Chair for Communication NetworksAachen University of TechnologyProf. Dr.-Ing. B. WalkeDiploma ThesisEvaluation of the OFDM MulticarrierTransmission Scheme for Radio Channelsby Means of Ray-TracingofStefan MangoldMatriculation Number: 185820Aachen, 3rd Dec. 1997

Supervised by:o. Prof. Dr.-Ing. B. WalkeDr. D.H. EvansDipl.-Ing. M. LottThis publication is meant for internal use only. All rights reserved. No liabilities withrespect to its content are accepted. No part of it may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of the publisher.

I assure, that this work has been done solely by me without any further help from othersexcept for the o�cal attendance by the Chair for Communication Networks and PhilipsResearch Laboratories. The literature used is listed completely in the bibliography.Aachen, 3rd Dec. 1997(Stefan Mangold)

CONTENTS1 Introduction 52 Indoor Radio Channel Modelling 72.1 Channel Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Empirically Derived Channel Modelling . . . . . . . . . . . . . . . . . . . . 122.2.1 Ray Tracing based on Geometrical Optics . . . . . . . . . . . . . . . 132.2.1.1 Ray Launching Method . . . . . . . . . . . . . . . . . . . . 132.2.1.2 Predicting the Radio Channel by Ray Launching . . . . . . 142.2.2 Predicting the Radio Channel by Channel Sounding . . . . . . . . . 162.2.3 RACE LEVEL-2 Data Format . . . . . . . . . . . . . . . . . . . . . 202.3 Statistical Description of Indoor Channels . . . . . . . . . . . . . . . . . . . 202.3.1 The Rayleigh and Ricean Multipath Channel . . . . . . . . . . . . . 202.3.2 The Modi�ed Poisson Model [5] . . . . . . . . . . . . . . . . . . . . . 222.3.3 The Neymann-Scott Clustering Model . . . . . . . . . . . . . . . . . 232.3.4 Other Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.5 Suggested Model for OFDM analysis . . . . . . . . . . . . . . . . . . 242.4 The ComNets Indoor Radio Channel Model . . . . . . . . . . . . . . . . . . 252.4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.1.1 Deterministic Part . . . . . . . . . . . . . . . . . . . . . . . 282.4.1.2 Line Splitting . . . . . . . . . . . . . . . . . . . . . . . . . 302.4.1.3 Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Orthogonal Frequency Division Multiplexing 353.1 Multicarrier Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1.1 Classical Frequency Division . . . . . . . . . . . . . . . . . . . . . . 353.1.2 The Water-Pouring Theorem . . . . . . . . . . . . . . . . . . . . . . 363.1.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 The OFDM Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.1 Basic Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.2 The Guard Interval Tg . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2.2.1 Cyclic Extension . . . . . . . . . . . . . . . . . . . . . . . . 41

2 Contents3.2.2.2 Bandwidth E�ciency . . . . . . . . . . . . . . . . . . . . . 423.2.3 Advanced OFDM Techniques, COFDM and MC-SS . . . . . . . . . 443.2.3.1 Coded OFDM and Frequency Diversity . . . . . . . . . . . 443.2.3.2 Spread Spectrum Techniques, MC-SS . . . . . . . . . . . . 463.2.4 History and Applications . . . . . . . . . . . . . . . . . . . . . . . . 473.2.4.1 Digital Audio Broadcasting (DAB) . . . . . . . . . . . . . . 483.2.4.2 Terrestrial Digital TV (DVB-T) . . . . . . . . . . . . . . . 493.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3 The Analytical Model of OFDM Systems . . . . . . . . . . . . . . . . . . . 513.3.1 The Orthogonality Condition . . . . . . . . . . . . . . . . . . . . . . 513.3.2 Multipath Channel Model . . . . . . . . . . . . . . . . . . . . . . . . 533.3.3 Maximum Excess Delay smaller than Tg (� � Tg) . . . . . . . . . . . 533.3.4 Maximum Excess Delay longer than Tg (Tg < � � T 0b) . . . . . . . . 553.3.5 Generalising to the Multipath Channel . . . . . . . . . . . . . . . . . 573.3.6 The Statistical Distributions of �0k;k, �0l;k and �0l;k . . . . . . . . . . . 593.3.7 The C/I Ratio of Subchannel k . . . . . . . . . . . . . . . . . . . . . 614 RESULTS: Indoor Radio Channel Characteristic at 5.2GHz 634.1 Validation of Ray Tracing Simulations by Measurements . . . . . . . . . . . 634.2 Improving the Ray Tracing Results . . . . . . . . . . . . . . . . . . . . . . . 664.3 Channel Classi�cation and Evaluation Environments . . . . . . . . . . . . . 674.4 Results for Di�erent Environments . . . . . . . . . . . . . . . . . . . . . . . 685 RESULTS: Performance of the OFDM System 715.1 SPW Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Optimal Guard Interval for 16-Point FFT . . . . . . . . . . . . . . . . . . . 735.3 The Analytically Derived Parameters . . . . . . . . . . . . . . . . . . . . . . 756 Conclusion 77Bibliography 79List of Abbreviations 81A Calculations 83A.1 The Sub-Channel Interference Ek(n)ICI . . . . . . . . . . . . . . . . . . . . 84A.1.1 l = k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Contents 3A.1.2 l 6= k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84A.2 The Inter-Symbol Interference Ek(n)ISI . . . . . . . . . . . . . . . . . . . . 85A.2.1 l = k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85A.2.2 l 6= k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85B Channel Models 87B.1 Res A 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88B.2 Res B 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89B.3 Res C 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90B.4 O� A 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91B.5 O� B 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92B.6 O� C 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93C SPW Implementation 95List of Figures 101List of Tables 103Acknowledgements 105

4 Contents

CHAPTER 1IntroductionThe multicarrier transmission scheme Orthogonal Frequency Division Multiplexing(OFDM) is investigated in this thesis as the transmission format for a wireless ATM-LAN(Asynchronous Transfer Modus - Local Area Network). It is proposed as the preferred ra-dio transmission format and modulation scheme within the ETSI RES 10 standardisationcommittee for Hiperlan (High Performance LAN), type 2.OFDMRadio transmission within o�ce and residential buildings su�ers from multipath e�ects,leading to severe inter-symbol interferences (ISI) between adjacent symbols due to thesignal delay spread. Multicarrier modulation (MCM) techniques such as OFDM are basedon transmitting data by dividing the high rate stream into several low rate streams, andby using these substreams to modulate di�erent subcarriers. The symbol duration of eachsubstream will be much higher than the channel time dispersion. By using a large num-ber of carriers, a high immunity against multipath dispersion can be provided. OFDM,having densely spaced subcarriers with overlapping spectra of the modulated subcarriers,abandons the use of steep bandpass �lters to detect each subcarrier as it is used in clas-sical frequency division multiplexing (FDM) schemes. It o�ers therefore a high spectrale�ciency.A multicarrier based wireless LAN needs only to have a limited number of carriers sincethe required distances between transmitters and receivers are only a few tens of meters,and thus, small delay spreads occur in local environments. In this work, the investigatedsystem is a 16-carrier OFDM scheme with DQPSK (Di�erential Quadrature Phase ShiftKeying) modulation of the subcarriers.Channel ModellingHiperlan is proposed to work at 5:2GHz. For this frequency, channel models of the indoorradio propagation channel, which are necessary for simulations of OFDM systems, are notavailable. Therefore, a key aspect of this thesis is to derive representative models of theradio channels, based on empirical propagation data.Ray tracing as well as frequency domain measurements are performed to empirically de-termine the channel characteristics for the Hiperlan channel. One of the scopes of thiswork is to evaluate the accuracy and suitability of radio channel predictions based on raylaunching algorithms, which are applied by the ComNets ray tracing tool.From the resulting individual channels statistical models are derived by means of a newmethodology. This way of parameterising the channel models is based on established al-gorithms which can be found in the literature.The created channel models are used to investigate the 16-carrier OFDM system to assessthe multipath e�ect on the multicarrier transmission. Furthermore, an analytical descrip-tion of OFDM is introduced, which can be used in conjunction with the channel modelsto determine the reliability of OFDM in terms of bit-error rates (BER).

6 1. IntroductionOutlineIn the next chapter, empirically derived channel modelling is discussed. The developedHiperlan/2 channel model as well as the methodology to parameterise it, are explained indetail.Chapter 3 gives an overview over OFDM. The principle of OFDM and some prominentapplications such as the European digital audio broadcasting (DAB) are explained. Fur-thermore, the detailed analytical model of OFDM is derived.Chapter 4 compares the applied measurements with results of ray tracing simulations.Further, channel models for individual scenario classes are issued and discussed.Chapter 3 presents the consequences and the optimal con�guration of a 16-carrier OFDMsystem for the investigated channels, by interpreting extensive simulations of OFDM. Somecalculations by means of the analytical OFDM model are presented to illustrate the useof OFDM in multipath environments.Finally, a conclusion and an outlook are given in chapter 6.Note, that for sake of clari�cation a table of all symbols used in the analytical descriptionsis given in appendix A.

CHAPTER 2Indoor Radio Channel ModellingThe e�ective design, assessment, and installation of a wireless radio network within build-ings requires an accurate characterisation of the radio channel. The channel character-istics vary from one environment to another and they determine the feasibility of usinga proposed communication technique in a given environment. With an accurate channelcharacterisation and with a detailed mathematical model of the channel, the speci�c per-formance attributes of a transmission scheme are predictable. For example, the achievabledata rate and the optimum antenna location of the radio stations can be found.Hiperlan/2 is proposed to work at 5:2GHz with a 23:5MHz channel bandwidth.Frequencies of this band are known to have several features for use in wireless local areainformation networks. For example, ray tracing simulations show that at these frequenciesa station transmitting signals with a power of less than 1W can provide coverage for sev-eral oors and through several walls within a building. Fig. 2.1 shows a typical wirelessresidential scenario.

multipathcomponents

reflection

diffractedwaves

transmission

heavilyobstructedLOS

Figure 2.1: Radio transmission within buildings.In the next section, fundamentals of radio channel characteristics are brie y discussed.Section 2.2 describes two ways of determining the radio channel. In section 2.3, some wellknown channel models are explained, which are often quoted in literature. In section 2.4,the indoor radio channel model developed in this work is described in detail.

8 2. Indoor Radio Channel Modelling2.1 Channel ParametersRadio propagation in indoor environments is complicated since the direct path betweentransmitter and receiver (line-of-sight, LOS) is often obstructed by intervening structures.Furthermore, due to re ection, di�raction, and scattering of indirect radio waves by struc-tures inside the building, the transmitted signal reaches the receiver by more than onlythe LOS path, from various directions. This is known as multipath fading. Except for theLOS path, all paths go through at least one order of re ection, transmission or di�ractionbefore arriving at the receiver. The fading is caused by constructive and destructive in-terference between the individual signal waves. They combine at the receiver antenna togive a resultant signal which can vary widely in amplitude and phase.In wide-band pulse transmission, the multipath phenomenon produces a series of delayedand attenuated echoes for a transmitted pulse. A channel can be modelled as a time varying�lter for a given transmitter and receiver location in space. In indoor environments, whenemploying local area radio networks with high data rates, it can be assumed that thechannel is slowly time varying and linear. For this reason, the impulse response can beassumed to be time invariant for short time intervals and the channel may be interpretedas wide sense stationary (WSS,[16]).m δ mA e (t-t )

m=1

jM

n(t)

y(t)

ΘmΣx(t)+Figure 2.2: The multipath channel as time invariant linear �lter with additive noise.Let the baseband complex channel impulse response be composed of M echoes. It can bewritten as h(t) = MXm=1Amej�m�(t� �m) + n(t) (2.1)where M is the total number of re ected paths, Am, �m, and �m are magnitude, delaysand the phase rotation of each path, respectively. The phase rotation includes the individ-ual phase shift and the rotation due to the Doppler e�ect. Indoor channels are assumedstationary for at least short time intervals and thus the Doppler e�ect only results in aphase rotation. The term n(t) is the lowpass complex valued additive Gaussian noise.The individual multipath components are mutually independent (uncorrelatedscattering, US). Assuming uncorrelated paths, the channel impulse response can be writtenin terms of power as jh(t)j2 = MXm=1A2m�(t� �m) (2.2)where the Gaussian noise is neglected for the sake of simplicity. The term jh(t)j2 is referredto as power delay pro�le (PDP). For wide-band signals, incoming paths are modelled asideal impulses with uniform distributed phase shifts �m. In this case, the total received

2.1. Channel Parameters 9power is simply related to the sum of the powers in the multipath components. TheComNets Raytracer, described in section 2.2.1, calculates such PDPs with the additionalinformation about the phase shift of the individual paths.Directly related to the received power of respective transmitter to receiver distances is thepath loss. The suggested model in [8] separates the free space loss from the loss due topenetration. In free space, and with a �xed transmitter power (Pt), the received power(Pr) decreases with distance (d), asPr(d) = PtGtGr(4��)2d��; � = 2 (2.3)where � is the exponent of the power-distance relationship and Gt, Gr are the gain of thetransmitter and receiver antennas, respectively. Taking the logarithm of (2.3), the linearrelationship10 log10 [Pr(d)] = 10 log10 [C]� 10� log10 [d] ; C = PtGtGr(4��)2 (2.4)between power in decibels and the distance is found. This equation can be expanded tomodel the particular impacts on the penetration loss for indoor characteristics, such as oorsizes and wall con�gurations [8]. Di�erent scenarios like o�ce or residential buildings resultin di�erent parameters. For free space, � equals 2. The values of � for o�ce environmentsare usually between 2 and 3. The path loss model roughly characterises buildings such asresidential, o�ce and factory buildings.Several multipath channel parameters are derived from the power delay pro�le. The im-portant parameters excess delay, rms delay spread, delay window, coherence bandwidthare brie y discussed below. Furthermore, the Doppler spread and the coherence time, twoimportant values which are not derived from pro�les are explained below.In Fig 2.3, some de�nitions of time domain parameters can be seen.

Figure 2.3: A power delay pro�le with rms delay spread, mean excess delay, maximumexcess delay, and the power threshold.The time dispersive properties of wide band multipath channels are quanti�ed by the mean

10 2. Indoor Radio Channel Modellingexcess delay � and root mean square (rms) delay spread �rms. The mean excess delay isthe �rst moment of the power delay pro�le with respect to the �rst arriving path:� = MPm=1(�m � �0) jAmj2MPm=1 jAmj2 (2.5)The rms delay spread is de�ned as the square root of the second central moment of apower delay pro�le: �rms =vuuuuuut MPm=0(�m � � � �0)2 jAmj2MPm=0 jAmj2 (2.6)These delay parameters are calculated relative to the �rst signal of the LOS path. Theydo not rely on the absolute power level of the received signal.Because in general the rms delay spread cannot directly be related to the system perfor-mance, the delay window parameterWq is often used to describe the time dispersion. Withrespect to the air interface design, it is a more established parameter. The delay windowis de�ned as width Wq of a time window for which the energy within the window relatedto the energy outside the window has a given ratio q. The energy of the signal fractionoutside the delay window is assumed to cause interferences and thus q can be consideredas the interference ratio. If a threshold is given for q (e.g. q = 20dB), the correspondingdelay window Wq indicates some of the required �lter parameters for the receiver. Thede�nition of the delay window is illustrated in Fig. 2.4.

W

01 02(E + E )i

|h( )|2

E

E0201E

q

τ

τ

E i

q=10log

WFigure 2.4: De�nition of the delay window WqThe coherence bandwidth Bc is a statistical measure of the range of frequencies overwhich the channel can be considered as at, which means that the spectral componentshave an approximately equal gain and a linear phase versus frequency. Bc is calculated asthe 3dB width of the complex autocorrelation function of the frequency channel responseH(f) ��� h(t). Two transmitted signals with a frequency separation greater than Bc are

2.1. Channel Parameters 11a�ected di�erently by the channel. The relationship Bc � 1=(��rms) with � of about 5 canbe found for various indoor environments. The value of � is not a constant, it depends onthe instantaneous channel impulse response. The coherence bandwidth is of great impor-tance for OFDM transmission schemes. If Bc is of the order of a carrier spacing (1=Tb),then it can be assumed that adjacent OFDM carriers are a�ected by uncorrelated ampli-tudes in the frequency domain. The subchannels can then be assumed to be statisticallyindependent which gives way to many optimum coding schemes, see section 3.2.3.1. OFDMis explained in detail in chapter 3.The time varying nature of the channel caused by either relative motion between thetransmitter and the receiver, or by movements of objects in the transmission path isdescribed by the Doppler spread BD. The well known Doppler e�ect causes frequencyshifts in the transmitted signal. BD is a measure of the spectral broadening caused bythe time rate of changes of the radio channel. The larger the velocities of the stations orscattering objects the larger the Doppler spread. If a pure sinusoidal tone with frequencyfc is transmitted, the signal at the receiver will have spectrum components in the rangeof fc � BD=2 where BD = vfc=c. The velocity of scatterers or of the antenna is given byv and c is the speed of the electromagnetic waves.The coherence time Tc is a measure of the average time duration over which the radiochannel is essentially stationary. The Doppler Spread and the coherence time are inverselyproportional to one another (Tc � 1=BD). In wireless ATM radio networks for indoorenvironments, the baseband signal bandwidth is much greater than the Doppler spreadand the e�ects of time variations are negligible at the receiver. Therefore, and in accordancewith the WSS channel, the wide-band propagation characteristics of radio waves withinbuildings can be characterised as slowly fading channels which are stationary for a symbolduration.It is important to note that di�erent data rates occur in OFDM systems. The short symbolduration Ts determines the high rate of the serial symbols before multiplexing, whereas thee�ective block duration Tb � Ts indicates the lower rate for the N parallel subchannels.The channel characteristic and the data rate determine the signal fading process at thereceiver antenna. In the following sections, it is assumed that(i) the symbol duration Ts of the signal, but not the block duration Tb, is smaller thanthe rms delay spread �rms(ii) the transmitted baseband signal bandwidth Bs is larger than the coherencebandwidth Bc(iii) the symbol duration Ts and the block duration Tb are smaller than the coherencetime Tc(iv) the transmitted baseband signal bandwidth Bs is much larger than the Dopplerspread BD.The �rst two items are equivalent to each other and imply that the channel is frequencyselective rather than at. With the additional assumption of uncorrelated multipath com-ponents (US), frequency diversity results and leads to powerful algorithms, such as codedOFDM or spread spectrum, to improve the performance of the applied transmissionscheme. Diversity methods in conjunction with OFDM are explained in section 3.2.3.1.The items (iii) and (iv) determine the channel to su�er from slow fading rather than fastfading (WSS). Furthermore, signal spectrum spreading due to the Doppler e�ect do notsigni�cantly occur in indoor scenarios and are neglected in the following. However, general

12 2. Indoor Radio Channel Modellingchannel model implementations should include the Doppler spread with regard to stationand scatterer velocities. The model classi�cation, proposed for in section 4.3 allows themodelling of the indoor channel with respect to slow antenna motions.2.2 Empirically Derived Channel ModellingToday, when developing new transmission techniques, the signal processing is the objectiveof extensive simulations. Source and channel coding, the modulation, and issues such assignal spectrum e�ciency are investigated by simulation tools for speci�cation and designof capable modem techniques. When simulating data transmission, a radio channel mustbe modelled statistically as a time varying �lter. Changes in the indoor environment suchas the opening of a door, small movements or rotations of the antennas or shadowing due tomoving objects between the stations result in serious changes of the channel characteristic.An empirically derived channel model represents an individual channel with respect tothese changes. Empirically derived models are based on, e.g., measurements or ray tracingsimulations where a large set of PDPs for a speci�c environment is found by means ofchannel sounding or site speci�c calculations, respectively.It is important to note that the channel parameters such as �rms should be de�ned fromPDPs which are a temporal or spatial average of consecutive impulse response measure-ments or calculations collected and averaged over a local area. Typically, many measure-ments or simulations are made at many local areas in order to determine the channelparameters. In this work, sixty PDPs are found by measurements and several hundreds ofPDPs are calculated by means of ray launching. Ray launching is a typical approach ofsite-speci�c modelling. Fig. (2.5) shows investigated locations in a domestic environmentwhich has been used to parameterise a channel model.

R_0_1 R_0_2

R_0_3

R_0_5

Tx4

BUILDINGRESIDENTIAL

GROUND FLOOR

R_0_0

R_0_6

11m

15 m

R_0_4

Figure 2.5: Ray tracing simulations within residential buildings. For large-scalevariations of the receiver location, PDPs are calculated.In the following sections, ray tracing, channel sounding by means of a vector analyser anda data format useful for data storage of the resulting pro�les, are described.

2.2. Empirically Derived Channel Modelling 132.2.1 Ray Tracing based on Geometrical OpticsSite-speci�c models perform computer simulations of the radio propagation processes withthe geometric structure of the building and the objects inside the rooms and their elec-tromagnetic characteristics as an input.Using geometrical optics principles, the propagation of the electromagnetic wave is de-scribed by lines - called rays. The rays are de�ned along the path where electromagneticpower travels from transmitter to receiver. In the described simulation tool both re ectiv-ity of the objects and transmissivity through walls are considered.As output value the impulse response is calculated considering the direct ray from trans-mitter to receiver and the rays re ected on the superstructure walls (ceiling, oor andside-walls) and on the objects inside it. Each object surface is characterised by the dielec-tric permittivity and loss tangent.In the ray tracing tool two algorithms are implemented; the ray launching and the imag-ing method. Both algorithms trace rays between transmitter and receiver using Snell`s lawwhich states that the angle of incidence is equal to the angle of departure. The re ectionorder is an input parameter which the user can choose. At each re ection point, the am-plitude and phase of the re ected ray are calculated using polarisation dependent Fresnelre ection coe�cients (or Landau formulas) which also in general depend on the angle ofincidence. The amplitude of each ray, beyond the attenuation due to re ections, decreaseso� linearly as the inverse of the ray-path length, which is comparable to the free-spacepath loss. Each ray is weighted by the transmitter and receiver antenna gain functions.The polarisation states of both antennas and the incoming rays are considered. At thereceiving end, all rays arriving at the same time bin are vectorially added.The following subsection describes the ray launching method in detail, since this algorithmis used in this work for predicting the indoor radio channel.2.2.1.1 Ray Launching MethodWith ray launching methods, rays are traced from the transmitting location in predeter-mined discrete directions and checks if an object intersection occurs. If no intersection isfound, the process stops if the ray energy falls below a speci�ed threshold due to path lossor the ray hits the environment of the receiver and a new source ray at the transmitter isinitiated.Once an intersection has occurred, a re ected and transmitted ray are initiated dependingon material, angle of incidence and su�cient energy from this point. These two rays aretreated in the same way as the initial one, resulting in a recursive algorithm which buildsup a binary tree of rays and is visualised in Fig. 2.6.One problem of the method is the resolution of rays per volume, because generally no raywill hit the receiver position directly, so that a detection environment around the receiverhas to be introduced.A ray that hits this environment is assumed to hit the receiver only under marginalchanges. Problems occur with multiply detection of this environment on a speci�ed re ec-tion depth, when the detection environments overlap. If the environments are too small,the receiver position cannot be detected.These requirements lead to an detection environment which has to be adaptable and is

14 2. Indoor Radio Channel Modellingk = 1

k = 2

k = 3

k = 4

TransmissionTransmission

T

Reflection Transmission

Reflection Reflection

k - Recursion depth

Partial radio path

Figure 2.6: Re ection tree of the ray launching algorithmcalculated according to the length of the ray up to this position and according to thenumber and density of sent rays, see Fig. 2.7, left.Ray

Detection gap

Transmitter

Detection range

Ray

Ray

Detection range

Detection range

Ray

Detection cone

Wall

Source

Spherical receiverdetection range

Figure 2.7: Adaption of the detection range and misdetection due to shadowing at acorner.Problems occur also with this solution due to the size of the environment. In the rightpart of Fig. 2.7 the ray is detected by the receiver due to the size of its environment faraway from the transmitter, though there is the edge in between the direct line of sightbetween receiver and transmitter.2.2.1.2 Predicting the Radio Channel by Ray LaunchingIn Fig. 2.8, the signal attenuation in a single room, calculated by means of ray launchingalgorithms is shown.In order to predict the signal energy from signi�cant paths between the transmitter andthe receiver the ray launching method is a simple but computationally time consumingapproach.Both, the transmitter and the receiver antennas are modelled as vertically polarised and

2.2. Empirically Derived Channel Modelling 15

BUILDINGSCENARIO

OBSTACLES

WINDOWS

DOOR

RWTH Aachen Communication Networks PROSIT - PROpagation SImulaTor

Attenuation

-100.00 dB -95.00 dB -90.00 dB -85.00 dB -80.00 dB -75.00 dB -70.00 dB -65.00 dB -60.00 dB -55.00 dB -50.00 dB -45.00 dB -40.00 dB -35.00 dB -30.00 dB -25.00 dB -20.00 dB -15.00 dB -10.00 dB -5.00 dB 0.00 dB

0

|

1

|

2

|

3

|

4

|

5

|

6

|

[m]

6.95|

0 --

1 --

2 --

3 --

4 --

5 --

6 --

7 --

[m]

7.45--

Basestation

Figure 2.8: Ray tracing simulationideal isotropic antennas.Using the ray tracer, channel impulse responses are calculated as complex valued PDPs.A typical predicted pro�le is shown in Fig. 2.9.At the receiver location, the arriving rays are assumed to be mutually uncorrelated evenif rays arrive at the same time. Each ray represents a respective multipath componentwhich su�ers from individual attenuations and phase shifts. However, even if the multipathcomponents are independently a�ected, they will interfere with each other at the receiverantenna. The ComNets Indoor Radio Channel Model, introduced in 2.4, is parameterisedby line splitting with respect to this e�ect, see 2.4.1.2.

0 10 20 30 40 50 60 70 80 90 100

−150

−140

−130

−120

−110

−100

−90

−80

−70

excess delay [ns]

dB

Delay Profile

Figure 2.9: Typical power delay pro�le,with respect to the LOS. The �rst ray arrives att = 0.A pro�le calculated by the ray launching method can be written as given in Eqn. (2.2),where the phase shifts are neglected. It is calculated only for the distinct frequency 5:2GHzand the received rays are interpreted as ideal and not band-limited impulses. Table 2.1

16 2. Indoor Radio Channel Modellingshows the dielectric permittivity and the conductivity of the modelled building materials.�0 �00wood 0:65 0:01glass 6:3 0:06concrete 6:95 0:74steal 0 1Table 2.1: Dielectric characteristics of the modelled materials at 5:2GHz.2.2.2 Predicting the Radio Channel by Channel SoundingFor the validation of ray tracing results, a vector network analyser has been used.Because of the dual relationship between time and frequency domain techniques, it ispossible to measure the channel impulse response in the frequency domain.Coherent wide-band frequency domain measurements provide magnitude and phase ofthe frequency response of the channel. As a result, the exact time domain response is alsoobtained by taking the inverse Fourier transform of the measured data. The block diagramof the measurement system used for frequency domain characterisation of the indoor radiochannel is shown in Fig 2.10.The main component of the measurement system is a vector network analyser that outputsa swept frequency signal and analyses the complex valued received signal. Measurementsfor validating the ray tracing results have been performed in a laboratory room at PhilipsResearch Laboratories and sixty measured complex valued PDPs are now available. Inthese measurements, the time to sweep 801 distinct frequency points was set to 180ms.Care was taken to select an appropriate time span large enough to capture all signi�cantpower delay components.The signal generated by the network analyser is propagated by a dipole antenna, whichwas chosen for its wide bandwidth and its good omnidirectional properties. The signalfrom the receiver antenna, which has the same properties as the transmitter antenna, isreturned to the network analyser to determine the frequency and time response of thechannel. The measured data is then read and stored by the RS9000 controller for furtheranalysis and channel modelling.In contrast to the ray launching simulations, a 2GHz band centered at 5GHz was inves-tigated. The 2GHz bandwidth in the frequency domain gives an equivalent resolution inthe time domain of about 1ns which is better than most of the time domain measurementsystems are capable to produce. Time domain measurements determine the channel im-pulse response by sending a narrow pulse and by observing the e�ect of the channel onthe received signal.When sweeping a 2GHz band with 801 points, two systematic limitations have to bementioned. A sweep time of 180ms means that the overall recording time is approximately140 seconds. In o�ce buildings, the channel frequency response changes during this longinterval, resulting in an erroneous impulse response measurement. To mitigate the e�ect,and to achieve a stationary channel, measurements were performed during weekends and atnight. To further avoid variations of the channel during the recording time, the surroundingenvironment was kept stationary by preventing movements close to the transmitter and

2.2. Empirically Derived Channel Modelling 17the receiver. However, if the number of swept frequencies is reduced, e.g., from 801 to 401,the recording time decreases. In this case due to the periodicity of the Fourier transform,the period of the resulting response in time domain decreases to values near the maximumexcess delay. If a 2GHz band is swept, with 801 points a periodicity of T = 400ns resultsand with 401 points, the periodicity is T = 200ns which might be in the range of largeexcess delays. The HP8510 analyser allows channel sounding with 51, 101, 201, 401 or 801frequency points.S-parameter test set

HP 8516 A

45MHz .. 40GHz

Vector Network AnalyserHP 8510

Swept Frequency Oscillatorwith

X( )ω Y( )ω

X( )ωY( )ωωH( )=

ωh(t)=FT [H( )]−1

Tx Rx

Port 1 Port 2

InverseDFT Processor

Figure 2.10: Frequency domain channel sounding, block diagram.Another drawback occurs due to the frequency dependence of the dielectric constants ofmaterials like concrete and brick walls. The re ection and transmission constants of ob-structing planes vary over the 2GHz frequency interval. Hiperlan/2 radio transmissionwill only occupy a band of 23:5MHz for one Hiperlan channel. Hence, the signal char-acteristic of the individual paths in real Hiperlan scenarios will di�er from the measuredand broadband pro�les.Fig. 2.11, 2.12 and 2.13 show plots of the magnitude and phase of a typical frequencyresponse H(f; x) measured at a location x, and the corresponding magnitude of the timedomain response jh(t; x)j obtained from the inverse Fourier transform. The magnitude ofthe frequency response in decibels, the phase of the frequency response in degrees, andthe magnitude of the time response on a linear scale are shown.The frequency response consists of 801 complex samples at a frequency spacing of 2:5MHzfor a frequency span of 2GHz, which is centered at 5GHz. To exemplarily show thefrequency selective fading for the proposed relevant Hiperlan/2 band, only the intervalbetween 5:0GHz and 5:4GHz is shown in Fig. 2.11 and 2.12. From the frequency response,a periodic time response of 400ns is derived. The time response in Fig. 2.13 is truncatedto only that portion with signi�cant energy. The frequency selective nature of the channelis seen to result in deep nulls at certain frequencies. The phase is linear for most ofthe frequency band, except for those frequencies at deep nulls where a phase jump isobserved. The time domain response illustrates the multipath propagation which causesthe frequency selectivity. Table 2.2 summarises the channel sounding con�guration.

18 2. Indoor Radio Channel Modelling

Figure 2.11: Frequency selective channel, magnitude in dB. The frequency range isfrom 5:0GHz to 5:4GHz. The normalised signal envelope is indicated witha 5dB=unit scale.

Figure 2.12: Phase response in degree. The frequency range is from 5:0GHz to 5:4GHzand the signal phase is scaled as 50 degrees/unit.

2.2. Empirically Derived Channel Modelling 19

Figure 2.13: Time domain response of the multipath channel with linear scaling. Theenvelope of the normalised S21 parameter is shown for the delay intervalfrom 0ns to 100ns.Number of Pro�les 60Center Frequency 5.0 GHzFrequency Span 2 GHzNumber of Points 801Tx Antenna Height 1.7 mRx Antenna Height 1.45 m / 1.35 m / 1.25 mAntenna Characteristic �=2-dipoleTx-Rx Distance 4.5 m ... 5.5 mEnvironment Laboratory, very good LOSTable 2.2: Con�guration of the channel sounding measurements.

20 2. Indoor Radio Channel Modelling2.2.3 RACE LEVEL-2 Data FormatThe RACE LEVEL-2 format is a common �le format for propagation data which is ob-tained by measurements or simulations [11]. This format has not been used in this workfor the data management, and the format of the ComNets ray tracer was adopted formeasurement data storage. This incomplete format only contains information on the fre-quency, the antenna separation distance, and the pro�le data itself. No information onthe simulation or measurement environment is included. The RACE LEVEL-2 format wasonly used to classify resulting PDPs, since it suggests a rough classi�cation of propagationdata. In further projects, this proposed way of data storage should be considered for boththe description of the scenario environment as well as the measured or calculated pro�ledata.When performing ray tracing or channel sounding, a set of pro�le instances with all relevantdata to specify the individual scenario con�guration can be found for creating a datarepository. The repository instances can be classi�ed as described in section 4.3. For theresulting pro�le classes, representative channel models have to be de�ned.RACE LEVEL-2 �les are simple ASCII-�les, with �xed line lengths. They are outlinedin several blocks where the blocks provide information on the environment, antenna andmeasurement characteristic, and the analyser con�guration such as the frequency range.The last block includes the real and imaginary parts of the measured or predicted impulseresponse samples.The RACE LEVEL-2 format is simple but meets the requirements for describing measure-ment results as well as performed ray launching simulations. The simplicity is the mainadvantage. Using this format, data analysis and channel modelling is possible based onempirical data, independently of the way in which the pro�le data was found.2.3 Statistical Description of Indoor ChannelsThe indoor channel model must be appropriate for use in simulation tools like SPW (SignalProcessing Workbench) and for use in analytical models. There is an inherent trade o�between the simplicity and accuracy of models. For simulation purposes the model cannotbe too complex due to time constraints. On the other hand, to satisfy the demand ofrepresenting the real channel, it should be as errorless and authentic as possible, resultingin complicated and time consuming simulations.Typical channel models use bins or taps to describe the multipath channel in time domain.In these models, bins represent the delayed power at the receiver for certain time intervals.Often quoted ways of modelling channels can be found in [2], [3], [7], and [5].In the following, the Ricean channel is introduced and some important channel modelsare discussed. None of them has been used for simulations in this work, instead a moreaccurate and simple model has been developed, which is described in section 2.4.2.3.1 The Rayleigh and Ricean Multipath ChannelThe fading of the magnitudes of received signals in a multipath environment may followdi�erent distributions depending on the covered area and the presence or absence of adominating strong signal component. It is not in the scope of this work to �nd distributions

2.3. Statistical Description of Indoor Channels 21with the best �t to the empirical data. Only the most commonly used, the Rayleigh andthe Ricean distributions are considered here.In indoor radio channels, the Rayleigh distribution of bin magnitudes or envelopes iswidely used to describe the statistical time varying nature of the received envelope of themultipath components [4]. The individual path phases are very sensitive to the path length,changing by 2� when the path length changes by a wavelength. A wavelength is about6cm at frequencies of 5:2GHz. Therefore, signal phases at arbitrary receiver locationsare uniformly distributed over [0; 2�). The in-phase and quadrature components of thereceived signal envelope are assumed to be independent and Gaussian distributed randomvariables. The joint distribution of the magnitude x = p=2 + <2 is found as Rayleighdistributed. The probability density function (PDF) is given byp(x) = x�2 e� x22�2 ; x � 0 (2.7)where � is the rms value of the magnitude (the most probable value). Fig. 2.14 shows twoRayleigh distributions.p(x)

x

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5

sigma=1sigma=0.8

Figure 2.14: The Rayleigh probability density function for � = 0:8 and � = 1:0.When there is a dominant stationary signal component present, such as the LOS path,the fading signal magnitude distribution is Ricean. A strong component may also occur ifthere are paths which go through much less attenuation compared to other arriving paths,even compared to an obstructed LOS. When such a strong path exists, the received signalcan be a sum of two vectors, a scattered Rayleigh vector with random amplitude andphase and a vector which is deterministic in amplitude and phase. Assuming the phasesto be uniformly distributed, the Ricean PDF is given asp(x) = x�2 e�x2+v22�2 I0 �rv�2� ; x � 0 (2.8)where I0 is the zeroth-order modi�ed Bessel function of the �rst kind, v is the magni-tude of the deterministic component and �2 is proportional to the power of the Rayleighcomponent. The Ricean distribution is often described in terms of a parameter K whichis de�ned as the ratio between the deterministic signal power and the variance of themultipath components. It is also called the Ricean factor and is given by

22 2. Indoor Radio Channel ModellingK[dB] = 10logpower of the deterministic componentpower of the Rayleigh component dB (2.9)As v ! 0, K ! 1, the Ricean distribution degenerates to a Rayleigh distribution. IfK � 1, the Ricean PDF is approximately Gaussian about the mean. In Fig. 2.15 theimpact of the Ricean K-factor on the resulting distribution is displayed.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5

sigma=1, v=0sigma=1, v=3

x

p(x)

Figure 2.15: The Ricean probability density function for K !1 (v = 0) and forK � 1 (v = 3).2.3.2 The Modi�ed Poisson Model [5]This model, also called �-K channel model takes into account the clustering property ofpaths caused by the grouping of scatterers and objects without complete randomness. Itis a discrete time impulse response model with N multipath components. The time axis isdivided into small intervals. Each impulse response can be described by a sequence of 0sand 1s, where a 1 indicates the presence of a ray in a given interval and a 0 represents theabsence. A magnitude and phase value is associated with each 1. The number of multipathcomponents for the pro�les is assumed to follow a normal distribution where the meanvalue decreases with increasing antenna separation. The standard deviation is assumedto increase with increasing antenna separations which can be explained due to the factthat there are greater variations in the environment for larger antenna separations. Thedistribution of the path arrival time sequence is modelled by a second-order modi�edPoisson process. It takes into account the fact that scatterers inside a building causing themultipath dispersion are not located with complete randomness. The process is describedby transitions between two states representing di�erent mean arrival rates. Initially, theprocess starts in state 1 with a mean arrival rate �0(t). If a path arrives at time t, atransition is made to state 2 with a mean arrival rate K�0(t). If no further paths arrivein the interval [t; t + �], a transition is made back to state 1 at the end of the interval.For K > 1, the incidence of a path at time t increases the probability of receiving anotherpath in the interval [t; t+�]. Thus, the process exhibits a clustering property.In [5], the Modi�ed Poisson model proves to be a good �t to the empirical data collected inseveral urban mobile environments, and for radio transmission within buildings. In [2], thismodel is recommended as the model of choice for Hiperlan/2 simulations of the physical

2.3. Statistical Description of Indoor Channels 23layer. However, to �t such a model to the ray tracing results, a large set of calculatedpro�les are needed. Several thousand PDPs were used in [5]. For this reason, and becauseof the complicated �tting algorithms for cluster models, the Modi�ed Poisson model wasrejected for use in this work.2.3.3 The Neymann-Scott Clustering ModelSaleh and Valenzuela developed a multipath model for indoor channels based on timedomain measurement results [3]. The model assumes that the multipath components arrivein clusters. The amplitudes of the received clusters are independent Rayleigh randomvariables. The cluster and the multipath components within a cluster form Poisson arrivalprocesses with di�erent rates. The formation of the clusters is related to the buildingstructure, while the components within the cluster are formed by multiple re ections fromobjects in the vicinity of the transmitter and receiver.In Fig. 2.16, a schematic representation of the model is shown.

0 T1 TnT

β2 (t)

...t

-T/

−τ/γ

Γe

e

Figure 2.16: The exponentially decaying ray and cluster average powers. The decay isde�ned by the parameters � and .The model starts with the physical realisation that rays which model the multipath com-ponents arrive in clusters. The cluster arrival times, i.e., the arrival times of the �rst raysof the clusters, are modelled as a Poisson arrival process with the rate �. Within each clus-ter, subsequent rays also arrive according to a Poisson process with another �xed rate �.Typically, each cluster consists of many rays (�� �). The arrival time of the lth clusteris denoted by Tl, where l = 0; 1; 2; 3; � � �. The arrival time of the kth ray measured fromthe beginning of the lth cluster is denoted by �kl, where l = 0; 1; 2; 3; � � �.Setting the arrival time for the �rst cluster to T0 = 0 and for the �rst ray within the lthcluster to �k0 = 0, the arrival times are described by independent interarrival exponentialprobability density functions.The complex lowpass impulse response of the channel, given in Eqn. 2.1 is rewritten inthis model as h(t) = 1Xl=0 1Xk=0�klej�kl�(t� Tl � �kl) (2.10)where � is the phase and � the amplitude related to an incoming ray. The additive noise is

24 2. Indoor Radio Channel Modellingnot part of the model. The phases are independent uniform random variables over [��,�).The amplitudes are statistically independent positive random variables whose mean squarevalues f�2klg decrease with increasing Tl and �kl.In general, clusters overlap and typically, � > , which means that the expected powerof the rays in a cluster decay faster than the expected power of the �rst ray of a possiblefollowing cluster, see Fig. 2.16.The Neymann-Scott clustering model can be interpreted as a simpli�cation of the Modi�edPoisson model.2.3.4 Other ModelsRappaport and Seidel developed an empirically derived statistical model both for indoorand outdoor channels [7]. They characterise fading and the variation in the number andarrival times of multipath components. The average number of multipath componentsranges between 9 and 36 and is based on an empirical �t to the measurements. Theprobabilities for multipath arrivals are modelled as piecewise functions of the excess delay.The channel simulator, SIRCIM, calculates multipath pro�les with 7:8ns excess delayresolution of multipath signals. Excess delay spreads of up to 500ns are simulated.Rappaport's way of calculating the representing impulses, the line splitting technique, isadopted and implemented in this work for parameterising the channel model.The HIPERLAN type 1 channel model selected by RES10/TTG is described in [9]. Chan-nel impulse responses are modelled in time domain as tapped-delay line models. 128 uni-formly spaced taps represent the impulse responses with a total maximum excess delaytime of 1�s. Each tap correspond to a Rayleigh fading path. No static line of sight compo-nent is included and multiple clusters of paths are not modelled. The average power delaypro�le is assumed to decay with an exponential form. The average rms delay spread isused as the parameter to de�ne the decay. Three values are used, 50ns, 100ns, and 150ns,however, during simulations the rms delay spread for an instantaneous impulse responsemay di�er widely from these. In Fig. 2.17, a resulting impulse response of this model isshown. Due to the long excess delay of 1000ns, obviously many of the delayed taps donot signi�cantly contribute to the received signal energy, if an indoor scenario at a highfrequency such as 5:2GHz is modelled. To reduce the simulation time, the taps must notbe computed and can be neglected. Models with more than 100 taps are computationallytime consuming, resulting in long simulation times.2.3.5 Suggested Model for OFDM analysisThe scope of this thesis is to evaluate OFDM transmission techniques by means of sim-ulations and analytic descriptions. For this reason, a channel model which is based onray tracing results has been selected. It must be simple, exible, and accurate. To �t oneof the cluster models to the PDPs may be possible, if several thousand pro�les will beavailable. However, to implement such a model in simulation tools and, furthermore, touse it in analytic descriptions of OFDM, is not applicable. In chapter 3, parameters de-scribing systematical interferences of OFDM systems are extracted. The distributions ofthese noise-like interferences are calculated and determined. This can only be done and ismore feasible if a basic and exible channel model with Rayleigh distributed magnitudesand with a constant and small number of modelled multipath components is used.

2.4. The ComNets Indoor Radio Channel Model 25

Figure 2.17: Typical power delay pro�le (squared magnitudes of taps) of theHIPERLAN/1 channel model.A new exible channel model suitable for the 5:2GHz indoor channel is introduced in thenext section. The model is described in detail and compared to the other approaches. Amethod to extract and �t the model characteristic to empirical derived pro�les is explained.2.4 The ComNets Indoor Radio Channel ModelThe ComNets indoor radio channel model for HIPERLAN type 2 is very similar to themodel for HIPERLAN type 1. It is also a discrete tapped-delay line model where the tapsnow are called bins. The number of bins depends individually on the modelled channelscenario with its speci�c delay spread. The goodness of the �tting algorithms at the end ofthe modelling and the system bandwidth determine whether the resulting model is usefuland whether the chosen number of bins is satisfactory. In general, some iterations arenecessary until an accurate resulting model is found.All bins, except the �rst one, are equally spaced in time and represent the received signaland its corresponding delay interval. Uniform spacing of bin delays produces periodicity ofthe channel transfer function in the frequency domain. However, if the delays are smallerthan the reciprocal of the signal bandwidth, this e�ect will be negligible. Spaces of about10ns are used for a 25MHz signal bandwidth resulting in models with about 10 bins. Forsimulation purposes the model must not be too complex and for this reason the spacesshould be as large as possible. In accordance with the WSSUS channel approach, the binpowers are assumed to be uncorrelated and their phases are assumed to be identically andindependently distributed (i.i.d. uniform) over [0; 2�). The resulting bin powers have anexponential probability density function, or, equivalently, the magnitudes are distributedwith a Rayleigh probability density function. For large-scale variations in antenna locationscurve �tting algorithms show that the Rayleigh distribution of the magnitudes �t theempirical data well.In contrast to the HIPERLAN/1 model, a deterministic bin is extracted in every pro�leto represent the steady power of the channel response. Thus, the channels are modelled

26 2. Indoor Radio Channel Modellingas Ricean channels. Fig. 2.18 shows the SPW symbol block of the �nal model, whichwas used in OFDM simulations. The deterministic fragments of the channel responseand the statistic parts are independently written to di�erent channel block outputs. Theoutput called "OUT" includes the complete signal response and the additive noise. In SPWsimulations, if a respective channel model is necessary, the parameters of the channel, e.g.,the number of paths, must be changed according to the model inside the block layer.

Figure 2.18: The SPW symbol of the channel model. Statistical and deterministicoutputs are independently given. See appendix C for the details of theimplementation.For the sake of simplicity, cluster arrival processes as suggested in [2], [8] are not part ofthe model. Since no distinct decaying is de�ned by the model and since the bin powersare not correlated to each other, the signal strength due to the delayed bins can be higherthan the strength of the �rst bins during a stationary period. This allows modelling oflarge instantaneous rms delay spreads even with small excess delays. In HIPERLAN/2scenarios, a mobility with velocities of up to 10m=s is assumed. Due to motion of scatterersor antennas the transmission of an unmodulated carrier is received as a multipath signalwhose spectrum is not a single carrier frequency, but contains frequencies spread due tothe Doppler e�ect. A typical spectrum is given in [26]. This was used in GSM speci�cations[12] for mobile channels with up to 12 bins and can be also adopted for the ComNets modelimplementations in this thesis. However, the Doppler e�ect is not signi�cant and can beneglected for the indoor environment, as explained in section 2.1.A channel model is determined by the number of bins, the maximum excess delay and theexpected values of bin magnitudes. Further, the power of the deterministic bin determinesthe steady signal power whereas the delayed bins represent the interference power. Thus,the average Ricean K-Factor of a channel model is known. Channel characteristics likethe average expected rms delay spread and the delay window can be calculated from themodel too.In Fig. 2.19, both the static and the statistical part of the channel model are shown.The delayed and mutual independently attenuated bins of the statistic part represent themultipath e�ect which introduces interference in the receiver. The deterministic bin with aconstant attenuation and an assumed phase shift of 0 represents the useful signal fragment.

2.4. The ComNets Indoor Radio Channel Model 27A e j0

LOS

NN-1k321time

[dB]bin magnitude

NN-1k321

: Uniform Distr.φ

bin magnitude

Rayleigh

time

[dB]

Figure 2.19: The deterministic bin (left) and the statistical bin pro�le (right) model theRicean fading multipath channel.2.4.1 MethodologyIn this section the methodology of developing channel models based on the simulationand measurement results is described. To show the correctness of the models each step isexplained in detail.empirically derived

delay profile classes

CDF

data

SPW, C++ ...ASCII-Files MATLAB

Curve Fitting

Line Splitting

Extract LOS

(not available)

Repository

Channel Models

Other Sources

Channel Sounding

Ray-Tracing

RACE LEVEL-2 Figure 2.20: Developing the channel models.Large-scale variations of the receiver location are investigated by means of measurementsas well as ray launching. Large-scale rather than small-scale variations are modelled ifthe distances between the distinct investigated points are chosen larger than a signalwavelength.When using simulations or measurements to determine power delay pro�les, a repositoryis created. A repository can be interpreted as a set of pro�le instances. Each pro�le in-stance represents a complex valued PDP with information on the receiver and transmitterlocations and with all relevant data to specify the scenario con�guration.When performing the methodology to measured rather than simulated pro�les, the pro�ledata must �rst be converted to a pro�le similar to the ray tracing results. The channelsounding results are present in the frequency domain and have to be transformed with theinverse Fourier transform of the measured parameter S21. This parameter is equal to thechannel transfer function, S21 = jH(j!j. Fig. 2.21 shows a typical measured PDP for adistinct receiver location.Measured pro�les are represented by 801 equally spaced points. To convert the PDP, �rstthe points before the LOS delay are cut out. In Fig. 2.21 these are the points at times

28 2. Indoor Radio Channel Modelling

0 10 20 30 40 50 60 70 80 90 100

1

2

3

4

5

6

7

8

9

10x 10

−4

Figure 2.21: A measured S21 parameter of the channel versus time [ns]. The localmaxima are treated as mutually uncorrelated multipath components.< 18ns, which equals to approximately 5:4m. They are obviously due to thermal noise.Then, only the local maxima of the function are used for the analysis, the other pointsare neglected. The local maxima of the measured pro�les are interpreted as mutuallyuncorrelated impulses. Thus, the pro�le is given as a set of independent impulses whereeach impulse represents a di�erent multipath component.The applied modelling methodology is subdivided into the steps "extracting the deter-ministic part", "line splitting", and "curve �tting". Before using these algorithms, somebasic de�nitions according to the model precision have to be done. The number of binsmust be selected as a main parameter for the resulting model. Thresholds in power andtime specify the amount of valuable impulses in the pro�les and a decision area must bede�ned for the extracting of deterministic signal fragments.Before the deterministic signal strength of the PDPs is calculated, three basic matrixtransformations of the pro�le data are done in order to simplify the following calculations.� The pro�les have to start with the LOS. Therefore, earlier impulses are neglectedand the delayed ones are time-shifted such that the �rst impulse arrives at t = 0, ifthe LOS is not obstructed.� Impulses with high attenuation with a power below a certain threshold and impulseswhich arrive later than the maximum excess delay are neglected. The maximumexcess delay and the minimum power threshold are selected by the user and have tobe carefully adjusted at the beginning of the modelling iterations.� All pro�les are normalised to the power of 0dB, i.e. the sum of the impulse magnitudesmust be 1.2.4.1.1 Deterministic PartIt is likely for indoor scenarios that the received signal power includes a steady part ratherthan only the obstructed and delayed impulses. A steady signal fragment is determinedby either the line-of-sight paths or -if the LOS is heavily obstructed- by delayed paths

2.4. The ComNets Indoor Radio Channel Model 29where only re ections at good conductors with low attenuations occur. If in a given pro�lethe �rst impulses are dominant, they are assumed to be deterministic and contribute tothe steady and deterministic part. A decision area given by time and power thresholdsde�nes whether or not impulses donate to the extra bins. In both ways of deriving thepro�les, measurements and simulations, not only the �rst impulse arrives through the line-of-sight path and there is more than one impulse which determines the deterministic signalstrength. Note that this can occur especially in ray tracing simulations, even if the delaysof the LOS rays are very small. Due to the theory of geometrical optics, small time shiftsof the rays which travel on the direct line were observed, when the LOS is obstructed bythin planes, such as windows. For this reason, a decision area with a small time intervalis introduced rather than assuming that only the very �rst impulse arrives deterministic.In Fig. 2.22, the extracting is indicated.detected

3 deterministical rays

MinPowerLOS

decision area

obstructed rays

MaxExcessLOS< bin time interval length1

2

+

e.g. -100dBm

time

ray power[dBm]

PowerThreshold

Figure 2.22: Rays or measured samples within the decision area are assumed to bestatic and contribute to the deterministic bin.The decision area is userde�ned and depends on the magnitude of the strongest path.De�ning the length of the time period and the tolerated attenuation of the decision area isdue to the user of the model. First seed values should be, e.g., �3dB attenuation thresholdand half a bin interval time for the duration of the decision interval, see Fig. 2.22. Notethat the attenuation is de�ned with respect to the strongest multipath component, even ifthis component is outside the decision area. In this case, it is automatically assumed thatthe pro�le has no deterministic signal fragment and the corresponding bin is set to 0.Hence, each power delay pro�le is divided into the extra deterministic bin and into thestatistic fragments which represent the excess delay pro�le due to the scattered paths. Inother words, in addition to the obstructed paths, an extra bin with �xed magnitude andphase and without any excess delay represents the deterministic power.When deterministic signal fragments have been found in power delay pro�les, the channelmodelled out of the pro�les is given as a Ricean channel. Since the ratio of the power ofthe extra bin to the power of the obstructed bins depends on the Ricean K-factor, this

30 2. Indoor Radio Channel Modellingfactor also can be easily quanti�ed, as shown in Fig. 2.23.NN-1k321

= K

bins

2

2

Figure 2.23: Calculating the Ricean factor with the resulting bin powers.The deterministic bin of the �nal model is found by averaging the magnitudes of all deter-ministic bins extracted from the pro�les and is representative of the respective simulationenvironment. This way of calculating the deterministic power can be precisely applied toray tracing simulation results and to measured pro�les.2.4.1.2 Line SplittingThe number of rays in simulation results and the number of local maxima in measuredpro�les are not limited. Typically, pro�les with several hundreds of impulses are calculatedby the ray tracer. To reduce the number of multipath components in a time domainmodel without losing the important information about signal impairments, a simpli�cationtechnique is adopted in this methodology.The line splitting technique of Rappaport [7] is used to create individual bin representa-tions for each pro�le. This averaging technique reduces the amount of delayed multipathcomponents to a small number of time variant and delayed bins.The bin magnitudes are calculated by a vector summation, adding all ray impulses withinthe corresponding time excess interval. The summation of the impulses is calculated tak-ing into account the phases and the time shifts of each impulse. Therefore this techniqueassumes a slight correlation between adjacent impulses of the pro�les. Furthermore, be-cause of the possible correlation between impulses in the vicinity of the bin interval, theimpulses from half the adjacent intervals are weighted with 0:33 and contribute to the�nal result. This may be interpreted as a smoothing convolution with a lowpass �lter forreducing the signal bandwidth, resulting in a physically adequate model.However, the impulses inside the decision area only contribute to the deterministic binand are rejected for the line splitting calculations. Thus, the �nal channel models maybe composed of the deterministic bin and a �rst statistical bin with a very low signalpower, even lower than the power of the following bins. This occurs in environments witha very good LOS and a large Ricean K-factor (K � 1). Note that the line splitting isonly performed with the delayed and non-deterministic impulses. Due to the line splittingtechnique, there is no averaging of the dominant impulses which contribute to the �rststatic bin. Furthermore, no correlation is assumed between impulses inside the decisionarea and the impulses close to the decision area.A �ne subdivision in time with large excess delays results in a model with many bins.Thus, simulations or numerical calculations using the model may be time consuming and

2.4. The ComNets Indoor Radio Channel Model 31

NN-1k321

lost due toPowerThreshold

MaxExcessNoOfBins

MaxExcessNoOfBins

k

(k-1)

Bin Interval time

0

x xx

N intervalsN=NoOfBins

MaxExcess

lost due toMaxExcess

PowerThreshold

ray power

e.g. -100dBm

[dBm]

weight 0.66

weight 0.33

Figure 2.24: Impulses within the marked excess delay interval are added to �nd therepresentative model bin for this interval. The �gure also depicts thathighly attenuated impulses and impulses with a large excess delay areneglected and lost for the sake of simplicity.no longer applicable if a high model resolution in time domain is requested.2.4.1.3 Curve FittingSo far, the PDPs are reduced to corresponding bin pro�les each with 1 deterministic binandM�1 statistical bins, whereM is the required number of bins for the resulting model.If the LOS was heavily obstructed in a PDP, the deterministic bin magnitude is set to 0.The deterministic bin of the �nal model is calculated as the mean of the �rst bins of thebin pro�les.The pool of all the bin pro�les is summarised to one normalised model by means of a curve�tting technique. Rayleigh distributions of the bin magnitudes are �tted to the empiricallyderived bin magnitudes of the individual pro�les, as depicted in Fig 2.25.The distributions of the bin magnitudes have to be found. Fortunately, since this is aclassic problem in numeric quadratic programming, MATLAB o�ers such a method to �ta function to a set of data. The algorithm is called the Nelder-Mead simplex algorithmfor minimising a non-linear function of several variables. It calculates a least square �t,which minimises the sum of the squares of the data deviations to the function. This canbe written as Z 1�1 (cdf(x)� data(x))2 dx �!MIN (2.11)where x is the bin magnitude. Note that the cumulative distribution function (CDF)of a Rayleigh distribution is completely determined by the variances of the zero mean

32 2. Indoor Radio Channel ModellingRayleigh Distribution (CDF)

fits empirical data

x

P(x)

time

[mV]bin magnitude

x (=magnitude)

Figure 2.25: The magnitudes of the bins are assumed to be independent Rayleighrandom variables and are �tted to the empirical data.quadrature components.The CDF is the probability P (x < X) that the bin magnitude does not exceed a speci�edvalue. The CDF of a Rayleigh distributed variable is given asP (x < X) = 1� e�X2� (2.12)where � = �n is the variance of the Gaussian random noise having zero mean. ThisGaussian distribution determines the in-phase and quadrature components. The parameter� is calculated for each time interval by the curve �tting algorithm. For an eight bin model,this is shown in Fig. 2.26.It can be seen that the Rayleigh distribution �ts the empirical data well. The eighth andlast bin shows a bad �t, which indicates that in this model the maximum excess delay waschosen too long or the power threshold for neglecting highly attenuated rays was chosentoo high. Another modelling iteration with slight changes of the seed values such as thepower threshold is necessary for this channel model.The received signal strength, i.e. the ratio between the signal power and the additivenoise, depends on the distance between transmitter and receiver and the path loss due tothe indoor environment. In addition to the normalised model obtained by means of thecurve �tting, the signal-to-noise ratio (SNR) must be calculated. This can only be doneif the noise �gure of the receiver and the power of the transmitted signal is known. Withthe known SNR, an adaptive additive Gaussian noise source can be used in simulationsto add the noise to the channel response. In this thesis, the following assumptions andcalculations are done to calculate the resulting SNR:� The signal power at the transmitter is Pt = 100mW � 20dBm� The temperature within the buildings is T = 293K� The channel bandwidth B = 23:5MHz� The receiver noise �gure Nf = 9:9dBW� The Boltzman constant is 1:38 � 10�23Ws=KThe resulting noise power � of the additive white Gaussian noise (AWGN) is therefore

2.4. The ComNets Indoor Radio Channel Model 3310

−50

0.5

1

x

P(x

)

Bin 1

10−5

0

0.5

1

x

P(x

)

Bin 2

10−5

0

0.5

1

x

P(x

)

Bin 3

10−5

0

0.5

1

x

P(x

)

Bin 4

10−5

0

0.5

1

x

P(x

)

Bin 5

10−5

0

0.5

1

x

P(x

)

Bin 6

10−5

0

0.5

1

x

P(x

)

Bin 7

10−5

0

0.5

1

x

P(x

)

Bin 8

Figure 2.26: Rayleigh distributions of a typical 8-bin model �tted to the data.found as � = 10log10 (kTB) +Nf = �120:32dBW = �90:32dBm (2.13)The received signal power is calculated as the summation of the impulse powers of allarriving impulses, when one single impulse has been sent from the transmitter.Pr = MXm=1A2mand the SNR for a distinct antenna con�guration is found asSNR[dB] = Pr[dBm]� �[dBm]The resulting SNR for a channel model is calculated as the average of all investigatedreceiver locations.

34 2. Indoor Radio Channel ModellingFinally, a typical result of the modelling methodology is shown below. The resulting valuesare written to a �le and are directly used in simulations for calculating the delays and theweights of the multipath components.===========================Power Delay Profile Model===========================Created at/by:12-Nov-1997 14:05:59 mangoldRay Trace output file *.pdp: Tx1.pdpNumber of statistical bins: 8Maximum excess delay of latest ray: 100nsMinimum ray power: -159dBMaximum excess delay of line-of-sight rays: 8.75nsPower difference to main ray for LOS decision: -3dB------------------------------Deterministic Bin Magnitude:(steady /specular part)0.699842 (-3.1dB)------------------------------Statistical Bin Magnitudes:(random /scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 6.25ns | -7.1742 |2 | 18.75ns | -14.0117 |3 | 31.25ns | -24.4453 |4 | 43.75ns | -30.3915 |5 | 56.25ns | -24.4631 |6 | 68.75ns | -27.4893 |7 | 81.25ns | -26.2823 |8 | 93.75ns | -32.1971 |----------------------------------Ricean Factor: 2.0056Signal to Noise Ratio (SNR): 49.7089dBAverage r.m.s. delay spread: 10.89nsExample of a resulting channel model for use in SPW simulations.

CHAPTER 3Orthogonal Frequency Division Multiplexing3.1 Multicarrier ModulationIn a conventional serial data system, the symbols are transmitted sequentially, with thefrequency spectrum of each data symbol allowed to occupy the entire available bandwidth.Due to the bursty nature of the indoor radio channel, several adjacent symbols may becompletely destroyed during a fade. In indoor environments, the propagation channelconsists of several obstacles and re ectors. The received signal arrives as an unpredictableset of re ections and direct waves each with its own degree of attenuation, delay and phaseshift.Higher data rates can be achieved in a serial system by using higher order modulations (forexample QPSK instead of BPSK) at the expense of a degradation in performance, or, atthe expense of increased channel bandwidth, by decreasing the symbol interval. However,decreasing the symbol interval is equivalent to increasing the symbol rate and makes thesystem more susceptible to delay spread impairments.If the speci�ed symbol rate increases, the time dispersion is generally much greater thanthe rate and, hence, inter-symbol interference (ISI) results from the non-ideal frequencyresponse characteristics of the channel. In this case an equaliser is necessary, to reduce thechannel distortion.To completely prevent ISI in single carrier systems, the data rate must be reduced to arate much less than the reciprocal of the delay spread.3.1.1 Classical Frequency DivisionA parallel or frequency multiplexed data system o�ers possibilities for alleviating manyof the problems encountered with serial systems in the presence of channel distortion.Fig. 3.1 shows the basic principle of frequency division. The channel signal to noise ratiois depicted as the ratio of the squared channel frequency response jC(f)j2 to the powerdensity of the additive noise �nn(f).A parallel system is one in which several sequential streams of data are transmitted si-multaneously, so that at any instant many data elements are being transmitted. In sucha system, the spectrum of an individual data element normally occupies only a smallpart of the available bandwidth, such that each subchannel is nearly ideal. These systemsare called Multicarrier Modulation (MCM) schemes. In a classical MCM system, the to-tal signal frequency band is divided into N non-overlapping frequency subchannels. Eachsubchannel is modulated with a separate symbol and, then, the N subchannels are fre-quency multiplexed. This scheme is called Frequency Division Multiplexing (FDM). Tooriginate orthogonality between adjacent subchannels a guard band is introduced betweenthe subbands. For this reason, steep �lters for truncating each subband are needed.The use of the �lters and the poor bandwidth e�ciency of conventional FDM schemes

36 3. Orthogonal Frequency Division Multiplexingfrequency

channel bandwidth

guard band

P(f)

channel signal to

2

noise ratio SNR

|C(f) |

Φ (f)n n

Figure 3.1: The available channel bandwidth is subdivided into a number ofsubchannels, each subchannel is nearly ideal.means that these systems are not applicable for modern communication systems. Preciousbandwidth is wasted due to the guard band and the relatively large distances of the narrowsubbands.3.1.2 The Water-Pouring TheoremIn an MCM link, the receiver and the transmitter can cooperate by adaptively distributingtheir power budget over the individual subcarriers. The signal-to-noise ratios on eachsubcarrier selected according to Gallagar's water-pouring theorem [23] of the informationtheory has been proven theoretically to be optimum under certain conditions [22]. InFig. 3.2, the water �lling interpretation is graphically explained. Note that in contrast toFig. 3.1 the ordinate now indicates the inverse channel signal to noise ratio.|C(f) |2

Φn n(f)

frequency selective

W

P(f)

frequency

AWGN channel

Figure 3.2: Interpreting the distortion as the bottom of a bowl: when an amount ofwater is poured into the bowl, the water will distribute itself so as to achievecapacity.E�cient loading of the various subcarriers can signi�cantly enhance the performance ofMCM over frequency selective fading channels. Suppose that C(f) is the frequency re-sponse of a frequency selective, bandlimited channel with bandwidth W and that �nn(f)

3.1. Multicarrier Modulation 37is the power spectral density of the additive white Gaussian noise. Let P (f) be the trans-mitted signal power to be distributed in frequency. It is well known, that for a given signalto noise ratio the capacity of an ideal, band-limited, AWGN channel is limited, where thecapacity is measured in bits=s. When evaluating the maximum achievable capacity of thenon ideal channel [28], P (f) has to be chosen so thatP (f) + �nn(f)jC(f)j2 = const 8 f 2W:This solution for optimising channel capacity agrees with Shannon's argument for achiev-ing capacity [27]. The result can be interpreted as if the transmitted signal power insidethe channel band will be high where the ratio of the additive noise to the squared channelimpulse response is low. For example, if there is a deep fade in a small fraction of thefrequency spectrum, the transmitter should adaptively decrease the signal power for thissubband concerning the power density of the additive noise. Whereas at frequencies fgoodwith a good transmission ratio the power P (fgood) of the transmitted signal should beincreased to obtain a better performance. Obviously this constraint is easy to meet inmulticarrier systems with independent narrow subchannels. It is generally called a water-�lling interpretation, since the term �nn(f)= jC(f)j2 can be thought as the bottom of acontainer of unit depth, see Fig. 3.2. When pouring in an amount of water (substitutingthe power), the water will distribute itself in a way as to achieve capacity (constant levelof water surface).3.1.3 EvaluationClassical MCM systems perform at the highest theoretical limits of the channel capacity.They have the advantage of spreading out a wide fade over many symbols. This e�ectivelyrandomises the burst errors caused by, e.g., shadowing in the indoor environment. Insteadof several adjacent symbols being completely destroyed, many symbols are only slightlydistorted. This allows precise reconstructions of most of them. Since MCM systems spreadout the total symbol duration, the sensitivity of the signals to the delay spread is therebyreduced. Parallel approaches like MCM systems have the additional advantage of ideal atfading subchannels and thus reduce the need for equalisation of the modulated subcarriers.However, the classical parallel approach has some severe drawbacks. Since there is noperfect bandwidth �lter, mutual interference among the subchannels cannot entirely beprevented. MCM requires high quality steep decaying �lters to separate the subchannels.But the limitation of �lter implementation forces the bandwidth of each subband to beequal to (1 + �)fm, where � is the roll-o� factor and fm is the Nyquist subchannel band-width. Furthermore, since in the transmitter and receiver robust oscillators are required,a high complexity of the equipment to implement the system is needed.When performing adaptive power loading algorithms in accordance to the water-�llingtheorem, the channel response and the noise power must be known in the transmitter.To prevent a large overhead due to the reloading, the channel characteristic should bestationary for at least short periods (slow fading), which de�nitely occurs in indoor radiochannels.

38 3. Orthogonal Frequency Division Multiplexing3.2 The OFDM ApproachA more e�cient use of the frequency band can be obtained with a parallel system if thespectra of the individual subchannels are permitted to overlap. The transmission schemeOrthogonal Frequency Division Multiplexing (OFDM) allows consecutive spectra to shiftinto each other while still maintaining orthogonality between subchannels.3.2.1 Basic PrincipleConsider the signals of Fig. 3.3. In (a), N = 4 cosine signals or not modulated carriers aremultiplied with a rectangular pulse. This e�ectively means a truncation of the signal tothe interval (0::Tb).An ideal rectangular pulse shape transforms to a sinc-function in frequency domain withzeros at multiples of 1=Tb. Multiplying with a cosine in time means convolution with twoideal impulses in frequency. In the following, the negative shadow impulse is neglected forthe sake of simplicity and only the right and positive side-band is shown in Fig. 3.3 (b).

Time

Sig

nals

s0

s1

s2

s3

0

Frequency

Car

rier

Spe

ctra

f0

f1

f2

f3

f0=f

c

f1=f

c+1/T

bf2=f

c+2/T

bf3=f

c+3/T

b

Figure 3.3: Four unmodulated and orthogonal carriers (a) in time and (b) in frequencydomainIf the duration Tb of the pulse is accurately set to half a period of the lowest carrier,the resulting sinc functions in frequency domain are shifted in a way that the individualmaxima of the main lobes meet the �rst zero-crossing points of the adjacent carriers. Thecarriers are modulated in parallel by individual symbols Xk during a pulse interval, andthis interval is called the block duration.In OFDM, N symbols are transmitted in parallel. In this report, the parallel symbols arereferred to as a block. Therefore, Tb is the e�ective block duration and Ts is called thethe symbol duration. Tb is called the e�ective block duration since it does not include theredundant OFDM guard interval, see section 3.2.2.The relationship between the centre frequency f0 of the lowest carrier and that of carrierk (0 < k < N � 1), fk, is given by fk = f0 + k=Tb.However, the orthogonality between OFDM-subchannels may also be assured if the blockduration Tb has been extended to nTb with n = 1; 2; 3 � � � and thus if the maxima of thenarrowed sinc functions have been moved to the next zero-crossing points of the othercarriers. It has to be mentioned that in this case one of the major advantages of OFDM,

3.2. The OFDM Approach 39the accurate bandwidth e�ciency, is lost.ωcos ( t) sin ( t)ω0

Serial-

To-

Parallel

Converter

0

X (n)+jX (n)

. . .

X (n)

X (n)

X (n)

X (n)

. . .

cos ( t)ωk ωksin ( t). . .

. . .

j tω

S

P

. .

Multiplex

Data Encoder

to channel

HF-Modulator

datan

n

0

0

’

’

’’

’’

. .

e

’’’ kk

RF

Figure 3.4: OFDM TransmitterIn Fig. 3.4, the principle of an OFDM transmitter including the phase shift keying mod-ulation block and the modulation to the intermediate frequency (IF) is shown in detail.Let the number of complex-valued subcarriers be N . Hence, N symbols are collected inthe serial-to-parallel converter and then transmitted over N complex carriers. The blockduration Tb as the e�ective signalling interval has been increased which makes the systemless susceptible to delay spread impairments. After multiplexing, the summation signal inbaseband is given asN�1Xk=0 �X 0kcos(2�fk)�X 00k sin(2�fk)� = Re(N�1Xk=0 Xkej2�fkt) (3.1)where X 0k and X 00k are real sequences representing the in-phase and quadrature componentsof Xk, respectively.The FDM is achieved, not by bandpass �ltering as it is common in conventional systems,but by baseband processing.The right term of Equation (3.1) can exactly be interpreted as an inverse N -point discreteFourier transform (IDFT). Thus, the system complexity, e.g., the use of oscillators andsub�lters, can be greatly reduced by eliminating any pulse shaping and �ltering. This isdone by using the fast Fourier transform (FFT) to implement the modulation processes.The summation signal after the multiplexer is e�ectively the Fourier transform of theoriginal data stream and the bank of the coherent modulators can be interpreted as anIDFT.On the receiver side, the received signal is demodulated, sampled at the block rate 1=Tb,and passed to a discrete Fourier transform (DFT) operator which converts the signal backto the frequency domain. Fig. 3.5 shows a simpli�ed diagram of a receiver where the DFTis depicted as a �lter bank of short-time integrators. A reconstructed decision variable Ykon subchannel k can be written asYk(n) = 1Tb TbZ0 y(t)e�j2�fktdt (3.2)Understanding the receiver as a �lter-bank of short-time integrators and multipliers, each

40 3. Orthogonal Frequency Division Multiplexing

k

ω

ωkcos ( t)ω

0

Y (n)

Y (n)

cos ( t) sin ( t)ω0

sin ( t)

. . .

. . .

. . .

. . .

. . .

. . .

. . .

Y (n)

Y (n)

j t

Short Time Integrators

(Integrate & Dump)

to DQPSK

Demodulation

Converter

Serial

To-

Parallel-

e RF

HF-Demodulator

ω

y(t)

P

S

n

n

0

0

’

’from Channel

’’

’’

Figure 3.5: OFDM Receiverof the receiver �lters has to be matched to its corresponding carrier. This is done bymatching the oscillator frequencies of the multiplication signals to the carrier frequencies.In the receiver, the entire signal as the sum of all the modulated subcarriers is multipliedwith the di�erent and matched frequencies. The results are then integrated on each receiver�lter. Because of the orthogonality between the carriers due to the suitable carrier spacing,the integration results in the receiver depend only on the matched and relevant carriers.The basic impulses of [20] show the way of recovering the symbol on a subcarrier. Onlythe k-th carrier contributes to the result of the k-th sub�lter. Short-time integrators canalso be explained as rectangular functions in time domain. The impulse responses of thetransmitter �lters as well as the receiver �lters are then interpreted as rectangular functionswith the interval (0::Tb). When multiplying these functions with the orthogonal frequenciesand after convoluting the transmitter with the receiver �lter, the normalised results arefound as basic impulses, see Fig. 3.6.0.5-1

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

t / T

l=k

0 1-0.5

l=k

Figure 3.6: Orthogonality Condition depicted as basic impulse. The �gure shows thenormalised time-domain results of the convolution of a transmitter �lterwith receiver �lters.Due to recent advances of digital signal processing (DSP) and integrated circuit technolo-gies, a cost e�ective implementation of an OFDM system with its massive computationand the need of high speed memory is possible. The availability of e�cient IFFT/FFTalgorithms is one of the major reasons for making OFDM systems applicable.

3.2. The OFDM Approach 41OFDM su�ers from some systematic limitations. In comparison to single carrier systems,it introduces inter-channel interference (ICI) between the subchannels when transmittedover a non ideal radio channel.Concerning synchronisation issues, it can be shown that sensitivity of OFDM to carrierfrequency errors is by several orders higher than that of single carrier systems, due to theoverlapping subbands.With N su�ciently large, OFDM signals can be seen as the summation of many in-dependent subcarrier signals. Therefore, the amplitude of the resulting signal becomesapproximately Gaussian. Thus, an OFDM signal has a noise like amplitude with a verylarge dynamic range (large crest-factor). Therefore, it requires power ampli�ers to workwith a high peak to average power ratio. Transmitters have to work with a high powerback-o� to maintain linearity.Another drawback results from the DFT transform theory. The calculated waveform aftera DFT is a continuously repetitive sequence and the minimum information required isone cycle of this pattern. In other words, the DFT output has a periodic spectrum withperiod N=Tb, each period being composed of N pulses with a frequency separation of 1=Tb.In order to limit the transmitted signal spectrum and to assign one sinc frequency pulseto each of the individual N symbols comprised in a given DFT block, a lowpass �lter isneeded. A physically realisable and non-ideal �lter must be employed. Assuming raised-cosine spectral shaping of this �lter, the outer carriers on the edges of each side of a DFTblock are severely attenuated. Depending on the �lter quality these carriers may not beusable and have to be set to zero. They are then referred to as \virtual carriers" and �rstintroduced in [25].3.2.2 The Guard Interval Tg3.2.2.1 Cyclic ExtensionIn indoor radio environments, signals coming from multiple indirect paths added to thedirect path mean that the condition of orthogonality between subcarriers is no longerful�lled, which results in ICI. Furthermore, the multipath e�ect causes inter-symbol in-terference (ISI). In terms of the modelling approach described in the following, this e�ectshould particularly be called inter-block interference (IBI). Since the expression \ISI" iswell known, this shall be used in this report.Both the e�ects can be circumvented by adding a guard interval Tg before the block periodTb. A new block duration, T 0b = Tg + Tb is then obtained. The guard interval is generallysmaller than Tb=4. If Tg is longer than the maximum channel excess delay, the subcarriersare still mutually orthogonal inside the e�ective block interval (Tg::T 0b). Fig. 3.7 shows theprinciple of adding a guard interval, where the cyclic extension of two carriers is shown onthe left side.The guard interval is chosen longer than the excess delay of the given power delay pro�le.Thus, there is no multipath distortion during the useful period (Tg::T 0b). On the right sideof Fig. 3.7, the integration periods of the transmitter and the receiver �lters are shown.Note that the block duration is now increased from Tb to T 0b and thus the data rate ona subchannel decreases. To obtain the same overall data rate like it was without theextension, the number of carriers in the OFDM system must be increased.

42 3. Orthogonal Frequency Division Multiplexing

TBTG

B transmitter

time

receiver

TG

T ’

1/T ’

1/T ’

B

timeB

B

T ’

T ’

B

elementary signaluseful periodguard

interval

symbol duration

power delay profile

t

Figure 3.7: Cyclic extension of the block duration and impulse responses of thetransmitter and receiver �lters.Again, the basic impulses of Fig. 3.8 are useful to indicate the gain of introducing theguard time. When using the guard interval in a multipath radio channel, the resultingimpulses are less susceptible to ISI and ICI and it becomes more important to maintainthe orthogonality.0.4

0.2

0

-0.2

-0.4

0 1-0.5 0.5-1

0.6

0.8

1

1.2

l=k

l=k

t / T

Tg=01.2

l=k1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

0 1-0.5 0.5-1

t / T

l=k

Tg>0

Figure 3.8: Basic impulses after introducing the guard interval.3.2.2.2 Bandwidth E�ciencyThe carrier spacing between the OFDM subcarriers is given asfl � fk = nTb n = 1; 2; 3; � � �N � 1 (3.3)where l; k = 1; 2; 3; � � �N .This expression points out that the carrier spacing only depends on the e�ective blockduration and does not rely on the total block duration T 0b or the guard time Tg.

3.2. The OFDM Approach 430

Frequency

Car

rier

Spe

ctra

f0

f1

f2

f3

f4

f5

f6

f7

Tg=0

0

Frequency

OF

DM

Pow

er S

pect

rum

f0

f1

f2

f3

f4

f5

f6

f7

Tg=0

Figure 3.9: Spectra of an 8-carrier OFDM system with Tg = 0. The modulated carriersare assumed to be uncorrelated, thus, the overall spectrum is the sum of thecarrier spectra.The spectrum of the transmitted signal of an 8-carrier OFDM system without any guardtime (Tg = 0) is shown in Fig. 3.9. The orthogonality is clearly visible since the cen-tre frequencies of the subchannels meet exactly the zero crossing points of the adjacentcarriers.Introducing the guard interval, there are some systematic disadvantages for the use ofOFDM in multipath environments. Some of the transmitted signal energy is lost for thesignal recovering. The OFDM receiver only uses the signal inside the e�ective block dura-tion. Thus the e�ective useful signal energy decreases if the guard interval is introduced.ERx(Tg>0) < ERx(Tg=0)An excessive guard space will reduce the throughput of the system, or conversely increasethe transmission bandwidth. There are two ways of introducing the periodical extension:� Tb stays constant and T 0b = Tb + Tg is the new block duration.� T 0b is set to Tb and then Tb is set to T 0b � Tg.In [17], the �rst way is investigated by analysing the use of a guard interval in OFDMfor a two path channel with white Gaussian noise. It is shown that the e�ective blockduration Tb decreases when a guard interval is used. To maintain the same data rate thetotal block duration T 0b must stay constant. The carrier spacing must increase to keep theorthogonality between the subcarriers. Thus, the required bandwidth of the entire systemincreases and the signal power is not constantly distributed over the channel bandwidth,see Fig. 3.10.In the second way, a similar problem occurs after increasing the total block durationT 0b = Tg+Tb. Since now Tb stays constant, the carrier spacing does not have to be changed.But since the data rate decreases the width of the power density spectra of the modulatedcarriers decreases, too. This also results in deep power density gaps in frequency betweenthe carriers.This remarkable result is the reason for the loss of bandwidth e�ciency when introducing

44 3. Orthogonal Frequency Division Multiplexing0

Frequency

Car

rier

Spe

ctra

f0

f1

f2

f3

f4

f5

f6

f7

Tg=T

b*20%

0

Frequency

OF

DM

Pow

er S

pect

rum

f0

f1

f2

f3

f4

f5

f6

f7

Tg=T

b*20%

Figure 3.10: Spectra of an 8-carrier OFDM system with Tg = 0:2Tb. In this case, Tbstays constant and T 0b is increased to Tg + Tb.the guard interval. In this case, the signal power is not constantly distributed over thechannel band. When measuring the power spectrum of an entire OFDM signal, small gapsare visible between adjacent carriers. Therefore, the number of useful subchannels can bemeasured by counting the local maxima of the signal spectrum inside the channel band.In Fig. 3.11 to 3.13, this is shown for a 4-carrier OFDM signal, where the averaged signalspectra (logarithmic scale, 10dB/unit) for di�erent guard intervals can be seen. The centrefrequency of the shown band is 480MHz and the frequency span is 50MHz.In the OFDM demonstrator system, 4 adjacent carriers are spaced 2:625MHz apart (Tb �380ns). The centre frequency (IF) is 479:5MHz. The carriers are randomly DQPSK-modulated where the four symbol streams are mutually uncorrelated. In Fig. 3.11, noguard time is used. In Fig. 3.12 the guard interval is set to Tg = 0:25Tb and in Fig. 3.13the guard interval is set to half the block duration Tb. Note that when Tg increases, visiblegaps between the subchannels occur (10dB for Tg = 0:5).3.2.3 Advanced OFDM Techniques, COFDM and MC-SS3.2.3.1 Coded OFDM and Frequency DiversityTransmission schemes in a multipath channel su�er from frequency selective fading. InOFDM systems, the use of channel coding taking into account the correlation betweenthe individual subchannels, gives a great improvement in the system's BER performance.If the number of arriving paths inside the guard interval is large, the frequency fadesof the narrow subchannels become uncorrelated. This gives way for employing frequencydiversity techniques, interleaving and channel coding.Frequency diversity may be implemented in OFDM systems by duplicating the modu-lated information symbols on carriers spaced the maximum distance apart. So any fadinga�ecting one carrier is less likely to a�ect the other one carrying the same data.Block codes are forward error correction (FEC) codes that enable a limited number oferrors to be detected and corrected without retransmission. Parity bits are added to blocksof message bits to make code blocks. A total of � � � redundant bits are added to the �

3.2. The OFDM Approach 45

Figure 3.11: 4-Carrier demonstrator spectrum. The carriers are randomly modulatedand no guard interval is applied.

Figure 3.12: The Spectrum with an introduced Tg = Tb=4

46 3. Orthogonal Frequency Division Multiplexing

Figure 3.13: Tg increased to Tb=2information bits for the purpose of detecting and correcting errors. The code is referredto as a (�; �) code.Reed-Solomon (RS) codes are block codes capable of correcting errors which appear inbursts (whereas BCH coding is usually considered more e�ective for random errors), see[13]. Currently, in OFDM prototypes developed at P.R.L., RS codes are used since cost-e�ective implementations of RS coding/decoding systems are available.When interleaving the symbols to the subchannel, another degree of freedom is introduced.In [19], Turbo codes are suggested for a large interleaving size. Turbo codes are created byconcatenating classical codes, e.g. BCH-codes. They are known to work at near optimumperformance (near the Shannon capacity).Coding as well as frequency diversity techniques imply transmission of redundant data. InWireless ATM applications, padding is required to ensure that there are su�cient bits to�ll the last input codeword and to �ll the last OFDM block. Thus, when applying thesetechniques, the transmission bandwidth of the system increases.3.2.3.2 Spread Spectrum Techniques, MC-SSThe advantages and success of multicarrier (MC) modulation and of the spread spectrum(SS) technique are the reasons for recent investigations of the suitability of the combinationof MCM with SS, known as multicarrier spread spectrum (MC-SS) for cellular systems[24]. The combination bene�ts from the advantages of both schemes: Higher exibility,higher spectral e�ciency, simple detection techniques.A multiple access scheme based on direct sequence spread spectrum, known as direct se-quence code divisionmultiple access (DS-CDMA) relies on spreading the data stream usingan assigned spreading code for each user in the time domain. Cross- and auto-correlation

3.2. The OFDM Approach 47properties of the spreading codes o�er the capability to distinguish one component fromothers in the composite received signal.Di�erent multiple access concepts based on the combination of MCM with DS-CDMA havebeen introduced during the last years. They di�er in spreading and frequency mappingstrategies, but they are all based on the same principle.ωcos ( t) sin ( t)ω0

cos ( t)ωk ωksin ( t)

c (t) X (n)

X (n)

X (n)

X (n)

. . .

0

. . .

. . .

. . .

S

P

freq

to channeln

n

0

0

’

’

’’

’’

DS

data

time time

freqFigure 3.14: MC-CDMA multicarrier spreaderOne common concept, known as MC-CDMA, is based on a serial concatenation of DSspreading with MC modulation [18], [24]. The high rate DS spread data stream is MCmodulated in the way that the chips of a spread data symbol are transmitted in parallelon each subcarrier. Thus, many users may occupy the total bandwidth for the transmissionat the same time. The separation of the signals is performed in the code domain. The datasymbols are �rst multiplied with the chips of the spreading code assigned to speci�c usersand then serial parallel converted. This re ects that the MC-CDMA system performs thespreading in the frequency domain.Other MC-SS concepts, known as MC-DS-CDMA and multi-tone-CDMA (MT-CDMA)are based on �rst converting the data stream onto parallel low rate subchannels beforeapplying the DS spreading on each substream.3.2.4 History and ApplicationsThe concept of using parallel data transmission and frequency division multiplexing waspublished more than three decades ago. An United States patent on OFDM was issuedin 1970. The initial applications were in military communications. Recent advances indigital signal processing technologies have led the way for the massive implementationof OFDM techniques in the telecommunication electronics �eld. One recent successfulimplementation of OFDM is in asymmetric digital subscriber line (ADSL) technologythat has been selected in the United States for transmission of digitally compressed videosignals over telephone lines.In the next two sections, two European OFDM applications are brie y discussed. In section3.2.4.1, digital audio broadcasting (DAB) is explained. DAB was developed in Europe forterrestrial and satellite broadcasting of multiple digital audio programs to mobile receivers.OFDM has been evaluated in Europe for digital television terrestrial broadcasting. A pan-European project Digital Video Broadcasting (DVB) was launched in 1993 for specifying

48 3. Orthogonal Frequency Division Multiplexingsatellite, cable and terrestrial digital TV (DVB-S, DVB-C and DVB-T, respectively). Somedetails of the adopted OFDM transmission scheme in DVB-T are explained in section3.2.4.2.3.2.4.1 Digital Audio Broadcasting (DAB)Current analogue FM radio broadcasting systems have reached the limits of technical im-provement. The digital audio technology has set technical standards which are far beyondthose which are currently available to radio broadcasting transmitted over analogue FMsystems.The DAB standard was developed to solve this problem. By using modern data reduc-tion techniques, e.g., psychoacoustic source coding, large bandwidth requirements are pre-vented. For the transmission technique, COFDM was adopted with channel coding usinga convolutional code. Three modes are de�ned according to di�erent applications:� Mode 1 is speci�ed for the use in single frequency networks (SFN) for a carrierfrequency up to 375MHz.� Mode 2 is designed for local broadcasting and also includes the local single frequencynetwork. The RF frequency can be up to 1:5MHz� Mode 3 has been developed for terrestrial and satellite con�gurations and a hybridsatellite/terrestrial application. The mode is suitable for RF carrier frequencies upto 3GHz.Table 3.1 gives an overview over the main OFDM parameters speci�ed for DAB.Mode 1 Mode 2 Mode 3application SFN local coverage satellitetotal block duration T 0b 1:25ms 312:5�s 156:25�sblock duration Tb 1:0ms 250�s 125�sguard interval Tg 250�s 62:5�s 31:25�snumber of carriers N 1536 384 192Table 3.1: DAB parameters in modes 1, 2 and 3Because the DAB system has been designed to be relatively immune to multipath e�ects,the receiver can operate successfully when two or more signals are received. Several trans-mitters can therefore be used on the same frequencies without causing interference. On thisbasis a hybrid system can be used where land-based transmitters supplement the coverageof a satellite service. The satellite would give coverage to rural and urban areas, while theterrestrial transmitters are available for heavily screened areas, for example city centres.A mobile receiver in these areas may receive more than one signal, from the satellite andfrom the local transmitter. Provided the relative delay between the signals is not too great(�t < Tg), the system will operate without ISI and ICI.

3.2. The OFDM Approach 493.2.4.2 Terrestrial Digital TV (DVB-T)The European digital terrestrial television system (DVB-T) released by ETSI is based on2K/8K-point OFDM. In the 8K-Mode, up to 6818 non virtual subcarriers are available forthe lower bit-rate transmission. In order to help the receiver to recover the signal and toadapt it to the modulation and channel coding parameters, the transmitted OFDM signalincludes continual pilot carriers carrying signalling parameters. They are transmitted attwice the normal power level and modulated by a reference sequence.The applied modulation scheme is a non-uniform quadrature amplitude modulation (QAM),characterised by a greater distance between the adjacent states of di�erent quadrants thanbetween adjacent states in the same quadrant. This allows the simultaneous transmissionof (�rst) a high priority bitstream, modulating the most signi�cant bytes of a 16- or 64-QAM, which can be interpreted as a simple and robust QPSK modulation, and (second)a bitstream with lower priority modulating the remaining least signi�cant bytes, whichrequires a more sophisticated but less robust QAM demodulation.The implementation of the 8K mode is complex, which makes receivers expensive, but itslong block period used with the maximum guard interval allows a satisfactory receptioneven in the presence of very long multipath delays, such as in single frequency broadcastingnetworks. The 2K mode is simpler and the receiver is less expensive, but the shorter blockperiod reduces the performance in the presence of long echoes.Table 3.2 gives an overview over some of the OFDM parameters speci�ed for DVB-T.8K Mode 2K Modeapplication SFN local coverageblock duration Tb 896�s 224�sguard interval Tg Tb=4, Tb=8 or Tb=32 Tb=4, Tb=8 or Tb=32number of carriers N 8192 2048number of virtual carriers 8192 � 6818 2048 � 1706Table 3.2: Main parameters of the DVB-T system3.2.5 SummaryThe advantages and drawbacks of the OFDM transmission scheme are summarised in thissection. The advantages are:� OFDM makes e�cient use of the spectrum by allowing overlap.� The use of the cyclic pre�x (guard interval) reduces ISI and ICI.� The nearly ideal narrowband subchannels su�er only from at fading. Channel equal-isation becomes simpler than adaptive techniques in single carrier systems.� By adaptively distributing the power budget over the individual subcarriers, OFDMperforms at the highest theoretical limits of the channel capacity.

50 3. Orthogonal Frequency Division Multiplexing� Cost-e�ective implementations of OFDM systems with several thousands of subcar-riers are available by using e�cient IFFT/FFT algorithms.� Provided that the number of arriving paths inside the guard interval is large, powerfulcoding and diversity techniques are available to reduce the BER.� The combination of OFDM with spread spectrum techniques (MC-SS) bene�ts fromthe advantages of both schemes, e.g. exibility, spectral e�ciency and simple detec-tion techniques.In terms of drawbacks it must be mentioned:� MCM systems su�er from ICI due to the loss of orthogonality between the subcarriers.� OFDM signals have a noise like amplitude with a very large range (large crest-factor). Therefore, nonlinearities or peak-limitations of the channel and ampli�erscause severe signal distortions.� Due to the periodicity of the IFFT output, some outer carriers are severely attenuatedand have to be set to zero. These virtual carriers reduce the bandwidth e�ciency.� Applying the guard interval to suppress the ISI and ICI result in loss of bandwidthe�ciency.� FEC and diversity techniques imply transmission of redundant data. Padding is re-quired if the codes do not �t to the OFDM blocks. Thus, the transmission bandwidthincreases.� Because incoming data is processed in blocks, OFDM systems introduce a trans-mission delay which can be incompatible with WATM applications like Hiperlan/2,where the turn-around time is required to be very short.� Synchronisation is di�cult in OFDM, it is sensitive to carrier frequency o�sets anddrifts.It is important to note that OFDM is much more sensitive to frequency dependent dis-tortions than its single carrier counterpart. Without coding, the performance of OFDMover a frequency selective channel is substantially worse than an equivalent single carriersystem using linear equalisation.

3.3. The Analytical Model of OFDM Systems 513.3 The Analytical Model of OFDM SystemsThe following calculations are made as a basic framework for modelling an OFDM trans-mission system. They are based on the work of Viterbo and Fazel [14]. In appendix A, thebelow used symbols are listed in a table.Let fk = fc + kTb for k = 0 : : : N � 1 (3.4)be the N subcarrier frequencies, where fc is the carrier frequency and Tb is the e�ectiveOFDM block duration. Since all calculations are done in the baseband the carrier frequencyfc shall be assumed to be 0: fc = 0 (3.5)Let Tg be the duration of the guard interval and T 0b = Tb + Tg be the total block durationdue to the cyclic extension. The orthogonal basis functions are�k(t) = ( ej2�fkt : �Tg � t < Tb0 : else (3.6)The transmitted OFDM baseband signal in time domain is given asx(t) = 1Pn=�1N�1Pk=0 Xk(n)�k(t� nT 0b) (3.7)where Xk(n) are the DQPSK symbols transmitted on the k-th subcarrier in the n-th block.For the receiver detection, the way of decoding the decision variables of each subchannelcan be written asYk(n) = 1Tb Tb+nT 0bZnT 0b x(t)�k�(t� nT 0b)dt = 1Tb Tb+nT 0bZnT 0b x(t)e�j2�fk(t�nT 0b)dt (3.8)where the asterisk means complex conjugation. The detection can be easily done by ap-plying the DFT.3.3.1 The Orthogonality ConditionTwo channels are orthogonal, if they do not interfere with each other, which may bemaintained in time, frequency or code domain. Here, the orthogonality condition is givenin the time domain as1Tb TbZ0 �l(t)�k�(t)dt = 1Tb TbZ0 ej2�(fl�fk)tdt = ( 1 : l = k0 : l 6= k (3.9)

52 3. Orthogonal Frequency Division Multiplexingwhich is referred to as the inner product of the basis functions [28]. According to (3.8),the correct receiver detection for the k-th subchannel at the 0-th block (n = 0) is given asYk(0) = 1Tb TbZ0 x(t)�k�(t)dt (3.10)and assuming no impact of the preceding blocks (perfect channel), this can be calculatedas Yk(0) = 1Tb TbZ0 x(t)e�j2�fktdt= 1Tb TbZ0 N�1Xl=0 Xl(0)ej2�(fl�fk)tdt (3.11)With (3.9) the received symbol is found:Yk(0) = Xk(0) (3.12)In (3.11), if l 6= k, the result of the integration has to be 0 to achieve orthogonality. Toful�ll this constraint, the spacing between adjacent subcarriers must be set to a value ascalculated below. For l 6= k, the inner product of the basis functions must be 0:0 = 1Tb TbZ0 N�1Xl=0 Xl(0)ej2�(fl�fk)tdtand the required carrier spacing can be calculated:0 = 1Tb TbZ0 N�1Xl=0 Xl(0)ej2�(fl�fk)tdt= 1Tb "N�1Xl=0 Xl(0)# 1j2�(fl � fk) hej2�(fl�fk)Tb � 1i) 0 = ej2�(fl�fk)Tb � 1) 2�(fl � fk)Tb = 2�n n = 1; 2; 3; � � �Hence, the carrier spacing for maintaining the orthogonality between adjacent subchannelsis found as fl � fk = nTb n = 1; 2; 3; � � � (3.13)

3.3. The Analytical Model of OFDM Systems 533.3.2 Multipath Channel ModelThe channel is assumed to be a WSS multipath channel with the impulse response [16]h(t) = 1pM MXm=1Amej(�m+2�fDmt)�(t� �m) (3.14)where M is the total number of the re ected paths, Am, �m, �m and fDm are magnitude,excess delay to the Line-Of-Sight, phase rotation and Doppler frequency of each path. Thefactor p1=M ensures convergence as N !1.If the Doppler frequencies are small compared to 1=T 0b (fDT 0b � 1) which is usually thecase in indoor scenarios an important simpli�cation can be done. The phase rotation dueto the Doppler frequency can then be replaced by a constant phase shift in the integrationinterval of each block.The linearity of this model enables the e�ect of each single path to be considered separately.In the following, �rst the simple case with one direct path and one echo is analysed. Second,the results are extended and generalised to the multipath channel given in (3.14).The received signal of the two-paths model is given byy(t) = x(t) +Aej(�+2�fDt)x(t� �) (3.15)Again, A, � , � and fD are magnitude, excess delay, phase rotation and Doppler frequencyof each path, respectively. Hence, the output of of the k-th subchannel for the n-th blockcan be written as the sum of two termsYk(n) = Xk(n) +Ek(n) (3.16)where the �rst term is due to the direct path and the second one is the interfering termproduced by the echoes of the delayed paths.Because it is assumed that � � T 0b only the (n � 1)-th block will interfere with the n-thblock and only these two cases have to be analysed:� � Tg and Tg < � � T 0b3.3.3 Maximum Excess Delay smaller than Tg (� � Tg)Consider the two-path assumption indicated in Fig 3.15. The second path arrives with andelay smaller than the guard time Tg.If � � Tg there is no impact of the preceding blocks on the current block. The receiveronly uses the signal from t = 0. The received signal can be written asYk(n) = 1Tb Tb+nT 0bZnT 0b x(t)e�j2�fk(t�nT 0b)dt+Ek(n)= 1Tb Tb+nT 0bZnT 0b x(t)e�j2�fk(t�nT 0b)dt+ 1Tb Tb+nT 0bZnT 0b Aej(�+2�fDt)x(t� �)e�j2�fk(t�nT 0b)dt

54 3. Orthogonal Frequency Division MultiplexingTx

time

time

path 1

...

path 2

...

block (n-1) block n

Rx

<ττ Tg

Tb’bT

t

TgFigure 3.15: Sent and received blocks with 2-paths channel model and � � Tg.Using (3.8) the second term due to the echo is obtained asEk(n) = ATb Tb+nT 0bZnT 0b ej(�+2�fDt) 24 1Xi=�1N�1Xl=0 Xl(i)�l(t� iT 0b � �)35 e�j2�fk(t�nT 0b)dt (3.17)It is assumed that only one preceding block impacts the current block. Hence, with(nT 0b � Tg) < (t� iT b0 � �) < (nT 0b + Tb) and � � Tg, Eqn. (3.17) can be rewritten asEk(n) = ATb Tb+nT 0bZnT 0b ej(�+2�fDt) "N�1Xl=0 Xl(n)ej2�fl(t�nT 0b��)# e�j2�fk(t�nT 0b)dt= ATb N�1Xl=0 Xl(n)e�j2�fl� Tb+nT 0bZnT 0b ej(�+2�fDt)ej2�(t�nT 0b)(fl�fk)dt (3.18)Substituting u = t� nT 0b with dudt = 1 it follows thatEk(n) = ATb ej(�+2�fDnT 0b) N�1Xl=0 Xl(n)e�j2�fl� TbZ0 ej2�fDuej2�(fl�fk)uduPremising fDT 0b � 1 as mentioned above, the phase rotation due to the Doppler e�ect canbe replaced by a constant phase shift that can be set to 0. Hence,Ek(n) = ATb ej(�+2�fDnT 0b) N�1Xl=0 Xl(n)e�j2�fl� TbZ0 ej2�(fl�fk)udu (3.19)Using the orthogonality conditions (3.9) the echo term can be written asEk(n) = Aej(�+2�fDnT 0b)e�j2�fk�Xk(n) (3.20)

3.3. The Analytical Model of OFDM Systems 55Finally, the received symbols are obtained asYk(n) = Xk(n) +Ek(n) = h1 +Aej(�+2�fDnT 0b)e�j2�fk� iXk(n) (3.21)For the general channel model with M paths it can be concluded thatYk(n) = " 1pM MPm=1Amej(�m+2�fDmnT 0b)e�j2� kTb �m#Xk(n) (3.22)3.3.4 Maximum Excess Delay longer than Tg (Tg < � � T 0b)Now, if � > Tg the preceding block interferes with the current block and this results inboth ISI and ICI, as shown in Fig. 3.16. The resulting e�ect is that the orthogonalitybetween the carriers is lost.time

Tx

path 1

time

...

path 2

...

block (n-1) block n

Rx

τ TbTg

Tb’Tg

t

<

τ

ISI ICI

Figure 3.16: Sent and received blocks with 2-paths channel model and � > Tg.The received and distorted symbols areYk(n) = 1Tb Tb+nT 0bZnT 0b x(n)(t)�k�(t� nT 0b)dt+ � � �+ 1Tb Tb+nT 0bZ��Tg+nT 0b Aej(�+2�fDt)x(n)(t� �)�k�(t� nT 0b)dt+ � � �+ 1Tb ��Tg+nT 0bZnT 0b Aej(�+2�fDt)x(n�1)(t� �)�k�(t� nT 0b)dt (3.23)where x(n)(t) is the signal of the current block n and x(n�1)(t) the signal of the precedingblock n� 1.

56 3. Orthogonal Frequency Division MultiplexingThis can be written as Yk(n) = Xk(n) +Ek(n)ICI +Ek(n)ISI (3.24)After some basic calculations (see appendix A), the inter-channel interference Ek(n)ICIcan be written as Ek(n)ICI = Aej(�+2�fDnT 0b) N�1Xl=0 Xl(n)�l;k(�) (3.25)and the inter-symbol interference Ek(n)ISI asEk(n)ISI = Aej(�+2�fDnT 0b) N�1Xl=0 Xl(n� 1)�l;k(�) (3.26)with �l;k(�), �l;k(�) given in (3.27) and (3.28). Note that the term Ek(n)ICI also includesthe fading of the carrier with itself due to interference. This is given as �l;k(�) with l = k.In appendix A, the parameters �l;k(�) and �l;k(�) are determined. The results can besummarised to�l;k(�) = 8><>: Tb��+TgTb e�j2�k� 1Tb : l = ke�j��2 lTb ��(l�k)Tb+��TgTb � sin��(l�k) 1Tb (Tb��+Tg)��(l�k) : l 6= k (3.27)�l;k(�) = 8><>: ��TgTb e�j2�k(��T 0b) 1Tb : l = ke�j��2 lTb (��T 0b)�(l�k) ��TgTb � sin��(l�k) ��TgTb )��(l�k) : l 6= k (3.28)�k;k(�) describes the loss of orthogonality in the k-th subcarrier (l = k). Due to the mul-tipath channel the carriers are distorted. This results in deep fading during transmission.Note that if Tg increases, Tb decreases for a constant T 0b. Thus, the term Tb + Tg in 3.27is constant and independent of Tg, if the data rate and the number of carriers is constant(T 0b; N = const).The interference between two di�erent channels is expressed in �l;k(�) with l 6= k. Someof the power transmitted in one subchannel is transferred into the adjacent subchannelsduring transmission.�l;k(�) shows the impact of the preceding blocks on all the simultaneously transmittedcurrent blocks. However, if l = k, this e�ect is obvious since the preceding block of thek-th subcarrier distorts the current block of the k-th subcarrier. If l 6= k, the ISI betweendi�erent subchannels is shown in (3.28).Calculating the limits for � ! Tg, the error term Ek(n)ISI + Ek(n)ICI equals the errorterm of (3.21) in section 3.3.3, where the excess delay of the second path is smaller thanTg(� � Tg).

3.3. The Analytical Model of OFDM Systems 57lim�! Tg �k;k(�) = e�j2� kTb �lim�! Tg;l 6=k�k;l(�) = 0lim�! Tg �k;k(�) = 0Calculating these limits is a way to validate the parameters by comparing the resultinginterferences with Ek(n) of Eqn. 3.21. There, the second and delayed multipath componentis assumed to arrive inside the guard interval. When � ! Tg, the interference termsdegenerate to Ek(n) of Eqn. 3.21, thus, a general model with more than one delayed pathcan be found as is done in the next section. In the general model below, signal componentswithin the guard interval and components with excess delays larger than Tg are modelledto �nd a representative description of real transmission scenarios.3.3.5 Generalising to the Multipath ChannelBy generalising the multipath channel model of (3.14) the received symbols are given asYk(n) = 1pM MXm=1;�m�TgXk(n)Amej(�m+2�fDmnT 0b)e�j2�fk�m + � � �+ 1pM MXm=1;�m>Tg "Amej(�m+2�fDmnT 0b) N�1Xl=0 Xl(n)�l;k(�m)#+ � � �+ 1pM MXm=1;�m>Tg "Amej(�m+2�fDmnT 0b) N�1Xl=0 Xl(n� 1)�l;k(�m)# (3.29)The complex path weights of the delayed paths (Amej(�m+2�fDmnT 0b)) are equivalent tothe bin weights Hm of the ComNets indoor channel model. Every bin represents a set ofdelayed paths in a given excess delay. The �rst bin H0 is called the deterministic bin anddoes not follow any distributions.Using the bin weights, the received symbol can be expressed asYk(n) = 1pM MXm=1;�m�TgXk(n)Hme�j2�fk�m + � � �+ 1pM MXm=1;�m>Tg "Hm N�1Xl=0 Xl(n)�l;k(�m)#+ � � �+ 1pM MXm=1;�m>Tg "Hm N�1Xl=0 Xl(n� 1)�l;k(�m)# (3.30)where Hm = Amej(�m+2�fDmnT 0b)Reordering the terms the three impacts of an OFDM system in a multipath channel, thesymbol interference with itself, the ISI and the ICI can be expressed:

58 3. Orthogonal Frequency Division MultiplexingYk(n) = 1pMXk(n) MXm=1;�m�TgHme�j2�fk�m + 1pMXk(n) MXm=1;�m>TgHm�k;k(�m) + � � �+ 1pM MXm=1;�m>Tg 24Hm N�1Xl=0;l 6=kXl(n)�l;k(�m)35+ � � �+ 1pM MXm=1;�m>Tg "Hm N�1Xl=0 Xl(n� 1)�l;k(�m)# (3.31)In the �rst line of (3.31) the fading due to interference is shown. In a multipath environmentevery symbol interferes with itself. Bins inside the guard interval (� � Tg) only contributeto this e�ect and do not cause ISI or ICI. The orthogonality is maintained. However, thebins later than Tg also carry power of the symbol Xk(n) itself and thus contribute to thisinterference fading e�ect.Severe distortion due to the loss of orthogonality between the subchannels is expressed inthe second term of (3.31). If the excess delay of a bin is longer than the guard time Tg, theadjacent subchannels do interfere with each other. Some energy of the symbol Xl(n) willthen be received at Yk(n) with l 6= k. This is called the inter-channel interference (ICI).The third term in (3.31) clari�es the impact of the preceding block n� 1. If there are binswith an excess delay longer than Tg, the preceding symbols interfere with the current andpresent symbols. Not only some energy of the symbol Xk(n� 1) will be received at Yk(n)but also some energy of the adjacent symbols Xl(n� 1) with l 6= k of the preceding block.These symbols also contribute to this e�ect, called inter-symbol interference (ISI).In section 3.3.2 it was assumed that �m � T 0b. Thus, only the last preceding block interfereswith the present block.Let �0k;k = MXm=1;�m�TgHme�j2� kTb �m + MXm=1;�m>TgHm�k;k(�m)represent the interference of the symbols. Let�0l;k = MXm=1;�m>TgHm�l;k(�m) for l 6= krepresent the e�ects due to ICI and let�0l;k = MXm=1;�m>TgHm�l;k(�m)represent the ISI e�ects. Now Yk(n) can be rewritten asYk(n) = �0k;kpMXk(n) + N�1Pl=0;l 6=kXl(n) �0l;kpM + N�1Pl=0 Xl(n� 1) �0l;kpM (3.32)The three above derived parameters completely describe the systematical errors in thecase that multipath components arrive with delays larger than the guard interval. The

3.3. The Analytical Model of OFDM Systems 59constructive or destructive fading of di�erent signal waves at the receiver antenna occurregardless of the chosen guard interval. The ISI and ICI parameters are e�ected by Tg anddecrease to 0 if the guard interval has been set to a value larger than the excess delay ofthe last received signal fragment.3.3.6 The Statistical Distributions of �0k;k, �0l;k and �0l;kIn [21], the bit error rate of a �4 -DQPSK modulated signal in a Rayleigh fading channelis analytically derived. These calculations need to know the distributions of the in-phaseand quadrature components of the distortion due to the radio channel.In (3.32) the received decision variable for the DQPSK demodulation is shown. If thedistributions of the three terms are known, the expected bit error rate on each subchannelcan be calculated using [21].The terms in (3.32) denote the fading, the ICI and the ISI. In a more general channelmodel, a fourth term for the additive noise (AWGN) has to be considered. This term isneglected for the sake of simplicity.Using the ComNets Indoor Radio Channel, the statistical distribution of the in-phasecomponent of �0k;k is derived in the following. Calculating the distributions of �0l;k and �0l;kcan be done in the same way and is not presented below.The channel model is based on independently Gaussian distributed quadrature componentsof the bin magnitudes. Only the �rst and static bin does not follow any distribution. Letthe channel be a three path channel with one static bin and two uncorrelated Rayleighfading bins. The �rst bin is modelled without excess delay (�1 = 0). The excess delay �2of the second bin is assumed to be smaller than the guard time Tg and the delay �3 of thethird bin is assumed to be greater than Tg (Tg < �3 < Tb). The fading parameter, �0k;k,can thus be written as�0k;k = 2Xm=1Hme�j2� kTb �m +H3�k;k(�3)= H1e�j2� kTb �1 +H2e�j2� kTb �2 +H3Tb � �2 + TgTb e�j2� kTb �3Whereas H1 is deterministic and constant during transmission, the magnitudes H2 and H3are Rayleigh distributed and thus their quadrature components are zero-mean Gaussiandistributed. H1 = constH2 = <fH2g+ j=fH2gH3 = <fH3g+ j=fH3gTo determine the in-phase and quadrature components of �0k;k, some basic calculationshave to be done and, e.g., the real part is found as<f�0k;kg = H1 + <fH2g cos�2� kTb �2�+ =fH2g sin�2� kTb �2�+ � � �

60 3. Orthogonal Frequency Division Multiplexing+ <fH3gTb � �2 + TgTb cos�2� kTb �3�+ =fH3gTb � �2 + TgTb sin�2� kTb �3�By generalising to the general channel model with M bins, the in-phase component canbe obtained as<f�0k;kg = H1 + MXm=2;�m�Tg �<fHmg cos�2� kTb �m�+=fHmg sin�2� kTb �m��+ � � �+ MXm=2;�m>Tg <fHmgTb � �2 + TgTb cos�2� kTb �m�+ � � �+ MXm=2;�m>Tg =fHmgTb � �2 + TgTb sin�2� kTb �m�This term can de�nitely be understood as a Gaussian distributed variable since the bincomponents are already Gaussian distributed. Because of the zero-mean distributions, H1is the expected value of <f�0k;kg and using the basic identity depicted in Fig. 3.17, thevariance of <f�0k;kg can be found asE[(<f�0k;kg �H1)2] =MXm=2;�m�Tg �E[<fHmg]2 cos2 �2� kTb �m�+E[=fHmg]2 sin2 �2� kTb �m��+ � � �+ MXm=2;�m>Tg E[<fHmg]2 �Tb � �2 + TgTb �2 cos2 �2� kTb �m�+ � � �+ MXm=2;�m>Tg E[=fHmg]2 �Tb � �2 + TgTb �2 sin2 �2� kTb �m�

22

zero-mean

Gaussian distr.

var=

K

σ var= K

real scalar const

X Y

zero-mean

Gaussian distr.

σ 2Figure 3.17: Calculating the variance after weighting of a statistical variable.Note that the Hm are mutually statistically independent.In the same way the variances of the quadrature component and of the two parametersfor ISI and ICI are obtainable. These parameters, �0l;k and �0l;k, are Gaussian distributedif the Rayleigh fading bin model is used to determine the channel. Thus, a combination

3.3. The Analytical Model of OFDM Systems 61of the OFDM model based on the radio channel model with the model of [21] is a way toestimate the bit error rate of the DQPSK-OFDM system.3.3.7 The C/I Ratio of Subchannel kWith the assumption that the transmitted symbols are statistically independent, the C/Iratio can be calculated. For this, it is assumed that the preceding blocks are accuratelyknown (they have been correctly decoded in the previous interval) and that the channeldoes not change signi�cantly during a block duration T 0b.The C/I ratio is the ratio between the useful signalE 24����� �0k;kpMXk(n)�����235and the uncorrelated distortion signal due to the interference termsE 264������ N�1Xl=0;l 6=kXl(n) �0l;kpM + N�1Xl=0 Xl(n� 1) �0l;kpM ������2375where E[:] means the expected value of the statistic process.Since Xl(n) and Xk(n�1) for all k; l = 0::N �1 are not correlated, the interference powercan be expressed asE 264������ N�1Xl=0;l 6=kXl(n) �0l;kpM ������2375+E 24�����N�1Xl=0 Xl(n� 1) �0l;kpM �����235 (3.33)The symbols Xl(n), Xl(n) and Xk(n) represent DQPSK modulated symbols with an ab-solute value of 1. Since M is a constant value and the channel is assumed not to changesigni�cantly during a block duration, the ratio between the signal power and the interfer-ence power of each subchannel is obtained as(C=I)k = ����0k;k���2N�1Pl=0;l 6=k ����0l;k���2 + N�1Pl=0 ����0l;k���2 (3.34)If the channel characteristics change during a block duration, the parameters in (3.34)become statistic variables and their expected values have to be used instead.Using the OFDM model, the system performance is analytically derived for Ricean fadingmultipath channels as a function of the guard interval and the number of carriers. Thesensitivity of the OFDM system to the interference caused by echoes exceeding the guardtime can be analysed.

62 3. Orthogonal Frequency Division Multiplexing

CHAPTER 4RESULTS: Indoor Radio Channel Characteristic at 5.2GHzChannel models have been created for typical residential and o�ce scenarios. Factorybuildings, which are assumed to have di�erent characteristics, are not investigated inthis thesis. All models are based on pro�le classes developed by means of ray tracing. Inaddition, one model is created based on measurements. This model gives an impression ofthe accuracy of the ray tracing results.In the next section, the consequences of the validation of ray tracing by means of channelsounding are discussed. Channel classes, as proposed in [1] for the new Hiperlan/2 stan-dard, are described in section 4.3. Finally, in section 4.4, the resulting channel models forthe individual classes are presented and their characteristics are discussed.4.1 Validation of Ray Tracing Simulations by MeasurementsIn Fig. 4.1, a scenario de�nition �le is shown. It is the input �le for the ray tracingcalculations. A part of the P.R.L. o�ce and laboratory building, the 3rd oor of theCordless Communications Group, is modelled and used for prediction of the radio channelcharacteristic. The �gure and some additional scaling informations determine the site-speci�c environment for ray launching simulations. Di�erent line widths and patterns inthe �gure are associated with respective materials, walls, windows, doors and obstaclessuch as tables, shelfs and computer desktops.Tx5cTx5bTx5a

Tx

F213 F215 F217 F219 F221 F223 F227F225

F232F230F226F220

F216 F218

F236

Conference Room

OFFICE BUILDING (P.R.L. Cordless Comms)Figure 4.1: Three typical areas for large-scale variations of receiver locations, named asTx5a, Tx5b, Tx5c. The transmitter (Tx) is placed in room F218.The scenario area Tx5a was chosen for the measurements, since the room F218 is built

64 4. RESULTS: Indoor Radio Channel Characteristic at 5.2GHzas a measurement room with a constant climate. The measurement devices in this roomare calibrated for a distinct room temperature, which is assured even if the equipmentitself produces leakage heating. In principle, also antenna locations within the rooms inthe vicinity of F208 are of interesting for channel sounding measurements. For example,the areas named Tx5b and Tx5c, model heavily obstructed scenarios with relative largeantenna distances. Coherent measurements, which provide the phase shifts for the sweptfrequencies, are possible for large antenna separations, if linear ampli�ers at the sweeperports are used to mitigate the high attenuation of the long cables between the ports andthe receiver antenna.To reduce the expenditure of calibrations, which are obviously more feasible with a com-plete passive test set, only the area Tx5a with a good LOS is investigated by means ofchannel sounding.Measurements, as described in section 2.2.2, were performed in F208. The room hasa height of 3:26m and a oor space of 3 � 8m. The concrete ceiling is attenuated bypolystyrene plates. The walls are made of wood with a thickness of about 5cm. One frontwall includes a large window. The door is made of wood and has a large window. Thecupboard in the upper left corner of F208 with a height of about 2:3m is made of steal.Many randomly located scatterers such as computers and measurement test sets are ob-served in the room. In ray launching simulations of the respective scenario, the analyserdevices and the computers are modelled as blocks of steal. Desks and shelfs are interpretedas closed massive wooden blocks.The resulting channel models derived from ray launching simulations and frequency do-main measurements are given in Table 4.1. Interpreting the results, the limitations as wellas the advantages of ray launching simulations in conjunction with the modelling method-ology are obtained. Both models result in 1 deterministic and 8 statistical bins, where thedelay of the last bins were equally set to 64ns.The decision area must be chosen with respect to the pro�le data. In measured pro�les,the exact antenna distance is not known due to uncertainties of a few cm in the antennalocations. Knowing that the sweeping frequency band was set to 2GHz, it can be assumedthat impulses in measured pro�les (the local maxima), which are more than 2ns apart,are mutually uncorrelated. Thus, the decision area interval is set to 2ns to determine thestatic signal fragment based on measurements.For the pro�les resulting from ray tracing simulations, the LOS is perfectly known andonly a small interval of 0:5ns is chosen for the decision area.In Tab. 4.1, the magnitude of the deterministic bin in the 7th row, and the resulting valuesin the rows below, are calculated by the modelling script rather than chosen by the userof this tool. Thus, these values can be used for interpreting the reliability of applied raytracing simulations.The �rst and deterministic bin is not as dominant as expected, which was assumed forthis environment with a very good LOS. Scatterers with a good conductivity, such asmetal cases and devices, in the near vicinity of the antennas determine that the �rst twostatistic bins have nearly the same expected value. This e�ect is more obvious in themeasurement model, since obstacles and scatterers were only roughly modelled in the raytracing simulations, see Fig. 4.1. The low attenuation of delayed rays can be explained bythe fact that in the ray launching algorithms, the re ection coe�cient is set to r = �1for steal. Thus only the attenuation due to free space loss is calculated for rays which are

4.1. Validation of Ray Tracing Simulations by Measurements 65obstructed by such planes.Interestingly, the Ricean factor, which determines the power ratio of the �rst bin to thepowers of the eight statistic bins, is nearly the same for both channel models. This indicatesthat the modelling step of extracting the deterministic bin works relatively accurately andreliably, if the decision areas are carefully set with respect to the way of deriving the PDPs.The limitation of the ray tracing approach can be seen when comparing the resulting SNRsand the resulting delay spreads for both models. The average power of all incoming raysis comparable to the average power of the local maxima of the measured pro�les. Bothmodels result in a SNR of about 50dB, where the noise power in both cases is assumedto be �120dBW . But the temporal distribution of the power in the simulated pro�les,given as rms delay spread, di�ers widely from the measured value. This can be explainedby the limited simulation time in ray tracing. The number of re ections and transmissionswas set to 3 to obtain feasible simulations. Thus, late but strong paths are not calculated,resulting in severe gaps in late excess delay intervals between 30 and 100ns, where only afew rays arrive at the receiver. These non existing signal fragments at large excess delayslead to the aberration in rms delay spread values.Channel Models, Scenario Tx5abased on: Ray Tracing MeasurementsPro�le Data File *.pdp Tx5a2.pdp mTx5a.pdpNumber of statistical bins 8 8Maximum Excess Delay 64ns 64nsMinimum Power -130dB -130dBDecision Area Interval 0.5ns 2nsDecision Area Attenuation -3dB -3dBDeterministic Bin -7.563dB (0.418) -5.218dB (0.548)Ricean Factor 0.268 0.234SNR 50.8dB 54.1dBRMS Delay Spread 4.33ns 9.54nsStatistical Bins Delay Magn. E[x] Delay Magn. E[x]1 4ns -2.69dB 4ns -4.75dB2 12ns -10.35dB 12ns -2.06dB3 20ns -20.45dB 20ns -8.18dB4 28ns -31.87dB 28ns -9.04dB5 36ns -28.67dB 36ns -16.10dB6 44ns -19.83dB 44ns -16.15dB7 52ns -42.63dB 52ns -25.98dB8 60ns -38.94dB 60ns -41.79dBTable 4.1: Resulting channel models for ray launching versus channel sounding.Summarising the results, the following issues have to be mentioned:� Ray tracing simulations have to be performed with a large depth in re ection itera-tions to accurately model signal fragments with large excess delays.

66 4. RESULTS: Indoor Radio Channel Characteristic at 5.2GHz� The decision area must be carefully chosen with respect to the pro�le data. In raytracing pro�les, rays travelling over the direct path have negligible excess delays,resulting from the area that is used to determine whether a launched ray hits thereceiver or not. This is an e�ect of the ray launching method, which is explained indetail in section 2.2.1. The decision area interval must be set to several tenths of ananosecond. For models based on measurements, the decision area must be increasedto about 2ns, depending on the swept frequency band.� The rms delay spread values derived from ray tracing are too optimistic, the resultingvalues of the models in appendix B are too small compared to measured delay spreads.4.2 Improving the Ray Tracing ResultsIn the previous section, it is shown that the signal fractions which arrive through higherorders of re ections and transmissions, are important for the signal power distribution overthe time. With a depth of a maximum of 3 transmissions and 3 re ections, the obtainedpro�les do not result in accurate models. The small rms delay spread of about 4:33nscompared to the 9:54ns which results from channel sounding, indicates that a highernumber of delayed rays is necessary in simulations. The problem is ruled out by increasingthe limited number of re ections and transmissions. In Fig. 4.2, two pro�les are comparedwith each other. They are calculated by means of ray launching for the Tx5a scenarioand show the received signal for an equal receiver location. The pro�le on the left sideis created with a depth of 3, similar to those simulations which were compared to themeasurements. It is clearly visible that for excess delays > 40ns the number of incomingrays is too small.-120

-100

-80

-60

-40

-20

0

0 50 100 150 200 250 300ns

dB

-120

-100

-80

-60

-40

-20

0

0 50 100 150 200 250 300ns

dB

Figure 4.2: Power delay pro�les calculated by means of ray launching with a simulationdepth of 3 (left) and 10 (right). Both pro�les are obtained for the samescenario at a distinct location. The rms delay spread are 2:59ns and 8:56ns,respectively.When calculating the signal spread with a depth of 10, resulting pro�les of equal receiverlocations become more precise, according to the measurements. A typical pro�le is shownon the right side of Fig. 4.2. There, due to expendable and time consuming simulations,delayed signal fragments are modelled with a su�cient number of bins. The rms delayspread of the left PDP is 2:59ns whereas the right PDP results in 8:56ns. Measurementsindicate an expected rms delay spread of about 9:54ns for this antenna con�guration.It must be concluded that in ray tracing simulations for a scenario with a lot of obstructingscatterers like computer screens, metal desks and technical devices, as is given in this

4.3. Channel Classi�cation and Evaluation Environments 67evaluation scenario, care must be taken that a su�cient number of considerably delayedrays arrive at the receiver antenna. The simulation depth must be increased to at leastapproximately 8 re ections and transmissions, leading to time consuming simulations. Insection 4.4, it is shown that this problem can be slightly reduced by means of the linesplitting algorithm. When employing the line splitting method, the resulting delay spreadmodelled by the bins becomes more suitable, even if the number of calculated rays is lowfor large excess delays.4.3 Channel Classi�cation and Evaluation EnvironmentsAccording to the RACE LEVEL-2 data format, the channel models are classi�ed for therespective scenarios. Obvious di�erences in channel characteristics are observed in res-idential, o�ce and factory buildings and these three types of buildings determine theclassi�cation. For respective buildings, the classes are divided into di�erent scenarios ac-cording to their environments. These are scenarios with a non-obstructed LOS (type A,very good LOS), those with a typical LOS condition (type B, fair LOS) and worst casescenarios with obstructed direct paths (type C, LOS heavily obstructed). The subdividingof the channel classes is indicated in Tab. 4.2.Classi�cationName Environment LOS DopplerRes X v Residential Building X=A,B,C v=0..10O� X v O�ce Building X=A,B,C v=0..10Fac X v Factory Building X=A,B,C v=0..10Table 4.2: Channel model classes.The class names are encoded using the format 'scenario X v' where the �rst three lettersdetermine the building ('Res', 'O�' or 'Fac'). The parameter 'X' indicates the extent ofobstruction (X=A: very good LOS; X=B: fair LOS; X=C: direct path heavily obstructed),and 'v' denotes the station velocity between 0m=s and 10m=s. In SPW libraries, adaptiveblocks are provided to model the Doppler spread of individual paths as well as of thetotal signal due to moving antennas. Here, mobilities of stations or scatterers are notinvestigated, and the calculated models are issued for v= 0. The mentioned blocks are notused in SPW channel implementations.Some calculated parameters, the Ricean factor, the excess delay, and the rms delay spreadcharacterise the channel classes. For the individual classes, typical ranges are expectedin accordance to the values which can be found in the literature [4], [8]. However, todate only few information is available about the radio characteristics within buildings forcarrier frequencies of about 5:2GHz. Performing the modelling methodology of section2.4.1, some assumptions about the channel characteristic were done before deriving theresulting channel classes. The assumed and expected ranges of the Ricean factor, the excessdelay, and the rms delay spread are summarised below in Tab. 4.3.Obviously, in very good LOS scenarios, which are modelled as Res A x and O� A x classes,

68 4. RESULTS: Indoor Radio Channel Characteristic at 5.2GHzExpected RangesClass Ricean Factor RMS Delay Spread Max. Excess DelayRes A 0 � 1 < 5nsRes B 0 � 1 5 � � � 10ns � 80nsRes C 0 ! 0 10 � � � 30nsO� A 0 � 1 10 � � � 30nsO� B 0 � 1 20 � � � 50ns � 200nsO� C 0 ! 0 40 � � � 100nsTable 4.3: Expected characteristic for the channel classes.the Ricean factor can be assumed to be large, because of the expected dominance of thedirect path. The rms delay spread is expected to increase with increasing room sizes,since the individual paths are longer in o�ces with larger room sizes than in domesticenvironments. Furthermore, the stronger the attenuation of the LOS, the larger the rmsdelay spread.The maximum excess delay, i.e., the time interval between the �rst arriving path and thelast one with signi�cant power, is expected to be large in large rooms, such as o�ces. Nodependence of the maximum excess delay to the power ratio of the direct to the scatteredsignals is expected. It must be remarked that the maximum excess delay of the channelmodels is set to adequate values during the modelling iterations, rather than calculatedwith respect to the pro�les. The results of the �tting algorithms for the magnitudes of thelast bins are used to determine whether a delay of the last bin,i.e., the maximum excessdelay, has been suitably chosen.4.4 Results for Di�erent EnvironmentsIn appendix B, resulting channel models for six scenario classes of residential and o�ceenvironments are summarised. For these models, the most important channel parameters,which characterise the classes, are shown in Tab. 4.4. Note that the number of bins and themaximum excess were designated during the modelling whereas the rms delay spread andthe Ricean factor only depend on the accuracy of the simulations and the line splitting andcurve �tting algorithms. None of the models is based on channel sounding measurements.The o�ce models are based on simulation results of the scenarios called Tx1, Tx2 andTx3, see Fig. B.1. For the residential models, see Fig. 2.5, which indicates performed raytracing simulations in domestic environments.When comparing Tab. 4.4 with the expected ranges, it can be observed that the rmsdelay spread values are not as large as expected. Obviously, the delay spread increasesfor decreasing Ricean factors, since in heavily obstructed transmissions less power travelsthrough the LOS paths, resulting in higher delay spread values. The rms delay spreadvalues of the residential models show appropriate values with respect to the assumptionsof Tab. 4.3. The curve �tting results depicted in Fig. B.2, B.3, and B.4 show that even forrelatively large delays (bins 4 � � � 6), enough rays are obtained. This results in an accurate�t to the empirical data. Thus, it can be concluded that the rms delay spread values forthe three residential values are correct, since an adequate number of rays is obtained for

4.4. Results for Di�erent Environments 69ResultsClass Environment No. Max. Excess RMS Delay Riceanof Bins Delay Spread Factorresidential,Res A 0 very good LOS 1+6 48ns 5.016ns 0.5132residential,Res B 0 fair LOS 1+6 54ns 6.985ns 0.265residential,Res C 0 obstructed LOS 1+6 54ns 7.777ns 0.1995o�ce,O� A 0 very good LOS 1+8 64ns 4.326ns 1.431o�ce,O� B 0 fair LOS 1+10 100ns 10.89ns 0.9565o�ce,O� C 0 obstructed LOS 1+10 100ns 13.51ns 0.1924Table 4.4: Results for residential and o�ce environments.large excess delays.Problems due to limitations in ray tracing simulations occur for o�ce scenarios. Theresulting rms delay spread values are far smaller than expected. Observing the curve�tting results for the channel class O� A 0 in Fig. B.5, it can be seen that the empiricalmagnitude distributions of the delayed bins do not �t very well to a Rayleigh CDF. Thereason for this is the lack of calculated rays with large delays at the receiver locations. Thesimulations Tx1, Tx2 and Tx3 were performed with a simulation depth of 3. For largerand more suitable delay spread values, more rays have to be calculated.The models of appendix B are derived for use in SPW simulations and analytical models ofOFDM transmission systems. The line �tting algorithm of the modelling method assumesa correlation between adjacent rays. Thus, if at least a couple of rays occur at largeexcess delays, the bin power for the respective interval will model a representative pro�le,resulting in more accurate delay spread values.Note that the rms delay spread values in Tab. 4.4 are calculated based on ray pro�les,where the rays are assumed to be mutually uncorrelated. They are not based on the binmodels. When calculating the r.m.s. delay spread from the bin models instead of from theray pro�les, the results increase from 4:33ns to 5:96ns for the channel sounding scenarioTx5a2, from 5:02ns to 12:66ns for the class Res A 0 and from 4:33ns to 6:37ns for theO� A 0 channel class.The accuracy of the bin models and not the accuracy of the ray tracing pro�les is importantfor the SPW simulations. Due to the line splitting, more convenient bin models are found,even if only a small number of rays are calculated for larger excess delays.However, it must be mentioned that the rms delay spread values of the bin models arestill too small, compared to measured delay spreads. The channel sounding measurementswhich are performed in this work indicate that ray launching prediction of indoor radiochannels can only be done with a large depth of re ection iterations.

70 4. RESULTS: Indoor Radio Channel Characteristic at 5.2GHz

CHAPTER 5RESULTS: Performance of the OFDM SystemScope of this thesis is to investigate the reliability of the OFDM transmission scheme forindoor radio channels.Ray tracing is used to calculate the sets of power delay pro�les. Based on the ray tracingresults, the modelling method with line splitting and curve �tting is used to create channelmodels for the scenario classes. The simulation tool SPW is used to �nd the resulting bit-error-rate (BER) for the 16 carrier OFDM system, with di�erent guard intervals Tg.The simulations of the OFDM system are explained in the next section. With respect tothe BER performance, the optimal Guard interval Tg is determined in section 5.2.In section 5.3, the performance of OFDM systems is analytically derived and discussed bymeans of the results of chapter 3. It is shown that the systematic errors of multicarriersystems in multipath environments, namely ISI and ICI, are eliminated by means of thecyclic extension of the OFDM blocks.5.1 SPW SimulationsAppendix C depicts the channel implementation in SPW. A general channel model withup to 16 bins and variable bin weights and delays is used for simulations of multipathchannels, see Fig. C.2. The channel contains the adaptive AWGN block, which determinesthe power ratio of the scattered signal to thermal noise. Fig. 5.1 shows the simulatedmultipath signal at the output of the channel. It is important to note that here the channelis assumed stationary for a cell duration. For each ATM cell a new channel impulse responseis calculated. Thus, adjacent cells are mutually uncorrelatedly a�ected by the channel.From Fig. 5.1, it is visible how the time varying channel is modelled. It can be seen thatthe channel is implemented as stationary over an ATM cell duration. Between ATM cells,where a null block is sent, the distortion due to the multipath delays and the additivenoise can be observed.The quadrature components of the channel bins are independently distributed as whiteGaussian random processes. Thus, the channel can be used for slow fading simulationswhere the channel characteristics change slowly, but constantly. For this, the Gaussiandistributions have to be coloured rather than white by passing the bin weights througha lowpass �lter with a very low critical frequency. New channel impulse responses arestill calculated for each ATM cell duration. But now the distortion of consecutive cells iscorrelated, as it is reasonable for indoor radio channels with its slow mobilities. Estimatingparameters of error source models for the channel is thus possible, and the description ofbursty error statistics in indoor communication channels can be derived.For indoor scenarios, with velocities of up to 10m=s, a typical critical frequency of thecoloured Gaussian distributions is in the range of less than 1Hz.The simulated OFDM system is based on a 16 point FFT. Some con�guration parameters

72 5. RESULTS: Performance of the OFDM System

Figure 5.1: The OFDM signal, severely a�ected by the radio channel. Note that thechannel is modelled as stationary for a cell duration. No correlation isassumed between the distortion of adjacent ATM cells.are issued below.� For one channel, the data arrives at the physical layer as cells with 53 octets (424bits) at a rate of 23:5294Mbit=s.� The applied coding scheme is the RS-(56,76) coding, leading to an RS padding of 24bits. Padding means that the data is extended with zeros, until the number of bitsis divisible by 56.� To the 448 bits the coding redundancy and a reference symbol are added resultingin 640 bits.� The 640 bits are DQPSK modulated to 320 symbols, which �t in 20 16-pnt OFDMblocks, calculated by an IFFT.� The calculated symbols (16 symbols per block) are interleaved to the subcarriers toensure that adjacent symbols are randomly distorted due to frequency diversity. Theinterleaving algorithm applied in the simulation needs another OFDM padding block.� The duration of the cyclical extension of the OFDM blocks depends on the guardinterval Tg. Repeating some points of the IFFT outputs, discrete values are possiblefor the duration, leading to a redundant overhead.� Finally, a null block is added to the extended OFDM blocks. No further synchroni-sation issues are considered in the simulations, and up to 3 SYNC-blocks might haveto be attached in the real demonstrator system.At the air interface, an MPDU has a duration of about 16:5�s at a guard interval of 2points. A data rate of 47:25Mbits=s, or a complex sampling rate of 23:625MSamples=soccurs.The e�ective OFDM block duration Tb is 667ns. The guard interval Tg can be set tomultiples of 20:8ns in simulations and multiples of 41:7ns in the real system.

5.2. Optimal Guard Interval for 16-Point FFT 735.2 Optimal Guard Interval for 16-Point FFTFig. 5.2, 5.3 and 5.4 show the resulting BER versus Tg=Tb, obtained by simulations ofthe OFDM system. The simulations were performed for a 32-pnt FFT, which causes abetter resolution for the choice of the guard interval. However, as indicated in the �gures,the 16-carrier system only allows a cyclical extension of the block duration by multiplesof Tb=16.It must be mentioned that the used channel models are all based on ray tracing withoptimistic results and relatively small delay spreads.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510

−5

10−4

10−3

10−2

1−pnt 2−pnt 3−pnt

BER vs. Guard Interval / Tx4 / 16 Carriers

BE

R

Tg / T

b

o: uncoded +: RS−coded

Figure 5.2: BER versus guard interval for the residential scenario Tx4.The results for radio transmission within domestic buildings are shown in Fig. 5.2. Thisscenario, Tx4, is modelled as residential with fair LOS and without mobility (Res B 0).The applied ray tracing simulations and the respective receiver locations for this scenarioare shown in Fig. 2.5. By observing the BER of coded and not coded bits, the optimalguard interval for this channel is a 2-pnt extension, which means that Tg = 80ns. Notethat the maximum excess delay rather than the rms delay spread determines if the lossof orthogonality and the inter-symbol interference is ruled out by the guard interval.Even if the last incoming multipath components are weak compared to the �rst arrivingcomponents, they still introduce severe ICI and ISI in the multicarrier transmission.The optimal guard interval for o�ce scenarios can be determined from Fig. 5.3 and Fig. 5.4.The receiver locations for the scenarios are shown in Fig. B.1, appendix B. The power delaypro�les for these locations result in models with fair LOS, namely O� B 0.Here, since the decay of the BER with increasing Tg=Tb is not as steep as for residentialmodels the optimal guard space in the 16-carrier system is a 3-pnt extension, resultingin Tg = 120ns. This means that Tg � 0:2Tb which is a typical value for OFDM systems.In o�ce environments, multipath components arrive with larger delays than in residentialenvironments. This leads to the necessity of a slightly longer extension of the block durationwithin o�ce scenarios than within domestic buildings.

74 5. RESULTS: Performance of the OFDM System

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510

−5

10−4

10−3

10−2

1−pnt 2−pnt 3−pnt

BER vs. Guard Interval / Tx1 / 16 Carriers

BE

R

Tg / T

b

o: uncoded +: RS−coded

Figure 5.3: BER versus guard interval for the o�ce scenario Tx1.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.3510

−5

10−4

10−3

10−2

1−pnt 2−pnt 3−pnt

BER vs. Guard Interval / Tx3 / 16 Carriers

BE

R

Tg / T

b

o: uncoded +: RS−coded

Figure 5.4: BER versus guard interval for the o�ce scenario Tx3.

5.3. The Analytically Derived Parameters 755.3 The Analytically Derived ParametersThe three parameters �kk, �lk, and �lk are evaluated by using 30 PDPs of residentialscenarios.In chapter 3.3.5, the in uence of a multipath channel on DQPSK symbols, which aretransmitted by applying OFDM , are analytically derived. Error terms due to ICI, ISI,and the at fading on the subcarriers are extracted. Received DQPSK-symbols are writtenas Yk(n) = �0k;kpMXk(n) + N�1Xl=0;l 6=kXl(n) �0l;kpM + N�1Xl=0 Xl(n� 1) �0l;kpM (5.1)The parameter �kk determines the fading. The parameter �lk denotes the in uences ofthe ICI and �lk indicates the impairments due to ISI. As shown in 3.3.7, the three termsin Eqn. 5.1 can be used to determine the ratio between the signal and the interference onsubcarrier k to (C=I)k = ����0k;k���2N�1Pl=0;l 6=k ����0l;k���2 + N�1Pl=0 ����0l;k���2 (5.2)In this equation, the additive noise is ignored for the sake of simplicity. For a set of 30power delay pro�les, which are obtained by simulations in residential environments, thethree parameters are calculated for OFDM multicarrier systems with 8, 16, 32, and 64subchannels. The resulting values are averaged over the subchannels to express the meanimpairments of the transmitted symbols. Note that a set of only 30 pro�les is not enoughfor a reliable statement about the system behaviour. Nevertheless, the �gures below showthe suitability of the analytic expressions, which are derived in chapter 3.In Fig. 5.5, the averaged values of �lk and �lk versus Tg are depicted for di�erent numbersof subchannels.

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2x 10

−5

Tg [ns]

mue

lk

N=8 N=16N=32N=64

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5

2x 10

−5

Tg [ns]

lam

bda lk

N=8 N=16N=32N=64

Figure 5.5: The error parameters �lk and �lk versus Tg, exemplarily calculated for 30pro�les and averaged over the subchannels.

76 5. RESULTS: Performance of the OFDM SystemExtending the block duration by introducing the guard interval Tg yields in suppressionof the ISI as well as the ICI. It can be seen in Fig. 5.5 that, if Tg is chosen larger than theexcess delay of the last arriving multipath component, both parameters, �lk for ISI and�lk for ICI, are entirely reduced to 0. This indicates that the cyclical extension is a simplebut e�cient way to maintain orthogonality and to suppress the ISI.The at fading of the transmitted DQPSK symbols is not a�ected by the guard interval,as it is shown in Fig. 5.6, where �lk is depicted versus Tg in the left diagram.

0 5 10 15 20 25 30 35 40 45 50

10−2

10−1

Tg [ns]

mue

kk

N=8 N=16N=32N=64

0 5 10 15 20 25 30 35 40 45 5040

50

60

70

80

90

100

110

120

130

Tg [ns]

C/I

N=8 N=16N=32N=64

Figure 5.6: The at fading, �lk, averaged over the subchannels and the C/I-ratio versusTg.In Fig. 5.6, it can be seen that the interference of a symbol on a subcarrier with itself,which leads to severe fading, is not in uenced by the guard interval. Note that the resultsare found as the average over 30 channel impulse responses. For the 64 carrier system,only 20 responses are used to reduce the time-consuming calculations. For this reason, aslight dependence of �lk is observed for N = 64 which can be neglected compared to thedistinct in uences of Tg on ISI and ICI. In the right diagram of Fig. 5.6, the resultingC/I-ratio, averaged over all subchannels is shown versus Tg, where it is observed that thisratio increases with increasing guard interval. Note that the additive noise is not part ofthe calculations and thus that the resulting ratio increases to in�nity for Tg > �max, where�max means the delay of the last arriving multipath component.Summarising the results, OFDM ensures reliable data transmission even in harsh multi-path environments such as the indoor radio channel. If the guard interval is set to a valuegreater than the excess delay of the last arriving multipath components, the orthogonalitybetween the subchannels is maintained and no impact of preceding symbols is experi-enced. Without employing equalisation of the subchannels, the modulated symbols onlysu�er from at fading. However, in real systems, Tg cannot be too large resulting in ISIand ICI. Furthermore, the impacts of the AWGN occur, which are here neglected.The results show that the analytical description of chapter 3 is a suitable model of theOFDM transmission scheme, where the applied coding method such as the RS-coding isnot part of the model. With the ComNets indoor radio channel model as the channelof choice, the statistical distributions of the error terms are extracted, see section 3.3.6.Hence, in conjunction with the DQPSK-model of [21], the analytical description of OFDMcan be used for BER calculations, without employing SPW simulations of OFDM.

CHAPTER 6ConclusionChannel ModellingA simple and accurate Ricean fading multipath channel model for the Hiperlan/2 indoorradio channel is presented in this work. It is appropriate for use in simulation tools andanalytical models and satis�es the demand of representing the channel. A methodologyto characterise the channel models using ray tracing results is developed based on thethree steps (i) extracting the deterministic part, (ii) line splitting, and (iii) curve �tting.The results of the �tting method show that the Ricean multipath channel model �ts theempirical data well.This model, together with the methodology to derive it from ray tracing results is pre-sented to the ETSI RES 10 standardisation committee as the model of choice for the newHiperlan/2 standard [1].Residential and o�ce environments are classi�ed with respect to the obstructing of theLOS, and models are derived for the individual classes.The evaluation of the ray tracing results by means of extensive frequency domain mea-surements within o�ce buildings show that the channel impulse responses derived fromthe ray launching simulations are too optimistic in terms of the rms delay spread, if theiteration depth of the recursive ray launching algorithm is chosen too small.OFDMUsing the channel models in OFDM simulations, the optimal guard interval of the16-carrier OFDM system is determined with respect to the di�erent environments. It isshown that introducing the cyclical extension of the OFDM blocks yields in a betterperformance of the data transmission in terms of BER.The analytical model of OFDM determines the systematic error terms due to multipath,such as ICI and ISI. The C=I-ratio for the individual subchannels is extracted. The modelcan be used in conjunction with the analytical description of DQPSK of [21] to quantifythe symbol distortion and thus to evaluate the BER.OutlookOFDM systems exploit the frequency diversity of indoor channels by transmitting con-secutive symbols at frequencies which are mutually uncorrelated. Thus, e�cient codingand interleaving schemes are employed in OFDM to reduce BER, and are important forthe transmission scheme. Channel Coding is not analytically described in this thesis, fora more representative model, this must also be included in the model.In further projects, when performing ray tracing within environments with a large set ofobstacles, care must be taken to select the appropriate depth of iterations.Estimating parameters of error source models and describing the bursty error statisticsin indoor communication channels is one of the key aspects for the physical layer of theWATM system. Using coloured rather than white Gaussian random processes for the

78 6. Conclusionquadrature components of the bin magnitudes, a temporal correlation of the respectiveenvironment can be modelled, and error source models such as Markov-chain models canbe parameterised. This is not scope of this thesis, but possible by means of the channelmodels and the analytical description of OFDM.This thesis covers the issues of multipath radio channels, the statistical description ofsuch a channel, and the evaluation of OFDM by means of derived channel models. Theresults may be useful for decisions concerning the reliability of OFDM for WATM localarea networks.

BIBLIOGRAPHY[1] S. Mangold, M. Lott, D. Evans, R. Fi�eld, "A simple/accurate Propagation Model forthe 5.2GHz Indoor Radio Channel", ETSI EP BRAN, Temporary Document wg3td73[2] S.N. Hulyalkar, "Indoor Channel Model", Philips Research internal deliverable D2.11,Nov. 1996[3] A.A.M. Saleh and R.A. Valenzuela, "A Statistical Model for Indoor Multipath Prop-agation" , IEEE Journ. Select. Areas Commun., vol. SAC-5, no. 2,Feb. 1987[4] H. Hashemi, "The Indoor Radio Propagation Channel", Proc. IEEE, vol. 81, no. 7,pp. 942-967[5] H. Hashemi, "Impulse Response Modelling of Indoor Radio Propagation Channels" ,IEEE Journ. Select. Areas Commun., vol. 11, no. 7, Sep. 93[6] H. Suzuki "A Statistical Model for Urban Radio Propagation", IEEE Trans. Com-mun., vol. COM-25, no. 7, July 1977[7] T.S. Rappaport, S.Y. Seidel and K. Takamizawa, "Statistical Channel Impulse Re-sponse Models for Factory and Open Plan Buildings Radio Communication SystemDesign", IEEE Trans. Commun., vol. 39, no. 5, May 1991[8] M. Lott, R. Fi�eld, D. Evans, S. Hulyalkar, "Radio Channel Characteristics for typicalEnvironments at 5.2GHz", ACTS Mobile Comm. '97 , vol. 1, pp. 252-257[9] G. Halls/PT41, "HIPERLAN radio channel models and simulaion results",RES10TTG 93/58 ETSI EP BRAN[10] G. Halls/PT41, "Software implementation of the HIPERLAN channel model",RES10TTG 93/46[11] G. Kadel, "RACE LEVEL-2 �le format for wideband propagation data", ETSI EPBRAN, Temporary Document wg3td40[12] GSM 0.50.5 (ETS 300 577): Digital cellular telecommunication system(Phase 2), "Radio transmission and reception", March 1996, pp. 36-37[13] A.C. Caswell and T.J. Mousley,"Multicarrier Transmission for Wireless ATM", P.R.L.Technical Note No. 3494, 1996[14] E. Viterbo, K. Fazel, "How to combat long echoes in OFDM transmission schemes:sub-channel equalization or more powerful channel coding", Globecom'95, pp. 2069-74, vol. 3[15] R.F. Ormondroyd, J.J. Maxey, "Comparison of Time Guard-Band and Coding Strate-gies for OFDM Digital Cellular Radio in Multipath Fading", VTC '97, pp. 850-854[16] Peter Hoeher, "A Statistical Discrete-Time Model for the WSSUS Multipath Chan-nel", IEEE Trans. Veh. Techn., vol. 41, no. 4, Nov. 1992, pp. 461-468[17] A. Vahlin, N. Holte, "Use of a Guard Interval in OFDM on Multipath Channels",Electronic Letters, vol. 30, no. 24, pp. 2015-2016

80 Bibliography[18] N.Yee, J.P.M.G. Linnartz and G. Fettweis, "Multi-Carrier-CDMA in Indoor WirelessNetworks", Conference Proceedings PIMRC '93, Yokohama, Sept, 1993. p 109-113[19] Damien Castelain, Dominique Lacroix, Philippe Madec, "Channel Coding and Num-ber of Carriers for a COFDM Air Interface", ETSI EP BRAN Temporary Documentwg3td85[20] K.D. Kammeyer, "Nachrichtenuebertragung", B.G. Teubner Stuttgart 1996[21] P. Seidenberg, "Entwicklung eines Empfaengermodells fuer das BuendelfunksystemTETRA unter Beruecksichtigung der Funkkanaleigenschaften", thesis work, ComnetsRWTH Aachen, 1997[22] Irving Kalet, "The Multitone Channel", IEEE Trans. Commun., vol. 37, no. 2, Feb.1989[23] Robert G. Gallagar, "Information Theory and Reliable Communication",New York: Wiley, 1968[24] Khaled Fazel, Gerhard Fettweis, "Multi-Carrier Spread-Spectrum", Kluwer AcademicPubl., 1997[25] H.Sari, G. Karam, I.Jeanclaude "Analysis of Orthogonal Frequency-Division Multi-plexing for Mobile Radio Applications", VTC '94, vol. 3, June 1994, pp.1635-1693[26] W.C. Jakes, "Microwave Mobile Communications" IEEE Press, 1993[27] H.D. Lueke, "Nachrichtenuebertragung", Springer, 1995[28] J.G. Proakis, "Digital Communications", New York: McGraw Hill, 1995[29] T.S. Rappaport, "Wireless Communications, Principles and Practice",Prentice Hall, 1996

LIST OF ABBREVIATIONSADSL Asymmetric Digital SubscriberLineATM Asynchronous Transfer ModusAWGN Additive White Gaussian NoiseBCH Bose-Chadhuri-HocquenghemBER Bit-Error RateBPSK Binary Phase Shift KeyingCDF Cumulative Distribution FunctionCDMA Code Division Multiple AccessDAB Digital Audio BroadcastingDFT Discrete Fourier TransformDVB Digital Video BroadcastingDVB-C DVB-cableDVB-T DVB-terrestrialDQPSK Di�erential Quaternary PhaseShift KeyingDS-CDMA Direct Sequence CDMADSP Digital Signal ProcessingFDM Frequency Division MultiplexingFEC Forward Error CorrectionFFT Fast Fourier TransformHIPERLAN High Performance LANIBI Inter-Block InterferenceICI Inter-Channel InterferenceIDFT Inverse DFTIF Intermediate Frequency

IFFT Inverse FFTISI Inter-Symbol InterferenceLAN Local Area NetworkLOS Line-Of-SightMC MulticarrierMCM Multicarrier ModulationMC-SS Multicarrier Spread SpectrumMT-CDMA Multi-Tone-CDMAOFDM Orthogonal Frequency DivisionMultiplexingPDF Probability Density FunctionPDP Power Delay Pro�lePRL Philips Research Labs, RedhillQAM Quadrature AmplitudeModulationQPSK Quaternary Phase Shift KeyingRF Radio FrequencyRMS Root Mean SquareRS Reed-SolomonSFN Single Frequency NetworkSNR Signal-to-Noise RatioSPW Signal Processing WorkbenchSS Spread SpectrumUS Uncorrelated ScatteringWSS Wide Sense Stationary

82 List of Abbreviations

APPENDIX ACalculationsSymbol Meaningt timefc carrier frequency, assumed to be 0k; l sub-channel indices in frequency domainfk sub-carrier frequency in basebandn block index in time domainN number of sub-channelsTb e�ective OFDM block durationT 0b total block durationTg guard interval duration� excess delay of second path in two path approach�m excess delay of path mA real magnitude of second path in two path approachAm real magnitude of path m� phase rotation of second path in two path approach�m phase rotation of path mfD Doppler frequency of second path in two path approachfDm Doppler frequency of path mHm Complex value of bin mXk(n) DQPSK symbol at k-th carrier in n-th block�k(t) k-th basis functionYk(n) reconstructed symbol at k-th carrier in n-th blockEk(n) interference at k-th carrier in n-th blockEk(n)ISI ISI at k-th carrier in n-th blockEk(n)ICI ICI at k-th carrier in n-th blockx(t) transmitted OFDM baseband signalM number of paths or bins�k;l(�) describes the ICI impacts in two paths approach�k;l(�) describes the ISI impacts in two paths approach�0k;k interference variable in multi-path model�0k;l ICI variable in multi-path model�0k;l ISI variable in multi-path modelTable A.1: Table of symbols

84 A. CalculationsA.1 The Sub-Channel Interference Ek(n)ICIUsing (3.6) and from (3.23) it follows thatEk(n)ICI = 1Tb Tb+nT 0bZ��Tg+nT 0b Aej(�+2�fDt)x(n)(t� �)e�j2�fk(t�nT 0b)dtThis can be simpli�ed toEk(n)ICI = 1Tb Tb+nT 0bZ��Tg+nT 0b Aej(�+2�fDt) "N�1Xl=0 Xl(n)ej2�fl(t�nT 0b��)# e�j2�fk(t�nT 0b)dt= ATb N�1Xl=0 Xl(n)e�j2�fl� Tb+nT 0bZ��Tg+nT 0b ej(�+2�fDt)ej2�(fl�fk)(t�nT 0b)dt= ATb N�1Xl=0 Xl(n)e�j2�fl� TbZ��Tg ej(�+2�fD(u+nT 0b)ej2�(fl�fk)udu= Aej(�+2�fDnT 0b) N�1Xl=0 Xl(n)�l;k(�) (A.1)with �l;k(�) = 1Tb e�j2�fl� TbZ��Tg ej2�(fl�fk)udu (A.2)A.1.1 l = kWith fk = kTb , it follows that�k;k(�) = Tb � � + TgTb e�j2�k� 1Tb (A.3)A.1.2 l 6= k �l;k(�) = 1Tb e�j2� lTb � ej2�( lTb� kTb )Tb � ej2�( lTb� kTb )(��Tg)j2�( lTb � kTb )Substituting a = 2�Tb (l � k)�l;k(�) = 1Tb e�j2� lTb � 1ja hejaTb � eja(��Tg)i= e�j��2 lTb ��(l�k)Tb+��TgTb � sin��(l � k) 1Tb (Tb � � + Tg)��(l � k) (A.4)

A.2. The Inter-Symbol Interference Ek(n)ISI 85A.2 The Inter-Symbol Interference Ek(n)ISIUsing (3.23) it follows thatEk(n)ISI = 1Tb ��Tg+nT 0bZnT 0b Aej(�+2�fDt)x(n�1)(t� �)e�j2�fk(t�nT 0b)dt (A.5)In the same way like the sub-channel interference, this is simpli�ed toEk(n)ISI = Aej(�+2�fDnT 0b) N�1Xl=0 Xl(n� 1)�l;k(�) (A.6)with �l;k(�) = 1Tb e�j2�fl(��T 0b) ��TgZ0 ej2�(fl�fk)udu (A.7)A.2.1 l = kWith fk = kTb , �k;k(�) = � � TgTb e�j2�k(��T 0b) 1Tb (A.8)A.2.2 l 6= k �l;k(�) = 1Tb e�j2� lTb (��T 0b) ej2�( lTb� kTb )(��Tg) � 1j2�( lTb � kTb )Substituting a = 2�Tb (l � k)�l;k(�) = 1Tb e�j2� lTb (��T 0b) 1ja heja(��Tg) � 1i= e�j��2 lTb (��T 0b)�(l�k) ��TgTb � sin��(l � k) ��TgTb )��(l � k) (A.9)A.3 ResultsSummarising the results,�l;k(�) = 8><>: Tb��+TgTb e�j2�k� 1Tb : l = ke�j��2 lTb ��(l�k)Tb+��TgTb � sin��(l�k) 1Tb (Tb��+Tg)��(l�k) : l 6= k (A.10)�l;k(�) = 8><>: ��TgTb e�j2�k(��T 0b) 1Tb : l = ke�j��2 lTb (��T 0b)�(l�k) ��TgTb � sin��(l�k) ��TgTb )��(l�k) : l 6= k (A.11)

86 A. Calculations

APPENDIX BChannel ModelsIn Fig. B.1, the used transmitter and receiver locations in o�ce environments are shown.The depicted antenna con�gurations are used to calculate power delay pro�les, which thenare classi�ed, with respect to the obstructing of the LOS. The receiver is located in largeand small o�ce rooms, as well as the corridor, to �nd representative sets of resultingchannels.See Fig. 2.5 for the respective con�gurations in domestic environments.y

x

Tx_1

5.23

4.16

4.17

4.184.19

5.285.29 5.30

5.31

5.3

5.2

5.1

5.18

5.46 5.47 5.48

5.225.21

5.20

5.19

5.49

Tx_2

5.50

5.26

5.51

5.25

5.32 5.33 5.34

5.35

5.4 5.5 5.6

3.18

5.17

5.43 5.44

5.36

5.37 5.38 5.39

5.95.12

5.15

5.14

5.13

5.41 5.42

Philips Research Laboratories, Redhill, UK(detail drawing)

5.45

5.65.5

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5.7

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ReceiverLocations

ReceiverLocationsFigure B.1: Large-Scale variations of the receiver location in o�ce environments.On the next pages, the 6 channels for residential and o�ce buildings are given. The resultsof the curve �ttings, which are also shown, indicate the accuracy of the models. Note thatthe channels for o�ce environments do not show good �ts for the last bins, because of theoptimistic results derived from ray tracing.

88 B. Channel ModelsB.1 Res A 010

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Figure B.2: Curve �tting of Rayleigh distributions to emoirically derived magnitudes.===========================Power Delay Profile Model===========================Ray Trace output file *.pdp: res_a_0.pdpNumber of statistical bins: 6Maximum excess delay of latest ray: 48nsMinimum ray power: -130dBMaximum excess delay of line-of-sight rays: 0.1nsPower difference to main ray for LOS decision: -3dB----------------------------------Deterministic Bin Magnitude:(steady/specular part)----------------------------------0.52814 (-5.54503dB)----------------------------------Statistical Bin Magnitudes:(random/scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 4ns | -6.00906 |2 | 12ns | -11.8922 |3 | 20ns | -16.2931 |4 | 28ns | -8.80763 |5 | 36ns | -11.4246 |6 | 44ns | -30.1408 |----------------------------------Ricean Factor: 0.51329Signal to Noise Ratio (SNR): 59.2873dBAverage r.m.s. delay spread: 5.016nsResulting Channel Model, for use in SPW

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Figure B.3: Curve �tting results.===========================Power Delay Profile Model===========================Ray Trace output file *.pdp: res_b_0.pdpNumber of statistical bins: 6Maximum excess delay of latest ray: 54nsMinimum ray power: -130dBMaximum excess delay of line-of-sight rays: 0.1nsPower difference to main ray for LOS decision: -3dB----------------------------------Deterministic Bin Magnitude:(steady/specular part)----------------------------------0.55483 (-5.1168dB)----------------------------------Statistical Bin Magnitudes:ray power:(random/scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 4.5ns | -4.76838 |2 | 13.5ns | -2.26304 |3 | 22.5ns | -8.21267 |4 | 31.5ns | -11.0838 |5 | 40.5ns | -23.0383 |6 | 49.5ns | -37.9118 |----------------------------------Ricean Factor: 0.26506Signal to Noise Ratio (SNR): 53.545dBAverage r.m.s. delay spread: 6.985nsChannel Model

90 B. Channel ModelsB.3 Res C 00

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Figure B.4: Curve �tting results.===========================Power Delay Profile Model===========================Ray Trace output file *.pdp: res_c_0.pdpNumber of statistical bins: 6Maximum excess delay of latest ray: 54nsMinimum ray power: -130dBMaximum excess delay of line-of-sight rays: 0.1nsPower difference to main ray for LOS decision: -3dB----------------------------------Deterministic Bin Magnitude:(steady/specular part)----------------------------------0.525807 (-5.58348dB)----------------------------------Statistical Bin Magnitudes:(random/scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 4.5ns | -6.29754 |2 | 13.5ns | -0.671609 |3 | 22.5ns | -6.25593 |4 | 31.5ns | -12.7134 |5 | 40.5ns | -24.1837 |6 | 49.5ns | -34.3921 |----------------------------------Ricean Factor: 0.1995Signal to Noise Ratio (SNR): 38.1051dBAverage r.m.s. delay spread: 7.777nsChannel Model

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Figure B.5: Curve �tting results.===========================Power Delay Profile Model===========================Ray Trace output file *.pdp: off_a_0.pdpNumber of statistical bins: 8Maximum excess delay of latest ray: 64nsMinimum ray power: -159dBMaximum excess delay of line-of-sight rays: 0.1nsPower difference to main ray for LOS decision: -3dB----------------------------------Deterministic Bin Magnitude:(steady/specular part)----------------------------------0.773642 (-2.23089dB)----------------------------------Statistical Bin Magnitudes:(random/scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 4ns | -7.83166 |2 | 12ns | -10.3457 |3 | 20ns | -20.4443 |4 | 28ns | -31.8849 |5 | 36ns | -28.6604 |6 | 44ns | -19.825 |7 | 52ns | -42.5363 |8 | 60ns | -38.8715 |----------------------------------Ricean Factor: 1.43086Signal to Noise Ratio (SNR): 50.7495dBAverage r.m.s. delay spread: 4.326nsChannel Model

92 B. Channel ModelsB.5 O� B 010

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Figure B.6: Curve �tting results.===========================Power Delay Profile Model===========================Ray Trace output file *.pdp: off_b_0.pdpNumber of statistical bins: 10Maximum excess delay of latest ray: 100nsMinimum ray power: -159dBMaximum excess delay of line-of-sight rays: 0.1nsPower difference to main ray for LOS decision: -3dB----------------------------------Deterministic Bin Magnitude:(steady/specular part)----------------------------------0.568304 (-4.90838dB)----------------------------------Statistical Bin Powers:(random/scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 5ns | -5.41097 |2 | 15ns | -14.3954 |3 | 25ns | -22.8103 |4 | 35ns | -29.4581 |5 | 45ns | -30.1915 |6 | 55ns | -27.0721 |7 | 65ns | -28.3381 |8 | 75ns | -30.3737 |9 | 85ns | -27.4802 |10 | 95ns | -37.6972 |----------------------------------Ricean Factor: 0.95652Signal to Noise Ratio (SNR): 49.7089dBAverage r.m.s. delay spread: 10.89nsChannel Model

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Figure B.7: Curve �tting results.===========================Power Delay Profile Model===========================Ray Trace output file *.pdp: off_c_0.pdpNumber of statistical bins: 10Maximum excess delay of latest ray: 100nsMinimum ray power: -159dBMaximum excess delay of line-of-sight rays: 0.1nsPower difference to main ray for LOS decision: -3dB----------------------------------Deterministic Bin Magnitude:(steady/specular part)----------------------------------0.411062 (-7.72186dB)----------------------------------Statistical Bin Powers:(random/scattered part)----------------------------------Bin | Excess-Delay | E [dB] |----|--------------|-------------|1 | 5ns | -1.0519 |2 | 15ns | -13.105 |3 | 25ns | -15.8709 |4 | 35ns | -29.8016 |5 | 45ns | -36.9214 |6 | 55ns | -27.1137 |7 | 65ns | -22.6011 |8 | 75ns | -26.6687 |9 | 85ns | -23.5118 |10 | 95ns | -25.0407 |----------------------------------Ricean Factor: 0.19242Signal to Noise Ratio (SNR): 41.976dBAverage r.m.s. delay spread: 13.51nsChannel Model

94 B. Channel Models

APPENDIX CSPW ImplementationIn Fig. C.1, the channel implementation is shown. The SPW block contains 1 deterministicand 16 delayed and weighted paths. The individual delays are constant and depend on thenumber of used bins and the maximum excess delays. The complex bin magnitudes aremodelled as random processes The expected values of the Rayleigh distributed weightsdetermine the instantanteneous bin weights. On a raising edge at the external input NEWRESPONSE, new values are calculated for the weights.

Figure C.1: SPW symbol of the channel model.An adaptive random noise generator is used to add the thermal noise (AWGN). For this,the average SNR must be known and is extracted in the channel models.The channel must be accurate in time, for this reason the sampling frequency of thechannel must be high. Therefore an interpolation �lter at the input and a decimation�lter at the output are included. The simulations in performed in baseband, with a signalbandwidth of about 25MHz. A 32 point DFT was used rather than a 16 point DFT, andthe base rate at the input of the radio channel was set to 47:25MHz. This results in an 4times oversampling of the transmitter and the receiver. The interpolation factor was setto 8 � � � 10, resulting in time-consuming simulations and low simulation e�ciency.The next gigure shows the implemented channel details. If models with a smaller numberof bins is modelled, such as the three residential channels, the upper bins are automaticallyswitched o�. Fig. C.3 and Fig. C.4 show the calculation of the complex bin weights. Thecomplete simulation system of OFDM with the ComNets indoor radio channel is given inFig. C.5.

96 C. SPW Implementation

Figure C.2: Channel Details.

97

Figure C.3: Rayleigh distributed weights.

Figure C.4: Details of the weights. The Rayleigh distribution is calculated by twomutually uncorrelated white Gaussian quadrature components. The phase isuniformly distributed.

98 C. SPW Implementation

Figure C.5: The OFDM system and the channel model.

LIST OF FIGURES2.1 Radio transmission within buildings. . . . . . . . . . . . . . . . . . . . . . . 72.2 The multipath channel as time invariant linear �lter with additive noise. . . 82.3 A power delay pro�le with rms delay spread, mean excess delay, maximumexcess delay, and the power threshold. . . . . . . . . . . . . . . . . . . . . . 92.4 De�nition of the delay window Wq . . . . . . . . . . . . . . . . . . . . . . . 102.5 Ray tracing simulations within residential buildings. For large-scale varia-tions of the receiver location, PDPs are calculated. . . . . . . . . . . . . . . 122.6 Re ection tree of the ray launching algorithm . . . . . . . . . . . . . . . . . 142.7 Adaption of the detection range and misdetection due to shadowing at acorner. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.8 Ray tracing simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.9 Typical power delay pro�le,with respect to the LOS. The �rst ray arrives att = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.10 Frequency domain channel sounding, block diagram. . . . . . . . . . . . . . 172.11 Frequency selective channel, magnitude in dB. The frequency range is from5:0GHz to 5:4GHz. The normalised signal envelope is indicated with a5dB=unit scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.12 Phase response in degree. The frequency range is from 5:0GHz to 5:4GHzand the signal phase is scaled as 50 degrees/unit. . . . . . . . . . . . . . . . 182.13 Time domain response of the multipath channel with linear scaling. Theenvelope of the normalised S21 parameter is shown for the delay intervalfrom 0ns to 100ns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.14 The Rayleigh probability density function for � = 0:8 and � = 1:0. . . . . . 212.15 The Ricean probability density function for K !1 (v = 0) and for K � 1(v = 3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.16 The exponentially decaying ray and cluster average powers. The decay isde�ned by the parameters � and . . . . . . . . . . . . . . . . . . . . . . . . 232.17 Typical power delay pro�le (squared magnitudes of taps) of the HIPER-LAN/1 channel model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.18 The SPW symbol of the channel model. Statistical and deterministic outputsare independently given. See appendix C for the details of the implementation. 262.19 The deterministic bin (left) and the statistical bin pro�le (right) model theRicean fading multipath channel. . . . . . . . . . . . . . . . . . . . . . . . . 272.20 Developing the channel models. . . . . . . . . . . . . . . . . . . . . . . . . . 27

100 List of Figures2.21 A measured S21 parameter of the channel versus time [ns]. The local maximaare treated as mutually uncorrelated multipath components. . . . . . . . . . 282.22 Rays or measured samples within the decision area are assumed to be staticand contribute to the deterministic bin.The decision area is user de�ned anddepends on the magnitude of the strongest path. . . . . . . . . . . . . . . . . 292.23 Calculating the Ricean factor with the resulting bin powers. . . . . . . . . . 302.24 Impulses within the marked excess delay interval are added to �nd the rep-resentative model bin for this interval. The �gure also depicts that highlyattenuated impulses and impulses with a large excess delay are neglected andlost for the sake of simplicity. . . . . . . . . . . . . . . . . . . . . . . . . . . 312.25 The magnitudes of the bins are assumed to be independent Rayleigh randomvariables and are �tted to the empirical data. . . . . . . . . . . . . . . . . . 322.26 Rayleigh distributions of a typical 8-bin model �tted to the data. . . . . . . . 333.1 The available channel bandwidth is subdivided into a number of subchannels,each subchannel is nearly ideal. . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Interpreting the distortion as the bottom of a bowl: when an amount of wateris poured into the bowl, the water will distribute itself so as to achieve capacity. 363.3 Four unmodulated and orthogonal carriers (a) in time and (b) in frequencydomain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4 OFDM Transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5 OFDM Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.6 Orthogonality Condition depicted as basic impulse. The �gure shows thenormalised time-domain results of the convolution of a transmitter �lterwith receiver �lters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.7 Cyclic extension of the block duration and impulse responses of the trans-mitter and receiver �lters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.8 Basic impulses after introducing the guard interval. . . . . . . . . . . . . . . 423.9 Spectra of an 8-carrier OFDM system with Tg = 0. The modulated carriersare assumed to be uncorrelated, thus, the overall spectrum is the sum of thecarrier spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.10 Spectra of an 8-carrier OFDM system with Tg = 0:2Tb. In this case, Tbstays constant and T 0b is increased to Tg + Tb. . . . . . . . . . . . . . . . . . 443.11 4-Carrier demonstrator spectrum. The carriers are randomly modulated andno guard interval is applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.12 The Spectrum with an introduced Tg = Tb=4 . . . . . . . . . . . . . . . . . . 453.13 Tg increased to Tb=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.14 MC-CDMA multicarrier spreader . . . . . . . . . . . . . . . . . . . . . . . . 473.15 Sent and received blocks with 2-paths channel model and � � Tg. . . . . . . 543.16 Sent and received blocks with 2-paths channel model and � > Tg. . . . . . . 55

List of Figures 1013.17 Calculating the variance after weighting of a statistical variable. . . . . . . . 604.1 Three typical areas for large-scale variations of receiver locations, named asTx5a, Tx5b, Tx5c. The transmitter (Tx) is placed in room F218. . . . . . . 634.2 Power delay pro�les calculated by means of ray launching with a simulationdepth of 3 (left) and 10 (right). Both pro�les are obtained for the samescenario at a distinct location. The rms delay spread are 2:59ns and 8:56ns,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.1 The OFDM signal, severely a�ected by the radio channel. Note that thechannel is modelled as stationary for a cell duration. No correlation is as-sumed between the distortion of adjacent ATM cells. . . . . . . . . . . . . . 725.2 BER versus guard interval for the residential scenario Tx4. . . . . . . . . . 735.3 BER versus guard interval for the o�ce scenario Tx1. . . . . . . . . . . . . 745.4 BER versus guard interval for the o�ce scenario Tx3. . . . . . . . . . . . . 745.5 The error parameters �lk and �lk versus Tg, exemplarily calculated for 30pro�les and averaged over the subchannels. . . . . . . . . . . . . . . . . . . . 755.6 The at fading, �lk, averaged over the subchannels and the C/I-ratio versusTg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76B.1 Large-Scale variations of the receiver location in o�ce environments. . . . . 87B.2 Curve �tting of Rayleigh distributions to emoirically derived magnitudes. . . 88B.3 Curve �tting results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89B.4 Curve �tting results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90B.5 Curve �tting results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91B.6 Curve �tting results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92B.7 Curve �tting results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93C.1 SPW symbol of the channel model. . . . . . . . . . . . . . . . . . . . . . . . 95C.2 Channel Details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96C.3 Rayleigh distributed weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . 97C.4 Details of the weights. The Rayleigh distribution is calculated by two mu-tually uncorrelated white Gaussian quadrature components. The phase isuniformly distributed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97C.5 The OFDM system and the channel model. . . . . . . . . . . . . . . . . . . 98

102 List of Figures

LIST OF TABLES2.1 Dielectric characteristics of the modelled materials at 5:2GHz. . . . . . . . 162.2 Con�guration of the channel sounding measurements. . . . . . . . . . . . . 193.1 DAB parameters in modes 1, 2 and 3 . . . . . . . . . . . . . . . . . . . . . 483.2 Main parameters of the DVB-T system . . . . . . . . . . . . . . . . . . . . . 494.1 Resulting channel models for ray launching versus channel sounding. . . . . 654.2 Channel model classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3 Expected characteristic for the channel classes. . . . . . . . . . . . . . . . . 684.4 Results for residential and o�ce environments. . . . . . . . . . . . . . . . . 69A.1 Table of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

104 List of Tables

ACKNOWLEDGEMENTSI would like to thank my advisors, Prof. Dr.-Ing. B. Walke of ComNets, andDr. D.H. Evans of Philips Research Labs. Their friendly support and cooperation en-abled my stay in Redhill and made it a great and valuable experience together with mywork here in Aachen. Further, special thanks to Dipl.-Ing. Matthias Lott, who has signif-icantly contributed to the ideas and contents of this thesis by his advice and inspiration.It was a great pleasure to work with Matthias.I am grateful to all colleagues of the Cordless Communications Group at Philips ResearchLabs for a friendly and inspiring atmosphere and their o�ered support at any time. Inparticular, I am deeply indebted to Robert Fi�eld and Dave Evans for their encouragementand their contribution to the thesis by an uncountable number of fruitful discussions,helpful suggestions and comments.In addition, there are several others, who helped me in di�erent ways. I would like tothank Anne Caswell for taking the time to checking large parts of the report and givingso many useful advices, Markus Knoch for his support during all stages of the thesis andour common years of studies, and all friends I have got to know at P.R.L. and at ComNetsfor spending such a great time together.Finally, I would like to send special thanks to my family and Hella. Their support andencouragement have been highly appreciated during the whole time of my studies.Aachen, December 1997