WCDMA radio channel classification

2007:013 CIV

M A S T E R ' S T H E S I S

WCDMA RadioChannel Classification

Markus Andersson

Luleå University of Technology

MSc Programmes in Engineering Media Technology

Department of Computer Science and Electrical EngineeringDivision of Signal Processing

2007:013 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--07/013--SE

WCDMA Radio Channel Classification

Markus Andersson, Me

January 19, 2007

Abstract

When studying channel properties in cellular networks two key parametersare the delay spread and the type of fading. The delay spread holds infor-mation about the time dispersion the channel induces, whereas the effectthe channel has on the power of propagating waves is reflected in the fading.Line-of-sight communications results in Rician fading whereas non-line-of-sight means Rayleigh fading. Measurements and classification of channelenvironments have, to the writer’s knowledge, so far only been done withthe use of complex sounding devices. In this work, channel classification isperformed using low-level data from a regular cell phone.

Measurements were performed with a real cell phone in a controlled mi-lieu where different radio environments were emulated. With the use ofchannel estimates from the cell phone, probability density function parame-ter estimations were performed with both maximum likelihood and methodof moments techniques. The Rician K-factor, which expresses the ratio ofline-of-sight components to scattered waves, was calculated with the resultsfrom the estimation.

The K-factor calculations showed, as expected, obvious differences be-tween various simulated environments. The K-factor increases with strongerline-of-sight component, which is in line with theory. For weak direct waves,the estimate often becomes zero which is due to the difficulty of detecting aweak direct wave in lots of scattered waves. To achieve better results, otherestimation techniques might therefore be necessary.

For repeated measurements with the same settings the variance of theK-factor estimates is quite high. Also, the variance increases with strongerdirect wave. This might be due to additive noise during measurement. Themean of the K-factor estimates seems to be 3dB higher than expected. Thisoffset is possibly due to the difference in the noise power between complexand real noise, which is exactly 3dB, or internal differences in the powerlevel of the channel simulator. The reason for the difference is not clear butpower measurements confirms it.

With compensation for this, the calculated K-factors aligns much betterto the expected K-factors. Although they are not exactly the same, theyare so close that with further studies, classification of radio channels withthe use of cell phone channel estimates should be possible.

Preface

This report is the result of a master thesis study carried out at EricssonResearch in Lulea, Sweden. It has evolved from an idea of radio channelclassification with the use of low-level cell phone data.

As the writer, I would like to thank all of you that have supported meduring this project. First of all Kjell Larsson at Ericsson Research for beingmy supervisor, Sven-Olof Jonsson, also at Ericsson Research, for giving methis opportunity. Anders Hedlund, Ericsson Skelleftea, which have beenmore than helpful with his low-level coding. James LeBlanc and MagnusLundberg at Lulea University of Technology which have been extremelypatient and answered at lot of questions. Also, thanks to all the coworkersat Ericsson Research that have helped me in troubled times.

CONTENTS CONTENTS

Contents

1 Background 3

2 Introduction 42.1 Wired networks . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Cellular networks . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Impulse response and convolution . . . . . . . . . . . . . . . . 52.4 WCDMA basics . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4.1 Radio access technologies . . . . . . . . . . . . . . . . 62.4.2 Direct sequence spreading . . . . . . . . . . . . . . . . 72.4.3 Rake receiver . . . . . . . . . . . . . . . . . . . . . . . 72.4.4 Physical channels . . . . . . . . . . . . . . . . . . . . . 72.4.5 Power control . . . . . . . . . . . . . . . . . . . . . . . 8

3 Theory 93.1 Propagation of radio waves . . . . . . . . . . . . . . . . . . . 93.2 Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3.1 Frequency selective and flat fading . . . . . . . . . . . 113.3.2 Fast and slow fading . . . . . . . . . . . . . . . . . . . 12

3.4 Probability density function . . . . . . . . . . . . . . . . . . . 133.4.1 Rayleigh distribution . . . . . . . . . . . . . . . . . . . 133.4.2 Rician distribution . . . . . . . . . . . . . . . . . . . . 14

3.5 Channel types . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.5.1 Typical urban . . . . . . . . . . . . . . . . . . . . . . . 163.5.2 Rural area . . . . . . . . . . . . . . . . . . . . . . . . . 173.5.3 Hilly terrain . . . . . . . . . . . . . . . . . . . . . . . . 18

3.6 Cell phone channel estimator and sample data . . . . . . . . 193.7 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . 20

3.7.1 Method of moments . . . . . . . . . . . . . . . . . . . 203.7.2 Maximum likelihood estimation . . . . . . . . . . . . . 213.7.3 Cramer-Rao lower bound . . . . . . . . . . . . . . . . 23

4 Method 244.1 Simulating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2 Measuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . 254.4 Estimating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Results 265.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.3 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . 29

1

CONTENTS CONTENTS

5.4 Modified K-factor estimates . . . . . . . . . . . . . . . . . . . 335.5 Proposed presentation of results . . . . . . . . . . . . . . . . . 35

6 Discussion 366.1 Measurement difficulties . . . . . . . . . . . . . . . . . . . . . 366.2 Cell phone limitations . . . . . . . . . . . . . . . . . . . . . . 36

7 Conclusions 37

8 Further studies 38

2

1 BACKGROUND

1 Background

Cellular networks, such as GSM and 3G, are today available all over theworld. Properly set, these networks have the capability of providing highperformance wireless connectivity. To achieve that; planning, tuning, op-timization and troubleshooting are done by the mobile operators. For thelatter tasks, they use field test tools which are built for maintenance ofwireless networks. An example of such tools is TEMS Investigation.

In mobile networks, the radio channel characteristics differ dependingon location of base stations and handheld devices, movement of the latterand also obstacles in the surrounding. Urban and rural areas will not havethe same channel characteristics; neither will two different places within abuilding. Different channels could affect the performance for the end user.Therefore, information and knowledge about the radio channel characteris-tics would be very helpful and make it possible to better understand andtroubleshoot new 3G services.

The purpose of this project was to investigate if it is possible to char-acterize and classify different radio channels based on measurements froma modified cell phone. If possible and implemented in TEMS, such classi-fication would give important information to the user regarding the radiochannel properties. Information about how the cell phone perceives thechannel could be useful during field tests. Areas in an environment canbe tested to see if the radio channel characteristics in fact is what one ex-pects them to be. Such information could also be useful as input during cellplanning.

3

2 INTRODUCTION

2 Introduction

Communication systems in general, whether they are mobile or not, consistof at least one transmitter and one receiver. The path between these two,usually named channel, is the medium used for the transport of signals. Thechoice of medium to use, differs in various networks.

2.1 Wired networks

In fixed systems, e.g. land line phones and computer networks, copperwires or fiber optic cables are often used as channels. As the purpose oftransmission systems is to move information it is desirable that the receiveddata is the same as the transmitted.

In a perfect system, the channel would only transport the signal withno modifications, but in real world applications this is not the case. Ev-ery signal sent through a channel is to some extent distorted. The amountof channel induced distortion is highly dependent on the channel itself andtechniques for undoing this distortion must be implemented in every com-munication system. Luckily, when it comes to channels like copper wiresand fiber optic cables both have one important property which is invari-ance. Except for small changes in the properties of the copper due to, forexample, temperature variations, the copper wire is regarded as an invariantmedium. Hence, every signal sent through one copper wire will experiencethe same channel and be affected in the same way. Therefore, mitigationof the channel distortion is quite easy. Unfortunately, it is not as easy incellular communication.

2.2 Cellular networks

1 2 3

654

987

#0*

Figure 1: Example of wireless channels.

One of the biggest differences between fixed and mobile networks is thechannel itself. Instead of electrons moving in copper cables, mobile networksmake use of electromagnetic waves which propagate in air, see Fig. 1 fora simple example of two mobile channels. The entire environment betweentransmitter and receiver is the channel and herein lays also the difficulty.All objects that make up the channel are not stationary. Cars and busesmove, people are walking and trees are swaying in the wind. Besides, in a

4

2 INTRODUCTION 2.3 Impulse response and convolution

cellular network, transmitter and receiver are not usually on fixed locations,e.g. a person using a cell phone is not always sitting completely still. Allthis means that the transmission channel is variant, i.e. it changes in time.One signal sent through a mobile network at two different time instanceswill not experience the same channel. Remediation of the channel effectscaused by a variant channel requires other methods than those for invariantchannels.

2.3 Impulse response and convolution

The distortion that different channels cause is highly correlated with theirunique physical characteristics. Mathematically these properties are con-tained in the channel’s impulse response, IR. This is a time representationof the channel’s output, or response, when the input is an impulse. Hereinlays a lot of information. The impulse response describes how the channelamplifies, attenuates and modifies the amplitude and phase of the inputsignal and also how the channel disperses the signal in time.

x(t) y(t) = x(t) h(t)∗h(t)

Figure 2: Block diagram of a transmission system.

Transmission systems in time invariant channels are often described as inFig. 2. The transmitted signal x(t) is being sent through a channel with IRh(t). This will result in the received signal y(t). If the input signal and theIR is known, the output of the system can be calculated as y(t) = x(t)∗h(t)where ∗ denotes convolution1. In the one sided continuous time case it isdefined according to Eq. 1.

x(t) ∗ h(t) =∫ ∞0

x(τ)h(t− τ)dτ (1)

As the process of convolution may be invertible, this means that in trans-mission systems with known IRs, the sent signal can often be calculatedfrom the received one. For this to work with wireless channels, which aretime-variant, IR estimation has to be performed regularly. With the use ofpredetermined code sequences, so called pilot symbols, an estimate of theIR can be calculated. This, so called channel estimate, can then be used tocounteract the channel induced distortion.

1For detailed information about convolution see [11] on page: 84-92

5

2 INTRODUCTION 2.4 WCDMA basics

2.4 WCDMA basics

Implementation of communication systems can be done in a number of ways.Regardless technique, optimization of performance and efficient use of thelimited bandwidth is of great importance. The available bandwidth must beshared between multiple users and how to share it differs between varioustypes of radio access technologies.

2.4.1 Radio access technologies

FDMA, Frequency Division Multiple Access, allows a portion of the totalbandwidth to be used by each user during the entire transmission, see leftpart of Fig. 3. This technique is easy to implement, does not introduce ISI2

and makes synchronization easy. The drawbacks are that one must use astatic spectrum allocation and frequency reuse is difficult. Also, users areassigned a part of the spectrum even if they don’t need it at all times.

Another technique is TDMA, Time Division Multiple Access, seen in themiddle of Fig. 3. Here each user is given a part of, or the entire bandwidth,for a short period of time. This means the users take turns using the channel.This gives an increase in capacity but requires at the same time, strictsynchronization. The GSM system makes use of a combination of FDMAand TDMA. Users are assigned a part of the spectrum for a short time butthe spectrum for each user can change between transmissions. This is knowsas frequency hopping.

Time

FDMA

Time

Freq

uenc

y

Freq

uenc

y

CDMA

Freq

uenc

y

Time

TDMA

Figure 3: Radio access technologies

Since the available bandwidth is constricted it is therefore very expensiveand efficient use of the spectrum is of great importance. This, together withthe demand for higher bitrates for new services, led to the use of CDMA,Code Division Multiple Access. CDMA is an old military technique, usedamong other things in the Global Positioning System, GPS. It makes use ofspreading codes which make it possible to allow all users to communicateon all frequencies at all times, right part of Fig. 3. With the right codesthe receiver can extract the sent signal belonging to a certain user. This

2Inter-symbol interference

6


technique makes higher transfer rates possible and allows for more usersthan FDMA and TDMA.

CDMA2000 and Wideband-CDMA, are radio access techniques thatuse CDMA technology. The difference between them is the width of thespectrum. WCDMA uses a 5 MHz wide signal whereas CDMA2000 uses1.25MHz. A wider spectrum gives the advantage of even higher bit ratesand is more robust against fading.

2.4.2 Direct sequence spreading

In WCDMA, simultaneous transmission for users is possible due to the uti-lization of direct sequence spreading codes. These codes are pseudo-randomnoise codes with a much higher rate than the information signal. Multiplica-tion with these codes results in a spread spectrum signal which for WCDMAis 5 MHz wide. The rate of the resulting signal is referred to as chip raterather than bit rate and the chip rate in WCDMA is 3.84 Mcps3. Sinceeach user has a unique code, separation between users is possible. Aftertransmission through the channel, de-spreading is performed with the samecode that was used in the spreading and the sent data is retained. Moreinformation about spreading and de-spreading can be found in [6] on page27-30.

2.4.3 Rake receiver

The spread transmitted signals will, due to reasons explained in Chapter 3.1,be dispersed in time. The signals will arrive at the receiver after propagationon multiple paths. There the signal parts will add up either constructivelyor destructively, which means that the received energy will be changing intime. The Rake receiver, which is used in WCDMA, assigns one Rake fingerat the delay positions that have significant energy. The channel estimate isthen used to remove or at least reduce the channel induced distortion. Eachfinger will then contain a ”part” of the sent and time dispersed signal. Thefinal step is to combine these parts of signal energy to maximize the usefulenergy. This is done with something called maximum ratio combining, see[6] on page 30-33. The steps that are performed in the Rake receiver aremore or less like those in a matched filter.

2.4.4 Physical channels

The transmission of data between the base station, BS, and the user equip-ment, UE, is done on a number of different channels. These are not to bemistaken for the physical channel itself, i.e. the environment where the ra-dio waves propagate. Some channels are for transport of actual data and

3Mega chips per second

7


some are only needed for controlling the transmission system. An exampleof the latter is the Common PIlot CHannel, CPICH, which only sends pilotsymbols for use in the channel estimate procedure, see Chapter 3.6. Thischannel is used by all users in the cell.

As the purpose of the CPICH channel is to gain knowledge about how theradio channel affects the transmitted signals, there are no quality controlssuch as power control on the CPICH. Other channels like the DedicatedPhysical CHannel, DPCH which is used for transmitting user data, mustretain a constant quality. Measures that strive to counteract the channelinduced distortion are therefore necessary and each user makes use of theirown power controlled dedicated physical channel.

2.4.5 Power control

On the up link, i.e. communication from the UE to the BS, the goal withthe power control is for the BS to receive equal signal quality from eachuser, regardless of the distance. If a user close to the BS transmits withtoo high power, signals from users transmitting at a greater distance mightbe overshadowed. The WCDMA BSs utilize a power control that measuresthe received signal quality, commands an increase or decrease in power fromthe UE, and does this 1500 times per second. As this is faster than anysignificant change in path loss, the signal quality can be controlled.

From the UE point of view, i.e. the down link, the power control followscommands that the UE sends. If there is need for more power, e.g. at theedge of a cell, the UE demands it.

8

3 THEORY

3 Theory

3.1 Propagation of radio waves

Transmitted electromagnetic waves that propagate in air behave like wavesin water in that they can change direction, are stopped etc. depending onwhich type of obstacle they encounter. There are three basic mechanismsthat have impact on the propagation, i.e. reflection, diffraction, and scat-tering [13].

When radio waves impinge something that has a smooth surface and isvery large compared to the wavelength of the wave itself, they are reflected.If the radio path is obstructed with a large dense object between the trans-mitter and the receiver, secondary waves can be formed after the object.This is named diffraction or shadowing since the waves actually can reach areceiver even though the line-of-sight propagation path is shadowed. Withsome obstacles, radio waves can also propagate through them, though thisresults in attenuation. Scattering is when radio waves hit obstacles withsmall dimensions or larger objects with a rough surface. If the dimensionof the obstacle is in the order of one wavelength or less, the signal will bescattered in all directions.

3.2 Delay

0 100 200 300 400 500

−105

−100

−95

−90

−85

Excess Delay [ns]

Rec

eive

d P

ower

[dB

]

Power Delay Profile

RMS Delay spread

Mean excess delay

Maximum excess delay < 10 dB

Noise threshold

Figure 4: Power delay profile.

Reflection, diffraction and scattering of electromagnetic waves will leadto a multipath propagation of the sent signal, i.e. each sent signal will besplit in numerous rays that all travel on their own path to the receiver. Sincethese paths will have unequal distances, the received signal will be dispersedin time. A signal sent from a transceiver at some time instance will start

9

3 THEORY 3.2 Delay

to arrive at the receiver at time t0. From that point on, the received energywill be the sum of all incoming rays as a function of the excess time τ . Theamount of time dispersion that the channel induces affects the time it takesbefore the received energy fades away. The power delay profile in Fig. 4shows an example of this.

From this profile it is possible to calculate time dispersion measures suchas mean excess delay and root mean square (RMS) delay spread. Mean excessdelay is a measurement of the extra delay that the channel introduces afterthe first part of the signal arrives at t0. RMS is the standard deviation of thedelayed reflections, weighted by their respective energy. Both mean excessdelay and delay spread differs widely between channel types which makesthem important channel characteristics. Fig. 4 also show the maximumexcess delay which is where the signal level has dropped 10 or 20 dB fromthe maximum received level. Basically, this is the time it takes to receivethe ”whole” signal. There is also a noise threshold under which everythingthat is received is seen as noise.

−5 0 5 10 15 20 25 30 35 40 45−40

−35

−30

−25

−20

−15

−10

−5

0

5Power Delay Profile

τ − Excess Delay [µs]

Rec

eive

d P

ower

[dB

]

Mean excess delay: 2.81 µsDelay spread: 6.83 µs

Figure 5: Discrete Power delay profile.

Fig. 5 show a Power delay profile in the discrete case. Here calculationof mean excess delay, denoted τ and root mean square (RMS) delay spread,denoted στ can be done according to Eq. 2, Eq. 3 and Eq. 4 where ak isthe amplitude, P (τk) the power and τk the time index.

τ =∑

k ak2τk∑

k ak2

=∑

k P (τk)τk∑k P (τk)

(2)

τ2 =∑

k ak2τk

2∑k ak

2=∑

k P (τk)τk2∑

k P (τk)(3)

στ =√

τ2 − (τ2) (4)

10

3 THEORY 3.3 Fading

3.3 Fading

The power delay profile shows how the received energy varies in time. Thiseffect, caused by multipath propagation, is called fading. The instantaneousreceived power is the sum of many rays arriving with different amplitudeand phase. Hence, a moving antenna will experience a strong signal wherethe superposition of the rays is constructive and, unfortunately, a very weaksignal if it is destructive. This abrupt loss of signal strength, which can beas much as 30 dB, will unless mitigated, result in high bit error rate overthe channel.

The cause of these deep fades is actually very small position changes,those in the order of one wavelength. Changes in position will cause bothtime dispersion of the signal and time variance of the channel. Each result-ing in two types of so called small-scale fading. Time dispersion of the signalleads to frequency selective or flat fading whereas time variance results infast or slow fading.

Besides this small-scale fading, motion over large areas results in large-scale fading. This is an attenuation of the signal power as a function ofdistance. Hence, the instantaneous power is the combination of small-scalefading superimposed on large-scale fading. Though, it is the small-scalefading that causes the most severe problems.

The sections below, which discuss various types of fading, talk abouttransmission of symbols. In WCDMA transmission of data is done in chipsbut the theory of fading applies to both.

3.3.1 Frequency selective and flat fading

Performance degradation due to time dispersion of the signal can be dividedin two categories, frequency selective fading or flat fading. Both are depen-dent on the relationship between, Ts, the symbol time and Tm, the maximumexcess delay. Ts is the time duration for each sent symbol and Tm is themaximum excess delay. Channels with Tm > Ts, will spread the symbols intime so that they interfere with each other, causing inter-symbol interfer-ence, ISI. Such a channel will be experiencing so called frequency selectivefading. The opposite, with Tm < Ts, will result in flat fading. Frequencyselective fading will cause serious performance degradation so mitigation isnecessary [14].

Another way of looking at the degradation due to time dispersion is in thefrequency domain. This gives a better understanding for the name frequencyselective fading. In the frequency domain, the term coherence bandwidth,f0, is used to denote the range of frequencies over which a channel affectspassing signals with equal gain and linear phase. The coherence bandwidthis approximately the inverse of the maximum excess delay. This meansthat a channel will exhibit frequency selective fading if f0 < 1/Ts, i.e. all

11

3 THEORY 3.3 Fading

the spectral components of the signal are not affected equally since thebandwidth of the signal is greater than the coherence bandwidth. Hence, toavoid ISI the channel must be flat fading with f0 > 1/Ts.

3.3.2 Fast and slow fading

Just like time dispersion reflects in two types of fading, so does the timevariance of the channel. Movement of either the user equipment or objectsin the propagation path will result in changes in the impulse response. Inthe time domain the coherence time, T0, is the time over which the channel’simpulse response to a large extent is invariant. This means that channelswith T0 < Ts will be fast fading since the channel’s response will be changingduring the transmission of one symbol. Degradation caused by fast fadingis very severe and can result in irreducible error rates [13]. If the channelstate is invariant over the transmission time for one symbol, i.e. T0 > Ts,the channel will instead be slow fading.

In the frequency domain the time variations of the channel will lead toa spectral broadening of the signal [13]. A channel with low coherence timeis changing at a high rate. To understand the impact these changes have onthe signal it is often useful to draw a parallel to the effect of signal keying.An infinitely long sinusoid at a certain frequency is in the frequency domaincharacterized by an impulse. As soon as this sinusoid is limited in time,e.g. switched on and off as in keying, a spectral broadening will occur. Therapid changes in the channel’s impulse response can, in some sense, be seenas keying and thus resulting in a spread of the signal. This effect is namedDoppler spread or fading rate, and is approximately equal to the inverse ofthe coherence time fd ≈ 1/T0. Hence, if the symbol rate, 1/Ts < fd thechannel will change quicker than the symbols are sent, which will lead tofast fading.

To avoid the problems with frequency selective and fast fading the sig-naling rate must be contained within the coherence bandwidth, f0, and theDoppler spread. Too high symbol rate will introduce frequency selectivefading since the coherence bandwidth will be smaller than the signal spec-trum. A rate that is too low will result in fast fading since the channel’sresponse will change during the transmission of one symbol. Detailed infor-mation about fading can be found in [13] and mitigation techniques for theproblems described above are discussed in [14].

12

3 THEORY 3.4 Probability density function

3.4 Probability density function

Multipath propagation, time dispersion and the type of fading one will ex-perience highly depends on the physical properties of the channel. Denselybuilt areas with a large amount of buildings, lampposts, street signs, etc.,will produce a lot of scattered waves. The time dispersion in an environmentlike this is most certainly not minute. Neither is it likely that this environ-ment allows for a line-of-sight, LOS, communication between transmitterand receiver. At least not with roof top mounted BSs. On the other hand,sparsely built cities and rural areas induce less scattering and line-of-sightcommunication is often possible.

As the received signal consists of a mixture of delayed, reflected, andscattered waves, the physical differences in the radio channel will reflectin the amount of each type of wave the received signal contains. Thesevariations will affect the statistics of the fading.

3.4.1 Rayleigh distribution

In 1889, John William Strutt the 3rd Baron Rayleigh, published the Rayleighmodel [12]. This model assumes that a received multipath signal can beconsidered consisting of a large number of waves, possibly infinitely many,with independent and identically distributed, i.i.d., in-phase and quadraturecomponents. The central limit theorem supports, that with sufficiently manyarriving waves the IQ components will follow a Gaussian distribution asillustrated in Fig. 6(a).

−6 −4 −2 0 2 4 6−4

−2

0

2

4In−phase and Quadrature−phase components

Qua

drat

ure

In−phase

(a) Scattered waves.

0 1 2 3 4 50

0.2

0.4

0.6

Amplitude

Den

sity

Amplitude PDF

(b) Amplitude PDF.

Figure 6: Scattered waves in IQ representation together with the amplitudePDF.

If z = x + iy, where x and y are i.i.d. Gaussian with zero mean andvariance σ2, the probability density function, PDF, for the amplitude, |z|,can be derived as in [9]. The result

f(x|σ) =x

σ2exp

(− x2

2σ2

)(5)

13


is the Rayleigh distribution and has the characteristic form displayed in Fig.6(b). It has been shown that this model is in fact suitable for describingfading in areas with lots of scattered waves, such as densely built cities [4].The σ in Eq. 5 is a function variable and is the standard deviation from theone dimensional Gaussian distribution.

3.4.2 Rician distribution

Radio waves propagating in sparsely built cities or rural areas are, just likethose in densely areas, scattered and reflected. The big difference is thatusually a line-of-sight, LOS, wave reach the receiver. Since this wave oftenis strong compared to the scattered waves, the PDF of the amplitude willchange. The scattered waves will no longer have zero mean. This is displayedin 7(a).

−5 0 5

−5

0

5

In−phase and Quadrature−phase components

Qua

drat

ure

In−phase

(a) Scattered waves with LOS.

2 4 6 80

0.1

0.2

0.3

0.4

Amplitude

Den

sity

Amplitude PDF

(b) Amplitude PDF with LOS.

Figure 7: Scattered waves in IQ representation with a LOS componenttogether with the amplitude PDF.

Due to this shift in mean, the amplitude PDF will change form, see 7(b).This new form is the Rician distribution defined as

f(x|s, σ) =x

σ2exp

(− (x2+s2)

2σ2

)I0

(xs

σ2

)x > 0 (6)

where the non-centrality parameter s ≥ 0 and the scale parameter σ > 0.As in the Rayleigh PDF, the function parameter σ is the local standarddeviation of the one dimensional Gaussian distribution. I0 is the zero-ordermodified Bessel function of the first kind. The Rician K-factor which isdefined as

K =s2

2σ2(7)

expresses the ratio of dominant component to the scattered waves. In fact,as K →∞ the Rician PDF → Gaussian and as K → 0 the Rician PDF →Rayleigh. That is, the stronger the line-of-sight component is, the greaterwill the shift of mean be for the scattered waves. Such a shift will make

14


the Rician distribution approach Gaussian distribution. As the direct waveweakens the shift of mean will approach zero and the Rician PDF becomesRayleigh.

The representation in Fig. 7(a) is only valid in the stationary case.When there is relative movement between the transmitter and receiver theDoppler effect becomes an issue. This will lead to a phase shift in thereceived components, which results in a ”rotating” cloud in the IQ-plane,see Fig 8(a). However, the amplitude PDF will still be Rician as in Fig8(b).

−5 0 5

−5

0

5

In−phase and Quadrature−phase components

Qua

drat

ure

In−phase

(a) Scattered waves with LOS andDoppler.

2 4 6 80

0.1

0.2

0.3

0.4

Amplitude

Den

sity

Amplitude PDF

(b) Amplitude PDF with LOS andDoppler.

Figure 8: Scattered waves in IQ representation with a LOS componenttogether with the amplitude PDF, both with Doppler.

15

3 THEORY 3.5 Channel types

3.5 Channel types

The physics of multipath radio wave propagation makes the number of chan-nels in mobile communication almost infinite. To be able to do simula-tions and calculations in 3G-networks, standardization organizations, suchas ITU4 and 3GPP5, have decided upon a few channel types to describe themost usual channel environments. Each channel model has its own char-acteristics regarding fading and delay. All data describing these channelmodels are available in [1]. The mean excess delay and the delay spreadhave been calculated with Eq. 2, 3 and 4. There are more channel modelsthan the below mentioned but these are some of the most widely used. Also,observe the different scales on the x-axis.

3.5.1 Typical urban

In densely built cities the received signal usually consists of the sum of re-flected, scattered and diffracted waves with no line-of-sight component. Theradio channel will then be best described with the ”typical urban” model.The mean excess delay is moderate since the multipath propagation leadsto some time dispersion of the signal. The delay spread is also noticeable.Since there is no line-of-sight component, this means that all channel tapswill be Rayleigh distributed. Fig. 9 shows the impulse response for thischannel model.

0 0.5 1 1.5 2−40

−35

−30

−25

−20

−15

−10

−5

0Typical Urban Channel Model

Time Index [µs]

Ave

rage

Rel

ativ

e P

ower

[dB

]

Filter tapsMean excess delay: 0.50 µsDelay spread: 0.50 µs

Figure 9: Impulse response for Typical Urban Channel Model.

4International Telecommunication Union53rd Generation Partnership Program

16


0 0.1 0.2 0.3 0.4 0.5 0.6−40

−35

−30

−25

−20

−15

−10

−5

0Rural Area Channel Model

Time Index [µs]

Ave

rage

Rel

ativ

e P

ower

[dB

]


Figure 10: Impulse response for Rural Area Channel Model.

−2 0 2 4 6 8 10 12 14 16 18−40

−35

−30

−25

−20

−15

−10

−5

0Hilly Terrain Channel Model

Time Index [µs]

Ave

rage

Rel

ativ

e P

ower

[dB

]


Figure 11: Impulse response for Hilly Terrain Channel Model.

3.5.2 Rural area

On the country-side there are usually less buildings that interfere with thepropagation of radio waves. Therefore a dominant line-of-sight componentwill reach the receiver together with multipath reflections. The direct pathbetween transceiver and receiver is always the shortest. Hence, the ampli-tude of the first channel tap in the Rural Area channel model will be Riciandistributed. Since the traveled lengths of the multipath waves do not differas much as they do in urban environments they arrive with relatively smalldelay. This, together with the dominant line-of-sight component, leads tosmall excess delay and delay spread. The channel model’s impulse response

17


is depicted in Fig. 10.

3.5.3 Hilly terrain

Areas with large hills or mountains experience some reflected waves arrivingvery late. This leads to a high mean excess delay and, most significant, avery high delay spread. Large objects in the propagation path means noline-of-sight propagation, which equals Rayleigh fading channel taps. Fig.11 shows the impulse response for this model.

18

3 THEORY 3.6 Cell phone channel estimator and sample data

3.6 Cell phone channel estimator and sample data

To mitigate the effects caused by multipath fading, cellular networks usepilot symbols to estimate the channel impulse response. These are knownreference symbols that are transmitted through the channels. The purpose isto gain knowledge about the channel induced distortion that the transmitteddata have been subjected to. With the use of pilot symbols, comparisonscan be made between the received symbols and reference symbols. Withsome calculations a description of how the channel affects transmitted datais received in form of impulse response estimates. The estimates can thenbe used to counteract most of the channel distortion. The technique usedfor this and for calculating the estimates can differ between various mobileplatforms and various receiver types, but the purpose is the same.

In WCDMA, pilot symbols are sent primarily on two different channels.These are the CPICH and DPCH. The CPICH carries only pilot symbolswhereas on the DPCH, pilot symbols are being transmitted interleaved be-tween data and other signaling bits. The symbols from the channels areused during different parts of the estimation procedure, such as amplitudeand phase estimation.

The mobile hardware is, with special firmware, capable of deliveringdata from internal routines such as the channel estimation. Together with acomputer with logging capabilities, i.e. the right software, the following logpoints and many others can be recorded:

• DPCH symbols — The DPCH symbols as they arrive to the user afterpassing the channel.

• CPICH symbols — The CPICH symbols as they arrive to the userafter passing the channel.

• FD — Finger delay, time between fingers in the Rake receiver.

• AGC — In and output value of the Automatic Gain Control.

All of these log points are directly related to the physical propertiesof the channel. The finger delay measurements should be possible to usetogether with the amplitude of the channel estimates to calculate the timedelay and delay spread properties of the channel. To analyze the fading,other tools must be used.

19

3 THEORY 3.7 Parameter estimation

3.7 Parameter estimation

The cell phone channel estimator outputs are all samples from the calculatedimpulse response. As the probability density function (PDF) differs betweenvarious channel types, PDF parameter estimation could give important in-formation about the experienced channel.

Estimation can be done with numerous techniques. One way is to usethe, in statistics well known, Kolmogorov-Smirnov test, [8], [3]. Though, it ismore a goodness-of-fit technique than an actual estimation technique. Otheralternatives for finding the parameter estimates are method of moments, [7],[2] and maximum likelihood estimation, [17], [16], [15], [10] and [7]. Methodof moments make use of the moments of the PDF which often give simpleexpressions for the sought parameters. In maximum likelihood estimationthe likelihood function of observing the given data set is maximized.

3.7.1 Method of moments

The method of moments estimator has the advantage of being easy to findand simple to implement. The disadvantage is that is has no optimalityproperties. Though, as long as the data set is large enough it is still usefulsince it is most often consistent.6 Its simplicity also gives the advantage oflow calculation speed.

As the name implies, this technique is based on the moments of a PDF.It is often possible to use the moments to set up equations and from thesederive expressions for estimators to the function parameters in terms ofmoments. The theoretical moments can then be changed to the samplemoments that gives the estimate.

The general expression for the nth moment for the Rician PDF is givenin [15] as

E[Xn] = (2σ2)n/2Γ(

1 +n

2

)1F1

[−n

2; 1;− s2

2σ2

](8)

where Γ is the gamma function and 1F1 is a confluent hyper geometricfunction. Luckily, when n is even, the moments become simple polynomialsin s and σ, e.g.

E[X2] = s2 + 2σ2 (9)E[X4] = s4 + 8s2σ2 + 8σ4 (10)

Derivation of the estimators for s and σ in terms of E[X2] and E[X4] canbe done using only Eq. 9 and Eq. 10 as follows

2 E2[X2] = 2(s2 + 2σ2)2 = 2s4 + 8s2σ2 + 8σ4

6See [7] on page: 289-304

20


= E[X4] + s4 ⇒ s4 = 2 E2[X2]− E[X4] =⇒ (11)

s = 4

√2 E[X2]2 − E[X4], σ =

√(E[X2]− s2)/2

There are also other method of moments estimators that make use of lowerorder moments, such as the first and second moment that was used in [17].Estimators based on lower order moments usually give better results but arenot as easy to find as the estimators that are based on moments which aresimple polynomials.

3.7.2 Maximum likelihood estimation

The most popular practical estimator is based on the maximum likelihoodprinciple. It can be implemented even for complicated estimation problemsand for large enough data sets it minimizes the variance of the estimationerror to levels which makes its performance optimal7

The main idea with this estimation technique is to find the value ofthe unknown distribution parameter(s) that most likely have produced theobserved data [10]. To solve this problem one has to maximize the jointdensity for the given data set. If we define the likelihood function as L(σ|x) =f(x|σ), where f(x|σ) is the PDF for the distribution we seek parameters to,this function represents the likelihood of the parameter σ given sample datax. Finding the global maximum of this function, something usually done byderivation, will give us the most likely distribution parameter.

In the case with Rician distributed data the maximum likelihood estima-tors can be derived as described in [17]. Start with the Rician PDF, definedin Eq. 6. Let (x1, x2, . . . , xN ) be independent samples drawn from a Riciandistribution with unknown parameters s and σ. Then the joint density forthis outcome of N samples can be expressed as:

J = f(x1) . . . f(xN )

=(x1 . . . xN )

σ2Nexp

(−(x2

1 + . . . + x2N + Ns2)

2σ2

)(12)

∗ I0

(x1s

σ2

). . . I0

(xNs

σ2

)Finding the parameters that are most likely for the given set of samplesis done by finding the maximum of this likelihood function. To make thecalculations easier we take the natural logarithm of J and get

lnJ =N∑

i=1

ln(xi)− 2N lnσ − Ns2

2σ2−

N∑i=1

x2i

2σ2+

N∑i=1

ln(

I0

(xis

σ2

))(13)

7See [7] on page: 157-199

21


Rician s−parameter

Ric

ian

σ−pa

ram

eter

Log−likelihood surface for Rician distribution over s and σ

3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 3.5

2

2.05

2.1

2.15

2.2

2.25

2.3

−2026

−2024

−2022

−2020

−2018

−2016

Figure 12: Log-likelihood surface for different combinations of s and σ.

which is the log-likelihood function. To find the maxima of this function wehave to solve the system in Eq. 14 while ensuring that the solution is amaximum, e.g. with the second derivative test.8

∂

∂slnJ = 0,

∂

∂σlnJ = 0 (14)

Since the expression for the Rician PDF is quite complicated no closedform solution exists [17], [15] and [2]. Finding the solution of the resultingnonlinear equation is usually done using numerical processes. Although themaximum likelihood estimate is difficult to find, Eq. 13 together with Eq.14 lead to:

E[X2] = s2 + 2σ2 =1N

N∑i=1

x2i (15)

which shows that the maximum likelihood estimate for the second momentis the ”sample second moment” [17]. This can be used to speed up thesearch for the global maxima. The search becomes one dimensional sincethe maxima lies somewhere on the ellipse defined by Eq. 15.

The log-likelihood surface that lies on top of the parameter space [10]can be visualized as in Fig. 12. It has been calculated with Eq. 13 and the”X” is the result of a search process for the maxima.

82nd derivative test ensures a maximum at x when f ′′(x) < 0

22


3.7.3 Cramer-Rao lower bound

Regardless the choice of estimation technique all estimates will include anestimation error. According to Harald Cramer and Calyampudi Radhakr-ishna Rao, the variance of estimator b for B is always equal to or greaterthan I−1[B] where I[B] is the Fisher information for B. This limit, calledCramer-Rao lower bound, CRLB, is the lower limit for any unbiased esti-mator. As Rician distributed data are dependent on two parameters, theFisher information matrix is defined as

I [θ]i,j = E

[∂

∂θiln f(x|θ) ∂

∂θjln f(x|θ)

](16)

where f(x|θ) is the joint density defined in Eq. 12 and θ = [s σ2] is theparameter vector. The results from the derivations in Eq. 16 are presentedin [16] as

I(1, 1) =N

σ2

(Z − s2

σ2

)(17)

I(1, 2) = I(2, 1) =Ns

σ4

(1 +

s2

σ2− Z

)(18)

I(2, 2) =N

σ4

(1 +

s2

σ2(Z − 1)− s4

σ4

)(19)

which are the four elements in the Fisher information matrix with Z definedas

Z = E

x2

σ2

I21

(sxσ2

)I20

(sxσ2

) (20)

I21 is the first order modified Bessel function squared. From this follows that

the Cramer-Rao lower bound defined as I−1[B] becomes

CRLB =1

det I

(I(2, 2) −I(2, 1)−I(1, 2) I(1, 1)

)(21)

where CRLB1,1 and CRLB2,2 are the lower limits for the variance of theestimation error for s and σ2, respectively. For fixed parameter values anumerical calculation of Z can be performed. This gives simple expressionsfor the CRLB which can be used as a yardstick in performance tests forvarious estimation techniques.

23

4 METHOD

4 Method

The construction of a model for radio channel classification has been per-formed in a number of steps. First, a theoretical study was done on thesubject and related work was investigated. After finishing the theoreticalstudy, a radio network simulator in Matlab was used to check if classifica-tion would be possible based on channel estimates. Two different estimationtechniques were used and evaluated, most importantly in terms of accuracy,but also, to some extent, calculation speed. The performance of the estima-tors was analyzed and compared using the Cramer-Rao lower bound.

Measurements were then performed with a hardware channel emulator,a real UE and a BS emulator. The recorded data were post-processed and,finally, used in parameter estimation.

4.1 Simulating

Part of an Ericsson in house Matlab based radio network simulator wasused to investigate how the characteristics of different radio channels reflectin various types of fading. Estimation was performed on the first tap ofsimulated channel’s impulse responses as this is the one with direct wavecontribution. Performance tests were also done on the different estimationtechniques with Monte Carlo simulations.

4.2 Measuring

In Skelleftea, Sweden, Ericsson has a test lab, that is built for, amongstother things, radio channel simulations. The equipment there can be tunedfor simulations on different radio channel environments and with the rightcell phone software it is possible to record how a regular cell phone perceivesthese channels.

Rohde & SchwarzCMU200WCDMA Generator

HP / Agilent11759 RFChannel Simulator

SMIQGPS Sync10 MHzComputer K600

DL

UL

Figure 13: Cell phone measurement setup.

24

4 METHOD 4.3 Post-processing

Fig. 13 shows the setup and the equipment used for recording the cellphone channel estimates. The Rohde & Schwarz CMU200 WCDMA basestation generator was used to set up a call from the cell phone. The downlink from the generator was the input to the HP 11759 RF channel simu-lator which was set to use various types of fading, e.g. Rayleigh or directwaves. Different delays and various Doppler velocities could be set on eachchannel tap but this was not studied here. The output from the simulatorwas connected to the cell phone with use of external attenuation set to 30dBdue to the fact that attenuation of the down link decreased the variance ofthe measurements. The cell phone was then monitored from a computer.

With the use of modified cell phone software, data from a number ofsteps in the channel estimate procedure were written to log files. The mea-surements were done with the own cell registered in the neighbor cells list inthe WCDMA BS generator. This was necessary to receive data with varyingvalues.

To clearly be able to decide whether or not it is possible to use the cellphone’s pilot symbols as ground for classification, one tap impulse responseswere used. These were set to consist of different mixtures of line-of-sightand non-line-of-sight components, i.e. Rayleigh plus direct wave or onlyRayleigh. The channel estimates were recorded and post-processed. Therecording was done at a rate that allows for the assumption of independentsamples.

4.3 Post-processing

After the measurements, unwanted entries/log-points in the log files wereremoved with a Perl script and the remaining data were read into Matlab.There the data were cleaned and sorted. Duplicates were removed and onlylog points with the same time index were saved. The channel estimateswere then scaled with the resolution of the quantizer, i.e. 16-bit. To re-move the effect of the AGC, the estimates were also scaled with the relativeamplification.

4.4 Estimating

With the use of the post-processed channel estimates the PDF parameter es-timation was performed. This was done primarily with maximum likelihoodestimation but also, to some extent, with method of moments estimation.The estimated parameters were used to calculate the Rician K-factor.

25

5 RESULTS

5 Results

5.1 Simulations

The output from the Matlab radio network simulator shows obvious visualdifferences in the amplitude distribution of the channel estimates, see Fig.14(a) and Fig. 14(b). With parameter estimation, these differences arereflected in the Rician K-factor. To study the performance of different esti-

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

Amplitude

Den

sity

Typical Urban − Simulated

(a) Without LOS.

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

Amplitude

Den

sity

Rural Area − Simulated

(b) With LOS.

Figure 14: Amplitude distribution of simulated channel estimates.

mation techniques, repeated estimations were performed on simulated data.Fig. 15 shows the mean-square error for maximum likelihood and methodof moments estimation after a large number of estimations on randomlygenerated data of various sample sizes.

10 15 20 25 30 35 40 45 500

0.5

1

1.5

2

2.5

3

3.5

4

N [samples]

Mea

n S

quar

e E

rror

MSE as a function of samplesize Samples from Rician distribution with s=6 and σ=2

MoM − sMoM − σ2

MLE −sMLE − σ2

CRLB

Figure 15: Comparison of estimation techniques with CRLB.

26

5 RESULTS 5.2 Measurements

The curves could be smother if the calculations were done with moresimulations but that would be very time consuming. If we disregard the un-evenness of the curves it is obvious that the maximum likelihood estimationis indeed asymptotically optimal as stated in [7]. It approaches the Cramer-Rao lower bound for larger data sets. This can not be said about methodof moments which has no optimality properties. Though, the simplicity andcomputational speed of method of moments can be of greater importancethan the accuracy of maximum likelihood estimation. The calculation timehas not been thoroughly tested, but the method of moments technique isroughly 100 times faster.

5.2 Measurements

The differences in the physical properties of cellular environments shouldreflect in different types of fading. Fig. 16 shows some plots of the post-processed CPICH channel estimates for various mixtures of direct wavecomponents and scattered waves. These simulations was performed witha Doppler velocity of 3.6 km/h and the channel estimates are plotted in theIQ plane. The first figure, in the upper left corner, shows a mixture of scat-tered waves and a highly attenuated line-of-sight component. The scatteredwaves have, at least near, zero mean and equally distributed phase, just asin Fig. 6(a).

−0.4 −0.2 0 0.2−0.4

−0.2

0

0.2

R−0db + D−9dB

−0.4 −0.2 0 0.2−0.4

−0.2

0

0.2

R−0db + D−6dB

−0.4 −0.2 0 0.2−0.4

−0.2

0

0.2

R−0db + D−3dB

−0.4 −0.2 0 0.2−0.4

−0.2

0

0.2

R−3db + D−0dB

−0.4 −0.2 0 0.2−0.4

−0.2

0

0.2

R−6db + D−0dB

−0.4 −0.2 0 0.2−0.4

−0.2

0

0.2

R−9db + D−0dB

Figure 16: IQ representation of measured and post-processed channel es-timates for various mixtures of waves. R in the titles stand for Rayleighfading and D for direct wave. The amount of attenuation is specified foreach type.

The bottom right figure, shows the opposite, a strong direct wave com-ponent. Here the shift in mean is clearly visible. The channel estimates alsoproduce the characteristic ring shape due to movement between transceiver

27

5 RESULTS 5.2 Measurements

and receiver, remember Fig. 8(a). The additional figures describe variousmixtures of scattered and direct waves. The titles use R to denote Rayleighfading and D for direct wave. Each type is attenuated as specified, i.e.D-9dB means that the direct wave is attenuated 9dB.

0 0.1 0.20

10

20

Amplitude

Den

sity

R−0db + D−9dB

0 0.1 0.20

10

20

Amplitude

Den

sity

R−0db + D−6dB

0 0.1 0.20

10

20

Amplitude

Den

sity

R−0db + D−3dB

0 0.1 0.20

10

20

Amplitude

Den

sity

R−3db + D−0dB

0 0.1 0.20

10

20

Amplitude

Den

sity

R−6db + D−0dB

0 0.1 0.20

10

20

Amplitude

Den

sity

R−9db + D−0dB

Figure 17: Amplitude histograms for various mixtures of waves.

Histograms over the amplitude for these channel estimates are shownin Fig. 17. Here it is easier to see the shift in mean for the non-extremecombinations of direct wave and scattered waves. The case with little line-of-sight has as expected the characteristic Rayleigh form. The stronger thedirect wave component becomes the more will the distribution shift to theright and approach Gaussian, compare with Fig 7(b). All of this is in linewith theory.

28

5 RESULTS 5.3 Parameter estimation

5.3 Parameter estimation

0 0.05 0.1 0.15 0.2 0.250

2

4

6

8

10

12

14

Amplitude

Den

sity

Rayleigh−0dB + Direct wave−3dB Maximum likelihood estimation

DataMLE | s≈0.05, σ≈0.05

Figure 18: Maximum likelihood estimation on measured channel estimateswith a mixture of Rayleigh-0dB + Direct wave-3dB.

The results from the maximum likelihood estimation on the post-processedchannel estimates differed greatly between different log files. With recordeddata, based on settings in the channel simulator corresponding to a RicianK-factor of 0.5, the result after estimation can be visualized as in Fig. 18.The curve is the probability density function to which the estimated param-eters, s ≈ 0.05 and σ ≈ 0.05, correspond.

Fig. 19 and Fig. 20 show the spread of the estimations on measureddata for various K-factors with different sample sizes. There seems to bean offset between expected and estimated K-factor. This is the case regard-less of sample size, compare Fig. 19 and Fig. 20. With thorough analysisof the plots, the offset seems to be around 3 dB. As the amplitude of thescattered waves follows a Gaussian distribution, one solution for this couldbe the difference in calculating the variance of complex noise compared tothe variance of real noise. A calculation of the real noise variance only takesthe real part of our scattered waves into account and not the imaginarypart, which makes the real noise variance smaller than the complex noisevariance. This difference is exactly 3 dB. Another reason could of coursebe a badly calibrated channel simulator with an internal offset in the signalpower. In fact, power measurements of the output from the channel simu-lator confirmed that the mean of the power of the Rayleigh fading signal isnear 3dB lower than that of the direct wave. Whatever the reason for thisis, if it is due to real/complex noise or an internal design issue is of minorimportance. If it can be established that the offset is fixed at 3 dB, this caneasily be compensated for.

29


−10 −8 −6 −4 −2 0 2 4 6 8 10

0

2

4

6

8

10

12

14

16K−factor estimates with samplesize ≈ 220

Direct Wave Attenuation/Amplification [dB]

Est

imat

ed K

−fac

tor

EstimatesExpected estimateMean of estimates

Figure 19: K-factor estimation on log files with data sets of size ≈ 220.

−10 −8 −6 −4 −2 0 2 4 6 8 10

0

2

4

6

8

10

12

14

16K−factor estimates with samplesize ≈ 450


Est

imat

ed K

−fac

tor


Figure 20: K-factor estimation on log files with data sets of size ≈ 450.

Fig. 21 shows the variance and standard deviation of the estimates fortwo different sample sizes. As expected, the variance for larger data sets islower than for small data sets. Higher variance as the direct wave becomesstronger was not expected, though it is not entirely unlikely that this isa result from additive noise during measurements. With large K-factors,i.e. strong direct waves, the denominator in the K-factor calculation will besmall, at least compared to the nominator. If the noise then is independentfrom both the power of the direct wave and the power of the scattered waves,the effect of the noise will be greater, hence leading to high variance of K.

30


−10 −8 −6 −4 −2 0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Variance and Standard Deviation of K−factor Estimates


Var

ianc

e/st

d of

Est

imat

ed K

−fac

tors

σ2 for samplesize ≈ 450σ for samplesize ≈ 450σ2 for samplesize ≈ 220σ for samplesize ≈ 220

Figure 21: Variance and standard deviation of K-factor estimates on log fileswith data sets of varying sizes.

To better see the estimates in the region with weaker direct wave, Fig.22(a) and Fig. 22(b) show the lower left part of Fig. 19 and Fig. 20 ingreater detail. It is clear that many estimates equals zero, and that thenumber of zero estimates increases with weaker direct wave component.

−10 −8 −6 −4 −2

0

0.5

1

1.5K−factor est. | Samplesize ≈ 220


Est

imat

ed K

−fac

tor

(a) Sample size ≈ 220. 20 estimates foreach setting

−10 −8 −6 −4 −2

0

0.5

1

1.5K−factor est. | Samplesize ≈ 450


Est

imat

ed K

−fac

tor

(b) Sample size ≈ 450. 10 estimates foreach setting

Figure 22: K-factor estimation on multiple log files with data sets of varyingsizes.

Fig. 23, which shows an amplitude histogram of simulated data witha mixture of waves that corresponds to a K-factor equal to 0.5, clarifiesthis. One of the two probability density functions in the figure is fromestimation. The other is the real PDF. The density functions are very similarand hard to distinguish from each other even though the differences betweenthe real and estimated parameters are vast. The estimation resulted ins = 0.004, σ = 1.834 when the real parameters were s = 1.5, σ = 1.5.An s estimate so close to zero results in a very small K-factor, in this case

31


2.38 ∗ 10e− 6 , which is far from the expected 0.5.

0 1 2 3 4 5 6 70

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Amplitude

Den

sity

MLE on Simulated Data with K−factor = 0.5

DataEstimated PDFReal PDF

Figure 23: MLE estimation error.

Fortunately, this problem is only an issue for weak direct waves. A weakline-of-sight component easily disappears in the scattered waves and in thosecases, the estimate for the s parameter often becomes zero. This occurs forboth measured and simulated channel type estimates.

0 0.5 10

500

1000

1500

K−factor dist. from MLE estimates with real K−factor = 0.125

0 0.5 10

100

200

300


0 0.5 10

100

200

300


0 0.5 10

100

200

300

K−factor dist. from MLE estimates with real K−factor = 1

Figure 24: MLE estimation difficulties.

Fig. 24 illustrates the distribution of the resulting K-factor after 5000simulated estimations for a number of different K-factors. As the directwave becomes stronger and the K-factor increases the estimation becomesmore accurate.

32

5 RESULTS 5.4 Modified K-factor estimates

Sadly, from an application perspective, the region with weaker directwave components is of most interest. As the Rake receiver needs 1 chipspacing between assigned fingers, the ITU channel models has to be resam-pled to fit this time resolution. For the RA model this resampling results ina K-factor of 0.38 for the first channel tap. This value is a statistical meanthat can be expected when performing repeated measurements and estima-tions in a RA channel environment. With instantaneous measurements andestimation, the K-factor can very well be over 0.38. Nonetheless, for clas-sification between TU and RA, the most interesting interval for the RicianK-factor is low values up to, maybe 0.5. Estimation must therefore be ac-curate in this region which might require other estimation techniques. Onesolution could be Bayesian estimation [5], which could give better results forthe difficult cases.

5.4 Modified K-factor estimates

Modification of the results can be performed if the difficulty of estimatingparameters in mixtures with weak direct wave is taken into account. If thezero estimates are interpreted solely as a result of the estimation procedureerror they can be removed. This increases the mean of the K-factor esti-mates. This, together with compensation for the 3dB offset detected in theoutput power, leads to different results than before, see Fig. 25. Here themean of the K-factor estimates align better to what was expected but thereis still a deviation for some combinations of direct and scattered waves.

−10 −8 −6 −4 −2 0 2 4 6 8 10−1

0

1

2

3

4

5

6

7

8

9Compensated K−factor est. | Zero est. removed | Samplesize ≈220


Est

imat

ed K

−fac

tor


Figure 25: Compensated K-factor estimation on log files with data sets ofsize ≈ 220, zero estimates removed.

33

5 RESULTS 5.4 Modified K-factor estimates

Fig. 26 shows the difference between the expected and estimated K-factors for two different sample sizes. The offset is relatively small for all buttwo combinations of direct and scattered waves. With a 3dB amplificationof the direct wave the deviation from expected K-factor is about +0.5. Thisis not large enough to raise any particular concerns. On the other hand,9dB amplification results in an offset of -2. This is much higher than can beaccepted and the exact reason for this is not clear.

−10 −8 −6 −4 −2 0 2 4 6 8 10−2.5

−2

−1.5

−1

−0.5

0

0.5

1


Diff

eren

ce

Difference between estimated and expected K−factors

Sample size ≈ 450Sample size ≈ 220

Figure 26: Difference between estimated and expected K-factors.

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5 RESULTS 5.5 Proposed presentation of results

5.5 Proposed presentation of results

Based on calculations of mean excess delay and/or delay spread, which havenot been performed but should be possible with use of channel estimatesand finger delay, it is possible to compare the time dispersion characteristicsof the physical channel to the ITU models. The difference between TypicalUrban, TU, and Hilly Terrain, HT, are vast but the distinction betweenTypical Urban and Rural Area, RA, is more subtle. Since RA is the onlyITU model with line-of-sight communication, hence the only model withRician fading, an accurate estimation and calculation of the Rician K-factorcan be used to separate this model from TU.

To visualize the results from the calculations and estimations in com-parison to, e.g. ITU channel models, a two dimensional image could beused. Fig. 27 shows one example of this. The pointer placement displays

Amount of line-of-sight

Tim

e di

sper

sion

Low High

Radio Channel classification illustration

Hilly Terrain

Typical Urban

Rural Area

Low

Hig

h

Figure 27: Radio channel classification illustration.

the amount of line-of-sight and some type of time dispersion measure, e.g.the delay spread. As the calculated values most likely will fluctuate in time,low-pass filtering could be helpful. When the radio channel characteristicschange, a buffer is used to display older samples. These are the faded marksin Fig. 27. The color gradient background specifies the areas where thecombination of delay spread and Rician K-factor correspond to the specifiedchannel models. The value of the K-factor typically varies from zero for theTypical Urban model to 0.38 for the 1 chip resampled Rural Area model.Though this is a statistical mean that very well might be exceeded. Thetime dispersion measures for TU and HT varies between [0 3µs] for thedelay spread and [0 0.9µs] for the excess delay. Just as the interval for theK-factor, these are not absolute boundaries; rather intervals in which themean excess delay and the delay spread most likely will lie.

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6 DISCUSSION

6 Discussion

6.1 Measurement difficulties

The results in Fig. 19 and Fig. 20 show large variation between K-factorestimates of log files with the same mixtures of waves. Ideally, each estimatewould be alike and close to the theoretical value. In the region with low K-factor, the estimates are often close to zero due to reasons explained earlier.As this region is of importance in an application perspective, this issue mustbe resolved. Other estimation techniques might perform better [5].

During the measurements, too high signal power resulted in large vari-ance in the AGC and in the final K-factor estimation. With the use of exter-nal attenuation, the variance of the AGC could be lowered and that seemedto lower the variance of the estimates. With additional measurements atdifferent signal levels this error could be quantified and then hopefully alsoreduced.

Another peculiar thing was the settings needed in the BS generator tobe able to record data. The first recordings resulted in channel estimateswith the exact same value. To received data that varies, the own cell hasto be registered in the neighbor cells list. That means that the cell that theUE uses also has to be registered as a neighbor cell. The reason for this isat this point not clear.

6.2 Cell phone limitations

Another issue that might affect the estimation is some limitations in theRake receiver. The receiver often assigns two Rake fingers, even when theimpulse response only should have one tap. The second, so called ghost fin-ger, will contain parts of the signal energy. This could affect the estimationwhich is done on each finger separately. Unfortunately, this problem is notfixable until the receiver filter is exchanged.

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7 CONCLUSIONS

7 Conclusions

After performing theoretical studies, simulations in Matlab showed, as ex-pected, obvious differences between the impulse responses amplitude distri-bution for various fading types. For estimation, method of moments andmaximum likelihood estimation were identified as usable techniques andevaluated in terms of accuracy and speed. Maximum likelihood estimationturned out most accurate but method of moments is roughly 100 times fastercomputationally. With large enough data sets, method of moments shouldbe ”good enough”. How large data sets that must be used has not beenestablished.

The use of real data recorded from a cell phone showed that the am-plitude distributions of the channel estimates changes form with differentmixtures of scattered and direct wave components. The stronger the directwave, the more Gaussian-like distribution. The weaker, the more Rayleigh-like. Combinations with nearly equal power means Rician distribution. Allin line with theory. Parameter estimation and calculation of the RicianK-factor resulted in an increase of the K-factor with stronger direct wave.The mean values of the Rician K-factor estimates for various mixtures ofwaves are about 3 dB higher than expected, which could be due to the dif-ference in noise variance between complex and real noise or due to that thechannel simulator generates the power level of different signal componentsdifferently.

Estimation performed on mixtures with weak direct waves often resultedin zero estimates due to difficulty of detecting the weak direct wave in thescattered waves. As the Rician K-factors statistically is 0 for Typical Urbanand 0.38 for the 1 chip resampled Rural Area, the region with weak directwaves, i.e. K < 0.5, is of most interest from an application perspective.Other estimation techniques might therefore be necessary. With strongerdirect waves the variance of the K-factor estimates increased. The exactreason for this has not been established. Though, it is not unlikely that themeasurements are, to some extent, subjected to additive noise. Such noisewould, if independent from the power in the signal components, have greatereffect on the K-factor as the power of the scattered waves decrease.

Although not investigated in this work, the mean excess delay and thedelay spread should be possible to calculate from the cell phone channel esti-mates and the finger delay. This, together with the parameter estimates andthe Rician K-factor, could be used for comparing the measured radio envi-ronment with channel models, such as, but not limited to, those specified byITU. Even though an exact parallel between theoretical Rician K-factor, andpractical Rician K-factor has been hard to establish, the results are in linewith theory. Measurements on a real cell phone and PDF parameter esti-mation have shown that it should be possible to classify radio environmentsusing cell phone measurement data.

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8 FURTHER STUDIES

8 Further studies

Before the techniques in this report can be used for classification of radiochannels, there are some issues that require further studies.

• The variance of the estimated parameter for repeated simulations atthe same settings is high. To be able to draw accurate conclusionsabout the radio channel environment the variance must be lowered.For each slot, the variance of the channel estimates can be calculated.This might be possible to use to weigh the channel estimates beforeestimation. Also, external attenuation of the down link signal seemsto decrease the variance. Maybe the power of the output from thechannel simulator is too high for optimal UE performance.

• Overestimation of the Rician K-factor might be due to the dimension-ing of the power in the scattered waves. Additional tests needs to beperformed to ensure that the channel simulator output indeed is whatis should be. The channel simulator might be dimensioning the powerof the scattered waves with regard to complex noise instead of realnoise which all calculation has been based on. Also, it might need tobe re-calibrated.

• Estimation of the parameters when the line-of-sight component is weakmost likely requires other estimation techniques to avoid zero esti-mates. Bayesian estimation might improve the results.

With these issues resolved, a product for classification of radio channelsshould be possible.

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REFERENCES REFERENCES

References

[1] 3GPP. (2002). Technical Specification Group Radio Access Networks;Deployment aspects Release: 5. TR 25.943 v 5.1.0.

[2] Abdi, A.; Tepedelenlioglu, C.; Kaveh, M.; Giannakis, G. (2001). On theestimation of the K parameter for the Rice fading distribution. IEEECommunications Letters. Volume: 5. Issue: 3. Page: 92-94.

[3] Bain, Lee J.; Engelhardt, Max. (1987). Introduction to Probability andMathematical Statistics. Duxbury Press. Boston, MA 02116. ISBN 0-87150-067-1.

[4] Chizhik, D.; Ling, J.; Wolniansky, P.W.; Valenzuela, R.A.; Costa,N.; Huber, K. (2003). Multiple-input-multiple-output measurements andmodeling in Manhattan. IEEE Journal on Selected Areas in Communi-cations. Volume: 21. Issue: 3. Page: 321-331.

[5] Haug, A.J. (2005). A Tutorial on Bayesian Estimation and TrackingTechniques Applicable to Nonlinear and Non-Gaussian Processes. TheMitre Corporation.

[6] Holma, Harri.; Toskala, Antti. (2001). WCDMA for UMTS: Radio Ac-cess for Third Generation Mobile Communications, Revised Ed. JohnWiley & Sons, LTD. West Sussex, PO19 1UD, England. ISBN 0-471-48687-6.

[7] Kay, Steven M. (1993). Fundamentals of Statistical Signal Processing:Estimation Theory. Prentice Hall PTR. Upper Saddle River, NJ 07458.ISBN 0-13-345711-7.

[8] Kirkman, T. Kolmogorov-Smirnov Test.http://www.physics.csbsju.edu/stats/KS-test.htm (2006-09-21)[email protected]

[9] Linnartz, Jean-Paul M.G. (1995). Derivation of Rayleigh PDFhttp://wireless.per.nl/reference/chaptr03/fading/anspdf.htm (2006-10-16) [email protected]

[10] Myung, In. J. (2003). Tutorial on maximum likelihood estimation. Jour-nal of Mathematical Psychology. Volume: 47. Page: 90-100.

[11] Phillips, Charles L.; Parr, John M. (1999). Signals, Systems, and Trans-forms: Second Edition. Prentice Hall. Upper Saddle River, NJ 07458.ISBN 0-13-095322-9.

[12] Rayleigh, Lord. (1889). On the resultant of a large number of vibrationsof the same pitch and of arbitrary phase. Phil. Mag. Volume: 27. Page:460-469.

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http://www.physics.csbsju.edu/stats/KS-test.html

mailto:[email protected]

http://wireless.per.nl/reference/chaptr03/fading/anspdf.htm

mailto:[email protected]

REFERENCES REFERENCES

[13] Sklar, Bernard. (1997). Rayleigh fading channels in mobile digital com-munication systems: Part I. Characterization. IEEE CommunicationsMagazine. Volume: 35. Issue: 7. Page: 90-100. ISSN: 0163-6804.

[14] Sklar, Bernard. (1997). Rayleigh fading channels in mobile digital com-munication systems: Part II. Mitigation. IEEE Communications Mag-azine. Volume: 35. Issue: 7. Page: 102-109. ISSN: 0163-6804.

[15] Sijbers, J.; den Dekker, A.J.; Scheunders, P.; Van Dyck, D.(1998). Maximum-likelihood estimation of Rician distribution param-eters. IEEE Transactions on Medical Imaging. Volume: 17. Issue: 3.Page: 357-361.

[16] Sijbers, J.; den Dekker, A.J. (2004). Maximum Likelihood estimationof signal amplitude and noise variance from MR data. Magnetic Reso-nance in Medicine. Volume: 5. Issue: 3. Page: 586-594.

[17] Talukdar, Kushal K.; Lawing, William D. (1991). Estimation of the pa-rameters of the Rice distribution. The Journal of the Acoustical Societyof America. Volume: 89. Issue 3. Page: 1193-1197.

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LIST OF FIGURES LIST OF FIGURES

List of Figures

1 Example of wireless channels. . . . . . . . . . . . . . . . . . . 42 Block diagram of a transmission system. . . . . . . . . . . . . 53 Radio access technologies . . . . . . . . . . . . . . . . . . . . 64 Power delay profile. . . . . . . . . . . . . . . . . . . . . . . . . 95 Discrete Power delay profile. . . . . . . . . . . . . . . . . . . . 106 Scattered waves in IQ representation together with the am-

plitude PDF. . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Scattered waves in IQ representation with a LOS component

together with the amplitude PDF. . . . . . . . . . . . . . . . 148 Scattered waves in IQ representation with a LOS component

together with the amplitude PDF, both with Doppler. . . . . 159 Impulse response for Typical Urban Channel Model. . . . . . 1610 Impulse response for Rural Area Channel Model. . . . . . . . 1711 Impulse response for Hilly Terrain Channel Model. . . . . . . 1712 Log-likelihood surface for different combinations of s and σ. . 2213 Cell phone measurement setup. . . . . . . . . . . . . . . . . . 2414 Amplitude distribution of simulated channel estimates. . . . . 2615 Comparison of estimation techniques with CRLB. . . . . . . . 2616 IQ representation of measured and post-processed channel

estimates for various mixtures of waves. R in the titles standfor Rayleigh fading and D for direct wave. The amount ofattenuation is specified for each type. . . . . . . . . . . . . . . 27

17 Amplitude histograms for various mixtures of waves. . . . . . 2818 Maximum likelihood estimation on measured channel esti-

mates with a mixture of Rayleigh-0dB + Direct wave-3dB. . 2919 K-factor estimation on log files with data sets of size ≈ 220. . 3020 K-factor estimation on log files with data sets of size ≈ 450. . 3021 Variance and standard deviation of K-factor estimates on log

files with data sets of varying sizes. . . . . . . . . . . . . . . . 3122 K-factor estimation on multiple log files with data sets of

varying sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3123 MLE estimation error. . . . . . . . . . . . . . . . . . . . . . . 3224 MLE estimation difficulties. . . . . . . . . . . . . . . . . . . . 3225 Compensated K-factor estimation on log files with data sets

of size ≈ 220, zero estimates removed. . . . . . . . . . . . . . 3326 Difference between estimated and expected K-factors. . . . . 3427 Radio channel classification illustration. . . . . . . . . . . . . 35

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WCDMA radio channel classification

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