OFDM & Fading

8/13/2019 OFDM & Fading

1/23

OFDM & Fading

Digital Communication

17/12/2013


2/23

Outline

1. Introduction to OFDM

2. The Multipath Environments

3. The Principle of OFDM

4. OFDM Mechanism

5. Conclusion

6. Example


3/23

-New techniques for digital transmission have developed to meet the increasing demand

for higher data rates in communications is Orthogonal Frequency Division Multiplexing

(OFDM)

-Orthogonal Frequency Division Multiplexing (OFDM) is a Multi-Carrier Modulation

technique in which a single high rate data-stream is divided into multiple low rate data-

streams and is modulated using subcarriers which are orthogonal to each other.

-Advantages-high data rate and bandwidth efficiency.

-Easy and efficient in dealing with multipath

-robust against narrow band interference

-Disadvantages

-High PAPR

-Sensitive to frequency offset-Applications

Digital audio and video broadcasting Wireless LAN 802.11

Digital subscriber lines (DSL) WiMAX 802.16

LTE (Long term Evolution), 4G Cellular Networks

Introduction to OFDM


4/23

The Multipath Environments

-The transmission of the signal from the transmitter to the receiver is carried over multiple

paths

Fadingis the rapid fluctuation of the amplitude of a radio signal over a short Period of time

or travel distance, caused by interference between two or more versions of the transmitted

signal which arrive at the receiver at slightly different times

Flat Fading

If the transmitted channel is sufficiently narrow then all the frequency componentstransmitted in the channel will be attenuated by the same amount, this is known as flat

fading

Frequency Selective Fading

If the mobile channel has a bandwidth that is smaller than the bandwidth of transmitted

signal, then the channel creates frequency selective fading on the received signal. the

received signal includes multiple versions of the transmitted waveform which are attenuated

(faded) and delayed in time, Thus the channel induces inter symbol interference


5/23

Narrowband and Wideband Channels

A channel to be Narrow band Ts > Td

A channel to be WidebandTd > Ts

Coherence Bandwidth

a channel which passes all spectral components with approximately equal gain and linear phasewhich the channel considered to be flat .

Bc = 1/Td


6/23

The Principle of OFDM

- Multi-Carrier Modulation (MCM) is the principle of transmitting data by dividing the stream into

several bit stream and the corresponding subchannel bandwidth is much less than the total system

bandwidth

-The number of substreams is chosen to insure that each subchannel has a bandwidth less than the

coherence bandwidth of the channel, so the subchannels experience relatively flat fading. So, the

ISI on each subchannel is small.

-Consider a bandwidth B available, then the symbol time Ts=1/B-For multicarrier system dividing bandwidth B into N subcarrier .

Spacing

to subcarrier spacing N ( if we have

subcarrier then we have

2

system carrier.


7/23

Multicarrier Data Detection

y(t)= S(t)= Xi 2

where y(t) in absence of noise.

Multicarrier Transmission

Consider ith

subcarrier Fi=i

, center frequency of the i

thsubcarrier where

(

2 1)

2

XiData transmitted on ith subcarrier

Si(t)= Xi 2

Xi 2

There are now N-subcarrier Hence, there are N data stream(Xi).

S(t)= Si(t) where, S(t) composite transmit signal , Si(t) ith

data stream modulated into ith

subcarri

S(t)= Si(t) = Xi 2

= Xi 2

where, S(t) multi-carrier composite transmitted signal.


8/23

Detection Scheme[1]

- Coherent demodulated each stream with corresponding sub-carrier :

(2

/

0)*dt where f

lits l

itsubcarrier and the conject its match filer

=

(Xi 2

/

0)2

dt

=

Xi 2()

/

0 where, fo=

multiple of fundamental frequency by Fourier

series.Fundamental period To=

1

fo=

Xi 2

0

= 0

=

= Xl + ili Xi 2()

/

0dt

All subcarrier are orthogonal.- Fo= and time period of integration = 1/fo= N/B

=

(XL + il Xi

2()/

0

/

0) dt

=

XL.

+

ilXi

2()/

0dt

= 0 since, integrating in fundamental period


9/23

=

XL.

= XL where, Xl: information symbol transmitted on Lthsubcarrier.

Hence, XL can be recovered by coherently demodulating with 2

.

This scheme is a termed of multicarrier modulation system(MCM) , its however the basic for

orthogonal frequency division multiplexing. but not OFDM modulation .

Hense, MCM transmit N-symbol using N-subcarrier in time period N/B

Therefore, symbol rate =

/=

Single carrier , symbol rate =1

1/=

This, the overall symbol rate in single carrier Vs multicarrier system is unchanged.

MCM N-symbol on N-subcarrier

Single carrier One symbol on a carrier

Hense, single carrier system experience ISI . but the BW for MCM coherence BW each

subcarrier experience frequency flat fading.

Hense, there is No ISI in time domain.


10/23

What is the problem in MCM system[2]?

Sol: implementing bank of N-modulator and N-demodulator is challenging.

There is a key advancement made by ( Weinsten & fbert, Data transmitting by frequency

Division Multiplexing using the discrete Fourier Transformer.1971)

Consider the MCM transmit signal and this signal is band limited to B.

Hense, the Nyqist sampling rate is B, sampling time Ts=1/B

S(t)= Xi 2

MCM signal.

Consider the uth

sample at t=uTs= u/B

S(uTs) = X(u) = Xi

2

= Xi

2

X(u) = Xi 2

I DFT (Inverse Discrete Fourier Transform) of information symbol

X(0) X(1) .X(N-1)

The MCM transmit signal can simply be generated by employing IFFT (Inverse Fast Fourier

Transform) .


11/23

This proposed scheme generating the MCM transmit signal has mush lower complexity

compared to using bank of modulator) as a fast operation.

ow, at the receiver, to recover the information symbol one can corresponding employ an FFT

operation.

This is termed as OFDM ( Orthogonal Frequency Division Multiplexing)Due to the rectangular

shape of pulses in the time domain, the spectrum of each modulated carrier has a sin(x)/x shape.

The spectra of different modulated carriers overlap, but each carrier is in the spectral nulls of all

other carriers. Therefore, as long as the receiver does the appropriate demodulation (multiplying

by exp(j2fnt ) and integrating over symbol duration), the data streams of any two subcarriers

will not interfere.[3]


12/23

OFDM Mechanism

Transmitter schematic

The incoming data stream is first converted from serial data to parallel data(output of S/P isdiscrete frequency component) . The number of parallel data stream will depend on the

bandwidth of the overall channel and the number of sub-carriers available to carry the data. Eachof the parallel streams of data is then modulated on to each sub-carrier which then undergoes an

IFFT (Inverse Fast Fourier Transform) which transforms the frequency domain signal into a time

domain signal(Each input controls signal at one frequency). The complex time domain signal isthen added to produce a composite and complex waveform.

IFFT output is sum of signal samples

IFFT does modulation and multiplexing in one stepFiltering and D/A of samples results in baseband signal


13/23

Receiver schematic :

The captured and sampled signal is transformed to the frequency domain by applying an FFT.This effectively separates the sub-carriers so they may be demodulated independently.

DFT is means to generate samples of the OFDM signal in the frequency and time domainwithout the use of oscillators

Multipath fading causes some frequencies to be attenuated

Fading is approximately constant over narrow band

Multipath delay causes change in amplitude and phase of each subcarrier


14/23

Cyclic Prefix[2,5]

The multi-path environment through which the radio signals propagate creates temporal

distortions in the data carried by the radio channel. The differing propagation durations of each

of the multi-path components create inter-symbol interference (ISI). Inter-symbol interference in

OFDM systems cannot be tolerated since it reduces the orthogonality between the sub-carriers,

and increases the BER and reduces the performance of the channel. All of the information

important to the FFT (Fast Fourier Transform) is contained within the symbol time. Therefore it

is critical that there is no distortion during this period.Since the ISI cannot be eliminated from the channel, the information must be protected from its

effect. The solution in OFDM systems is to extend the length of each symbol by a factor

equivalent to the likely delay spread in the channel. This extension to the symbol is known as the

cyclic prefix (CP) .

The CP, which appears at the beginning of each symbol, is actually a copy of the last part of that

symbol


15/23

X^(0).X^(n-2)X^(n-1) X(0)X(1)X(2)..X(n-1)

Frequency selective channel can be modeled as:

h(0)h(1)h(L-1) multi tap channel.

First symbol corresponding to current OFDM symbol block is:

Y(o) = h(0)X(0) + h(1)X^(n-1) + h(2)X^(n-2) +..h(L-1)X^(n-l+1)

Initial sample are being subject to ISI

Y(1) = h(0)X(1) + h(1)X(0) + h(2)X^(0) + .+ h(l-1)X^(n-l+2)

X(0)X(1) .. X(n-1) X(n-2) X(n-l+1)

Current OFDM symbolPrevious OFDM symbol

L taps

This from previous OFDM symbol ( Interference from L-1 sample)

ISI from previous OFDM symbols

Cyclic Prefix


16/23

X(n-l+1)X(n-2)X(n-1) X(0)X(1) .. X(n-1)

Y(0) = h(0)X(0) + h(1)X(n-1) + + h(n-1)X(n-l+1)

[ y(0) y(1)y(n-1)] = [h(0) h(1) ..h(l-1)] [ X(0) X(1) ..X(n-1)]

Received sample multi tap channel models ISI N-samples of current OFDM

Symbols generated after IFFT

Y=H X this is possible because of additional of cyclic prefix

Y(k) = H(k)X(k) modulated information symbol at Kth

subcarrier

Where, Y(k):received symbol across Kth

subcarrier

H(k):channel coefficient corresponding to Kth

subcarrier

X(k): symbol loaded onto Kth

subcarrier

Hense, the frequency selective channel is converted into a group of Narrow band Flat fading

channel one channel a cross each subcarrier.

All samples belong to current OFDM


17/23

Y(0) = H(0) X(0)

Y(1) = H(1) X(1) N parallel Flat fading channel

Hense, OFDM essentially removes theIS

Y(N) = H(N-1) X(N-1)


18/23

Example

Let X(f) is the i/p of IFFT then, the o/p =


19/23

ExampleNoteThat:

- IFFT (Inverse Fast Fourier Transform) which transforms the frequency domain signalinto a time domain signal. IFFT output is sum of signal samples, sample at fundamental

period

- F(t) = 2 = cos2 + 0.5 cos4+0.5cos6.- 2 = cos2 + sin2 - cos2ft = 1

2[ f fo +f + f o]

For IDFT X(n) =

1

Xi

2

Let X X 0 X 1 X 2 X 3 1 1 1 1

n n n n3 j2i j2 j4 j6N N N N

i 0

1 1x n X i e X 0 X 1 e X 2 e X 3 e ,0 n N 1

4 4

n n n

j2 j4 j6N N N

1x n 1 e e e ,0 n N 1

4

1

x 0 1 1 1 1 14

3

j jj2 2

1x 1 1 e e e 0

4

j j2 j31

x 2 1 e e e 04

3 9

j jj32 2

1x 3 1 e e e 0

4

IDFT 1 1 1 1 1 0 0 0


20/23

Example- Now, at the receiver after S/P, to recover the information symbol one can

correspond employ an FFT operation.

X(k) = ()2

1

==0 K=0,1,.,N-1

WN= 2

If N = 4 N = 22

X(0) = X0 + X1 + X2 +X3

X(1) = X0 + X12

4 - X2 + X323

4

X(2) = X0 X1 + X2 X3

X(3) = X0 + X123

4 - X2 X323

4

X(k) = X(even) + WnX(odd)

By applied The CooleyTukey algorithm, ( Butterfly algorithm) per/bit

O(N Log2N) : number of branch , Log2N : number of level [10]


21/23

Example

Example. 2: Consider a multicarrier system with a total passband bandwidth of 1

MHz. Suppose the system operates in a city with channel delay spread Tm = 20s.

How many subchannels are needed to obtain approximately flat-fading in each

subchannel.

Solution: The channel coherence bandwidth isBc = 1/Tm = 1/.00002 = 50 KHz. To

insure flat-fading on each subchannel, we takeBN =B/N = .1Bc


22/23

Conclusion OFDM is a key broadband wireless technology support data in excess of 100 Mbps. Designed for NLOS operation Fixed size (256 carrier), variable subcarrier spacing to support multiple defined

bandwidth.

Adaptive modulation with BPSK , QPSK and 64-QAM defined. OFDM is an advanced modulation technique which is suitable for high-speed data

transmission due to its advantages in dealing with the multipath propagation problem,

high data rate and bandwidth efficiency.


23/23

References

[1] Theodore Rappaport, Wireless Communications: Principles and Practice,2002

[2] Andrea Goldsmith, Wireless Communications, Cambridge University Press.2005

[3] Andreas F. Molisch ,Wireless Communications, Second Edition 2011 John Wiley & Sons

[4] Yao Xiao, A Thesis of Orthogonal Frequency Division Multiplexing Modulation and Inter-

carrier Interference Cancelation ,2003

[5] Arun Gangwar1, Manushree Bhardwaj,An Overview: Peak to AveragePower Ratio inOFDM system & its Effect,2012

[6]Hwaei Company, Telecomm Academy, LTE Radio Interface

[7 ] Gongpu Wang, Feifei Gao, Yik-Chung Wu, and Chintha Tellambura, Joint CFO and

Channel Estimation for OFDM-Based Two-Way Relay Networks,2011

[8] Yajun Wang, Wen Chen, , and Chintha Tellambura, Genetic Algorithm Based Nearly

Optimal Peak Reduction Tone Set Selection for Adaptive Amplitude Clipping PAPR

Reduction,2012

[9] Xiaoqiang Ma, Hisashi Kobayashi. and Stuart C. Schwarrz, Effect of Frequency Offset On

BER of OFDM and Single carrier System ,2003

[10] Pavan Kumar, Priya Jain, Ravi Kiran, Rohith N, Ramamani K, FFT Algorithms: A

Survey,2013

OFDM & Fading

Documents

Transcript of OFDM & Fading