OFDM Transmission Over Wideband Channel

8/13/2019 OFDM Transmission Over Wideband Channel

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Wireless Access Tech. Lab.

OFDM Transmission over WidebandChannel

Gwo-Ruey Lee


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Outlines

OFDM Transmission over Wideband Channel

The Time Dispersive Channel Model

Effects of Time Dispersive Channels on OFDM

Channel Estimation Time Domain Channel Estimation

Frequency Domain Channel Estimation

Equalization

Comparisons of Time- and Frequency- DomainEqualization


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A time-dispersive channel can be characterizedby its channel impulse response

where

is the number of multipath components

is the path gain of path i

is the path delay of path i

1

0

( ) ( ) ( )L

i i

i

h t t t

L

( )i t

i

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Each path gain is a complex random variablewith uniformly distributed phases and Rayleighdistributed magnitude.

The average power of each path decaysexponentially.

( )i

t

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The mathematical model for the time dispersivechannel is

where is the sampling period, and is

the root-mean-squared (RMS) delay spread.sT RMST

3/3

2 21 1(0, ) (0, )

2 2i i i

N j N

2 2

0i /s RMS

iT Te

2

0 1

/s RMS

T Te


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Effects of Time Dispersive Channels onOFDM

The phenomenon of multipath fading causesprevious symbol to interfere with the lattersymbol. This is known as the inter-symbol

interference (ISI).

The received signal is the convolution ofthe transmitted symbols and the discrete-time

channel impulse response.

ISI ISI ISI

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Channel Estimation

Channel estimation is the task of estimating thefrequency response of the radio channel thetransmitted signal travels before reaching thereceiver antenna.

The channel estimation can be performed using thetime domain approach and frequency domainapproach. Time domain channel estimation

Frequency domain channel estimation

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Time Domain Channel Estimation

This channel estimation is performed using the timedomain approach, before FFT processing of thetraining symbols.

In this, the channel impulse response instead of thechannel frequency response, is estimated.

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The received time domain signals are

is the channel impulse response.

is the known symbol.

is noise.

nx

nw

nh

)1.4(;64,...,1, nwxhrnnnn

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The time domain convolution can be expressed asa matrix vector multiplication.

The parameter Lis defined as the maximum

length of the impulse response, L


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Then receive signal is expressed as

1

2

3

4

64

r

r

r

r

r

1 64 64 2

2 1 64 3

63 62 64

64 63 64 1

L

L

L

L

x x x

x x x

x x x

x x x

0

1

2

1L

h

h

h

h

1

2

3

4

64

w

w

w

w

w

n n nr h x w h wX

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The least square (LS) estimate for ish

rXXXh HH

LS

1)(

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This channel estimation is performed using thefrequency domain approach.

In this, the channel frequency response isestimated by using two repeat training sequences.

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We get (4.2) from (4.1) through FFT transform,

If we have two repeat sequences,

k k k k R X H W

1, 1,

2, 2,

k kk

k

k kk

R WXR H

R WX

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W l h b


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The least square (LS) estimate for eachis

,k LSH

1

, 1, 2,

1

2

H H

k LS k k k k k H X X X R R

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W l T h b


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Comparisons of Time- and Frequency-Domain Equalization

Time-domain Equalization Frequency-domainEqualization

Convolution One-tap multiplication

High complexity

when Lis lager

Low complexity

when Lis small

No FFT Required FFT Required

nn rh

kk RH *

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Wi l T h b


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Wi l A T h L b

References

[1] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadratureamplitude modulation Principles and applications for personalcommunications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2000.

[2] Mark Engels, Wireless Ofdm Systems: How to Make Them Work?KluwerAcademic Publishers.

[3] John Terry, Juha Heiskala, OFDM Wireless LANs: A Theoretical andPractical Guide, Sams.

Documents

OFDM Transmission Over Wideband Channel