Improved Equalization for Coded, Zero-Padded OFDM (ZP-OfDM) Systems

8/2/2019 Improved Equalization for Coded, Zero-Padded OFDM (ZP-OfDM) Systems

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IMPROVED EQUALIZATION

FOR

CODED, ZERO-PADDED OFDM(ZP-OFDM) SYSTEMS

SUBMITTED BY:

ANKIT SANCHETI

2011PEC5324


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INTRODUCTION

In order to combat the effect of multipath, OFDM systems is

mainly used.

Most common OFDM systems use cyclic-prefix so referred as

CP-OFDM.

a N sample OFDM symbol is cyclically extended by NG

samples where NG > L, and L is the length of the channel

impulse response.

OFDM symbol is cyclic convolution in the case of the CP-

OFDM system.2


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INTRODUCTION CONTINUED.

Another way to deal with multipath is to pad the N sample

OFDM symbol with NG zeroes, referred as Zero-padded

OFDM (ZP-OFDM) system.

One of the main advantages of ZP-OFDM as compared to

CP-OFDM is that the total transmitted energy can be reduced.

Equalization at the receiver needs to be performed differently

because the convolution of the channel with the OFDM

symbol is now a linear convolution than cyclic convolution.

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SIGNAL MODEL

For any L, let us first define a (L x L) Fourier matrix as follows:

Data vector of length N be a = [a0 a1 aN1]

The OFDM symbol derived by taking the IFFT of a be

= A = [A0 A1AN1]

The vector A is extended by NG zeroes, where NG is thelength of the guard interval.

A is transmitted over a channel with impulse response

denoted by

we have explicitly forced the impulse response of the channelto be at most NG +1 samples long.

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SIGNAL MODEL CONT.

The received vector r can be expressed in terms of the channel

h and transmitted vector A as follows:

2

The eigen-vector matrix is the Fourier matrix, Hc can be written

as: 5


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is a N +NGdimensional diagonal matrix of eigen values i ofHc.

These eigen values are also the FFT of the channel i.e.

The received vector is

..3

We will now describe a number of estimators for a based onequations (2) and (3).

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SIGNAL MODEL CONT.


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A. OVERLAP-ADD(OLA) EQUALIZER

Adding last NG samples of the received vector r to the first NGsamples, we get the signal model:

We get overlap-add (OLA) equalizer by taking N-point FFTs ofboth sides.

Exhibit similar performance as the CP-OFDM system, sincespectral-nulls will be inverted.

No performance improvement as compared to a CP-OFDM

system.

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B. LEAST-SQUARES(LS) EQUALIZER

For the transmitted signal vector a

LS equalizer is

The estimation noise is colored, which may have an effect oncoded systems.

For large N, the complexity can be high since the equalizerinvolves the inverse of a channel-dependent matrix that is not adiagonal matrix..

Guarantees symbol recovery even in the presence of spectralnulls.

Better performance than the OLA equalizer

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C. SUBOPTIMAL LEAST-SQUARES(SLS) EQUALIZER

First multiply R by 1 , and then do a LSestimator for a.

Much easier to implement than the LS equalizer.

If there is a spectral null, the estimate error will be

high. Performance is similar to the OLA equalizer.

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D. TRUNCATEDSUBOPTIMAL (TS) EQUALIZER

For the truncated, suboptimal (TS) equalizer:

Matrix T has been truncated to remove the small eigen

values. Hence the inverse will not cause excessive noise

enhancement.

For large N even this implementation would become

extremely complex. 10


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E. SIMPLIFIEDTRUNCATEDSUBOPTIMAL (STS)

EQUALIZER

It can be described as

It is very simple to implement, since there are no non-diagonal

channel-dependent matrix inversions required.

since the small eigen values have been removed from T ,

noise enhancement is suppressed.

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SOFT-METRIC CALCULATION FOR

CODED ZP-OFDM

Let us now consider a bit-interleaved-coded-modulation (BICM)

system.

One way to compute the soft-metrics of the bits is to first

equalize, using one of the above equalizers to form an estimate

a and then evaluate the soft-metric for the ith bit in the kth

symbol as follows:

where 2k is the variance of the kth component of the estimation

noise, which in general is colored.12


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SOFT-METRIC CALCULATION FOR

CODED ZP-OFDM CONT.

An alternative way would be to start with eqn (3)

These soft-metrics are then used in a Viterbi decoder

to decode the transmitted sequence.

The decoder using the above metric is the maximum

likelihood (ML) receiver and in general this will give us

a lower bound on achievable performance. 13


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SIMULATIONS

We consider two ZP-OFDM systems.

Un-coded 16-QAM ZP-OFDM

Coded 16-QAM ZP-OFDM

OFDM symbol length N = 64

The number of zero-padded samples NG = 16.

Channels :-

The first is defined by h = [1/2 0 0 0 0 1/2]T .

The second channel we consider is an exponentially Rayleigh fadedchannel with rms delay spread of 80ns.

Sample rate = 20 MHz.

Length of impulse response = 17 = (NG +1)14


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MSE performance of different equalizers in

h = [1/2 0 0 0 0 1/2] channel.

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MSE performance of different equalizers in exponentiallyfaded Rayleigh channel with 80ns rms delay spread.

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PER performance of non-iterative equalizers in

h = [1/2 0 0 0 0 1/2] channel.

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PER performance of iterative equalizers in

h = [1/2 0 0 0 0 1/2] channel.

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PER performance of non-iterative equalizers inexponentially faded Rayleigh channel with 80 ns rms delay

spread channel.

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PER performance of iterative equalizers in exponentiallyRayleigh faded channel with 80 ns rms delay spread

channel.

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CONCLUSIONS

We developed two new equalizers for ZP-OFDM: the TS and STSequalizers and showed their performance advantage over the more

commonly used OLA equalizer in channels with and without spectral

nulls.

STS equalizer can improve performance, especially in channels with

spectral nulls, using a larger FFT size.

STS initialization provides a faster convergence than the OLA

initialization especially for channels with spectral nulls.

It is feasible to obtain the performance of a LS equalizer in a coded

ZP-OFDM system without requiring matrix inverses of channel-

dependent non-diagonal matrices, by using the iterative method of

soft-metric calculation

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Improved Equalization for Coded, Zero-Padded OFDM (ZP-OfDM) Systems

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