Optimization of zero-padded systems - Signal Processing and Optimization for Transceiver Systems - page 577

Optimization of
zero-padded systems

18.1 Introduction

The zero-padded (ZP) transceiver was discussed at length in Sec. 7.2. In this
chapter we consider numerical examples of optimal ZP systems. Performance
plots are shown in Sec. 18.2 for the ZP system with minimum symbol error
probability (with and without the zero-forcing constraint). We also discuss the
effect of the block size M on performance of optimal transceivers (Sec. 18.3). It
will be found, unlike in cyclic-prefix systems, that the performance of optimal
ZP systems degrades as the block size M is increased. The interest in increasing
M arises from the fact that it reduces the bandwidth expansion factor (Sec. 7.2).
But in the zero-padded case, there is a clear prize paid in terms of performance
as we shall see.

18.2 Zero-padded optimal transceivers

The transceiver with zero-padded precoding is reproduced in Fig. 18.1. Through-
out the chapter the channel is assumed to be FIR with order ≤ L ,thatis,

L

c ( n ) z −n .

C ( z )= (18 . 1)

n =0

With L zeros inserted per block as indicated in the figure, the system shown in
Fig. 18.1 is equivalent to Fig. 18.2, where A is a full-banded Toeplitz matrix:

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