The lazy precoder with a zero-forcing equalizer - Signal Processing and Optimization for Transceiver Systems - page 295

8

The lazy precoder with

a zero-forcing equalizer

8.1 Introduction

The zero-padded precoder described in Chap. 7 is reproduced in Fig. 8.1. In
this system, C ( z ) is a scalar FIR channel:

L

c ( n ) z −n . C ( z )=

n =0

The input s ( n ) is transmitted in blocks of length M ,with L zeros padded to
each block. The precoder at the transmitter is represented by the matrix R 1
and the equalizer matrix is T . The special choice of the precoder given by

R 1 = I

is called the lazy precoder, and is shown in Fig. 8.2. Thus, the transmitter
merely pads zeros, but does not perform any transformation. All collaboration
between components happens at the receiver. As pointed out in Chap. 4, such a
scenario is applicable in multiuser transceivers operating in the multiple access
or uplink mode (Sec. 4.5). In Chap. 7 we showed (see Eq. (7.5)) that the
system from the vector s ( n ) to the vector y ( n ) is a linear system with a constant
transfer matrix. Including the additive noise contributed by the channel, this
equation takes the form

y ( n )= As ( n )+ q ( n ) , (8 . 1)

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