Channel equalization with transmitter redundancy - Signal Processing and Optimization for Transceiver Systems - page 244

7

Channel equalization with
transmitter redundancy

7.1 Introduction

In this chapter we consider the effect of introducing redundancy into the symbol
stream at the transmitter of a digital communication channel. The introduction
of a su cient amount of redundancy helps to equalize the channels more easily.
For example FIR channels can be equalized with FIR filters without the need
for oversampling at the receiver as in Secs. 4.7-4.8. Two types of redundancies
will be discussed here. The first one, discussed in Sec. 7.2, is zero padding (ZP),
where a block of zeros is inserted between adjacent blocks of input samples. The
second one, studied in Sec. 7.3, is called cyclic prefixing (CP), where a subset of
input samples is repeated in each block. In Sec. 7.4 we show how the CP system
can be represented in terms of a circulant matrix. Important variations of cyclic-
prefix systems such as single-carrier (SC-CP) systems and multicarrier systems,
also called orthogonal frequency division multiplexing (OFDM) systems, are
discussed in Sec. 7.5. Cyclic prefixing is commonly employed in OFDM systems,
and in discrete multitone (DMT) systems used in DSL technology. Some details
about the DMT system are discussed in Sec. 7.6.

7.2 Zero padding

Figure 7.1 explains the zero-padding operation on a discrete-time signal s ( n ) (the
symbol stream to be transmitted). We divide the signal into blocks of length
M and insert L zeros at the end of each block to obtain the zero-padded result
x ( n ) , which is then sent over the channel. By convention the k th block begins
at n = kP and ends at n = kP + P

− 1 , where

P = M + L. (7 . 1)

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