Wireless Communications

10Channel Decomposition Techniques

Abstract

In this chapter, we re-examine the nature of channel equalization in a more fundamental framework of channel decomposition. When a pulse sequence is transmitted over a temporally dispersive channel, the spread pulse waveforms overlap with each other, causing inter-symbol interference (ISI). Mathematically, it is the nondiagonal channel matrix that causes ISI among adjacent symbols. Therefore, the key to avoiding ISI is to diagonalize the channel matrix. Various channel equalizers use different techniques for channel decomposition. For example, the Tomlinson–Harashima equalizer has its roots in QR decomposition, whereas orthogonal frequency-division multiplexing (OFDM) is rooted in singular decomposition. Channel decomposition represents an early strategy in tackling impaired channels whereby to implement the philosophy of symbol-by-symbol detection.

10.1 Introduction

The radical reason for the generation of inter-symbol interference (ISI) lies in the nondiagonal structure of a temporally dispersive channel matrix. It is through this nondiagonal channel matrix that adjacent symbols interfere with each other. Various channel equalization techniques described in the preceding chapter represents passive and defensive strategies for combating ISI, in the sense that the transmitter arbitrarily transmits a message pulse sequence without taking the channel characteristics into consideration and the receiver tries to find remedy once ISI is ...