Introduction

In this chapter we review a number of well established ideas in digital communication. Section 5.2 revisits the matched filter introduced in Sec. 2.5 and discusses it from the viewpoint of information sufficiency and reconstructibility. We establish the generality of matched filtering as a fundamental front-end tool in receiver design. It is often necessary to make sure that the noise sequence at the input of the detector is white. The digital filter that ensures such a property, the so-called sampled noise whitening filter, is described in Sec. 5.3. A vector space interpretation of matched filtering is presented in Sec. 5.4, and offers a very useful viewpoint.

Estimation of the transmitted symbol stream from the received noisy stream is one of the basic tasks performed in any communication receiver. The foundation for this comes from optimal sequence estimation theory, which is briefly discussed in Sec. 5.5. This includes a review of maximum likelihood and maximum a posteriori methods. The Viterbi algorithm for sequence estimation is described in Sec. 5.6. While this is one of the most well known algorithms, simpler suboptimal methods, such as decision feedback equalizers (DFE), have also become popular. The motivation for DFE, which is a nonlinear equalizer, is explained in Sec. 5.7. A nonlinear precoder called the Tomlinson-Harashima precoder can be used as an alternative to the nonlinear equalizer at the receiver, and is described in Sec. 5.8.