Optimum Data Transmission

Abstract

In Chapter 4, we examined signal design for baseband pulse transmission, and described the compromises among the bandwidth of the transmitted signal, noise immunity, and mitigation of intersymbol interference inherent in any design. Peak and mean-square intersymbol interference were defined, and it was shown how linear channel distortion can degrade performance. This chapter describes system structures that are optimum, either with respect to maximizing the probability that a sequence of symbols is correctly received or minimizing the output mean-square error; these receivers are primarily designed to correct the degradation caused by noisy channels and linear distortion. It is not possible, except in certain singular cases, to achieve the performance of an impairment-free system, or that of a system which attains the matched filter bound (which is equivalent to the transmission of isolated pulses). A further limitation discussed in Chapter 2 was the assumption of pulse-by-pulse (i.e. symbol-by-symbol) detection, which is optimum only in the absence of intersymbol interference. In the case of partial response signaling, we described precoding operations that eliminated the intentional intersymbol interference, but with a penalty in noise immunity. This penalty can be avoided if pulse-by-pulse detection is replaced by a process (the maximum likelihood receiver) that uses the entire received sequence for detection. This technique, the Viterbi algorithm, was applied to the decoding of convolutional codes in Chapter 3 and to the decoding of trellis codes in Chapter 5. In this chapter, the same technique will be applied to the detection of a sequence of amplitude-modulated pulses.