Introduction

Up to now we have assumed that the transmitted signal is only degraded by AWGN. Even when it is subjected to filtering, as in the previous chapter, the filtering characteristics are known precisely by the receiver. This knowledge is exploited in the design of the modulator/ demodulator by employing Nyquist's criterion to avoid intersymbol interference (ISI), or by allowing a certain amount of ISI as in the case of partial response systems, or by using a maximum likelihood sequence detection based on the unavoidable ISI.

In practice, however, there arise communication channels where the received signal is not subjected to a known transformation or filtering. In particular the gain and/or phase of a digitally modulated transmitted signal is not known precisely at the receiver. These parameters can be modeled as either unknown but fixed over the period of transmission or as random. In the former case, one could transmit a known signal briefly at the beginning of transmission to estimate the parameter(s) and then use the estimate(s) for the remainder of the transmission, which would be the message of interest. However, in the more typical application, the parameters do change in time, so though they may remain reasonably constant over a bit interval, or several bit intervals, they do change over the course of the entire message transmission, typically unpredictably.