Transmission of Multiplexed PAM Signals Over Multiple Channel and Diversity Systems

It is well known that the optimum receiver for pulse-amplitude-modulated (PAM) signals, transmitted over a single channel, consists of a cascade of continuous and transversal filters. It is shown that an extended structure of this type is also optimum for the completely general case of
M
multiplexed PAM signals transmitted over random-time and frequency-dispersive multichannel systems with
I
inputs and
N
outputs, where each output is subjected to arbitrarily correlated additive noise. The random channels may also be arbitrarily correlated. In general, the receiver consists of
MN
continuous filters and
M
tapped delay lines with M
²
sets of taps. An adaptive version is also described. The results include, as special cases, the situations considered by Gonsalves and Tufts [8], Shnidman [5], and Kaye [3]. Also, included as special cases are new results for diversity systems, multi-input systems such as multipair cables, and multiple-terminal systems such as multiple access repeaters in which cochannel interference occurs.