Signal Design for Digital Multiple Access Communications

In this concise paper we examine the signal design problem associated with a multiple access communication channel in which several binary digital links are operated simultaneously over a common channel. Receiver noise is neglected but the channel is confined in dimension, so that signal crosstalk is the only source of bit errors. An encoder is assumed to exist prior to channel transmission for converting the bit waveforms from all transmitters into a common channel signal available to all receivers. The encoder selects the channel signal during each bit so as to maximize the average detection probability per bit, where the average is taken over all links and all possible bit patterns. Two classes of receivers are considered. In the first the receivers are confined to only signal correlations with the corresponding transmitter signals. In the second the encoder and receivers are matched to arbitrary signal sets. For both type receivers, optimal channel signal selection is shown to be related to minimal hamming distance mappings. Values and bounds for the resulting detection probabilities in terms of numbers of transmitters and channel dimension are reported.