Error probabilities for adaptive multichannel reception of binary signals

Description and performance are given for two slightly different forms of an adaptive receiver that is used with binary signaling in a multichannel communication system. Each channel has a non-dispersive, nonfading propagation path and additive white gaussian noise that is independent of, and equal in intensity to, the other channel noises. Either phase-independent orthogonal signaling (such as FSK) or phase-reversal-comparison signaling is employed to convey to the receiver both the message and information about the path strengths and phases. The receiver measures the path parameters and applies the results to the detection processing as though they were perfectly accurate; it is shown that this procedure is a natural extension of non-adaptive reception. Results are given without derivation for the probability of binary decision error, which depends on the type of signaling, the ratio of the total noise-exclusive signaling energy received to the noise intensity, the number of channels, and the ratio of the effective measurement time to the binary signal duration. The distribution of the received signaling energy among the channels is immaterial. Graphs of error probability are presented for selected system parameters. A novel by-product of the study is an error-probability expression for non-adaptive multichannel reception of quite general binary signaling. Optimal adjustment of the adaptive receiver for fading-path situations is also considered, but corresponding error probabilities have not yet been derived.