The optimum transmitters for maximum information throughput when two independent users share a dispersive channel are investigated. The channel is assumed to be linear and time invariant and is described by a2 \times 2matrix of transfer functions. The noise at each receiver is additive and Gaussian and may have a nonwhite spectrum. Assuming naive superposition (the interfering signal is treated as noise) it is shown that for many practical channels, frequency division multiplexing is optimum, and the structure of the optimum transmitters is obtained.

Optimum detection of binary DPSK yields a bit error probability, Peof (1/2) exp (-E_{b}/\eta), the classic result, but requires a reference carrier in-frequency but not necessarily in-phase with the received carrier. Any other detector will yield degraded results. Several well known textbooks give a derivation for a suboptimum detector with the above result but neglect intersymbol interference. In this paper the optimumM-ary DPSK receiver is shown and a derivation of Pefor the binary case given. Two suboptimum detectors are analyzed and their performance is shown to be 1 to 2 dB worse than the optimum.

Rice's click model for ideal FM detection is applied to systems with co-channel interference. Output noise terms consist of a high signal-to-noise ratio (SNR) term due to noise alone, a term due to the desired signal beating with the interferer, and a term due to the clicks. Click rates are determined with and without modulation and it is shown that in the computation of noise due to clicks the interferer can be treated as a simple sinusoid [i.e., an unmodulated carrier] Plots are given for detected SNR versus carrier-to-noise (CNR) with signal-to-interferer ratio (SIR) and modulation index as parameters. The effect of signal suppression is analyzed and for the range of parameters used in this paper it is found to be negligible.