Signal set design for band-limited memoryless multiple-access channels with soft decision demodulation

Signal sets are identified that maximize the cutoff rate region for a multiple-access channel with an additive white Gaussian noise, in which the demodulator output alphabet is allowed to be infinite ("infinitely soft decisions"). The optimizing designs consist of a simplex signal set for each sender, such that each sender's set is orthogonal to those of the other senders. For "second moment" and for "fractional out-of-band-energy" bandwidth constraints on the signals of each sender, conditions are derived under which mutually orthogonal simplex sets are still optimal. For the second moment constraint, simplex sets derived from sinusoidal functions yield an optimal design and, for the out-of-band energy constraint, simplex Sets derived from prolate spheroidal wave functions are optimal. Choices of signal sets that maximize the cutoff rate region for an additive shot-noise limited multiple-access optical channel, subject to average energy and peak amplitude constraints, are also identified.