Optimal signaling and detector design for power-constrained binary communications systems over non-Gaussian channels

In this letter, joint optimization of signal structures and detectors is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. First, it is observed that the optimal signal for each symbol can be characterized by a discrete random variable with at most two mass points. Then, optimization over all possible two mass point signals and corresponding maximum a posteriori probability (MAP) decision rules are considered. It is shown that the optimization problem can be simplified into an optimization over a number of signal parameters instead of functions, which can be solved via global optimization techniques, such as particle swarm optimization. Finally, the improvements that can be obtained via the joint design of the signaling and the detector are illustrated via an example.