Choice of signals for an optical digital channel

The synthesis of receiver and choice of signals according to the criterion of maximum likelihood distance are considered for an optical digital communications channel. An algorithm of optimal-receiver operation is obtained for signals of arbitrary form with random phase, and signals are chosen for a coherent optical channel and a channel with random phase. The optimality of simplex signals in the absence of thermal noise is shown for a fully coherent channel. Also demonstrated is the optimality of orthogonal signals for a channel with random phase both in the absence (the limiting quantum case) and in the presence of thermal noise.