Optimum Reception of Coded Multiple Frequency Keying in Presence of Random Variable Phases

Wide-band multiple frequency-shift keying is perturbed by random phases in the
M \geq 2
frequency slots. We consider a coded digital system, where the
M
phases can be treated as mutually dependent random variables. If their joint distribution is known, the optimum (maximum-likelihood) receiver is shown to be in general very complicated. We show that there are a few phase distributions and signal-to-noise-ratio extremes for which the optimum receiver and its performance can be simply described. If the joint phase distribution is not known, we give an appropriate minimax receiver with a guaranteed performance. This performance is evaluted for orthogonal coding, white Gaussian noise, and nonfading signals. It is valid for all joint phase distributions.