Capacity of noncoherent MFSK channels

Performance limits theoretically achievable over noncoherent channels perturbed by additive Gaussian noise in hard decision, optimal, and soft decision receivers are computed as functions of the number of orthogonal signals and the predetection signal-to-noise ratio. Equations are derived for orthogonal signal capacity, the ultimate MFSK capacity, and the convolutional coding and decoding limit. It is shown that performance improves as the signal-to-noise ratio increases, provided the bandwidth can be increased, that the optimum number of signals is not infinite (except for the optimal receiver), and that the optimum number decreases as the signal-to-noise ratio decreases, but is never less than 7 for even the hard decision receiver.