Error performance of noncoherent MFSK with L-diversity on correlated fading channels

Noncoherent diversity reception of M-ary frequency-shift keying (MFSK) signals becomes increasingly important due to its widespread use in wireless communications. Its error performance analysis, however, is not available in the literature except for the simple case using binary modulation. We address the problem directly based on the decision variables, ending up with closed-form solutions to both conditional and average error probabilities for a general noncoherent MFSK diversity system operating on Rayleigh, Rician, and Nakagami fading channels. The solutions involve some higher order derivatives, and efficient recursive algorithms have been derived for their calculation. The solutions are very general permitting arbitrary diversity order, symbol size, channel parameters, and antenna-array covariance matrix. Numerical examples are also presented for illustration.