Performance of coherent MFSK schemes over slow flat fading channels

Analytical solutions for the average symbol error rate of coherent M-ary frequency shift keying (MFSK) modulation schemes operating over frequency non-selective slow fading channels corrupted by additive white Gaussian noise (AWGN) are derived. Starting from the alternate expressions for integer powers (n < 5) of Gaussian Q function, the symbol error probabilities (SEP) are obtained using probability density function (pdf) based approach. The derived end expressions composed of finite range integrals can be numerically computed and gives either exact values or provide tighter lower bounds. Different small scale fading statistics such as Rayleigh, Rician (Nakagami-n), Hoyt (Nakagami-q), and Nakagami-m has been considered for channel modelling. Error probabilities are graphically displayed for each model with different values of modulation order M and also for corresponding fading parameters (K, q, and m). The theoretical results presented offers insight to assess the efficacy of relatively less studied coherent MFSK in context of the optimum modulation choice in wireless communication.