Error probability of Q-ary symbol consisting of multiple channel symbols under Rayleigh fading

Closed-form expressions for symbol error probabilities are derived for the case when modulation alphabet size M is smaller than symbol size Q. We consider slow Rayleigh fading channel where fading amplitudes and phases remain constant during one Q-ary symbol duration. An exact expression is obtained for noncoherent M-ary frequency-shift keyed (MFSK) modulation and the simple and accurate approximate expressions are obtained for M-ary phase-shift keyed (MPSK) and quadrature-amplitude modulation. Simulation results showed that the derived error probability are well agreed.