Error probabilities for MRC diversity reception of MDPSK in slow Nakagami fading

Abstract

New closed form error probability expressions for M-ary differential-phase-shift-keying (MDPSK) with maximal ratio combining (MRC) diversity reception in Nakagami fading, are derived. These expressions involve easily computable Legendre polynomials and Associated Legendre functions. By setting the fading severity parameter m to unity, the new general error probability formula reduces to the known results for MDPSK systems in slow Rayleigh fading. For binary DPSK, the bit error rate (BER) performance with MRC is compared with known results for selection diversity combining (SDC). It is shown that MRC is more effective than SDC in improving BER performance for the Nakagami channels, as expected. We also discuss the ranges of the fading severity parameter and diversity order, within which the error probability expressions can be computed efficiently.