Asymptotic BER Comparison of MPSK and MDPSK in Lognormal Fading Channels

The bit error rate (BER) performance loss of M-ary differential phase-shift keying (MDPSK) with respect to M-ary phase-shift keying (MPSK) in wireless fading channels has been extensively studied, but the understanding of this problem in lognormal fading channels has been limited. The most recent work has shown the asymptotic BER performance losses of BDPSK and QDPSK with respect to BPSK and QPSK, respectively, in the lognormal fading channels. However, it is not known how the modulation order increases. In this paper, we derive the general expression of the relative BER performance loss of MDPSK with respect to MPSK for arbitrary M over the lognormal fading channels in high signal-to-noise ratio regimes. We start our analysis by investigating the asymptotic BER performance losses of MDPSK with respect to MPSK for M = 4, 8, and 16. Using the regularity of these results, we obtain the general closed-form expression of the relative BER performance loss in the lognormal fading channels.