Average SER for M-ary modulation systems with space diversity over independent and correlated Nakagami-m fading channels

The average symbol error rate (SER) performance of M-ary modulation systems with space diversity over independent and correlated Nagakami-m fading channels is investigated. Simple closed-form expressions are derived, respectively, to evaluate the average SER for three modulation schemes employing both L-order maximal ratio combining (MRC) and selection combining (SC) diversity reception over independent Nagakami-/n fading channels. This includes M-ary phase shift keying (MPSK), M-ary differential PSK (MDPSK) and noncoherent M-ary frequency shift keying (MFSK). Further closed-form expressions are derived to calculate the average SER for noncoherent MFSK with dual-branch MRC, SC and switched combining (SWC) diversity reception over correlated Nagakami-m fading channels. The effects of branch correlation on the average SER are also examined. For L = 2, numerical results show that MRC outperforms SC by 1.4 dB at an average SER = 10^-2 for noncoherent MFSK over an independent channel with fading parameter m = 1. For a correlated channel with correlation coefficient ρ = 0.5, the respective gain marginally increases to 1.6 dB. The error performance of dual MRC, SC and SWC over a correlated channel with m = I is degraded by approximately 0.7 dB when ρ increases from 0 to 0.5, and the degradation increases to about 2.0 dB when ρ increases from 0.5 to 0.9