Simple closed-form asymptotic symbol error rate of selection combining and its power loss compared to the maximal ratio combining over Nakagami m fading channels

This paper derives closed-form asymptotic symbol error rates (ASERs) for MPSK and MQAM signals with selection combining (SC) over Nakagami-m fading channels. It also presents a closed-form expression for the power loss of SC compared to maximal ratio combining (MRC) over a Nakagami- m fading channel. It is found that this power gap is a function of only the number (L) of independent Nakagami-m channels and the fading parameter m. For a fixed m, the gap monotonically increases with L. For a fixed L, the gap monotonically increases with m and approaches 10 log₁₀ L dB (the asymptotic gap between MRC and SC in an AWGN channel) as m ¿ ¿. In addition, numerical results show the accuracy of the ASERs obtained from closed-form expressions for both MRC and SC with MPSK and MQAM signals for large SNRs. They also show that the SNR gap is identical to that predicted by the analysis for arbitrary L and m.