Simple BER Approximations for Generalized Selection Combining (GSC) over Rayleigh Fading Channels and its SNR Gap Properties

The paper presents two simple closed-form approximated BER expressions for GSC, where m diversity branches with the largest SNR are selected from L (1lesmlesL) total available branches, over both iid and non-iid Rayleigh fading channels. They contain only inverse SNR raised to the diversity order and asymptotically accurate as SNR increases. When m=L, the approximations are the same as the approximated BERs of MRC presented in J. Proakis (1983). The SNR gaps resulting from coherently combining a different number branches are easily derived from these approximations. It is found that not only does the gap increase monotonically with m as expected for a fixed L, but also, when m is fixed the gap, increases monotonically with L. In other words, a larger L provides not only a greater diversity gain but also a greater SNR gain. It is also found that the increasing rate of the gap monotonically decreases with both m and L which means the gap saturates as m and L increases. Finally we prove that as Lrarrinfin (fading channel becomes AWGN), the gap approaches to 10logm which is exactly the gap for the AWGN channel