The paper presents two simple closed-form approximated BER expressions for GSC, where m diversity branches with the largest SNR are selected from L (1 ≤ m ≤ L) 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 [4]. 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 L → ∞ (fading channel becomes AWGN), the gap approaches to 10 log m which is exactly the gap for the AWGN channel.
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