Minimum selection GSC in independent Rayleigh fading

We analyze the error performance of minimum selection generalized selection combining (MS-GSC), in which the minimum number of diversity branches are selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. A flat Rayleigh fading channel with independent and distinctly distributed branch SNRs is considered. By transforming the ordered instantaneous branch SNRs to their differences, we derive the distribution of the number of selected branches in closed form. We then modify the derivation of this distribution to get the characteristic function (cf.) of the combiner output SNR. This cf. is used to obtain the symbol error probability for different coherent digital modulation schemes.