Analysis of minimum selection GSC in Rayleigh fading

This paper analyzes the error performance of an improved generalized selection combining (GSC) technique called minimum selection GSC (MS-GSC) in flat Rayleigh fading for coherent digital modulation schemes. Here the minimum number of diversity branches is selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. The threshold chosen here is determined by the combiner output SNR rather than individual branch SNRs as done in absolute threshold GSC (AT-GSC) and normalized threshold GSC (NT-GSC). As a result, MS-GSC uses less resource than AT-GSC or NT-GSC to give the same performance. We obtain a closed-form expression for the distribution of the number of selected branches followed by a closed-form expression for the characteristic function (c.f.) of the combiner output SNR. This c.f. is used to obtain the symbol error probability for different digital modulation schemes. Numerical results for M-ary phase-shift keying are presented as an example.