Asymptotic gains of generalized selection combining

In this paper, employing the polynomial approximation of the fading channel probability density function (pdf) for large average signal-to-noise ratio (ASNR), we derive general asymptotic moment generating function (MGF) expressions of the GSC output signal-to-noise ratio (SNR) for generalized fading channels. Based on the MGF result, the asymptotic diversity and coding gains for GSC are derived. Our analytical results reveal that the diversity gain of GSC is equivalent to that of maximum ratio combining (MRC), for different modulations and generalized fading channels (including the case of correlated branches). We also show that the difference in the coding gains for different modulations is manifested in terms of a modulation factor defined in this paper. Asymptotic performance gap between GSC and MRC, and the gap between non-coherent and coherent GSCs respectively, are studied in terms of the coding gain.