Asymptotic performance of wireless communications with generalized selection combining

In this paper, we study the asymptotic performance of generalized selection combining (GSC) over different fading channels for large average signal-to-noise ratio (ASNR). Employing a moment generating function (MGF) method and the polynomial approximation of the fading channel probability density function (pdf), we derive general asymptotic MGF expressions for the GSC output SNR over generalized independent fading channels. The diversity and coding gains for GSC over different fading channels 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. 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, and thus the performance gaps between different modulations can be analytically predicted. Asymptotic performance gap between GSC and MRC is also studied in terms of the coding gain. Numerical examples are presented to illustrate the application of the new results.