Capacity and performance analysis for hybrid selection/maximal-ratio combining in Nakagami fading with unequal fading parameters and branch powers

We consider a hybrid selection/maximal-ratio combining (HS/MRC) diversity system and assume independent Nakagami fading on the diversity branches with unequal fading parameters and unequal signal-to-noise ratios (SNR's). We use the virtual branch technique and two series expressions for the characteristic function (CF) of the sum of independent gamma random variables to derive closed-form expressions for CF, the probability density function (PDF), the mean, and the variance of the instantaneous combiner output SNR. We also obtain closed-form expressions for the outage probability, the channel capacity under different transmission policies, and the average symbol error probability (SEP) for a general class of M-ary modulation schemes (including MPSK, MQAM, BFSK, and MSK) with coherent detection. Our approach provides a canonical structure for the closed-form expressions, which are the closed-form expressions for a single-branch system in different Nakagami fading environments.