Exact error probability expressions for MRC in correlated Nakagami channels with unequal fading parameters and branch powers

In this paper, we derive the symbol error probability (SEP) for maximal ratio combining with an arbitrary number of diversity branches in Nakagami fading with integer-order fading parameters, where the instantaneous signal-to-noise ratios (SNRs) of the diversity branches are not necessarily independent or identically distributed. We consider coherent detection of M-ary phase-shift keying and quadrature amplitude modulation. The proposed problem is made analytically tractable by: (1) transforming the physical diversity branches into a "virtual branch" domain; and (2) using alternative definite integral representations of the conditional SEP with finite limits; which results in a simple derivation. We further obtain a canonical structure for the SEP as a weighted sum of the elementary SEPs, which are the SEPs of a non-diversity (single-branch) system with appropriate fading parameters and average SNR, whose closed-form expressions are well-known.