Performance of MRC over Nakagami-m fading channels with arbitrary branch correlation, non-identical and non-integral fading orders

We derive the PDF and MGF of the sum arbitrarily correlated, non-identically distributed gamma random variates. The derived PDF and MGF include the case of non-identical but non-integral fading orders. The derived results can be used to analyze a number of performance measures of diversity combining techniques for wireless communications over Nakagami-m fading channels. We derive, as an example, the exact bit error probability of MRC receivers over Nakagami-m fading channels for arbitrary PSK and square QAM signal constellations with coherent detection.