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The performance of dual-branch equal-gain combining (EGC) and maximal-ratio combining receivers operating over a composite correlated fading environment, modelled by the generalised Gamma (GG) distribution, is analysed. The moments of the output signal-to-noise ratio are derived in closed form for both types of receivers, and by employing the Pade approximants method, the average bit error probability is studied for a great variety of modulation schemes. Furthermore, based on the statistic of the product of two correlated GG random variables, a tight union upper bound for the outage probability of the EGC is obtained, whereas for the special case of Weibull fading a simpler bound is derived in closed form. The proposed mathematical analysis is complemented by various, numerically evaluated performance results, whereas simulations verify the correctness of the proposed analysis.