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In this study, highly accurate closed-form approximations to the probability density function of the sum of independent identically distributed (i.i.d.) generalised-K fading envelopes are derived. These approximations are valid for a wide range of values of the distribution parameters and number of summands. Based on the previously derived formulas, simple precise approximations for the outage probability and the average bit error probability of equal-gain combining receivers operating on i.i.d. generalised-K fading channels are proposed. Extensive numerically evaluating and computer simulation results are presented to demonstrate the proposed analysis.