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We derive closed-form expressions of outage probability with asymptotic analysis for orthogonal frequency division multiplexing-based nonlinear amplify-and-forward multiple-relay systems using best-relay selection over independent and non-identically distributed Nakagami-m fading channels for integer values of fading parameter. We then investigate a novel closed-form expression of average symbol error rate for a general order rectangular quadrature amplitude modulation scheme by using the well-known cumulative distribution function-based approach. Numerically evaluated results are compared with Monte Carlo simulations and the accuracy of the derived expressions is verified.