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Bit error rate (BER) analysis of orthogonal frequency division multiplexing (OFDM) systems over frequency-selective Nakagami-m fading channels is considered in this work. The provided analyses are applicable for multipath channels with any number of taps and the Nakagami-m fading parameter can be finite or infinite. The results obtained demonstrate that the Gaussian approximation (GA) can be inaccurate if the number of channel taps is less than five. The analytical results confirmed by simulation demonstrated that the probability distribution functions for infinite fading parameter m are substantially different from those where m is finite. It was also found that the effect of m depends on the number of multipath components L. For even values of L, increasing m decreases the BER while the opposite happens for odd L values. Therefore, the worst case scenario for even L values occurs for m = 1, while for odd L values it occurs for m = ∞, i.e., the amplitudes of the multipath components are constants and equal.