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We derive very tight closed-form lower bounds of symbol/bit error probability for maximum-likelihood sequence detection (MLSD) on clipped OFDM channels with frequency- selective quasi-static Rayleigh fading. Contrary to common knowledge, we show that as a result of both clipping and channel frequency-selectivity, clipping at the transmitter leads to achievable frequency-diversity and performance gain over unclipped systems with MLSD. We derive closed-form expressions of the diversity and the performance gain over the no-clipping case, as well as the optimal clipping ratio for a given system. We consider both Nyquist-rate and oversampled OFDM systems with rectangular QAM signaling.