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Based on the likelihood ratio, we derive the maximum-likelihood (ML) receiver for a synchronous fast frequency-hopped multiple-access system employing M-ary frequency-shift-keying (MFSK) modulation over frequency-selective Rayleigh-fading channels. The derived ML receiver is proposed and analyzed to obtain bit-error rate (BER) expressions. Analytical results are then validated by computer simulations. All system users are assumed to experience independent frequency-selective Rayleigh fading. Performance comparison among several commonly-used receivers shows that the proposed ML receiver gives the best BER performance for different combinations of parameters of the analyzed system under various fading conditions.