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An optimum maximum-likelihood (ML) receiver is proposed and analyzed for fast frequency-hopped M-ary frequency-shift keying systems over frequency-selective Rayleigh-fading channels with multitone jamming and additive white Gaussian noise. The analytical bit-error rate expressions of the proposed optimum ML receiver are also derived based on the characteristic function approach, which is applicable for higher diversity orders. Analytical results, validated by simulation results, show that the proposed optimum ML receiver significantly outperforms some commonly used conventional receivers. Our analysis also shows that there exists an optimum diversity order under certain channel conditions.