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We propose the multicarrier on-off keying (MC-OOK) as a bandwidth-efficient modulation method for frequency-hopped multiple-access (FHMA) communications. The motivation for using MC-OOK is that a more bandwidth-efficient modulation scheme allows a larger number of frequency slots, and thus provides a higher immunity against multiple-access interference in FHMA systems. We analyze the average bit-error probability in slow frequency-nonselective Rayleigh fading channels with background noise. We find that the capacity gain that MC-OOK/FHMA system provides over the MFSK/FHMA system in an interference-limited region is more than 2.5 when the modulation alphabet size M is 8, and even a higher capacity gain can be obtained with a larger M.