On the capacity of the asynchronous T-user M-frequency noiseless multiple-access channel without intensity information

We discuss an achievable rate region for the asynchronous T-user M-frequency multiple-access channel without intensity information. The problem is formulated in terms of frequencies, but the results are also applicable to pulse position modulation (PPM) schemes. It is shown that the achievable sum rate for T users reduces from (M-1) bits per channel use in the synchronous multiple-access situation to at least (M-1)·ln (2) bits per channel use in the asynchronous situation. In particular, the result shows that for instance, for multitone M-ary frequency shift keying multiple access, in asynchronous operation, multiple user interference reduces the capacity maximally by a factor ln(2)=0.693 relative to the ideal TDMA system