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

We discuss the achievable ε-error throughput for the uncoordinated (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. We show that the achievable sum rate for T users reduces from (M-1) bits per channel use in the fully coordinated multi-access situation to (M-1)·ln(2) bits per channel use if we assume no coordination between users. In particular, the result shows that for multi-tone M-ary frequency shift keying multiple access in asynchronous operation for instance, multiple user interference reduces the capacity only by a factor ln(2)=0.695 relative to the ideal TDMA system