The Effect of Asynchronism on the Total Capacity of Gaussian Multiple-Access Channels

The degradation due to complete asynchronism (at the codeword and symbol levels) in the total capacity, maximum rate-sum, of white Gaussian multiple-access channels is investigated. It is shown that asynchronism reduces the total capacity of a /f-user channel by at most a factor of K. Moreover, this bound is achieved, in asymptotically high signal-to-noise ratios, by the TDMA signalling strategy. When the signalling strategies are optimally designed to maximize the asynchronous total capacity under bandwidth constraints, we find that in a two-user channel 1) for a certain set of signal-to-noise ratios there is no degradation due to asynchronism, 2) for any bandwidth and signal-to-noise ratios the asynchronous total capacity is at least 88% of the synchronous total capacity, and 3) asynchronism has a vanishing small effect on total capacity for both low and high signal-to-noise ratios. Index Terms: Multiple-access channels, asynchronous channels, code-division multiple-access, time-division multiple-access.