| The capacity regions of Gaussian multiple-access channels under various time-domain and frequency-domain constraints are obtained.;The capacity region of the root-mean-square (RMS) bandlimited white Gaussian multiple-access channel in which the input waveforms are subject to the RMS bandwidth constraint is found. Comparing to the strictly bandlimited channel, we find that capacities of bandlimited channels are not sensitive to bandwidth measures in low signal-to-noise ratios. However, in high signal-to-noise ratios, the RMS-bandlimited channel capacity increases with the cubic root, significantly larger than the logarithm, as in the strictly bandlimited channel, of the signal-to-noise ratios.;When the input waveforms are subject to time-domain structural constraints imposed by particular modulation schemes, an equivalent discrete-time channel model can usually be obtained. We obtain the capacity region of such a discrete-time Gaussian channel with intersymbol interference (ISI). The water-filling argument that gives the optimal input power spectral density (PSD) of the user for the single-user Gaussian channel with ISI is extended to the two-user case.;The discrete-time channel capacity region is used to obtain the capacity region of the white Gaussian code-division multiple-access (CDMA) channel. Further restricting the signature waveforms of the users to be RMS-bandlimited, we find the capacity region of the synchronous RMS-bandlimited white Gaussian CDMA channel. We find that the optimal RMS-bandlimited signature waveforms of the users are not mutually orthogonal and the total capacity with optimal signature waveforms is much larger than can be achieved by TDMA or FDMA in which orthogonal signature waveforms are used.;The capacity of the CDMA channel is found to be insensitive to frame-asynchronism while symbol-asynchronism can degrade a K-user CDMA channel capacity by a factor of K, and TDMA is one of the signalling schemes most sensitive to asynchronism. However, if the signature waveforms can be designed optimally and separately for the synchronous and the asynchronous channels, we find that asynchronism does not decrease the total capacity in both low and high signal-to-noise ratios, while the degradation is at most 12% in the two-user channel regardless of the signal-to-noise ratios. |
