Capacity of root-mean-square bandlimited Gaussian multiuser channels

Continuous-time additive white Gaussian noise channels with strictly time-limited and root-mean-square (RMS)-bandlimited inputs are studied. The capacity of the single-user and two-user RMS-bandlimited channels are found in easy-to-compute parametric forms and are compared to the classical formulas for the capacity of strictly bandlimited channels. In addition, channels are considered where the inputs are further constrained to be pulse-amplitude-modulated waveforms. The capacity of the single-user RMS-bandlimited PAM channel is shown to coincide with Shannon´s capacity formula for the strictly bandlimited channel. This shows that the laxer bandwidth constraints precisely offsets the PAM structural constraint and illustrates a tradeoff between the time-domain and frequency-domain constraints. In the synchronous two-user channel, the pair of pulses that achieves the boundary of the capacity region is derived, and it is shown that the shapes of the optimal pulses depend not only on the bandwidth but also on the respective signal-to-noise ratios.