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. RMS bandwidth is equal to the normalized second moment of the spectrum, which has proved to be a useful and analytically tractable measure of the bandwidth of strictly time-limited waveforms. 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 (PAM) 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 constraint precisely offsets the PAM structural constraint, and illustrates a tradeoff between the time domain and frequency domain constraints. in the synchronous two-user channel, we find the pair of pulses that achieves the boundary of the capacity region, and show that the shapes of the optimal pulses depend not only on the bandwidth but also on the respective signal-to-noise ratios.