Sampling a noisy multiple output channel to maximize the capacity

This paper deals with an extension of Papoulis' generalized sampling expansion (GSE) to a case where noise is added before sampling and the total sampling rate may be higher than the Nyquist rate. We look for the best sampling scheme that maximizes the capacity of the sampled channel between the input signal and the M sampled outputs signals, where the channels are composed of all-pass linear time-invariant (LTI) systems with additive Gaussian white noise. For the case where the total rate is between M-1 and M times the Nyquist rate, the optimal scheme samples M-1 outputs at Nyquist rate and the last output at the remaining rate. When M = 2 the optimal performance can also be attained by an equally sampled scheme under some condition on the LTI systems. Surprisingly, equal sampling is suboptimal in general. Nevertheless, for some total sampling rates where there is an integer relation between the number of channels and the total rate, a uniform sampling achieves the optimal performance. Finally, we discuss the relation between maximizing the capacity and minimizing the mean-square error.