Capacity of the mismatched Gaussian channel

Information capacity is determined for the additive Gaussian channel when the constraint is given in terms of a covariance different from that of the channel noise. These results, combined with previous results on capacity when the constraint covariance is the same as the noise covariance, provide a complete and general solution for the information capacity of the Gaussian channel without feedback. The results are valid for both continuous-time and discrete-time channels and require only two assumptions: the noise is due to a stochastic process with sample paths having finite energy over the observation period (w.p.1), and the constraint is given in terms of a Hilbert space norm. Such a constraint is implicit in any constraint giving finite capacity.