Up-link multi-user MIMO capacity in low-power regime

This paper studies the up-link of a multi-user Multiple-Input Multiple-Output (MIMO) system under a fairly general channel model, subsuming a number of situations of relevant practical interest. Concerning the available prior information, we consider the case of Prior Channel State Information at the Transmitter (PCSIT) wherein only a statistical channel characterization is available before transmission, while we assume perfect Channel State Information at the Receiver (CSIR). Under this assumptions, we characterize the sum-capacity-achieving input covariance matrix for such a system and we also examine the low-power regime in terms of both minimum energy contrast and multiple access slope region, validating our theoretical findings through a set of numerical results.