MAC Gaussian channels with arbitrary inputs: Optimal precoding and power allocation

In this paper, (i) we derive closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the Two-user multiple-access channel (MAC), (ii) we investigate the linear precoding and power allocation policies that maximize the mutual information for the two-user MAC Gaussian channels with arbitrary input distributions, capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). (i) enforces the fundamental relations between information theory and estimation theory. And (ii) enforces that the optimal design of linear precoders may satisfy a fixed-point equation as a function of the channel and the input constellation under specific setups. We provide an interpretation for the interference with respect to the channel, power, and input estimates of the main user and the interferer.