Optimum Transmission Through the Gaussian Multiple Access Channel
In this paper, the authors study the optimality of particular points in the capacity region of Gaussian Multiple Access Channels (GMACs) with various power constraints. The points of interest maximize general rate objectives that arise in practical communication scenarios. Achieving these points constitutes the task of jointly optimizing time-sharing parameters, input covariance matrices and the order of decoding used by the successive interference cancellation receiver. To approach this problem Caratheodory's theorem is invoked to represent time-sharing and decoding orders jointly as a finite-dimensional matrix variable. This variable enables them to use variational inequalities to extend results pertaining to problems with linear objectives to more general, potentially non-convex, problems.