Close-to-optimal partial decode-and-forward rate in the MIMO relay channel via convex programming

We study the optimization of the data rate achievable with partial decode-and-forward in the Gaussian MIMO relay channel and propose a new algorithm to find close-to-optimal input covariance matrices. Although the optimization is a non-convex problem in its original formulation, we can show that a reformulated version with slightly modified constraint set is convex. In particular, we replace a positive-semidefiniteness constraint by a strict positive-definiteness constraint. This may introduce an inaccuracy, but we conjecture this inaccuracy to be small so that the obtained solutions are close to the globally optimal ones.