Maximizing the Partial Decode-and-Forward Rate in the Gaussian MIMO Relay Channel

It is known that circularly symmetric Gaussian signals are the optimal input for partial decode-and-forward (PDF) coding scheme in multiple-input multiple-output (MIMO) relay channel, but there currently no method to find covariance matrices nor compute achievable PDF rate since optimization a non-convex problem its original formulation. In this paper, we show it possible convex reformulation of by means an approximation and primal decomposition. We derive explicit solution inner as well gradient outer problem, so efficient cutting-plane can be applied solving problem. Based on these ingredients, propose convergent algorithm whose output globally along with certificate accuracy terms maximum distance true global optimum. numerical simulations, converged values close zero all considered instances showing proposed manages optimum instances.