Information Rate Optimization for Joint Relay and Link in Non-Regenerative MIMO Channels

The optimization of the Relay Transform Matrix (RTM) in a two-hop relay network with an average relay power constraint and perfect channel state information at the relay is addressed in this paper. The study considers the most general case in terms of number of transmit and receive antennas at the source, relay, and destination, with arbitrary correlation of the received noise at all terminals. The optimization problem is reduced to a manageable convex form, which is solved by linear algebra transformation and the KKT equations. A parametric solution is given, which yields the power constraint and the capacity achieved with uncorrelated transmitted data. The solution is shown to be amenable to a \emph{water-filling-like} algorithmic implementation, which extends earlier literature results addressing the case without the direct link. Simulation results are reported concerning a Rayleigh relay network where, in particular, the role of the direct link SNR is precisely assessed.