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We consider the optimization of a two-hop relay network based on anamplify-and-forward Multiple-Input Multiple-Output (MIMO) relay. The relay isassumed to derive the output signal by a Relay Transform Matrix (RTM) appliedto the input signal. Assuming perfect channel state information about thenetwork at the relay, the RTM is optimized according to two different criteria:{\bf\em i)} network capacity; {\bf\em ii)} network capacity based on OrthogonalSpace--Time Block Codes. The two assumptions have been addressed in part in theliterature. The optimization problem is reduced to a manageable convex form,whose KKT equations are explicitly solved. Then, a parametric solution isgiven, which yields the power constraint and the capacity achieved withuncorrelated transmitted data as functions of a positive indeterminate. Thesolution for a given average power constraint at the relay is amenable to a\emph{water-filling-like} algorithm, and extends earlier literature resultsaddressing the case without the direct link. Simulation results are reportedconcerning a Rayleigh relay network and the role of the direct link SNR isprecisely assessed.

Information Rate Optimization for Non-Regenerative MIMO Relay Networks with a Direct Link