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Optimized beamforming problem in Amplify-forward wireless MIMO relay networks

Total relay transmit power minimization in Amplify-forward (AF) MIMO relay beamforming is naturally formulated as an indefinite quadratic (nonconvex) program and then semidefinite relaxation (SDR) technique can be used to locate their optimal solutions. Indeed, SDR often gives rank-one optimal solution within a low number of relaying antennas and communicating users. However, as the antennas number increases, the computational complexity of SDR grows up explosively that requires a huge amount of additional variables. In this paper, a more efficient problem formulation is introduced, which needs a much reduced number of auxiliary variables but the optimal solutions are still achieved iteratively. Furthermore, it works as well as for max-min relay power optimization, for which SDR seems to be powerless for solution. Simulation shows the viability of the proposed approach.