Spectral optimization for beamforming in MIMO relay wireless networks

The amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay beamforming problems are conventionally formulated as nonconvex quadratic programs, and then the semidefinite relaxation (SDR) technique can be used to locate their optimal solutions. Although this technique can obtain the optimal beamforming, it introduces a large number of additional variables. Therefore, the computational complexity of the SDR method is prohibitively high when the number of antennas is high. In this paper, we recast the MIMO relay beamforming problem as an optimization problem of spectral functions. As compared to previous SDR methods, our formulation significantly reduces the number of auxiliary variables while the optimal solutions are still achieved by an efficient iterative algorithm. Consequently, as shown by numerical simulations, our proposed method offers a lower computational time as compared to the SDR formulation.