Iterative D.C. Optimization of Precoding in Wireless MIMO Relaying

Optimizations of precoding matrices in precode-and-forward (PF) MIMO relaying are nonconvex programs in precoding matrix variables. The semidefinite relaxation (SDR) technique, which relaxes the concerned nonconvex quadratic constraints by (convex) semi-definite ones, can locate the optimal solutions, provided that the numbers of relaying antennas and users are very small. The computational complexity of the SDR grows explosively even with a very moderate increase in the numbers of relaying antennas and/or users, making the existing semidefinite programming (SDP) solvers incapable. In this paper, much more efficient problem formulations of precoding matrix design that exploit the spectral matrix optimization are developed. Such formulations have a low dimensionality and are computationally-tractable nonconvex matrix programs. Furthermore, by exploiting their partial convex structures in the d.c. (difference of two convex functions) framework, new effective iterative solutions are obtained. Extensive simulation results are presented to support the computational advantage of the proposed approach and show that the proposed approach can effectively handle all three considered optimization problems of precoding matrices in MIMO PF relaying, while the SDR approach either is computationally impractical or fails.