Relay Beamforming Designs in Multi-User Wireless Relay Networks Based on Throughput Maximin Optimization

Beamforming design for multi-user wireless relay networks under the criterion of maximin information throughput is an important but also very hard optimization problem due to its nonconvex nature. The existing approach to reformulate the design as a matrix rank-one constrained optimization problem is highly inefficient. This paper exploits the d.c. (difference of two convex functions) structure of the objective function and the convex structure of the constraints in such a global optimization problem to develop efficient iterative algorithms of very low complexity to find the solutions. Both cases of concurrent and orthogonal transmissions from sources to relays are considered. Numerical results indicate that the proposed algorithms provide solutions that are very close to the upper bound on the solution of the non-orthogonal source transmissions case and are almost equal to the optimal solution of the orthogonal source transmissions case. This demonstrates the ability of the developed algorithms to locate approximations close to the global optimal solutions in a few iterations. Moreover, the proposed methods are superior to other methods in both performance and computation complexity.