Optimized Solutions for Beamforming Problems in Amplify-Forward Wireless Relay Networks

Beamforming problems in amplify-forward (AF) wireless relay network can be formulated as nonconvex quadratically constrained quadratic programming (QCQP) problems which is very difficult to solve directly. Generally, by transforming a QCQP problem into a semi-definite program (SDP) and by relaxing rank-one constraints, the problem can be tackled essentially. If resulting matrices found after solving SDP problems are of rank-one then the task can be terminated. However, in some scenarios such as minimizing individual power constraints on relays, most of the rank-one dropped SDP solutions have rank higher than one. In this case, a nonsmooth reverse convex optimization technique is employed to solve the problem iteratively then rank-one solutions can be optimized numerically.