Reduced-complexity distributed beamforming algorithm for individual relay power constraints

This paper presents a distributed beamforming algorithm with a reduced computational complexity for a wireless relay network, where a source-destination pair is assisted by cooperating amplify-and-forward (AF) relays but suffers from additional interference. The relay weights are obtained by maximizing the signal-to-interference-plus-noise ratio (SINR) at the destination subject to individual relay power constraints. Mathematically, this problem is a quasi-convex constrained maximization of a fractional quadratic function, which is typically solved via semidefinite relaxation (SDR) along with a bisection search that requires several iterations. We, however, propose a method based on the SDR approach followed by a change of the optimization variables to convert the original quasi-convex problem into a convex problem. The resulting optimization problem can then be solved in one step without a bisection search, thereby significantly reducing the computational complexity. The effectiveness of the developed procedure is shown by simulations and a complexity analysis. It may also be applicable to similar problems in other applications.