A lowcomplexity algorithm for collaborative-relay beamforming

We consider cooperative transmission in wireless relay networks, in which a source communicates with the destination with the help of a set of N cooperating amplify-and-forward relays. The relay weights are obtained to maximize the received signal-to-noise ratio at the destination, subject to individual power constraint. We consider two schemes that have appeared in the literature, i.e., (i) the optimal weight vector design method, which has been solved via second-order cone programming plus a bisection search, with complexity of O(N^3.5), and (ii) the one-bit feedback phase control scheme, which has been formulated as a binary quadratic programming and has been solved for exact solution via exhaustive search. We propose algorithms for these two problems that have substantially reduced complexity, i.e., O(N log₂ N) or O(N) for the first problem, and polynomial time O(N log₂ N) for the second problem.