Multiple Relay Selection and Beamforming in Dual-Hop Amplify-and-Forward Relay Networks

In this paper, the problems of multiple relay selection and beamforming optimization are considered for a dual-hop amplify-and-forward relaying network under individual and total power constraints. The selection is performed based on maximizing the signal-to-noise ratio with computationally efficient algorithms. For the individual power constraint case, an iterative selection technique based on the use of the squared \ell -1-norm is proposed and investigated. We demonstrate that the proposed technique can converge to the same suboptimal solution proposed in the literature with up to 80\% reduction in the number of iterations. Furthermore, we derive numerical suboptimal beamforming and relay selection solutions based on eigenvalue decomposition for both total and individual power constraints without the need for solving semidefinite programing problems.