Exploiting Sparsity for Multiple Relay Selection with Relay Gain Control in Large AF Relay Networks

We propose a new approach for multiple relay selection in large amplify-and-forward (AF) relay networks based on exploiting the sparsity of the relay gain vector. We start by applying our design approach to formulate the problem of optimizing the selected relay index and gain under the mean squared error criterion and a sparsity constraint. Building on recent advances in sparse signal recovery theory, we propose a solution based on the orthogonal matching pursuit algorithm and investigate its performance-complexity tradeoffs. Then, we generalize our formulation to multiple-antenna large AF relay networks, which naturally leads to a joint multiple relay-antenna selection problem with sparse relay gain vector optimization. Simulation results demonstrate the performance gains of our proposed scheme over existing schemes for both single-antenna and multiple-antenna large AF relay networks. Alternatively, at the same performance level, our scheme selects fewer relays resulting in reduced implementation complexity.