Relay selection in FDD amplify-and-forward cooperative networks

In this paper, the problems of relay selection and distributed beamforming are investigated for bi-directional dual-hop amplify-and-forward frequency-division duplex cooperative wireless networks. When using individual per-relay maximum transmission power constraint, it has been proven that the relay selection and beamforming optimization problem becomes NP hard and requires exhaustive search to find the optimal solution. Therefore, we propose a computationally affordable suboptimal multiple relay selection and beamforming optimization scheme based on the ℓ1 norm squared relaxation. The proposed scheme performs the selection for the two transmission directions, simultaneously, while aiming at maximizing the aggregated SNR of the two communicating nodes. Furthermore, by exploiting the previous solutions to accelerate the algorithm's convergence, our proposed algorithm converges to a suboptimal solution compared to the exhaustive search technique with much less complexity.