Joint tomlinson-harashima source and multi-relay beamforming design in decode-and-forward cooperative relaying systems with relay selection

A joint Tomlinson-Harashima (TH) source and multi-relay beamforming design in decode-and-forward (DF) relaying systems with relay selection is proposed, which exploits the relationship between QR decomposition (QRD) and Gram- Schmidt orthogonalization (GSO) to jointly optimize the source precoder and relay beamforming vectors of multiple relays. Then we propose a correlation-based approach which leads to a significant reduction of forward overhead information from the source to the selected relays. Finally a “Best-Last” based relay selection approach is proposed which has a performance close to the optimal global relay selection approach with a significantly reduced computational complexity. Simulation results are provided to support the advantages of the proposed schemes.