A New Method for Robust Multiple Peer-To-Peer Relay Beamforming

This paper focuses on how to design the robust beamforming vectors of multiple peer-to-peer relay networks. In the context of imperfect channel state information at the relays, our goal is to minimize the transmit power at relay nodes subject to the quality of service at each receiver. A method based on real value Lorentz-positive maps and linear matrix inequalities is proposed, which converts the transmit power minimization problem at relay nodes into a convex optimization problem. The proposed method overcomes the disadvantages of traditional methods based on semi-definite programming relaxation, which sometimes result in solutions with rank greater than one. Simulation results show that the solution of the proposed method is consistent with those of conventional method based on semi-definite programming relaxation.