Multiple Peer-To-Peer Relay Network Robust Beamforming Based on Lorentz-Positive Matrices

Aiming at minimizing the total transmit power of relay nodes in the multiple peer-to-peer relay network in the presence of channel estimation error, a relay beamforming method based on Lorentz positive matrix is proposed. Firstly, assuming the channel state information of the second hop in the relay network is uncertain and the signal to noise ratios of the destination nodes are given, the expression of total relay nodes transmit power minimization optimization problem is deduced. Secondly, some real valued variables are defined and the concept of Lorentz cone is used to transform the optimization problem into a real valued problem. Finally, using the equivalent linear matrix inequality description of Lorentz positive matrices, the relay transmit power minimization problem is transformed into a real valued convex optimization problem. The proposed method overcomes the problem existing in the conventional robust relay beamforming methods based on semi definite relaxation technique, which sometimes yield solution matrix of with a rank greater than 1. Simulation results show that in the case of different relay nodes and channel error coefficients, the proposed method yields minimum relay transmit power in line with the results of the robust relay beamforming method based on semi definite relaxation technique, which validates the effectiveness of the proposed method.