Background & Objective: This paper considers a multi-pair wireless network, which communicates
peer-to-peer using some multi-antenna amplify-and-forward relays. Maximizing the throughput
supposing that the total relay nodes’ power consumption is constrained, is the main objective of this
investigation. We prove that finding the beamforming matrix is not a convex problem.
Methods: Therefore, by using a semidefinite relaxation technique we find a semidefinite programming
problem. Moreover, we propose a novel algorithm for maximizing the total signal to the total
leakage ratio. Numerical analyses show the effectiveness of the proposed algorithm which offers
higher throughput compared to the existing total leakage minimization algorithm, with much less
Results and Conclusion: Furthermore, the effect of different parameters such as, the number of relays,
the number of antennas in each relay, the number of transmitter/receiver pairs and uplink and
downlink channel gains are investigated.