1. INTRODUCTION
Relay networks are important for future mobile networks since they can improve the network performance by extending the coverage and increasing the network capacity. In contrast to one-way relaying, two-way relaying techniques can compensate the spectral efficiency loss due to the half-duplex constraint of the relay and, therefore, use the radio resources in a more efficient manner. The optimal beam-forming design for the sum rate maximization in two-way amplify and forward (AF) relay networks with one pair of users has been studied in [1] and [2]. Only a few references deal with multi-pair two-way AF relay networks, which include adaptive power allocation [3] and distributed beamforming [4]. Moreover, the optimum beamforming design for maximizing the sum rate of this system has not been studied prior to our work.