Distributed relay beamforming for fairness-aware amplify-and-forward relaying under correlated relays noise

This paper presents a distributed replay beam-forming design for interference-limited two-way relay networks (TWRNs) under correlated relay noise. This network consists of two transceivers end nodes and N parallel amplify-and-forward (AF) relay nodes, where noise at the AF relay nodes may be correlated due to common interference or propagation through multiple hops. This paper assumes a practical scenario with correlated relay noises in contrast to the majority of the related work that assumes independent relays noise. Our objective is to maximize the worst signal-to-noise power ratio (SNR) of the two end nodes under individual relay power constraints and total relay power constraint in order to improve the users fairness for the two end nodes. This relay beamforming design is a non-convex problem taking the form of max-min optimization which could be solved by decomposing it into a series of solvable sub-problems using bisection search. Semi-definite relaxation problem (SDR) is used for the reformulation of the problem. The effect of the noise correlation on the beamformer design is analyzed for two cases, i.e., the first case when a complete knowledge of the correlation structure, represented by the relay noise covariance matrix (K), is available to the relay and the second one when no knowledge is available to the relay. Simulation results show performance improvement in terms of users fairness in comparison with un-optimized AF relaying in both cases. The obtained result indicates that the knowledge of the correlation structure increases the system performance w.r.t the case where no knowledge is available.