Joint Multirelay Selection, Power Allocation, and Beamformer Design for Multiuser Decode-and-Forward Relay Networks

Consider a two-hop relay network that consists of multiple pairs of single-antenna users and multiple multiantenna relays. We assume that the relays employ a linear decode-and-forward (DF) strategy to cooperatively forward information from sources to their destinations. To provide fairness among users and alleviate the network backhaul load, we consider a signal-to-interference-plus-noise-ratio (SINR)-based max-min fairness (MMF) problem by jointly optimizing the power allocation at sources, the receive and transmit beamformers at relays, and the size of the cooperating relays. This problem is a nonlinear mixed-integer program, which is challenging to solve. As a compromise, we seek some efficient approximate solutions to it. Specifically, we first approximate the hard backhaul constraint by a group sparse constraint and then employ the uplink-downlink duality transformation, advocated by Luo et al. [IEEE Transactions on Wireless Communications 2015], to eliminate trivial nonsparse solutions. From there, a custom-made distributed algorithm is developed for the approximated problem by fitting it into the alternating direction method of multipliers (ADMM) framework. Each iteration of ADMM can be computed in closed form, thus giving it very low complexity. The effectiveness of the proposed algorithm was validated by extensive numerical simulations.