Distributed Multi-Stream Beamforming in MIMO Multi-Relay Interference Networks

In this paper, multi-stream transmission in interference networks aided by multiple amplify-and-forward (AF) relays in the presence of direct links is considered. The objective is to minimize the sum power of transmitters and relays by beamforming optimization under the stream signal-to-interference-plus-noise-ratio (SINR) constraints. For transmit beamforming optimization, the problem is a well-known non-convex quadratically constrained quadratic program (QCQP) that is NP-hard to solve. After semi-definite relaxation (SDR), the problem can be optimally solved via alternating direction method of multipliers (ADMM) algorithm for distributed implementation. Analytical and extensive numerical analyses demonstrate that the proposed ADMM solution converges to the optimal centralized solution. The convergence rate, computational complexity, and message exchange load of the proposed algorithm outperforms the existing solutions. Furthermore, by SINR approximation at the relay side, distributed joint transmit and relay beamforming optimization is also proposed that further improves the total power saving at the cost of increased complexity.