Distributed Robust Beamforming in Multi-User Relay Network

In this letter, a robust distributed amplify and forward (AF) relay beamforming problem is solved, using the stochastic approach with imperfect channel state information (CSI) at the relay nodes and destination terminals. Specifically, we model the channel estimation error as a Gaussian random vector with known statistical distribution. Our objective is to minimize the total relays transmit power subject to probabilistic quality of service (QoS) constraint at each receiver. It is shown that the original robust design is a nonconvex SDP problem with rank constraint, but it can be relaxed to a SDP convex problem using the semidefinite relaxation (SDR) technique. Then the optimal solution of the relaxed problem is utilized to generate an approximate solution of the original non-convex problem using well-known randomization technique. Simulation results are reported to corroborate our studies.