Robust Cooperative Beamforming and Its Feasibility Analysis in Multiuser Multirelay Networks

In this paper, we study the optimal cooperative beamforming problem in the amplify-and-forward (AF) multi-user and multi-relay networks, which face the challenges of rapid node number variations and per-node power limits. To achieve extra diversity gain, direct-link (source-to-destination) and distributed relay-link signals are jointly exploited. The optimal cooperative beamforming problem is formulated as the maximum relay transmit power minimization problem, subject to per-relay transmit power and the minimum destination signal-to-noise ratio (SNR) constraints. Since the problem is non-convex, we introduce a phase-regulation (PR) method to transform the non-convex problem into a tractable second-order cone programming (SOCP) problem. It is demonstrated that the proposed method can provide much more robustness against node number variations in terms of worst-case convergence rates than the Lagrange dual and the successive convex approximation (SCA) methods. Furthermore, the closed-form expressions of two necessary feasibility conditions are derived, by which the infeasible channels can be identified and excluded. Consequently, computational costs are reduced. The equivalence of the proposed Necessary Condition I (NC1) and the signal-to-interference ratio (SIR) condition is proved theoretically and numerically. The proposed Necessary Condition II (NC2) has a lower upper-bound than the SIR condition, thus reducing more computational costs. This method is applicable to both direct-link and non-direct-link scenarios.