An Efficient Algorithm for Robust Fractional QCQP and its Applications to Multiuser Beamforming With Bounded Channel Uncertainties

In this paper, we investigate a nonconvex robust fractional quadratically constrained quadratic problem (Robust Fractional QCQP), which has a wide application to the worst-cast resource allocation optimization in wireless multiuser beamforming systems. The state-of-the-art method is based on semidefinite relaxation (SDR), which possibly returns a high-rank solution and makes it difficult to recover a robustly feasible solution. To overcome this drawback, we propose an efficient algorithm for solving the robust fractional QCQP by employing the constrained concave-convex procedure and the cutting set method. When finding a robustly feasible initial point is nontrivial, we propose an effective method to deal with it. We also develop the parallel implementation of the proposed algorithm to speed up the computation aiming for real-time application scenarios. As a case study, in the second part of the paper we focus on two examples, namely: i) a novel robust nonorthogonal multiple access (NOMA) multiuser beamforming for physical layer security; and ii) the renowned robust signal-to-interference-and-noise ratio (SINR) balancing problem of cognitive radio multiuser beamforming systems. Numerical results are presented to verify the effectiveness of our proposed algorithm compared with the state-of-the-art methods.