Secure beamforming for max-min SINR in multi-cell SWIPT systems

We consider the downlink of a dense multicell network where each cell region is divided into two zones. The users nearby their serving base station (BS) in the inner zone implement simultaneous wireless information and power transfer (SWIPT), thus harvest energy and decode information using the power splitting approach. Further, they try to eavesdrop the information intended for other users within the same cell. The users in the outer zone of each cell only implement information decoding. Our objective is to maximize the minimum user equipment (UE) signal-To-interference-And-noise ratio (SINR) under constraints on the BS transmit power, minimum energy harvesting levels of near-by users, and maximum SINR of eavesdroppers in the presence of multi-cell interference. For such a highly non-convex problem, semidefinite relaxation (SDR) may even fail to locate a feasible solution. We propose two methods to address such a difficult problem. In the spectral optimization, we express the rank-one constraints as a single reverse convex nonsmooth constraint and incorporate it into the optimization objective. In the difference-of-convex-functions iteration method, we directly solve for the beamforming vectors via quadratic programming (QP), avoiding the matrix rank constraints. In each iteration of the proposed algorithms, we only solve one simple convex semidefinite program (SDP) or QP. Our simulation results confirm that the proposed algorithms converge quickly after a few iterations. More importantly, our algorithms yield the performance that is very close to the theoretical bound given by SDP relaxation with comparable computational complexity.