Optimization for Maximizing Sum Secrecy Rate in MU-MISO SWIPT Systems

Abstract

In this paper, we consider the sum secrecy rate maximization problem in multiuser multiple-input single-output (MUMISO) systems in the presence of multiple energy harvesters (EHs) which also have potential to wire-tap the information users (IUs). To facilitate delivering secure information to the IUs and increase the total harvested energy by the EHs simultaneously, we optimise the transmit beamforming vectors to direct the information signals toward the IUs and artificial noise (AN) toward the EHs. We assume that each EH relies on itself to decode the information signal intended for an individual IU. Therefore, the corresponding problem is to maximize the worst-case sum secrecy rate under transmit power and energy harvesting constraints. The problem is optimally solved by transforming it into a convex iterative program using a change of variables, semi-definite relaxation (SDR) and linearization of quadratic terms. We prove that rank-one optimal solutions for the IUs beamforming covariance matrices can be obtained from the optimal relaxed unconstrained solution. Also, we provide three sub-optimal solutions based on null space projection and power control of the beamforming vectors for the low and high harvested energy constrained regions. A special case of cooperative EHs in which the EHs can collaboratively cancel the signal of all IUs except the one they intend to eavesdrop is also investigated, and the optimal solution is derived in a comparable way as in non-cooperative EHs case. Our simulation results reveal an understanding of how the trade-off between the AN and information signal can jointly improve both the sum secrecy rate and the total harvested energy. We also show that, within the low total harvested energy region, the sub-optimal solution in which the AN is projected in the null space of the IUs channels outperforms the sub-optimal solution which ignores AN alignment at the IUs, and vice versa over the high total harvested energy region; and that the suboptimal solution that combines both of them achieves close to optimal performance.