Robust Optimization with Probabilistic Constraints for Power-Efficient and Secure SWIPT

Abstract

Abstract-In this paper, we propose beamforming schemes to simultaneously transmit data to multiple information receivers (IRs) while transfering power wirelessly to multiple energyharvesting receivers (ERs). Taking into account the imperfection of the instantaneous channel state information, we introduce a probabilistic-constrained optimization problem to minimize the total transmit power while guaranteeing data transmission reliability, secure data transmission, and power transfer reliability. As the proposed optimization problem is non-convex and has an infinite number of constraints, we propose two robust reformulations of the original problem adopting safe-convexapproximation techniques. The derived robust formulations are in semidefinite programming forms, hence, they can be effectively solved by standard convex optimization packages. Simulation results confirm the superiority of the proposed approaches to a baseline scheme in guaranteeing transmission security.

Robust Chance-Constrained Optimization for Power-Efficient and Secure SWIPT Systems

“…Proposition 1: If an M × M Hermitian matrix W i has a rank of K ≤ M, then it can be expressed as W i = K j=1 ν i,k a i,k a H i,k , where ν i,k and a i,k are the kth non-zero eigenvalue and the corresponding eigenvector of W i , respectively. 11 In the following, we prove the rank-one property of the solution of (41) by contradiction. Assuming that the optimal solution of (41), W ⋆ i , has rank K > 1, ∀i.…”

“…Solving problem (11) is challenging due to the fact that the probabilistic constraints neither have simple closed-forms nor admit convexity. 4 In other words, (11) is an NP-hard problem which cannot be solved in polynomial time. To overcome this challenge, our goal is to derive convex upper bounds for the chance constraints in (11).…”

“…The poor performance of Method III is due to the fact that its approximation tightness is sacrificed for improved computational efficiency. Since, in this paper, we are interested in developing power-efficient strategies, in the following, we adopt Methods I and II to derive two safe approximations for (11). It is noted that our optimization problem is fundamentally different from the one considered in [40] where the objective is to minimize the total transmit power subject to IR rate outage constraints for a multiple-input single-output (MISO) downlink system.…”

“…are two sets of beamforming matrices. Solving problem (11) is challenging due to the fact that the probabilistic constraints neither have simple closed-forms nor admit convexity. 4 In other words, ( 11) is an NP-hard problem which cannot be solved in polynomial time.…”

“…Therefore, such techniques may not be suitable for protecting information in SWIPT systems [2], [8] as SWIPT devices are usually energy limited. Instead, physical layer security [9]- [11], where fading, noise, and interference are exploited, is considered to be an effective method for providing secure information transmission in SWIPT systems [2], [12].…”