Optimal transmit power minimization in secure MU-MISO SWIPT systems

Abstract

We consider multiuser multiple-input single-output (MU-MISO) 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 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. For information eavesdropping, we assume two scenarios; in the first, each EH relies on itself to decode the information signal intended for one IU, while in the second scenario, the EHs cooperate to decode the information signal intended for one IU. The considered problem is to minimize the total transmit power subject to total harvested energy and minimum worst-case secrecy rate constraints. The optimization problems for both cooperative and non-cooperative EHs are not convex due to quadratic secrecy constraints. The optimization problems are optimally solved by transforming them into convex iterative programs using change of variables, semidefinite relaxation (SDR) and linearization of quadratic terms. We provide a proof of optimality for rank-unconstrained semidefinite programming (SDP) solutions by using dual multipliers which satisfy Slater's condition and the Karush-Kuhn-Tucker (KKT) conditions. Simulation results are provided to demonstrate the effectiveness of the proposed algorithms.