Robust Secrecy Energy Efficiency Optimization for Wireless Powered Heterogeneous Networks Using Distributed ADMM Algorithm

Under the case of imperfect channel state information (CSI), this paper investigates the robust secrecy energy efficiency (SEE) optimization for the heterogeneous networks (HeNets) supported by simultaneous wireless information and power transfer. Specifically, we first consider a two-tier HeNet composed of a macrocell base station (MBS) and several femtocell base stations (FBSs), where the MBS serves multiple macrocell users (MUs) while each FBS serves an information receiver (IR) and an multiple-antenna energy receiver (ER). Meanwhile, a malicious multiple-antenna eavesdropper (Eve) attempts to wiretap the downlink information of MUs and the ER acts as a potential Eve to eavesdrop the confidential information for IR in the same femtocell. To enhance the secrecy performance, artificial noise (AN) is injected into the downlink information beams of the MBS and FBSs. By considering the user fairness, the problem of SEE maximization of the whole network is formulated via a cross-tier multi-cell coordinated beamforming design. The resulting problem contains infinite constraints caused by CSI error, which is nonconvex and cannot be solved directly. To this regard, we resort to the successive convex approximation, S-procedure and semi-definite relaxation techniques to obtain a solvable form of it. Furthermore, to reduce the overhead of information exchange among coordinated BSs, we develop a distributed solution based on alternative direction multiplier method (ADMM) that can achieve a good approximation performance. Finally, simulation results verify the validity of the proposed AN-aided cross-tier multi-cell coordinated beamforming design and distributed ADMM-based design.