Robust secrecy energy efficiency optimisation in heterogeneous networks with simultaneous wireless information and power transfer: centralised and distributed design

With the ellipsoid-bounded channel state information (CSI) errors, this study investigates the robust secrecy energy efficiency (SEE) optimisation in a wireless powered heterogeneous network. Specifically, the authors consider the network where multiple femtocell base stations (FBSs) are deployed under the coverage of one macrocell base station (MBS). Meanwhile, the MBS serves multiple macrocell users in the presence of a malicious multiple-antenna eavesdropper (Eve) while each FBS serves a pair of information receiver (IR) and energy receiver (ER) with multiple antennas, where the ER attempts to wiretap the information of IR in the same femtocell. To promote the secrecy performance, artificial noise (AN) is aided into the downlink signal at the MBS and FBSs, and the problem of maximising SEE is formed in a cross-tier multi-cell AN-aided transmit beamforming design. This problem is non-convex while containing infinite constraints caused by CSI errors, which cannot be solved directly. In this regard, the authors resort to the successive convex approximation, semi-definite relaxation techniques and Lagrange duality theory to acquire its solvable form. Moreover, to reduce the overhead of information exchange among coordinated BSs, they further propose a distributed approach based on alternative direction multiplier method. Finally, simulation results validate the effectiveness of the proposed design.