Secrecy Energy Efficiency in Cognitive Radio Networks With Untrusted Secondary Users

The information security and energy efficiency in cognitive radio (CR) networks have been extensively studied. However, the practical scenario involving multiple untrusted secondary users (SUs) in CR networks under the underlay spectrum sharing mechanism has not been studied so far. This article considers the downlink secrecy energy efficient coordinated beamforming design for multiple inputs single output CR networks under this scenario. Our goal is to maximize the global secrecy energy efficiency (GSEE), defined as the ratio of the sum of secrecy rates of all the primary users (PUs) to the total power consumption, under requirements on quality of service of PUs and SUs as well as constraints on power budget at the primary transmitter (PTx) and the secondary transmitter (STx). To tackle the non-convex GSEE maximization (GSEEM) problem, an algorithm is proposed based on Dinkelbach method and successive convex approximation to jointly optimize beamforming vectors of the PTx and the STx. The convergence behavior and the computational complexity of the proposed GSEEM algorithm are analyzed, followed by the connection with the secrecy rate maximization design and the power minimization (PM) design in terms of GSEE. In view of significantly higher computational complexity of the proposed GSEEM algorithm than that of the PM design, a 2-step searching scheme is further designed to efficiently search for an approximate solution to the considered GSEEM problem based on the PM design and the golden search method. Simulation results demonstrate the efficacy of the proposed GSEEM algorithm and the searching scheme, and show that the spatial degrees of freedom (primarily determined by the antenna numbers of PTx and STx) is the key factor to the performance of the proposed GSEEM algorithm.