Optimal power allocation to increase secure energy efficiency in a two-way relay network

In this paper, a cooperative secure transmission in a two-way relay network is investigated. Due to untrusted relay, physical layer security is adopted to secure the user's messages from relay interruption. Considering the secure sum rate and power consumption for the network, we formulate an optimal power allocation (OPA) problem for the transmission to maximize the secure energy efficiency (EE). To lower the complexity of the optimization solution, an approximation based on Taylor expansion is introduced to achieve near optimal secure EE with acceptable errors. Finally, the numerical results are presented to validate the correctness and efficiency of the proposed algorithm and solution. The relative error of secure EE is not greater than 6% in the worst case, and about 1% in most cases, which is acceptable.