In this paper, energy-efficient secure communications via untrusted two-way relaying are investigated considering physical layer security to prevent the relays from intercepting the confidential information of users. The performance metric of secure energy efficiency (EE), defined as the ratio of the secrecy sum rate to the total power consumption, is maximized by jointly optimizing power allocation for all nodes, with the constraints of the maximum allowed power and the minimum target secrecy rate. To deal with this intractable nonconvex optimization problem, some optimization methods termed as fractional programming, alternate optimization, penalty function method, and difference of convex functions programming, are jointly applied to address a solution scheme with comparatively lower complexity. With these above-mentioned optimization methods, the primal problem is transformed into simple subproblems hierarchically so as to adopt the corresponding optimization algorithm. By simulations, the achievable secure EE, the secrecy sum rate and the total transmission power of the proposed scheme are compared with those of secrecy sum rate maximization. It is demonstrated that the proposed scheme can improve secure EE remarkably yet at the cost of secrecy sum rate loss. This fact also reveals the inherent tradeoff between energy and security.Index Terms-Energy efficiency, physical layer security, twoway relaying, secure green communications.
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