Energy Efficiency Region for Gaussian MISO Channels With Integrated Services

This letter studies energy efficient optimization problem for a two-receiver multiple-input single-output channel with two integrated service messages: one multicast message intended for both receivers and one confidential message intended only for one receiver and required to be perfectly secure from the other receiver. We aim to characterize the energy efficiency (EE) tradeoff between the two services, and more specifically, to find the Pareto boundary of the EE region. Such an EE region maximization problem is a nonconvex vector maximization problem, and we propose a method of scalarization to reformulate it into a scalar optimization problem. Despite the nonconvexity of the scalar problem, we show that it can be iteratively solved by combining fractional programming and difference-of-concave programming methods. Further, we prove that our obtained EE performance could always be achieved by simply using the single-stream beamforming for confidential message transmission. Finally, numerical results demonstrate the efficacy of our proposed methods in characterizing the EE tradeoff.