On Convexity of Fairness-Aware Energy-Efficient Power Allocation in Spectrum-Sharing Networks

The optimization of energy efficiency (EE) in spectrum-sharing networks has received increasing attention. While much effort has been devoted to the network-side overall EE, the fairness of EE among users has not been adequately concerned. Due to the complicated interference between different users, the global optimality of power allocation problems for achieving proportional, harmonic, and max-min fair EE with guarantees on users' quality of service has not been fully addressed. By introducing auxiliary variables, changing variables, and transforming the objective and constraint functions, we convert the proportional, harmonic as well as max-min fairness-aware problems to convex ones. As a result, mature algorithms, such as interior-point methods, can be applied to achieve the global optimality with considerable efficiency.