This paper focuses on the power optimization problem for the max-min fairness of energy efficiency (EE) among cognitive users (CUs) in an underlay massive multiple-input multiple-output (MIMO) cognitive radio network (CRN). We formulate this problem as the maximization of the minimum EE of CUs, subject to their minimum data rate requirements and transmit power constraints. However, the problem is nonconvex and NP-hard due to its non-convex fractional objective and the complicated intra-cell interference term. In order to tackle this issue, we address it by solving its equivalent auxiliary problem based on fractional programming, and achieve the optimal minimum EE by the bisection method. Wherein an efficient iterative power control algorithm based on sequential convex programming is devised to obtain the local optimal transmit power. Numerical results demonstrate that the proposed algorithm is convergent and insensitive to the initial transmit power, and verify that the max-min fair power control scheme can guarantee good fairness of EE among CUs with high EE.
['Manman Cui', 'Bin-Jie Hu', 'Hongbin Chen', 'Xiaohuan Li']
Max-min fair power control algorithm in massive MIMO cognitive radio networks