Energy-Efficient Joint Power Allocation in Uplink Massive MIMO Cognitive Radio Networks With Imperfect CSI

In this paper, a joint pilot and data power allocation problem with max-min fair energy efficiency (EE) guarantee in the uplink massive multiple-input multiple-output cognitive radio networks is investigated. Given the fractional objective function, channel estimation errors, and inter-user interference, the joint allocation problem is formulated as a nonconvex and NP-hard problem. To tackle this, we transform the original problem into its convex form by introducing auxiliary variables and variable substitution, and then address it with the help of the Lagrangian dual method. Since the optimization variables are interrelated and interact on each other, it is difficult to directly obtain the closed-form solution to this problem. To settle this issue, we propose an alternative iterative algorithm to achieve the optimal power policy by a gradient-based adaption method, with its corresponding optimal Lagrangian multipliers obtained by the subgradient method. Numerical results show that the proposed approach has the best minimum EE performance and decent spectral efficiency performance. Besides, compared with the other schemes, significant saving in total transmit power and good cognitive user fairness are achieved by the proposed algorithm.