Sum Energy-Efficiency Maximization for Cognitive Uplink Networks with Imperfect CSI

In this work, we investigate the robust energy efficient transmission for the cognitive uplink wireless system. Precisely, we propose an optimization framework for maximizing the sum energy efficiency while taking into account the uncertainty of the channel between the primary and secondary users. Here, we assume that the base station has multiple antennas and employs a zero-forcing receive filter to eliminate the inter-user interference. We handle the intractability of the probabilistic interference constraints by approximating them with convex and linear surrogate constraints. Despite the non convexity of the utility function, we propose a parametric convex programming approach to derive an optimal algorithm based on Newton method. Through numerical simulations, we show the convergence and effectiveness of the proposed method and analyze the effect of channel uncertainty on the energy efficiency of the cognitive uplink system.