Robust Energy Efficiency Maximization in Cognitive Radio Networks: The Worst-Case Optimization Approach

Energy efficiency (EE) is very crucial for future wireless communication systems, especially for cognitive radio networks (CRNs). The EE performance relies on channel state information (CSI) of channels. Besides, the interference from secondary users (SUs) to primary users (PUs) also closely depends on CSI in underlay CRNs. However, available works on EE usually assume that CSI is perfect, which is often inaccurate in practical systems. Thus, in this paper we investigate the robust EE maximization problem in underlay CRNs with multiple SUs and PUs. Assuming CSI error to be bounded, we consider that all channels lie in some bounded uncertainty regions. From the perspective of worst-case optimization, we formulate it as the max-min problem with infinite constraint, which is nontrivial even without this constraint. This is because that the outer-maximization problem is non-convex and the inner-minimization problem is a concave minimization problem known as NP-hard in general. We propose a scheme to handle this problem via the fractional programming and global optimization techniques. Particularly, we efficiently solve this problem in two special cases. Simulation results validate that our proposed scheme can improve the worst-case EE of SUs distinctly and strictly guarantee the quality-of-service (QoS) of PUs under all parameters´ uncertainties.