Non-convexity Of Objective Function Research Articles

A femtocell network which is supported by a macrocell base station and some femtocell base stations provides more reliable transmission, higher wireless capacity, and broader coverage. However, it may face eavesdropping risk, which provides an eavesdropper with a chance to overhear a macrocell user’s confidential information. In this paper, we study a secrecy transmission problem for a downlink two-tier femtocell network with imperfect channel state information (CSI), where an eavesdropper wiretaps the legitimate macrocell user. More specifically, we aim to maximize the secrecy rate by jointly optimizing the power allocation and quality-of-service (QoS) requirement in terms of outage probability. We consider two types of CSI, i.e., instantaneous and statistic CSI, respectively, which can robustly guarantee the QoS of users in a complex communication environment. For the instantaneous CSI communication environment, where there exist estimated errors between instantaneous channel gains and their estimated values, we propose a novel conversion method to extract the approximate closed-form expressions of outage probability constraints. For the statistic CSI communication environment, where channel gains obey Rayleigh fading, we design a new method to obtain deterministic expressions by considering the expectations and variances of instantaneous channel gains. Then, the uncertainty and non-convexity of objective function are solved with the aid of variable substitution and Taylor expansion. Moreover, two iterative algorithms are proposed to derive the optimal transmission powers. Finally, we evaluate the proposed algorithms using large scale simulations, and present extensive evaluation results to demonstrate the effectiveness of our proposed algorithms.