Energy Efficiency of Distributed Antenna Systems with D2D Communications under Imperfect CSI

Abstract

In this paper, we investigate the distributed antenna systems (DAS) based on device to device (DAS-DID) communications under the imperfect channel state information (CSI). Our aim is to maximize the energy efficiency (EE) of the D2D users equipment (DUE) under the constraints of the maximum transmission power of D2D pairs and the quality of service (QoS) requirements of the cellular user equipment (CUE). The worst-case design is considered so that the QoS of the CUE can be guaranteed for every realization of the CSI error in the ellipsoid region. The EE objective function of the optimization problem is non-convex and non-linear, and thus this problem cannot be solved by the traditional optimization methods. To solve this problem, first we transform it to an EE maximization problem without uncertain parameters by exploiting the Markov and Cauchy-Schwartz inequality. Then using the fractional programming theory and difference of convex functions optimization method, the robust EE maximization algorithms based on the hard and soft protection method are developed to maximize the system's EE performance, respectively. However, these two algorithms are designed at the cost of the reduced EE of the DUE. Therefore, in order to further improve the EE performance and make a trade-off between the EE performance and the robustness, the iterative update algorithms for the total power constraint and average interference constraint are developed to maximize the system's EE performance, respectively. Simulation results demonstrate the effectiveness of the four proposed EE algorithms and illustrate the trade-off between the EE performance and robustness for the iterative update algorithms.