Reliable Underlay D2D Communications over Multiple Transmit Antenna Framework

Abstract

Robust beamforming is an efficient technique to guarantee the desired receiver performance in the presence of erroneous channel state information (CSI). However, the application of robust beamforming in underlay device-to-device (D2D) communication still requires further investigation. In this paper, we investigate resource allocation problem for underlay D2D communications by considering multiple antennas at the base station (BS) and at the transmitters of D2D pairs. The proposed design problem aims at maximizing the aggregate rate of all D2D pairs and cellular users (CUs) in downlink spectrum. In addition, our objective is augmented to achieve a fair allocation of resources across the D2D pairs. Further, assuming elliptically bounded CSI errors, the formulation ensures maintaining signal to interference plus noise ratio (SINR) above a specified threshold. The derived optimization problem results in a mixed integer non-convex problem and requires exponential complexity to obtain the optimal solution. We perform a semi-definite relaxation (SDR) to handle the stochastic SINR constraints by using the S-Lemma, obtaining a number of linear matrix inequalities. The non-convexity is addressed by introducing slack variables and performing a quadratic transformation to obtain sub-optimal beamformers via alternating optimization. The solution for channel assignments to D2D pairs is obtained by convex relaxation of the integer constraints. Finally, we demonstrate the merit of the proposed approach by simulations in which we observe higher and more robust network throughput, as compared to previous state-of-the-art.