Robust Transmit Beamforming for Underlay D2D Communications on Multiple Channels

Underlay device-to-device (D2D) communications lead to improvement in spectral efficiency by simultaneously allowing direct communication between the users and the existing cellular transmission. However, most works in resource allocation for D2D communication have considered single antenna transmission and with a focus on perfect channel state information (CSI). This work formulates a robust transmit beamforming design problem for maximizing the aggregate rate of all D2D pairs and cellular users (CUs). Assuming complex Gaussian distributed CSI error, our formulation guarantees probabilistically a signal to interference plus noise ratio (SINR) above a specified threshold. In addition, we also ensure fairness in allocation of resources to D2D pairs. We accommodate the probabilistic SINR constraint by exploiting a Bernstein-type inequality.The resulting problem is a mixed integer non-convex problem, and we propose to approximately solve it by exploiting a semi-definite relaxation (SDR) and a quadratic transformation, which leads us to an alternating optimization method. Simulation results corroborate the merits of the proposed approach by illustrating higher network throughput and more reliable communication.