SINR-Outage Minimization of Robust Beamforming for the Non-Orthogonal Wireless Downlink

A probabilistically robust transmit beamforming problem is referred, when the wireless downlink (DL) communication is supported by a robust non-orthogonal transmission (NOT)-aided design. Realistic imperfect channel state information (CSI) is considered in the face of rapidly fluctuating vehicular wireless channels, when the road side unit (RSU) communicates with multiple vehicles. Our design objective is to keep the probability of each vehicle's signal-to-interference-plus-noise ratio (SINR) outage below a given threshold. Minimizing the outage probability presents a significant analytical and computational challenge, since it does not lend itself to tractable closed-form expressions. Assuming a Gaussian CSI uncertainty distribution, we provide an approximation method by resorting to the semidefinite relaxation (SDR) and then apply a convex restriction to the original SINR outage constraints. Furthermore, the infinite constraints are reformulated into linear matrix inequalities (LMIs) by exploiting the popular S-procedure. As a benefit, the reformulated program can be solved efficiently using off-the-shelf solvers. Computer simulations are performed for benchmarking our convex method both against the non-robust non-orthogonal as well as the classical orthogonal designs. The results show that our robust beamforming design offers excellent high-mobility performance.