Probabilistic-Constrained Robust Beamforming for RIS-Aided Dynamic TDD Systems

Dynamic time-division-duplexing (DTDD) and reconfigurable intelligent surfaces (RISs) have been proposed recently as solutions to meet the traffic fluctuations in small cells and to tune the wireless propagation channels in real time. In this paper, we propose robust transmission strategies for an RIS-aided DTDD wireless system with imperfect channel state information (CSI). The problem is formulated as a sum-power minimization problem for the downlink cells under individual users’ signal-to-interference-plus-noise-ratio (SINR) constraints, interference temperature constraints for the uplink cells, and unit-modulus constraints of the RIS in the presence of CSI errors. We consider the statistical CSI imperfection model and propose a probabilistic-constrained robust (PCR) beamforming design scheme. To this end, we adopt a Bernstein-type inequality and the relaxed semi-definite programming (SDP) technique to reformulate the statistical CSI model-based design problem into a tractable problem that can be solved efficiently. Numerical results are presented showing that the outage probability-based approach outperforms that of the bounded norm model.