Statistical CSI Based Robust and Secure Transmission via Reconfigurable Intelligent Surfaces with Eavesdropper Location Uncertainty

Reconfigurable intelligent surfaces (RIS), as new physical dimension transmission technology, can smartly adjust its reflection coefficients to achieve passive beamforming gains for signal enhancement and interference nulling. However, the instantaneous channel state information (CSI) is generally hard to obtain and involves huge training overhead. Besides, due to the passive and noncooperative manner of eavesdroppers, neither location nor CSI of the eavesdropping links can be perfectly known. Considering these practical restrictions, we propose a robust secure transmission strategy using only statistical CSI of the RIS assisted legitimate link with imperfect knowledge about the eavesdropper link. A bounded error model is established to characterize the uncertainty of eavesdroppers channel state information based on its potential location with uncertainty. The approximated ergodic secrecy rate is first derived in closed form, and then maximized by optimizing the active beamforming of the BS, the phase shifts of the RIS and the artificial noise (AN). To tackle this problem, a block coordinate descent (BCD) algorithm is proposed, and the original problem is decoupled into multiple subproblems, which are solved iteratively until convergence. Simulation results demonstrate that our proposed scheme can achieve approximately $59.1 \%$ secrecy gain compared to the benchmark schemes.