Enhancing Physical Layer Security With RIS Under Multi-Antenna Eavesdroppers and Spatially Correlated Channel Uncertainties

Reconfigurable intelligent surface (RIS) has the capability to significantly enhance physical layer security by reconfiguring the propagation in wireless communications. However, due to the cascaded channel brought by the RIS and the hostile nature of potential eavesdroppers, acquiring perfect channel state information (CSI) of the eavesdroppers is challenging. Worse still, if the eavesdroppers are equipped with multiple antennas and there exists spatial correlation at the RIS due to closely spaced RIS elements, the random channel matrices are complicatedly coupled with the phase shift and other wireless resources in the outage probabilistic constraint, making their optimizations intractable. To date, there has been no systematic and feasible approach to address such a challenge. To fill this gap, this paper for the first time reveals an analytical transformation for handling the intractable outage probabilistic constraint. It is theoretically established that when the maximum tolerable outage probability is smaller than a threshold around 0.4, which generally holds in practice, the proposed transformation is exact and suffers no performance loss. As an illustrative example of the developed constraint transformation, the secure energy efficiency maximization is selected as the objecitve function and the resultant resource optimization is handled by the alternating maximization framework. Numerical results are presented to show the rapid convergence behavior of the proposed algorithm and unveil that the proposed probabilistic constraint transformation has superiority over the Bernstein-Type Inequality approximation. Compared with several baseline schemes (e.g., random phase-shift, fixed phase-shift, RIS ignoring CSI uncertainty, and secure transmission without RIS), the proposed scheme significantly boosts the performance, underscoring the significance of appropriately managing the probabilistic constraint outage and optimizing RIS phase shifts for secure transmission against multi-antenna eavesdroppers.