Joint Transmissive and Reflective RIS-Aided Secure MIMO Systems Design Under Spatially-Correlated Angular Uncertainty and Coupled PSEs

This paper investigates a joint transmissive and reflective reconfigurable intelligent surfaces (RIS) -aided secure multiple-input multiple-output (MIMO) system, where both a RIS-assisted transmitter and a RIS-based reflector are deployed to defend against the simultaneous jamming attack and wiretapping threat. Our design focuses on maximizing the sum rate under the unknown jammer's beamforming, joint RISs' coupled phase shift errors (PSEs), and spatially-correlated angular channel uncertainties. Besides, we take into account the various quality-of-service (QoS) requirement constraints for guaranteeing the secure performance. Since the problem is non-convex and mathematically intractable, a new optimization framework is established to facilitate the solution development to the formulated problem. Specifically, armed with the Akaike information criterion, a novel diagonalization method is first proposed to estimate the unknown jamming covariance matrix. Then, a series of fractional-eliminated rate expressions is derived that facilitates the application of the proposed Double Deterministic Transformation (DDT) to tackle the coupled stochastic PSEs. Besides, regardless of the spatial correlation matrix, a general discretization method is proposed to convert the e spatially-correlatd angular uncertainties into a worst-case robust one. Subsequently, building upon the above transformations which transform the original problem into tractable one, a two-layer iterative Lagrange multiplier algorithm capitalizing a low-complexity dual method is proposed to obtain the globally optimal solution of the digital precoder, where the multiple QoS constraints are handled without iteration. Meanwhile, we develop a novel polyblock-based multiple penalty method to obtain the globally optimal solutions to RISs' phase shifts which can simultaneously satisfy the multiple QoS constraints. Moreover, to address the narrow feasibility region induced by the multiple QoS constraints, a heuristic initial optimization method is proposed, which strengthens the existing result. Finally, theoretical analysis and numerical results demonstrate the optimality and the excellent performance of our proposed optimization framework.