Secure and Fresh Beamforming Design for RIS-Assisted Multi-User MISO System with FBL

This paper investigates the secure and fresh beamforming design for reconfigurable intelligent surface (RIS) assisted multi-user multiple-input-single-output (MISO) system with finite blocklength (FBL). Specifically, to simultaneously guarantee the security and timeliness requirements, we employ the moment generating functions in stochastic network calculus to derive an approximate closed-form expression for the upper bound of secrecy age outage probability (SAOP) under statistical channel state information (CSI). The beamforming design problem is formulated to minimize sum SAOP under constraints of reliability, information leakage, power budget and unit modulus. To solve the intractable problem, we propose an alternating optimization algorithm based on semi-definite relaxation (SDR) and momentum stochastic successive convex approximation (M-SSCA), where SDR is used for a quadratically constrained quadratic programs problem to optimize transmit beamforming vector, M-SSCA is utilized for a stochastic non-convex problem to optimize RIS phase shift. Simulation results validate the derived expressions and our proposed algorithm. It is shown that compared with stochastic successive convex approximation (SSCA) and stochastic gradient descent (SGD) methods, the proposed optimization algorithm achieves a reduction in sum SAOP with faster convergence speed.