Joint Beamforming and Blocklength Optimization for URLLC in RIS-Aided Cell-Free Massive MIMO System

The integration of reconfigurable intelligent surfaces (RIS) with cell-free massive MIMO (CF mMIMO) represents a compelling paradigm for satisfying the stringent reliability and latency demands of ultra-reliable low-latency communication (URLLC). In this framework, distributed access points (APs) provide substantial macro-diversity gains, while dynamically controllable RIS elements facilitate enhanced signal propagation. This paper investigates a practical RIS-aided CF mMIMO system designed for URLLC applications, where communications occur through RIS-reflected links under realistic spatially correlated Rayleigh fading channels, with practical impairments such as RIS phase estimation errors and electromagnetic interference explicitly considered. To evaluate reliability in the short-packet regime, we adopt the decoding error probability (DEP) as the performance metric and derive its analytical expression based on user-side SINR. We formulate a non-convex optimization problem to minimize the maximum DEP among users by jointly optimizing AP beamforming, RIS phase shifts, and blocklength allocation. A hybrid solution framework is proposed, combining deep reinforcement learning for continuous variables with a differential evolution (DE) algorithm for discrete blocklength optimization. Simulation results demonstrate the superior performance of the proposed method over alternating optimization and genetic algorithm (GA) baselines. Notably, increasing the number of AP antennas and transmission blocklength improves network availability, although gains saturate due to inter-user interference and diminishing returns. Moreover, the proposed DE-based algorithm for blocklength optimization consistently outperforms the GA method in terms of both solution quality and computational efficiency.