Joint Design of Pilot Power and Phase Shifts in RIS-Aided Cell-Free Massive MIMO URLLC Systems

In the context of Internet of Things, this letter considers a cell-free (CF) massive multiple-input–multiple-output (MIMO) system for ultrareliability and low-latency communication (URLLC) assisted by multiple reconfigurable intelligent surfaces (RISs). We derive the closed-form expression of the downlink achievable rate under multiple correlated RISs and pilot contamination. To mitigate the impact of pilot contamination and improve the fairness among users, we minimize the maximum normalized mean-squared error (NMSE) of the channel estimation by jointly optimizing the pilot power coefficient and the RIS phase shifts. Due to the nonconvexity of the original problem, we design an alternating optimization algorithm to solve the substitutable two subproblems using fractional programming and sequential convex approximation. Numerical results validate the proposed algorithm in terms of decreasing the maximum user NMSE and converging. Moreover, the 95%-likely per-user downlink achievable rate is also improved.