Energy-Efficient Optimization in User-Centric Cell-Free Massive MIMO Systems for URLLC With Finite Blocklength Communications

In this paper, we investigate the energy efficiency (EE) optimization in the user-centric cell-free massive MIMO (CF mMIMO) systems for ultra-reliable low-latency (URLLC), where access points (APs) use maximum ratio transmission or Zero-Forcing precoding schemes for downlink transmission. To address the challenge of achieving high EE while considering the URLLC-mandated finite blocklength achievable rate, we formulate a joint power control and user association problem. We introduce a convex lower bound for the intractable achievable rate using successive convex approximation (SCA), enabling us to reformulate the original problem as a mixed-integer second-order cone programming (MISOCP) problem. To mitigate the high computational complexity associated with obtaining the optimal solution using Branch-and-Bound (BnB) algorithms, we propose a low-complexity iterative algorithm that leverages continuous relaxation of the binary variables. Simulation results demonstrate that our proposed algorithms achieve near-optimal performance compared to BnB and outperform the conventional CF mMIMO approach, which assumes equal power allocation and coherent transmission. Furthermore, we provide insights into the impact of system parameters, latency and reliability constraints on system EE, as well as the convergence performance of our approaches.