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Cell-free networks have emerged as a new paradigm for beyond-5G networks, offering uniform coverage and improved control over interference. However, scalability poses a challenge in full cell-free networks, where all access points (APs) serve all users. This challenge is addressed by user-centric clustering, where each user is served by a subset of APs, reducing complexity while maintaining coverage. In this paper, we provide an analysis of the relation between the user-centric clustering and pilot assignment problems in cell-free networks, and introduce a formulation which decouples both problems enabling each to be solved independently. We present a general problem formulation for the user-centric clustering problem, allowing the use of diverse per-user and network-wide performance metrics. Specifically, we focus on one instance of this framework, utilizing per-user spectral efficiency and network-wide sum spectral efficiency (SE) as metrics. Additionally, we formulate the pilot assignment problem to minimize overall channel estimation error while considering the user-centric clusters in evaluating the desirability of pilot assignments, which leads to better performing solutions. Both problems are classified as binary nonlinear programs that are at least NP-hard. To solve these optimization problems, our proposed methodology employs sample average approximation coupled with surrogate optimization for the user-centric clustering problem and utilizes the genetic algorithm for the pilot assignment problem. Numerical experiments demonstrate that the optimized solutions surpass baseline solutions, leading to significant improvements in spectral efficiency. 

This paper addresses the user-centric clustering and pilot assignment problems in cell-free networks, recognizing the need to solve both problems simultaneously. The motivation of this research stems from the absence of benchmarks, general formulations, and the reliance on subjectively designed objective functions and heuristic algorithms prevalent in existing literature. To tackle these challenges, we formulate stochastic non-linear binary integer programs for both the user-centric clustering and pilot assignment problems. We specifically design the pilot assignment formulation to incorporate user-centric clusters when evaluating the desirability of pilot assignments, resulting in improved efficiency. To solve the problems, the proposed methodology employs sample average approximation coupled with surrogate optimization for the user-centric clustering problem and the genetic algorithm for the pilot assignment problem. Numerical experiments demonstrate that the optimized solutions outperform baseline solutions, leading to significant gains in spectral efficiency.