Clustered cell-free networks have emerged as a promising architecture for sixth generation ultra-dense wireless communication systems by enabling local cooperation among base stations while controlling system complexity. For resource allocation and performance optimization of such networks, accurate and efficient estimation of the ergodic achievable downlink rate is a fundamental prerequisite. Existing rate estimation approaches mainly rely on computationally prohibitive Monte Carlo simulations or adopt random matrix theory-based methods, which have been well-developed for conventional cellular and cell-free networks. However, existing RMT-based methods have not addressed the unique inter-subnetwork interference in clustered cell-free networks, and therefore lack an efficient solution for accurate downlink rate estimation under both regularized zero-forcing and zero-forcing precoding. In this paper, we propose a stabilized element-wise rate estimation method for downlink rate estimation in clustered cell-free networks. We establish the diagonal element-wise convergence of resolvent matrices, which enables the derivation of deterministic equivalents for inter-subnetwork interference and the downlink ergodic rate. We further introduce a stabilized variable transformation to address the numerical instability when the regularization parameter is very small, hereby enabling a unified formulation applicable to both regularized zero-forcing and zero-forcing precoding. Simulation results show that the proposed method achieves a relative error below 6% while significantly reducing computational complexity compared with the Monte Carlo simulation.

翻译：集群无蜂窝网络通过使基站间实现局部协作并控制系统复杂度，已成为第六代超密集无线通信系统中有前景的架构。在此类网络的资源分配与性能优化中，准确高效地估计遍历可达下行链路速率是基本前提。现有速率估计方法主要依赖计算代价高昂的蒙特卡洛仿真，或采用已成熟应用于传统蜂窝与无蜂窝网络的随机矩阵理论方法。然而，现有基于RMT的方法未能解决集群无蜂窝网络中独特的子网络间干扰问题，因此在正则化迫零与迫零预编码两种场景下缺乏准确估计下行链路速率的有效解决方案。本文提出一种面向集群无蜂窝网络下行链路速率估计的稳定化逐元素速率估计方法。我们建立了预解矩阵的对角线逐元素收敛性，从而推导出子网络间干扰与下行链路遍历速率的确定性等价表达式。进一步引入稳定化变量变换以解决正则化参数极小时的数值不稳定性，由此建立适用于正则化迫零与迫零预编码的统一公式。仿真结果表明，与蒙特卡洛仿真相比，所提方法在显著降低计算复杂度的同时实现了低于6%的相对误差。