In this paper, we investigate the low-complexity distributed combining scheme design for near-field cell-free extremely large-scale multiple-input-multiple-output (CF XL-MIMO) systems. Firstly, we construct the uplink spectral efficiency (SE) performance analysis framework for CF XL-MIMO systems over centralized and distributed processing schemes. Notably, we derive the centralized minimum mean-square error (CMMSE) and local minimum mean-square error (LMMSE) combining schemes over arbitrary channel estimators. Then, focusing on the CMMSE and LMMSE combining schemes, we propose five low-complexity distributed combining schemes based on the matrix approximation methodology or the symmetric successive over relaxation (SSOR) algorithm. More specifically, we propose two matrix approximation methodology-aided combining schemes: Global Statistics \& Local Instantaneous information-based MMSE (GSLI-MMSE) and Statistics matrix Inversion-based LMMSE (SI-LMMSE). These two schemes are derived by approximating the global instantaneous information in the CMMSE combining and the local instantaneous information in the LMMSE combining with the global and local statistics information by asymptotic analysis and matrix expectation approximation, respectively. Moreover, by applying the low-complexity SSOR algorithm to iteratively solve the matrix inversion in the LMMSE combining, we derive three distributed SSOR-based LMMSE combining schemes, distinguished from the applied information and initial values.

翻译：本文研究了近场无蜂窝超大规模多输入多输出（CF XL-MIMO）系统的低复杂度分布式合并方案设计。首先，我们构建了CF XL-MIMO系统在集中式与分布式处理方案下的上行链路频谱效率（SE）性能分析框架。值得注意的是，我们推导了基于任意信道估计器的集中式最小均方误差（CMMSE）与本地最小均方误差（LMMSE）合并方案。随后，聚焦于CMMSE与LMMSE合并方案，我们基于矩阵近似方法或对称逐次超松弛（SSOR）算法，提出了五种低复杂度分布式合并方案。具体而言，我们提出了两种基于矩阵近似方法的合并方案：全局统计与本地瞬时信息辅助的最小均方误差（GSLI-MMSE）方案以及基于统计矩阵求逆的LMMSE（SI-LMMSE）方案。这两种方案分别通过渐近分析与矩阵期望近似，将CMMSE合并中的全局瞬时信息以及LMMSE合并中的本地瞬时信息替换为相应的全局与本地统计信息而推导得出。此外，通过应用低复杂度SSOR算法迭代求解LMMSE合并中的矩阵求逆问题，我们推导了三种基于SSOR的分布式LMMSE合并方案，其区别在于所应用的信息类型与初始值设定。