Low-Complexity Distributed Combining Design for Near-Field Cell-Free XL-MIMO Systems

TL;DR

The paper tackles uplink spectral efficiency in near-field CF XL-MIMO by addressing the high computational burden of MMSE combining. It develops a generalized channel-estimator framework and introduces five low-complexity distributed schemes: $GSLI$-$MMSE$, $SI$-$LMMSE$, and three SSOR-based LMMSE variants ($Ins$-$SSOR$-$LMMSE$, $Sta$-$SSOR$-$LMMSE$, $Ins$-$SI$-$SSOR$-$LMMSE$), using matrix-approximation and iterative inversion techniques. The proposed methods leverage global statistics or local statistics to reduce real-time computation while maintaining near-centralized performance; SE expressions and LSFD fusion are provided for both centralized and distributed processing. Numerical results show that $GSLI$-$MMSE$ and $Ins$-$SI$-$SSOR$ achieve SE close to the $CMMSE$ baseline with substantially lower complexity, and the guidance outlines when to deploy each scheme based on information availability and latency constraints. Overall, the work delivers scalable, practical strategies for deploying CF XL-MIMO in near-field regimes with mutual coupling, offering concrete design rules for ultra-large antenna deployments.

Abstract

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.

Figures (10)

• Figure 1: Illustration of the studied CF XL-MIMO network.
• Figure 2: Average SE performance for the GSLI-MMSE combining scheme against the number of antennas per side each BS $N_x$ with $M=4$, $K=20$, and $\Delta_x=\lambda/4$.
• Figure 3: Sum SE performance for the GSLI-MMSE combining scheme against the number of BSs $M$ with $N_x=16$, $K=20$, and $\Delta_x=\lambda/4$.
• Figure 4: Average SE performance evaluated by the UatF bound for the GSLI-MMSE combining scheme under different channel estimators with $M=8$, $N_x=8$, $K=20$, and $\Delta_x=\lambda/4$.
• Figure 5: Sum SE performance for the GSLI-MMSE combining scheme against $\lambda /\Delta _x$ with $M=8$, $N_x=8$, and $K=20$.

Theorems & Definitions (19)

• Remark 1
• Remark 2
• Corollary 1
• Corollary 2
• Corollary 3
• Remark 3
• Remark 4
• Corollary 4
• Remark 5
• Remark 6