In this paper, we propose the cross splitting based information geometry approach (CS-IGA), a novel and low complexity iterative detector for uplink signal recovery in extralarge-scale MIMO (XL-MIMO) systems. Conventional iterative detectors, such as the approximate message passing (AMP) algorithm and the traditional information geometry algorithm (IGA), suffer from a per iteration complexity that scales with the number of base station (BS) antennas, creating a computational bottleneck. To overcome this, CS-IGA introduces a novel cross matrix splitting of the natural parameter in the a posteriori distribution. This factorization allows the iterative detection based on the matched filter, which reduces per iteration computational complexity. Furthermore, we extend this framework to nonlinear detection and propose nonlinear CSIGA (NCS-IGA) by seamlessly embedding discrete constellation constraints, enabling symbol-wise processing without external interference cancellation loops. Comprehensive simulations under realistic channel conditions demonstrate that CS-IGA matches or surpasses the bit error rate (BER) performance of Bayes optimal AMP and IGA for both linear and nonlinear detection, while achieving this with fewer iterations and a substantially lower computational cost. These results establish CS-IGA as a practical and powerful solution for high-throughput signal detection in next generation XL-MIMO systems.

翻译：本文提出基于交叉分裂的信息几何方法（CS-IGA），这是一种用于超大规模多输入多输出（XL-MIMO）系统上行链路信号恢复的新型低复杂度迭代检测器。传统迭代检测器（如近似消息传递（AMP）算法和传统信息几何算法（IGA））的每次迭代复杂度随基站天线数量线性增长，形成计算瓶颈。为克服此问题，CS-IGA在后验分布的自然参数中引入了一种新颖的交叉矩阵分裂方法。该分解实现了基于匹配滤波器的迭代检测，从而降低了每次迭代的计算复杂度。此外，我们将该框架扩展至非线性检测，通过无缝嵌入离散星座约束提出了非线性CS-IGA（NCS-IGA），实现了无需外部干扰消除环路的符号级处理。在真实信道条件下的综合仿真表明，无论是线性还是非线性检测，CS-IGA在误码率（BER）性能上均达到或超越了贝叶斯最优AMP与IGA，同时以更少的迭代次数和显著降低的计算成本实现这一目标。这些结果确立了CS-IGA作为下一代XL-MIMO系统中高吞吐量信号检测的实用且强大的解决方案。