Low Complexity Detector for XL-MIMO Uplink: A Cross Splitting Based Information Geometry Approach

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.