Joint subcarrier two-stage compressed sensing with off-grid localization for 6G XL-MIMO systems

6G systems aim to support ultra-high data rates, low latency, and centimeter-level positioning to meet the demands of future intelligent networks. As a key enabler, XL-MIMO holds great promise due to its ability to enhance spectral efficiency and spatial resolution. However, in near-field scenarios, conventional far-field assumptions fail due to spherical wavefronts, leading to angular sparsity degradation and parameter coupling, which pose challenges to accurate channel estimation and localization. To tackle these issues, we propose a joint subcarrier two-stage compressed sensing algorithm with off-grid localization for 6G XL-MIMO systems. By exploiting the inherent polar-domain channel characteristics of XL-MIMO, we construct a polar-domain dictionary for initial sparse channel estimation, and then construct a joint subcarriers model. By analyzing the cross-subcarrier phase rotation induced by the delay taps, the proposed method overcomes the limitations of distance sampling sparsity, enabling high-precision parameter estimation of multipath propagation delays. Based on this, a gradient descent-based off-grid optimization algorithm is proposed, jointly optimizing the path gain, angle and distance parameters, significantly reducing the grid error and achieving precise positioning. Simulation results demonstrate that the proposed method significantly outperforms existing algorithms in both channel estimation accuracy and localization performance, achieving sub-meter-level distance precision in near-field scenarios.