Channel Estimation for Wideband XL-MIMO: A Constrained Deep Unrolling Approach

Extremely large-scale multiple-input multiple-output (XL-MIMO) enables the formation of narrow beams, effectively mitigating path loss in high-frequency communications. This capability makes the integration of wideband high-frequency communications and XL-MIMO a key enabler for future 6G networks. Realizing the full potential of such wideband XL-MIMO systems depends critically on acquiring accurate channel state information. However, channel estimation is significantly challenging due to inherent wideband XL-MIMO channel characteristics, including near-field propagation, beam split, and spatial non-stationarity. To effectively capture these channel characteristics, we formulate channel estimation as a maximum a posteriori problem, which facilitates the use of prior channel knowledge. We then propose an unrolled proximal gradient descent algorithm with learnable step sizes, which employs a dedicated neural network for proximal mapping. This design empowers the proposed algorithm to implicitly learn prior channel knowledge directly from data, thereby eliminating the need for explicit regularization functions. To improve the convergence, we introduce a monotonic descent constraint on the layer-wise estimation error and provide theoretical analyses to characterize the algorithm's convergence behavior. Simulation results show that the proposed unrolling-based algorithm outperforms the traditional and deep learning-based methods.