Title: Pilot Signal and Channel Estimator Co-Design for Hybrid-Field XL-MIMO

Abstract: This paper addresses the intricate task of hybrid-field channel estimation in extremely large-scale MIMO (XL-MIMO) systems, critical for the progression of 6G communications. Within these systems, comprising a line-of-sight (LoS) channel component alongside far-field and near-field scattering channel components, our objective is to tackle the channel estimation challenge. We encounter two central hurdles for ensuring dependable sparse channel recovery: the design of pilot signals and channel estimators tailored for hybrid-field communications. To overcome the first challenge, we propose a method to derive optimal pilot signals, aimed at minimizing the mutual coherence of the sensing matrix within the context of compressive sensing (CS) problems. These optimal signals are derived using the alternating direction method of multipliers (ADMM), ensuring robust performance in sparse channel recovery. Additionally, leveraging the acquired optimal pilot signal, we introduce a two-stage channel estimation approach that sequentially estimates the LoS channel component and the hybrid-field scattering channel components. Simulation results attest to the superiority of our co-designed approach for pilot signal and channel estimation over conventional CS-based methods, providing more reliable sparse channel recovery in practical scenarios.