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

This paper addresses the intricate task of hybrid-field channel estimation inextremely large-scale MIMO (XL-MIMO) systems, critical for the progression of6G communications. Within these systems, comprising a line-of-sight (LoS)channel component alongside far-field and near-field scattering channelcomponents, our objective is to tackle the channel estimation challenge. Weencounter two central hurdles for ensuring dependable sparse channel recovery:the design of pilot signals and channel estimators tailored for hybrid-fieldcommunications. To overcome the first challenge, we propose a method to deriveoptimal pilot signals, aimed at minimizing the mutual coherence of the sensingmatrix within the context of compressive sensing (CS) problems. These optimalsignals 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 channelestimation approach that sequentially estimates the LoS channel component andthe hybrid-field scattering channel components. Simulation results attest tothe superiority of our co-designed approach for pilot signal and channelestimation over conventional CS-based methods, providing more reliable sparsechannel recovery in practical scenarios.