Hierarchical Soft-Thresholding for Parameter Estimation in Beam-Space OTFS Integrated Sensing and Communication

In this work, we propose a compressed sensing framework for radar parameter estimation in an Integrated Sensing and Communication (ISAC) system employing a realistic and hardware-efficient Hybrid Digital-Analog (HDA) architecture which uses Orthogonal Time Frequency Space (OTFS) digital modulation. In such a setup, the co-located radar receiver uses multi-block measurements to perform parameter estimation. OTFS is widely considered as a robust modulation to deal with the doubly-dispersive channel in the high mobility scenarios expected in ISAC applications, however it suffers from leakage effects in the presence of fractional Doppler/delay (i.e., off-grid) shifts. By taking the inherent structure of the leakage effect into consideration and casting the multi-block measurements in a Multiple Measurement Vector (MMV) setting, we develop the Joint Hierarchical Sparsity concept based on which, we formulate a soft-thresholding iterative parameter estimation framework. This framework exploits the jointly hierarchical structure of the MMV setting for improved (radar-) parameter estimation. We provide numerical results to showcase the effectiveness of the proposed framework for parameter estimation.