Joint Angle-Delay Sparse Structured Compressed Sensing for ISAC Channel Estimation

In the upcoming 6G communications, radar sensing will be integrated with communication to support a wide range of application scenarios. However, in complex Integrated Sensing and Communication (ISAC) channels, radar targets and communication scatterers may overlap, leading to similar sparse distributions of the sensing and communication channels in both the angle and delay domains. Additionally, the increasing use of compressed sensing (CS) for estimating communication parameters has given rise to numerous CS algorithms based on the expectation maximization (EM) method. However, due to the unique characteristics of the channel in specific scenarios, designing the channel sparse structure has become a crucial aspect of EM-base algorithm. Therefore, there is an urgent need to develop an appropriate channel sparse structure and design a CS algorithm specifically for the ISAC scenario. In this paper, we address the problem of channel estimation in a time-division duplex multi-input multi-output ISAC system using a bi-static model. We introduce a Joint Angle-Delay Sparse Structure (JADSS) to capture the sparsity characteristics of the ISAC channel in both the angle and delay domains. Furthermore, we design a message passing estimator within the framework of an EM-based double-loop algorithm to estimate the ISAC channel. Through simulations, we demonstrate that the proposed CS algorithm utilizing JADSS achieves competitive error performance.