Joint Sparse Bayesian Learning for Channel Estimation in ISAC

In this letter, we investigate channel estimation in integrated sensing and communication and propose a joint sparse Bayesian learning (JSBL) algorithm for the estimation of sensing and communication (S&C) channels. To capture the joint sparsity between S&C channels arising from the commonalities between the sensing targets and communication scatterers, we conceive an adaptive pattern-coupled prior for S&C channel coefficients, which allows us to formulate the joint S&C channel estimation as a maximum a posteriori (MAP) problem. Then, a tailored expectation-maximization (EM) method including an E-step and an M-step is developed to solve the MAP problem. Specifically, in the E-step, we derive the sparse Bayesian estimates for S&C channels, while in the M-step, we dynamically update the off-grid channel angles and prior parameters. Simulation results demonstrate that the proposed JSBL algorithm can achieve improved S&C channel estimation performance over existing methods due to the exploitation of the joint sparsity between S&C channels.