ISAC Receiver Design: Joint DoA and Data Estimation in the Presence of Incomplete Signal Observations

Integrated sensing and communication (ISAC) receiver design involves the challenge of jointly estimating the communication signal together with the direction of arrivals (DOAs) of the transmitters. This letter proposes an off-the-grid estimator for the ISAC receiver that jointly estimates the DOAs of $K$ transmitters together with the communication data. We focus on the challenging case of incomplete observation, i.e., where only a subset of the received signals in space and time are available. We propose a convex optimization based on the dual of atomic norm minimization (ANM). Though the problem is non-deterministic polynomial time (NP)-hard, we leverage the Schur complement technique to develop semidefinite relaxations (SDRs) to implement it. Moreover, we study a fast algorithm based on the alternating direction method of multipliers (ADMM) technique. Finally, our numerical results explore the feasibility of the joint estimation with incomplete observations, while outperforming classical DOA estimators.