Near-Field Integrated Sensing and Communication with Extremely Large-Scale Antenna Array

This paper studies a near-field integrated sensing and communication (ISAC) system with extremely large-scale antenna array (ELAA), in which a base station (BS) deployed with enormous number of antennas transmits wireless signals to communicate with multiple communication users (CUs) and simultaneously uses the echo signals to localize multiple point targets in the three-dimension (3D) space. To balance the performance tradeoff between communication and target localization, we design the transmit covariance matrix at the BS to optimize the localization performance while ensuring the signal-to-interference-plus-noise ratio (SINR) constraints at individual CUs. In particular, we formulate three design problems by considering different 3D localization performance metrics, including minimizing the sum Cram\'er-Rao bound (CRB), maximizing the minimum target illumination power, and maximizing the minimum target echo signal power. Although the three design problems are non-convex in general, we obtain their global optimal solutions via the technique of semi-definite relaxation (SDR). It is shown that the three problems have low-rank solution structures depending on the sensing and communication channel matrices, helping reduce the complexity of the SDR-based solutions. Interestingly, we find that in the special case with a single collocated target/CU present towards the middle of a symmetric uniform planar array (UPA), the optimal solutions to the three problems become identical to the SINR-maximization design and have a closed form, while in other cases they can be different in general. Besides, when the target/CU moves away from the transmitter/receiver, the CRB may first decrease and then increase. These two phenomena differ from those in the far-field. Numerical results show the benefits of the proposed designs for near-field ISAC, by exploiting the beam focusing capabilities of ELAA.