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 a very large 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 near-field communication and 3D 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 Cramér-Rao bound (CRB) for estimating 3D locations, 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) by proving the tightness of such relaxations. It is rigorously shown that the optimal solutions to the three problems have low-rank structures depending on the sensing and communication channel matrices, which can be exploited to greatly reduce the computational 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 scenario. Numerical results show the benefits of the proposed near-field designs in optimizing both sensing and communication performance, by exploiting the beam focusing capabilities of ELAA, while the benchmark based on far-field design yields inferior results due to model mismatch.