This paper studies a near-field multiple-input multiple-output (MIMO) radar sensing system, in which the transceivers with massive antennas aim to localize multiple near-field targets in the three-dimensional (3D) space over unknown cluttered environments. We consider a spherical wavefront propagation with both channel phase and amplitude variations over different antennas. Under this setup, the unknown parameters include the 3D coordinates and complex reflection coefficients of the targets, as well as the noise and interference covariance matrix. First, by considering general transmit signal waveforms, we derive the Fisher information matrix (FIM) corresponding to the 3D coordinates and the complex reflection coefficients of the targets and accordingly obtain the Cram\'er-Rao bound (CRB) for the 3D coordinates. This provides a performance bound for 3D near-field target localization. For the special single-target case, we obtain the CRB in an analytical form, and analyze its asymptotic scaling behaviors with respect to the target distance and antenna size of the transceiver. Next, to facilitate practical localization, we propose two estimators to localize targets based on the maximum likelihood (ML) criterion, namely the 3D approximate cyclic optimization (3D-ACO) and the 3D cyclic optimization with white Gaussian noise (3D-CO-WGN), respectively. Numerical results validate the asymptotic CRB analysis and show that the consideration of varying channel amplitudes is vital to achieve accurate CRB and localization when the targets are close to the transceivers. It is also shown that the proposed estimators achieve localization performance close to the derived CRB under various cluttered environments, thus validating their effectiveness in practical implementation. Furthermore, it is shown that transmit waveforms have a significant impact on CRB and the localization performance.

翻译：本文研究近场多输入多输出(MIMO)雷达感知系统，其中配置大规模天线的收发设备旨在未知杂波环境下对多个近场目标进行三维空间定位。考虑球面波前传播机制，不同天线间的信道相位与幅度均存在变化。在此设定下，未知参数包括目标的三维坐标和复反射系数，以及噪声与干扰的协方差矩阵。首先，通过考虑通用的发射信号波形，我们推导了与目标三维坐标和复反射系数对应的费舍尔信息矩阵，并据此获得三维坐标的克拉美-罗界，这为三维近场目标定位提供了性能边界。针对单目标特殊情形，我们以解析形式推导了克拉美-罗界，并分析了其相对于目标距离及收发天线尺寸的渐近标度行为。其次，为促进实际定位，我们基于最大似然准则提出了两种目标定位估计器，即三维近似循环优化算法与三维白高斯噪声循环优化算法。数值结果验证了渐近克拉美-罗界分析的正确性，并表明当目标靠近收发设备时，考虑信道幅度变化对获得精确的克拉美-罗界与定位性能至关重要。同时，所提估计器在各种杂波环境下均能达到接近推导的克拉美-罗界的定位性能，验证了其在实际部署中的有效性。此外，研究还表明发射波形对克拉美-罗界及定位性能具有显著影响。