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 the complex reflection coefficients of the multiple 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 Cramér-Rao bound (CRB) for estimating the 3D coordinates. This provides a performance bound for 3D near-field target localization. For the special single-target scenario, 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 multiple 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) with lower complexity, respectively. Numerical results validate the asymptotic CRB analysis and show that the consideration of exact antenna-varying channel amplitudes is essential to achieve accurate CRB and accurate localization in practice 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 different cluttered environments and significantly outperform the benchmark based on Newtonized orthogonal matching pursuit (NOMP), thus validating their effectiveness in practical implementation. Furthermore, it is shown that transmit waveforms have a significant impact on CRB and the localization performance.

中文翻译：

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通过 MIMO 雷达进行近场 3D 定位：Cramér-Rao 边界分析和估计器设计


本文研究了一种近场多输入多输出（MIMO）雷达传感系统，其中带有大型天线的收发器旨在在未知的杂乱环境中定位三维（3D）空间中的多个近场目标。我们考虑不同天线上通道相位和幅度变化的球形波前传播。在此设置下，未知参数包括多个目标的 3D 坐标和复反射系数，以及噪声和干扰协方差矩阵。首先，通过考虑一般发射信号波形，我们推导了与3D坐标相对应的Fisher信息矩阵（FIM）和目标的复反射系数，并相应地获得了用于估计3D坐标的Cramér-Rao界（CRB）。这为 3D 近场目标定位提供了性能限制。对于特殊的单目标场景，我们以解析形式获得CRB，并分析其相对于目标距离和收发器天线尺寸的渐近缩放行为。接下来，为了促进实际定位，我们提出了两种基于最大似然（ML）准则的估计器来定位多个目标，即3D近似循环优化（3D-ACO）和带有高斯白噪声的3D循环优化（3D-CO- WGN）分别具有较低的复杂性。数值结果验证了渐近 CRB 分析，并表明当目标靠近收发器时，考虑精确的天线变化信道幅度对于在实践中实现精确的 CRB 和精确定位至关重要。 它还表明，所提出的估计器在不同的杂乱环境下实现了接近派生的 CRB 的定位性能，并且显着优于基于牛顿正交匹配追踪（NOMP）的基准，从而验证了其在实际实施中的有效性。此外，结果表明发射波形对 CRB 和定位性能有显着影响。