Herein, an atomic norm based method for accurately estimating the location and orientation of a target from millimeter-wave multi-input-multi-output (MIMO) orthogonal frequency-division multiplexing (OFDM) signals is presented for a two-dimensional space. A novel virtual channel matrix is introduced and an algorithm to extract localization-relevant channel parameters from its atomic norm decomposition is designed. Then, based on the extended invariance principle, a weighted least squares problem is proposed to accurately recover the location and orientation using both line-of-sight and non-line-of-sight channel information. The conditions for the optimality and uniqueness of the estimate and theoretical guarantees for the estimation error are characterized for the noiseless and the noisy scenarios. Theoretical results are confirmed via simulation. Numerical results investigate the robustness of the proposed algorithm to incorrect model order selection or synchronization error, and highlight performance improvements over prior methods. The resultant performance nearly achieves the Cramér-Rao lower bound on the estimation error.

中文翻译：

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基于原子范数最小化的毫米波 MIMO OFDM 系统中的联合定位和方向估计

本文针对二维空间提出了一种基于原子范数的方法，用于从毫米波多输入多输出 (MIMO) 正交频分复用 (OFDM) 信号中准确估计目标的位置和方向。介绍了一种新的虚拟通道矩阵，并设计了一种从其原子范数分解中提取与定位相关的通道参数的算法。然后，基于扩展不变性原理，提出了一个加权最小二乘问题，以利用视距和非视距信道信息准确恢复位置和方向。针对无噪声和有噪声的场景描述了估计的最优性和唯一性的条件以及估计误差的理论保证。理论结果通过仿真得到证实。数值结果调查了所提出的算法对不正确的模型顺序选择或同步错误的鲁棒性，并突出了与先前方法相比的性能改进。由此产生的性能几乎达到了估计误差的 Cramer-Rao 下限。