基于二次域上中国余数的互质感知，第二部分： 推广与应用

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摘要翻译：
本文给出了二次域上基于中国剩余定理(CRT)的一类新互质阵列的实际应用。所提出的CRT阵列是由互质二次整数嵌入的理想格子构造的。本文详细讨论了该阵列的几何结构和理论基础，并重点介绍了该阵列在二维遥感中的应用。提出了一种基于两个或两个以上互质理想格的CRT阵列的推广方法，给出了传感器位置、传感器总数和可达自由度的闭式表达式。本文还讨论了任意两个二次整数的互性问题，以探索所有可能的理想格。利用网格的对称性，讨论了在保持共阵不变的情况下的传感器降阶方法，以实现经济最大化。为了将传统的基于均匀分布阵列的角度估计方法扩展到基于网格的任意共阵结构的角度估计方法，本文引入了二维空间平滑的六边形到矩形变换，为寻找更紧凑的传感器阵列提供了可能。通过实例验证了所提方法的可行性。
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英文标题：
《Coprime Sensing via Chinese Remaindering over Quadratic Fields, Part II:
  Generalizations and Applications》
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作者：
Conghui Li, Lu Gan, Cong Ling
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最新提交年份：
2019
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  The practical application of a new class of coprime arrays based on the Chinese remainder theorem (CRT) over quadratic fields is presented in this paper. The proposed CRT arrays are constructed by ideal lattices embedded from coprime quadratic integers. The geometrical constructions and theoretical foundations were discussed in the accompanying paper in great detail, while this paper focuses on aspects of the application of the proposed arrays in two-dimensional (2D) remote sensing. A generalization of CRT arrays based on two or more pairwise coprime ideal lattices is proposed with closed-form expressions on sensor locations, the total number of sensors and the achievable DOF. The issues pertaining to the coprimality of any two quadratic integers are also addressed to explore all possible ideal lattices. Exploiting the symmetry of lattices, sensor reduction methods are discussed with the coarray remaining intact for economic maximization. In order to extend conventional angle estimation techniques based on uniformly distributed arrays to the method that can exploit any coarray configurations based on lattices, this paper introduces a hexagon-to-rectangular transformation to 2D spatial smoothing, providing the possibility of finding more compact sensor arrays. Examples are provided to verify the feasibility of the proposed methods.
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PDF链接：
https://arxiv.org/pdf/1808.07511

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关键词：Applications Optimization Conventional Construction maximization arrays ideal 共阵 based 情况