互质阵列信号处理研究进展:波达方向估计与自适应波束成形

阵列信号处理是雷达领域各类应用的核心技术之一。近年来,互质阵列的提出打破了传统方法受限于奈奎斯特采样速率这一瓶颈,其稀疏布设的阵列结构和互质欠采样的信号处理方式大幅降低了系统所需的软硬件开销,为当前不断提升的实际应用需求提供了理论基础和技术前提。鉴于其在自由度、分辨率及计算复杂度等方面的性能优势,互质阵列信号处理的理论和技术研究受到了国内外学者的广泛关注。该文分别从波达方向估计和自适应波束成形这两个阵列信号处理领域的基本问题出发,介绍了互质阵列信号处理方向的研究进展。在互质阵列波达方向估计方面,该文总结了互质子阵分解方法和虚拟阵列信号处理方法等两类典型技术路线,并以此为基础介绍了压缩感知和无网格化技术在低复杂度和超分辨估计等方面的最新研究工作。在互质阵列波束成形方面,该文剖析了其与互质阵列波达方向估计问题的区别与联系,并介绍了面向互质阵列的高效鲁棒自适应波束成形设计方法。该文旨在通过对互质阵列信号处理研究前沿的分类归纳和总结,探讨各类方法的优势和未来的研究方向,为其在雷达等领域的产业需求和实际应用提供理论和技术参考。      

Generalized Three Dimensional Coprime Array for Two-Dimensional DOA Estimation

Wireless Personal Communications - In this paper, we extend the coprime planar array to coprime cubic array and propose a three dimensional coprime array (TDCA) for two-dimensional direction of...     

基于原子范数的互质阵列协方差矩阵重构算法

针对互质阵列的虚拟阵列插值过程中协方差项的非均匀加权问题,将互质阵列协方差矩阵重构转换为低秩矩阵填充与原子范数重构,提出基于原子范数的互质阵列协方差矩阵重构算法。该算法先利用广义增广法得到非完备的互质阵列协方差矩阵,并利用截断的均值奇异值门限填充法得到虚拟阵列的协方差矩阵初值,然后对其进行原子范数最小化求解,实现稳健的正定Toeplitz协方差矩阵重构。该算法充分利用互质阵列协方差矩阵信息,有效提高互质阵列DOA估计算法的稳定性,降低计算复杂度。     

互质MIMO雷达的非圆信号降维DOA估计方法北大核心CSCD

针对传统互质阵列波达方向估计方法存在的自由度低、阵列孔径小、相位模糊等问题,提出了一种基于互质MIMO雷达的非圆信号降维波达方向(Direction of Arrival, DOA)估计方法。该方法结合了互质阵列与MIMO雷达的优点,利用非圆信号特性对阵列进行扩展,重构接收信号矩阵,然后进行降维处理,并利用噪声特征值的幂级数对噪声子空间进行修正,进一步提高算法精度。最后推导了文中方法的无相位模糊问题。仿真实验表明,文中方法能够有效避免相位模糊,大大提高自由度并扩大阵列孔径,与传统MUSIC算法以及互质阵列MUSIC算法相比,在估计成功率、DOA估计精度等方面均具有更好的性能。     

基于双向传播算子的互质面阵二维波达方向估计

针对谱峰搜索的二维波达方向估计中现有算法复杂度高,精度受搜索间隔影响较大的问题,给出了一种双向传播算子的互质面阵二维波达方向估计算法,实现了俯仰角和方位角的低复杂、高精度、无模糊联合估计.该方法首先将互质阵列引入到二维波达方向估计中,构造互质平面阵模型,然后采用两次旋转不变传播算子方法计算出不同阵列流型方向上的旋转因子矩阵,根据旋转因子矩阵解算出目标信号的俯仰角和方位角,同时利用互质理论消除了稀疏阵列角度估计的不确定性,证明了互质阵列模型下采用双向传播算子方法进行俯仰角和方位角估计的无模糊性.对算法的复杂度进行理论分析,并给出了平面阵列角度估计的克拉美罗界推导.理论分析与仿真结果表明,算法不需要进行角度匹配和谱峰搜索,在相同条件下的均方根误差性能优于均匀平面阵的多重信号分类算法,并且以较低的复杂度无模糊的达到了高维网格搜索的精度.     

基于稀疏互质电磁矢量阵列的MUSIC算法

为增加传统MUSIC算法可分辨的信号源数,该文构造了一对具有互质关系的2维稀疏电磁矢量阵列,并基于此阵列提出了一种基于3维平滑的MUSIC算法。该算法利用两个阵列间的互质关系形成具有更多自由度的互质差合成阵列,并基于3维(2维空域加极化域)平滑算法恢复其自相关矩阵的秩,达到应用于传统MUSIC算法的目的。该算法的最大优势是仅使用二阶统计量即可系统地增加了原阵列的自由度。计算机仿真结果表明所提算法能估计多于物理阵元数的信号且分辨率高。     

基于互质阵列雷达技术的近距离目标探测方法(英文)

一组(M, N)互质阵列由两组结构化排列的子阵列构成:一组包括M个天线单元, 另一组包括N个天线单元。互质阵列稀疏天线仅需要M+N1个收发天线单元就可实现对O(MN)个远距离目标的识别。在相同分辨条件下, 互质阵列雷达技术可利用更少的收发单元来识别更多的雷达目标。因此互质阵列雷达技术能够极大地降低传统雷达收发系统的复杂度。但是, 现有文献中所讨论的互质阵列雷达技术均基于远场近似假设, 当探测近距离目标时, 会由于目标邻近天线单元而产生严重的探测误差。为了解决上述问题, 该文将标准的互质阵列雷达技术的适用范围扩展到用于解决近距离目标探测。该文论证了(M, N)互质阵列雷达技术能够以4k0/MN空域分辨率恢复[2k0, 2k0]空域范围内的目标信息, 其中k0表示自由空间波数, 是场景因子。由此可见(M, N)互质阵列能够以/4的方位向分辨率获得O(MN)个近距离目标方位向位置信息。该文进一步论证了互质阵列雷达技术在穿墙成像中的适用性。最后, 该文提供了一组数值仿真实验结果, 验证了互质阵列雷达技术对于近距离目标探测的有效性。      

Blind signal separation for coprime planar arrays: An improved coupled trilinear decomposition method

In this study, the problem of blind signal separation for coprime planar arrays is investigated. For coprime planar arrays comprising two uniform rectangular subarrays, we link the signal separation to the tensor-based model called coupled canonical polyadic decomposition (CPD) and propose an improved coupled trilinear decomposition approach. The output data of coprime planar arrays are modeled as a coupled tensor set that can be further interpreted as a coupled CPD model, allowing a signal separation to be achieved using coupled trilinear alternating least squares (TALS). Furthermore, in the procedure of the coupled TALS, a Vandermonde structure enforcing approach is explicitly applied, which is shown to ensure fast convergence. The results of Monto Carlo simulations show that our proposed algorithm has the same separation accuracy as the basic coupled TALS but with a faster convergence speed.     

On the linear complexity of functions of periodic GF(q)sequences

It is proved that the product of arbitrary periodic GF(q) sequences attains maximum linear complexity if their periods are pairwise coprime. The necessary and sufficient conditions are derived for maximum linear complexity of the product of two periodic GF(q ) sequences with irreducible minimal characteristic polynomials. For a linear combination of products of arbitrary periodic GF(q) sequences, it is shown that maximum linear complexity is achieved if their periods are pairwise coprime and the polynomial x -1 does not divide any of their minimal characteristic polynomials; assuming only that their periods are pairwise coprime, the author establishes a lower bound on the linear complexity which is of the same order of magnitude as maximum linear complexity. Boolean functions are derived that are optimal with respect to the maximum linear complexity. Possible applications of the results in the design of sequence generators are discussed     

互质阵中基于降维求根的波达角估计算法

该文提出互质阵中基于降维求根的波达角(DOA)估计算法。互质阵包含两个稀疏均匀线性子阵,拥有互质的阵元间距和阵元数目。该算法基于子阵间的互协方差,利用较长子阵中的旋转不变性扩展较短子阵的虚拟孔径。然后通过矩阵分块构造噪声子空间,并将来自两个子阵的2维参数估计问题降维为1维求根问题,获得自动配对的2维模糊参数估计。最后由这2维模糊参数可恢复出两组参数,根据互质性从两组参数估计的交集中可以获得无模糊的高分辨率DOA估计。相比互质阵中的联合多重信号分类(MUSIC)算法和联合旋转不变技术(ESPRIT)算法,该算法无需特征分解,复杂度低,但可获得更精确的DOA估计,处理更多的信源,并且对色噪声有更强的鲁棒性。多个仿真结果均验证了所提算法的有效性。     

一种高效的延迟容忍移动传感器网络异步探测机制

针对延迟容忍移动传感器网络(Delay Tolerant Mobility Sensor Network, DTMSN)节点间连接探测开销大、错失率高的问题,该文提出一种高效的DTMSN异步探测机制(Efficient Asynchronous Probing Scheme, EAPS)。该机制面向随机路点(Random Way-Point, RWP)移动模型,在采用互质周期对的时隙睡眠机制基础上,通过对节点运动区域的合理划分和周期对的优化选择,保证了网络连接探测的高成功率和低能耗的特性。仿真结果表明,与现有的异步探测机制相比,该机制能够在低能耗下实现更高的探测成功率与更低的探测延迟。     

Computationally efficient DOA estimation for coprime linear array: a successive signal subspace fitting algorithm

ABSTRACT

In this paper, direction of arrival (DOA) estimation of multiple signals with coprime array is investigated and signal subspace fitting (SSF) method is linked to the coprime array, which achieves a better DOA estimation performance than the traditional uniform array. While the SSF method requires expensive computational cost in the case of multiple signals due to the multidimensional global angular searching, we propose a successive SSF (S-SSF) algorithm from a computationally efficient perspective. In the proposed algorithm, we employ rotational invariance and coprime property to obtain the initial estimates. Then, via a successive scheme, we transform the traditional multidimensional global angular searching problem into one-dimensional partial angular searching one. Consequently, the computational complexity has been significantly reduced. Specifically, the proposed S-SSF algorithm can obtain almost the same DOA estimation performance as SSF but with remarkably lower complexity. Finally, Cramer-Rao Bound (CRB) is provided and numerical simulations demonstrate the effectiveness of the proposed algorithm.     

On construction of coprime factorizations for nonlinear feedback control systems

In this paper we describe a family of operators for constructing nontrivial left and right coprime factorizations under rather weak conditions for a large class of nonlinear feedback control systems that has a stabilizable or unstabilizable plant, using a common criterion of input-output stability. The proposed sufficiency and construction method are based on a generalization of the nonlinear Lipschitz operator theory formulated by us for such systems. This class of generalized nonlinear Lipschitz operators constitutes a very large family (an infinite-dimensional Banach space) of bounded nonlinear operators that describe (part of) the underlying systems. One of the main difficulties in constructing coprine factorizations for nonlinear feedback systems has been in taking care of the nonlinear composite and inverse operators that appear in the closed-loop configuration such that the overall feedback system is well defined in the sense of stability, causality, and uniqueness of the internal signals and such that the coprime factorizations can be achieved. In this paper we show how these difficult issues can be handled nicely under our framework of generalized nonlinear Lipschitz operator theory, at least for a very large class of nonlinear control systems. We give a simple illustrative example to show how these coprime factorizations can actually be characterized and constructed to yield explicit closed-form solutions.This work was supported in part by ONR Contract No. N00014-88-K-0127.     

Unfolded coprime bistatic MIMO radar for joint DOD and DOA estimation: from viewpoint on aperture augment for sum coarray

Generally, the coprime linear array (CLA) consisting of two interleaved uniform linear subarrays can enlarge the array aperture to attain the better angle estimation performance compared with the uniform linear array (ULA). In this paper, we ulteriorly study the virtual sum coarray of the unfolded coprime (UC) bistatic multiple-input multiple-output (MIMO) radar whose transmitter and receiver array are both unfolded CLA from the viewpoint on the geometry and array aperture. The UC MIMO radar can be exploited to obtain the better joint direction of departure (DOD) and direction of arrival (DOA) estimation performance due to the larger array aperture. Furthermore, we propose an all sum coarray multiple signals classification (ASCA-MUSIC) algorithm for the UC MIMO radar. ASCA-MUSIC can fully exploit all the degrees of freedom (DOFs) in the sum coarray and can obtain the better estimation performance. We also prove that ASCA-MUSIC can avoid the phase ambiguity problem due to the coprime property. In addition, we devise a reduced complexity scheme for ASCA-MUSIC to reduce the high computational complexity and utilize Cramer–Rao Bound (CRB) as a benchmark for the lower bound on the root-mean-square error (RMSE) of unbiased angle estimation. Finally, the numerical simulations verify the effectiveness and superiority of the UC MIMO radar, ASCA-MUSIC and the reduced complexity scheme.     

Two-dimensional DOA estimation for generalized coprime planar arrays: a fast-convergence trilinear decomposition approach

Multidimensional Systems and Signal Processing - In this paper, we investigate the problem of two-dimensional (2D) direction of arrival (DOA) estimation of multiple signals for generalized coprime...     

基于互质阵列孔洞分析的稀疏阵列设计方法

针对互质阵列产生连续延迟较少且冗余度高的问题,该文提出了两种基于互质阵列的稀疏设计方法.首先,通过分析阵元位置对互质阵列差分共阵总延迟和连续延迟影响,得出互质阵列在去掉特定阵元后,将不改变连续延迟拓扑.然后,优化传感器阵列布局,在保持整个阵列的阵元数不变的条件下,增加阵列连续延迟数量.其后,分别推得了两种提出阵列设计方...     

An H<Superscript>∞</Superscript> Output Feedback Control for Discrete-Time State-Delayed Systems

A coprime factorization approach to H controller design for discrete-time state-delayed systems is developed. The coprime factors that are generated by the present factorization possess the same delayed state as that of the original system. This property, together with the well-known Youla parameterization and the chain-scattering matrix setting, provides a relatively simple method for obtaining a family of internally stabilizing H output feedback controllers. A numerical example is given to demonstrate the validity and applicability of the proposed approach.     

基于互质阵列的运动单站信号直接定位方法

信号直接定位方法是一种新型无源定位体制,具有适应低信噪比、无需参数关联等优势。为适应复杂电磁环境,该文提出了一种基于互质阵列的运动单站信号直接定位方法。以典型窄带信号为例,该文首先构建了互质阵列截获信号模型,然后推导了其差分共性阵对应的等效信号数学模型,最后使用空间谱技术构建了直接定位代价函数,实现了定位。经仿真分析验证,采用相同互质阵列时,该方法在分辨率和精度稍有损失的情况下可大幅提升传统直接定位方法的自由度,且与基于均匀线阵的直接定位方法相比,该方法在自由度、分辨率和定位精度等方面都具有优势。      

Single-shot dense depth sensing with frequency-division multiplexing fringe projection

In structured light illumination (SLI) systems, multi-shot fringe patterns can reach higher precision than a single-shot fringe pattern. However, multi-shot methods are not suitable for dynamic scenes while single-shot ones are limited in the measurement accuracy. In this paper, a novel single-shot depth sensing method with frequency-division multiplexing (FDM) framework is proposed. To achieve a simultaneous casting, two fringe patterns with coprime periods are modulated into a single pattern. The method of fringe pattern extraction is similar to the demodulation in communication systems. The Gabor filter is adopted to get the phase information in the pattern, and the coprime theorem is used to solve the phase ambiguity. Quantitative and qualitative evaluations have proved that our method achieves higher accuracy in depth sensing compared with the Kinect v1 and ToF camera. In addition, benefiting from the single-shot pattern, our method is suitable for dynamic scenes.     

High performance ultra-low speed servo system based on doubly coprime factorization and instantaneous speed observer

This paper proposes a new speed servo system for a wide speed range based on doubly coprime factorization and instantaneous speed observer. The proposed speed controller is a new two-degrees-of-freedom speed servo system considering the robust stability according to inertia variation, which is designed on the basis of doubly coprime factorization and disturbance observer. In an ultra-low speed range, a speed sensor based on a rotary encoder cannot detect a motor speed. In this paper, a speed information in a very low speed range is estimated by the proposed instantaneous speed observer which mounts the parameter identification algorithm to cancel out the estimation error caused by parameter variation. Therefore, the two-degrees-of-freedom speed servo system connecting the instantaneous speed observer regulates a motor speed robustly in a wide speed range including an ultra-low speed range, and it keeps the desired speed response for all speed reference including an ultra-low speed range.