A Real-Valued 2D DOA Estimation Algorithm of Noncircular Signal via Euler Transformation and Rotational Invariance Property

The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.

Low-Complexity DOA Estimation of Noncircular Signals for Coprime Sensor Arrays

This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.

WIDELY LINEAR RLS CONSTANT MODULUS ALGORITHM FOR COMPLEX-VALUED NONCIRCULAR SIGNALS

Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.

Polynomial-rooting based fourth-order MUSIC for direction-of-arrival estimation of noncircular signals

A polynomial-rooting based fourth-order cumulant algorithm is presented for direction-of-arrival（DOA） estimation of second-order fully noncircular source signals, using a uniform linear array（ULA）. This algorithm inherits all merits of its spectralsearching counterpart except for the applicability to arbitrary array geometry, while reducing considerably the computation cost.Simulation results show that the proposed algorithm outperforms the previously developed closed-form second-order noncircular ESPRIT method, in terms of processing capacity and DOA estimation accuracy, especially in the presence of spatially colored noise.

模型误差影响下基于CNN+BiLSTM神经网络的非圆信号目标直接跟踪算法

针对运动观测阵列状态误差与接收频率抖动同时影响下的非圆信号无源跟踪问题,提出了一种基于卷积神经网络(Convolutional Neural Network,CNN)+双向长短时记忆网络(Bi-directional Long Short-Term Memory,BiL⁃STM)的直接跟踪算法.该算法首先利用多运动观测阵列信号各频带间的相关性与辐射源信号的非圆特性,建立模型误差影响下的扩展多站观测矢量;接着利用多个观测时隙内扩展多站观测矢量的信号子空间构造空时特征输入序列;然后设计基于CNN与BiLSTM混合神经网络的直接跟踪模型,通过训练实现对非圆目标的轨迹矢量直接估计.本文算法是从原始数据信号子空间中估计轨迹矢量的直接跟踪模式,相比传统“观测参数估计+滤波轨迹跟踪”的两步估计模式,具有更高的估计精度.由于本文算法在神经网络训练过程中学习到模型误差的信息,因此能够实现对多种误差的校正.仿真结果表明,本文算法较传统两步跟踪算法与现有直接跟踪算法均具有更高的轨迹估计精度,能够明显提升模型误差影响下多站协同跟踪的鲁棒性.

Efficient tensor decomposition method for noncircular source in colocated coprime MIMO radar

An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing the transmitter and receiver into two sparse subarrays,noncircular property of source can be used to construct new extended received signal model for two sparse subarrays.The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero.To further exploit the multidimensional structure of the noncircular received model,we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor,respectively.Thus,the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained.Then,the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship.Specifically,the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property.Furthermore,a closed-form expression for the deterministic CRB under the NC sources scenario is also derived.Simulation results verify the superiority of the proposed estimator.

面向非圆信号的四阶累积量直接定位方法

针对现有基于四阶累积量的直接定位方法阵列孔径扩展不充分以及数据冗余等问题,提出了一种针对最大非圆率信号的四阶累积量直接定位方法。基于移动阵列在多个时隙对目标观测的定位场景,该方法构造了一系列去冗余四阶累积量矩阵。结合辐射源信号的非圆特性,利用阵列接收数据和共轭数据来构成扩展数据模型,实现了阵列孔径扩展,使等效阵元数增加,从而提升定位性能,并通过重新构造快速提取无冗余数据,大大降低矩阵运算维度。由于结合了信号的四阶累积量与非圆特性,该算法适用于信源个数大于阵元数与阵列色噪声的复杂环境。理论分析与仿真结果表明,该算法具有计算量小、高估计精度以及高分辨率等优势,并在高信噪比条件下能够达到相应克拉美罗界。

模型误差对非圆信号测向MUSIC算法性能的影响

近年来,针对非圆信号的测向算法已陆续提出,对这些算法的渐近性能及Cramer-Rao界的分析也已见报道,但仍未涉及模型误差对此类算法影响的分析.本文概括介绍了用于非圆信号测向的MUSIC(Multiple Signal Classi-fication)算法,对其空间谱函数进行一阶泰勒展开,得到了测向误差的表达式,从而求得测向均方误差统计意义上的表达式.仿真实验验证了推导的正确性,并由理论结果分析了模型误差条件下测向误差与角度间隔和非圆相位差的关系.

基于含噪复值ICA信号模型的快速不动点算法

复数快速不动点算法亦称为复数FastICA算法,是盲信号分离的一类重要算法。然而,该算法对被噪声污染的混合源的分离效果较差,尤其是在低信噪比的情况下。这主要是由于在噪声环境下,被白化过后的信号样本的相关矩阵不再是单位阵而是一个对角矩阵。该文基于复信号快速不动点算法,首先将基于含噪复值ICA信号模型的混合源投影到信号子空间,以便进行去噪和去相关处理,然后对现有的复数FastICA算法的学习规则做了修正,从而在迭代更新过程中考虑了噪声的影响,因此将显著提高复数FastICA算法的盲信号分离性能。文中给出了去噪非圆信号nc-FastICA算法的推导和步骤,仿真结果说明了该算法的有效性。

非圆信号二维DOA和初始相位联合估计方法

针对传统联合估计方法计算量大、需要多维谱峰搜索的问题,该文提出了一种基于垂直阵列结构的任意初始相位非圆信号2维DOA(Direction Of Arrival)和初相联合估计方法,利用垂直阵列特点,将3维参数估计问题转化为可并行处理的3个2维参数估计,在每一个子阵上,同时使用噪声子空间正交性和信号子空间旋转不变性,将2维参数估计进一步转化为1维估计问题,最终只需要对扩展协方差矩阵进行一次特征分解即可实现2维DOA和初相的联合估计及自动配对。该方法适用于空间信源处于过载的情形和低信噪比、短快拍环境,可估计信源数为2(M-1)。数值仿真验证了该算法的有效性。

非圆信号的四阶累积量测向新方法

针对传统基于四阶累积量的非圆信号测向方法存在阵列扩展不充分或者有数据冗余等问题,利用四阶累积量的阵列扩展特性,提出了一种阵列充分扩展且无数据冗余的非圆信号测向新方法.根据信号的非圆特性,新方法充分利用了阵列接收数据及其共轭数据来构造四阶累积量矩阵,实现了阵列的充分扩展并且使扩展后的等效阵元数进一步增加;此外,通过巧妙地利用四阶累积量矩阵的结构特征,降低了算法的计算量.理论分析和实验仿真结果表明,所提方法具有计算量小、阵列扩展能力强以及分辨率高等优良性能.

非圆信号多级维纳滤波DOA估计求根算法

针对非圆信号DOA估计的计算量问题,运用多级维纳滤波和信号子空间的多项式求根方法,提出了一种快速算法。首先利用非圆信号特性构造出扩展阵列输出矩阵,然后不需进行协方差矩阵的生成和分解,利用多级维纳滤波求出信号子空间,针对均匀线阵推导出信号子空间多项式求根方法,得出目标的DOA估计值。新算法的均方根误差性能与非圆信号求根MUSIC算法、非圆信号ESPRIT算法、非圆信号扩展传播算子算法等快速算法相仿,但是计算量小于已有的算法,特别是在阵元数较多的情况下算法的实时性优势更加明显。

修正的虚拟空间平滑算法

对虚拟空间平滑方法进行了修正,提出了一种适用于直线信号(如调幅、二进制相移键控信号等)的修正虚拟空间平滑解相干方法.该方法无需对信号初始相位作特别假定,并可在不损失阵列有效孔径和工作阵元的情况下完成信号解相干,经其预处理后的特征子空间分解信号波达方向(DOA)估计方法的性能要优于传统空间平滑方法.

用于非圆信号二维测向的扩展Root-MUSIC算法

利用双平行线阵的阵列结构,提出了用于非圆信号二维测向的扩展root-MUSIC(ERM)算法。ERM算法估计得到的俯仰角与方位角一一对应,自动配对,无需搜索,其可测向信号数大于子阵阵元数,方位测角精度优于同样基于双平行线阵的二维测向波达方向矩阵法(DOAM),俯仰测角精度在低信噪比下优于DOAM算法,俯仰角兼并时算法仍有效。

非圆信号扩展传播算子DOA估计求根算法

为有效降低非圆信号DOA估计算法的计算量,提出了一种非圆信号DOA估计快速算法。该算法运用扩展传播算子和多项式求根方法来降低计算量。首先根据非圆信号特性构造出扩展阵列输出矩阵,并生成扩展协方差矩阵,然后不需要对协方差矩阵的特征分解,使用扩展传播算子方法得到估计的扩展噪声子空间,再利用均匀线阵的多项式求根方法快速求出目标的DOA估计值。对算法的性能仿真和计算复杂度分析结果表明,提出的算法不但其均方根误差性能与NC-root-MUSIC、NC-ESPRIT、NC-MSWF-MUSIC等快速算法相似,同时提出的算法还大大减小了非圆信号DOA估计MUSIC算法的计算复杂度,而且其计算复杂度小于上述提到的快速算法,实现了非圆信号DOA估计算法的快速估计。

宽线性波束形成技术综述

在圆信号的假设条件下,传统的线性波束形成技术仅仅利用了天线阵列观测矢量的协方差矩阵。然而,现代通信领域中的很多人工调制信号具有非圆特性,观测矢量不仅存在协方差矩阵,还存在伪协方差矩阵。宽线性波束形成技术是针对非圆信号环境提出的一类新技术,该类技术通过构造一个包含天线阵列观测矢量及其共轭的扩展观测矢量,建立有利于特定方向信号接收的目标函数及约束,推导出相应的扩展权重矢量。同传统线性波束形成技术相比,宽线性波束形成技术对非圆信号的接收性能有了明显提升。本文介绍了圆信号和非圆信号定义,给出了阵列模型并介绍了最小方差无畸变响应波束形成,对各种宽线性波束形成算法进行了综述,并对宽线性波束形成技术的下一步研究方向进行了展望。

非圆传播算子DOA估计算法

传播算子方法(Propagator method,PM)是一种常用的波达方向估计算法,但传统PM算法在阵元数较小时估计精度较低。本文针对非圆信号,提出了一种非圆传播算子DOA估计算法。该算法首先对接收信号进行扩展,而后对扩展信号进行子阵划分,最后利用PM方法获得非圆传播算子。算法将信号的非圆特性与传统PM算法相结合,既具有传统PM算法无需计算协方差函数的特点,又去除了峰值搜索过程,减小了算法运算量。同时非圆特性的引入,使算法估计精度有了大幅度提高。通过计算量分析说明了算法的计算复杂度较小,并通过仿真验证了算法的有效性。

残缺电磁矢量阵列直线信号波达方向估计

该文提出了一种适用于残缺电磁矢量阵列的非圆极化-多重信号分类直线信号(如调幅、二进制相移键控信号等)波达方向估计方法,它可视为非圆-多重信号分类方法基于矢量阵列的推广,并可综合利用非圆信号的非零共轭矩信息以及极化敏感阵列的极化多样性。与传统极化-多重信号分类方法一样,该方法只需在角度参数空间进行搜索。此外,该文方法可直接推广于残缺声矢量阵列。计算机仿真结果验证了该文方法的有效性。

自适应复数信号独立分量分析算法

针对强不相关变化算法不适用于谱系数相同的非圆信号的问题,提出了一种自适应复数独立分量分析算法.利用非圆信号的二阶统计量都不为零的特点构造代价函数,在复数域中直接优化代价函数,推导出一种针对非圆信号的自适应算法.该算法不仅对谱系数相同的非圆信号有效,而且适用于任意包含有非圆信号的统计独立的信源信号,不需要计算特征向量和奇异向量,算法的结构简单.实验仿真结果验证了算法的有效性.

非圆信号与圆信号共存下的快速方位估计算法

针对非圆信号和圆信号共存时,信号的波达方向估计算法运算量较大的问题,提出了一种可同时估计非圆信号和圆信号DOA的快速算法。利用观测数据及其复共轭构造中心复共轭对称矩阵,通过双映射定理可将该矩阵转换为实矩阵;利用多级维纳滤波,无须计算阵列协方差矩阵及对其进行特征分解,仅通过对接收的实数据矩阵递推可快速求出观测数据的信号子空间;利用酉ESPRIT算法的实值性,不必谱峰搜索,在保证DOA估计精度的同时可大大降低算法的计算复杂度。仿真结果验证了算法的有效性。