引入参考信号的新峭度快速不动点算法

在盲源分离和独立成分分析中,峭度是衡量随机信号非高斯性的常用对比准则,通过不同类型的算法对其进行优化,找到非高斯性极大值点,即实现了源信号的提取或分离。例如,基于峭度的快速不动点算法,它是一种收敛速度很快的算法。最近,Marc Castella等人提出了一类基于所谓“参考信号”的对比准则,以及对应的梯度最大化优化算法,这些算法具有很好的收敛性能。受其启发,文章以一种类似的方式将“参考信号”思想应用到峭度中,得到一种新颖的对比函数,并基于该新峭度对比函数,提出了一种新的快速不动点算法。与经典的基于峭度的快速不动点算法相比,该算法极大地提高了收敛速度,尤其是随着信号样值点数的增加,该算法的优势会更加明显。文章分析和证明了该新峭度对比函数的局部收敛性,给出了新算法的详细推导过程,仿真实验验证了该算法的性能,并与经典算法进行了比较分析。      

基于四阶累积量的非圆信号测向方法

对通信系统中大量使用的BPSK等非圆信号测向,可以采用共轭扩展MUSIC(CE-MUSIC)算法,也可以采用基于四阶累积量的MUSIC-like算法。CE-MUSIC算法没有利用高阶信息,MUSIC-like算法没有利用信号的非圆信息,性能均受限。该文提出的四阶扩展MUSIC(FO-EMUSIC)算法利用了非圆信号在四阶累积量中的信息,分辨力和测角精度明显优于MUSIC-like算法,略优于CE-MUSIC算法,可测向阵元数大于CE-MUSIC算法和MUSIC-like算法。针对均布线阵,为减小计算量,还提出了FO-EMUSIC/ULA算法。仿真实验验证了FO-EMUSIC算法的优良性能。     

DOA estimation of noncircular signals for coprime linear array via locally reduced-dimensional Capon

We investigate the issue of direction of arrival (DOA) estimation of noncircular signals for coprime linear array (CLA). The noncircular property enhances the degree of freedom and improves angle estimation performance, but it leads to a more complex angle ambiguity problem. To eliminate ambiguity, we theoretically prove that the actual DOAs of noncircular signals can be uniquely estimated by finding the coincide results from the two decomposed subarrays based on the coprimeness. We propose a locally reduced-dimensional (RD) Capon algorithm for DOA estimation of noncircular signals for CLA. The RD processing is used in the proposed algorithm to avoid two dimensional (2D) spectral peak search, and coprimeness is employed to avoid the global spectral peak search. The proposed algorithm requires one-dimensional locally spectral peak search, and it has very low computational complexity. Furthermore, the proposed algorithm needs no prior knowledge of the number of sources. We also derive the Crámer-Rao bound of DOA estimation of noncircular signals in CLA. Numerical simulation results demonstrate the effectiveness and superiority of the algorithm.     

共形阵列非圆信号波达方向估计算法

受共形载体变曲率结构的影响,各天线单元指向不尽相同,使得共形天线阵列呈现极化多样性。因此,共形天线阵列的建模过程中需考虑不同阵元的极化响应特性。基于柱面共形天线阵列的快拍数据模型,利用非圆信号的特性对阵列输出进行扩展,基于秩亏理论和子空间原理实现信号波达方向（DOA）估计,所提方法估计精度高,不需要参数配对。存在相干信源时,提出对扩展后的虚拟阵列进行划分,对划分出的子阵进行虚拟的空间平滑,实现解相干的预处理操作。仿真结果表明该方法能有效应用于柱面共形阵列非圆信号DOA估计,并提高了空间分辨率。      

基于对称旋转不变性的非圆相干分布源直接定位算法

针对现有相干分布源直接定位方法中存在的依赖分布模型、计算复杂等问题,该文提出一种基于非圆信号特征的对称旋转不变直接定位算法。该方法首先根据分布源参数化假设建立基于数据域信息的直接位置估计模型,并利用非圆信号特征扩展接收信号的协方差矩阵。然后针对中心对称阵列,证明了相干分布源的确定性角信号分布函数矢量具有对称特性,基于这一特征建立了扩展方向矢量的旋转不变关系;构造了融合多个观测站信息的目标函数,直接估计目标位置,避免了对分布模型的依赖,且降低了待估计参数维度。仿真结果表明,与现有相干分布源定位算法相比,所提算法提高了分布源位置估计精度和效率,避免了对分布模型的依赖,更具实用价值。     

An auto-calibration method for spatially and temporally correlated noncircular sources in unknown noise fields

Angularly dependent gain and phase uncertainties are produced by the combined effects of multiple sensor errors. This paper proposes a direction-finding method for noncircular signals in the presence of angularly dependent gain/phase errors, which utilizes instrumental sensors to achieve auto-calibration and relies on an improved alternating projection procedure. By applying the principle of the extended 2-sided instrumental variable signal subspace fitting algorithm, the proposed method is effective for separating spatially and temporally correlated noncircular sources from the unknown colored (i.e., spatially correlated) noise. Considering that modeling errors of instrumental sensors are frequently encountered in practice, this paper also presents a theoretical derivation for the closed-form expression of the mean square error of the estimation under the influence of modeling errors of instrumental sensors in the first-order analysis. Finally, the results of two series of simulations are demonstrated. The first series of simulations verifies the effectiveness of the proposed auto-calibration method, and shows that noncircularity and temporal correlation of sources are informative for enhancing the calibration performance of our method. The results also prove that the proposed method performs better than the instrumental sensor method when applied to spatially and temporally correlated noncircular sources. Moreover, this performance advantage of our method is more prominent when signal-to-noise ratio is low, or in spatially correlated noise fields. The second series of simulations validates the theoretical prediction, and thus our statistical analysis has a high predictive value for calibration performance of the proposed method under the influence of modeling errors.     

采用方向域滤波的非圆信号测向方法

针对实际应用中多个非圆信号从某一先验已知角度范围内入射的情况,提出了一种采用方向域滤波的非圆信号测向算法。新算法首先利用非圆信号测向MUSIC(NC-MUISC)算法得到入射信号的空间谱,再利用信号先验入射角度范围将其空间谱函数在方向域进行滤波,得到虚拟扩展协方差矩阵,然后仿照NC-MUISC算法求得信号入射方向。仿真结果表明,新算法保持了NC-MUISC算法的阵列扩展能力,同时在分辨力和测向精度方面进一步提高,且先验角度范围越准确则算法性能越好,具有良好的实用价值。      

Efficient Variant of Noncircular Complex FastICA Algorithm for the Blind Source Separation of Digital Communication Signals

In this paper, an improved version of the noncircular complex FastICA (nc-FastICA) algorithm is proposed for the separation of digital communication signals. Compared with the original nc-FastICA algorithm, the proposed algorithm is asymptotically efficient for digital communication signals, i.e., its estimation error can be made much smaller by adaptively choosing the approximate optimal nonlinear function. Thus, the proposed algorithm can have a significantly improved performance for the separation of digital communication signals. Simulations confirm the efficiency of the proposed algorithm.     

基于非圆信号波达方向估计的最大似然算法

现有的非圆信号波达方向(DOA)估计算法基本都是子空间分解类的,如NC-MUSIC、NC-ESPRIT算法等。基于子空间拟合类的非圆信号DOA估计算法研究的不多。文中依据非圆信号的DOA估计数学模型,提出了基于非圆信号的DOA估计最大似然算法。通过计算机仿真,将基于非圆信号的最大似然算法与常规最大似然算法及基于非圆信号的MUSIC算法进行了性能比较。结果表明,该算法提高了方位估计的估计性能,对于估计精度要求很高、用户比较密集的场合,能发挥很大的作用。     

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 equali- zation performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.     

非圆信号方位、俯仰及初相联合估计

该文利用双平行线阵的阵列结构,提出了用于非圆信号二维方向和初相联合估计的扩展MUSIC(EN-MUSIC)算法。EN-MUSIC算法估计得到的方位角、俯仰角与初相一一对应,自动配对,其可测向信号数大于子阵阵元数,方位及俯仰测角精度与非圆信号二维测向酉ESPRIT(2D-NC-UESPRIT)算法大致相当,优于波达方向矩阵法(DOAM)。     

基于扩展传播算子的非圆信号测向方法

现代通信系统大量使用非圆信号,利用经典高分辨算法对其测向没有充分利用非圆信号的信息,因而性能受限.本文提出的扩展传播算子测向算法(EPM)先对数据进行共轭扩展,再利用传播算子方法(PM)测向,充分利用了非圆信号的特点,从而可对多于阵元数的信号进行测向,分辨力和测角精度优于OPM(正交传播算子测向算法)和MUSIC算法,同时保持了PM算法的特点,不需要特征分解(ED)或奇异值分解(SVD).文中还分析了EPM算法的均方误差性能和计算复杂度,得到了均方误差的解析表达式.仿真实验验证了EPM算法的优良性能,均方误差的理论结果与仿真值相符.     

Time-difference-of-arrival estimation for noncircular signals using information theory

This paper addresses the time-difference-of-arrival (TDOA) estimation problem for a noncircular source, which is usually encountered in the context of radio communications. To exploit the second-order statistics (SOS) noncircularity of such signals, an information-theoretical measure is employed in designing the new TDOA estimator. While the classical cross-correlation (CC) method uses only the correlation measure of a source, the proposed method simultaneously uses both the correlation and conjugate correlation measures of a source. Since the SOS of a noncircular signal is not only determined by the correlation function but also by the conjugate correlation function, the proposed method utilizes the SOS information of a noncircular signal more comprehensively than the popular CC method. Simulation results demonstrated the effectiveness of the new algorithm compared to the CC algorithm.     

一种自动匹配的分布式非圆信号二维DOA快速估计方法

在相干分布式非圆信号2维波达方向(DOA)估计中,针对利用非圆特性后维数扩展带来的较大复杂度问题,且现有的低复杂度算法均需要额外的参数匹配,该文提出一种基于互相关传播算子的自动匹配2维DOA快速估计算法。该算法考虑L型阵列,在建立相干分布式非圆信号扩展阵列模型的基础上,首先证明了L阵中两个子阵的广义方向矢量(GSV)均具有近似旋转不变特性,然后通过阵列输出信号的互相关运算消除了额外噪声,最终利用子阵GSV的近似旋转不变关系通过传播算子方法得到中心方位角与俯仰角估计。理论分析和仿真实验表明,所提算法无须谱峰搜索和协方差矩阵特征分解运算,具有较低的计算复杂度,并且能够实现2维DOA估计的自动匹配;同时,相比于现有的相干分布式非圆信号传播算子算法,所提算法以较小的复杂度代价获得了性能的较大提升。     

基于实值传播算子的非圆信号DOA估计求根算法

为有效降低非圆信号DOA(direction of arrival)估计算法的计算量,本文提出一种非圆信号DOA估计快速算法,借助实值扩展传播算子和多项式求根方法来降低计算量。首先利用信号非圆特性构造出实值的扩展阵列输出矩阵及扩展协方差矩阵,然后使用扩展传播算子方法代替扩展协方差矩阵的特征分解得到噪声子空间,再利用均匀线阵的多项式求根方法获得目标的DOA估计值。对算法的性能仿真和计算复杂度分析表明,新算法的均方根误差性能与Euler-root-MUSIC、NC-root-MUSIC等快速算法相近,但其计算复杂度小于上述非圆信号DOA估计快速算法。优良的性能和较低的计算量使新算法具有良好的实用价值。      

基于偶数阶累积量的非圆信号测向方法

提出了基于2q阶累积量的非圆信号测向MUSIC(Multiple Signal Classification)算法(称为NC-2q-MUSIC),作为2q-MUSIC算法利用非圆信息的一种扩展,在可测向信号数、分辨力和测角精度等方面的性能均优于2q-MUSIC算法.并且,q越大,NC-2q-MUSIC算法的可测向信号数越大,分辨力越高,对模型误差也越不敏感.针对均布线阵(ULA:Uniform Linear Array)提出的NC-2q-MUSIC/ULA算法减小了计算量.仿真实验验证了NC-2q-MUSIC算法的优良性能.     

基于非圆信号的MUSIC算法性能研究

传统DOA估计算法不能处理多于阵元数的信号源,而且估计精度也不能满足一些高估计精度的场合,近年来基于非圆信号的DOA估计算法由于其优良的估计性能,受到越来越多的关注。依据非圆信号的DOA估计数学模型,研究了基于非圆信号的MUSIC算法。通过软件仿真,将基于非圆信号的MUSIC算法的各项性能进行了仿真。结果表明,该算法的估计性能比传统MUSIC算法有了明显的提高。     

Direct tracking of noncircular sources for multiple arrays via improved unscented particle filter method

Direct tracking problem of moving noncircular sources for multiple arrays is investigated in this study. Here, we propose an improved unscented particle filter (I-UPF) direct tracking method, which combines system proportional symmetry unscented particle filter and Markov Chain Monte Carlo (MCMC) algorithm. Noncircular sources can extend the dimension of sources matrix, and the direct tracking accuracy is improved. This method uses multiple arrays to receive sources. Firstly, set up a direct tracking model through consecutive time and Doppler information. Subsequently, based on the improved unscented particle filter algorithm, the proposed tracking model is to improve the direct tracking accuracy and reduce computational complexity. Simulation results show that the proposed improved unscented particle filter algorithm for noncircular sources has enhanced tracking accuracy than Markov Chain Monte Carlo unscented particle filter algorithm, Markov Chain Monte Carlo extended Kalman particle filter, and two-step tracking method.     

2D-DOA estimation of noncircular signals for uniform rectangular array via NC-PARAFAC method

In this paper, we propose a two-dimensional direction of arrival (2D-DOA) estimation algorithm for uniform rectangular array via noncircular-parallel factor (NC-PARAFAC) method. Compared to the conventional parallel factor (PARAFAC) algorithm, the proposed algorithm exploits the property of noncircular signals to double the array aperture. Therefore, the angle estimation performance of the proposed algorithm is better than the conventional PARAFAC method. The proposed algorithm achieves automatically paired two-dimensional angle estimates, and has better 2D-DOA estimation performance than some conventional algorithms, which include estimation of signal parameters via rotational invariance technique (ESPRIT), propagator method (PM), PARAFAC algorithm, noncircular-ESPRIT (NC-ESPRIT) and noncircular-PM (NC-PM). We also derive the Cramér–Rao bound for the 2D-DOA estimation of noncircular signals with uniform rectangular array. Simulation results verify the effectiveness and improvement of the proposed algorithm.     

基于互相关抽样分解的分布式非圆信号DOA快速估计

在非相干分布式非圆信号波达方向(DOA)估计中,针对利用信号非圆特性后输出矩阵维数扩展带来的较大运算量问题,该文提出一种基于互相关抽样分解的DOA快速估计算法。该算法仅需要从子阵间的扩展互相关矩阵中抽样出少量行元素和列元素,构成两个低维子矩阵,进而通过低秩近似分解便可快速地同时求出左右奇异矢量,即分别对应两个子阵的信号子空间,避免了计算整个互相关矩阵及其奇异值分解运算;最后利用两个子阵信号子空间的旋转不变性通过最小二乘得到DOA估计。仿真分析表明,当行列抽样数大于信源数的两倍时,所提算法与直接基于互相关矩阵奇异值分解的非相干分布式非圆信号DOA估计算法性能相近,但复杂度得到了大幅度降低;而相比于传统的低复杂度非相干分布源DOA估计算法,所提算法利用信号非圆特性具有更高的估计性能。