基于MIMO技术的二维波达方向估计

传统的L型阵相比面阵精简了阵列结构,以较少的阵元实现二维波达方向估计,但是波达方向估计性能受到物理孔径限制。本文将MIMO技术和L型阵结合,提出一种基于MIMO技术的L型阵二维波达方向估计方法。该方法通过MIMO等效虚拟阵列原理,将L型阵等效为一矩形平面阵列,然后在等效矩形阵列的基础上,采用MUSIC进行二维波达方向估计,以L型阵的物理孔径实现矩形平面阵列的估计性能。本文推导了二维波达方向估计的CRB,计算机仿真实验证实了所提方法的有效性。      

水下目标方位估计的克拉美-罗界研究

该文首次给出了任意平面离散阵列对水下窄带源和宽带源进行近场测距的克拉美-罗界(CRB),并进一步全面地推导了相应远场测向的CRB表达式。由此揭示了近场测距和远场测向的CRB的影响因素和特点：(1)两者的影响因素均可分为两部分：阵列相关因素,如阵列结构和阵列孔径等;目标信号相关因素,如目标的相对方位、信号频率、带宽和信噪比等。(2)两者均与信号带宽和谱密度函数构成的一个联合量成反比。(3)近场测距的CRB与目标距离的四次方成正比。(4)近场测距的CRB与基阵参考点的选择有关,而远场测向的CRB则与其无关。(5)对于均匀直线阵,近场测距CRB大致与阵列孔径的五次方成反比,而远场测向CRB则大致与阵列孔径的三次方成反比;对于均匀圆周阵,两者均与阵列孔径成反比,且与目标的相对方位无关。Monte-Carlo仿真结果验证了理论分析和上述结论的正确性。该文CRB不仅给出了近场测距和远场测向的最佳估计性能,而且为阵列及信号的设计提供了理论指导,以达到最优的测距和测向效果。     

Advantages of nonuniform arrays using root-MUSIC

In this paper, we consider the Direction-Of-Arrival (DOA) estimation problem in the Nonuniform Linear Arrays (NLA) case, particularly the arrays with missing sensors. We show that the root-MUSIC algorithm can be directly applied to this case and that it can fully exploit the advantages of using an NLA instead of a Uniform Linear Array (ULA). Using theoretical analysis and simulations, we demonstrate that employing an NLA with the same number of sensors as the ULA, yields better performance. Moreover, reducing the number of sensors while keeping the same array aperture as the ULA slightly modifies the Mean Square Error (MSE). Therefore, thanks to the NLA, it is possible to maintain a good resolution while decreasing the number of sensors. We also show that root-MUSIC presents good performance and is one of the simplest high resolution methods for this type of arrays. Closed-form expressions of the estimator variance and the Cramer–Rao Bound (CRB) are derived in order to support our simulation results. In addition, the analytical expression of the CRB of the NLA to the CRB of the ULA ratio is calculated in order to show the advantages of the NLA.     

A note on the Cramer-Rao bound for 2-D direction finding based on2-D array

The authors present explicit expressions for the Cramer-Rao bound (CRB) for estimating the two-dimensional (2-D) direction of a single source based on 2-D arrays of identical omnidirectional sensors. Two commonly used models, random wave and unknown wave, are compared. It is shown that the CRBs for the two models have the same dependency on the array structure. A specialization of the CRB to two orthogonal uniform linear arrays (ULAs) is discussed. It is found that the joint CRBs of the direction angles based on the two orthogonal ULAs can be as low as one quarter (for a random waveform model with a large number of snapshots and low SNR) or one half (for both models with high SNR) of the CRBs based on each ULA     

基于拉伸式COLD 传感器的DOA 和极化参数估计*

同点正交配置磁环和电偶极子(Co-centered orthogonal loop and dipole, COLD)是一种最常用的二分量 电磁矢量传感器,但是COLD 传感器没有充分利用磁环和电偶极子分量的空间信息。本文针对由COLD 传感器组成 的均匀线阵(Uniform linear array ,ULA),将所有磁环和电偶极子分量分别沿两个正交方向均匀拉伸,形成L 形阵,扩 展阵列的空间孔径,并提出了基于广义旋转不变的降维多重信号分类算法(Dimension reduction multiple signal classi fication method based on generalized rotational invariance, GRIDR-MUSIC)。所提算法利用L 形阵的几何构形,将导向 矢量分隔成三部分,通过两个正交ULA 的广义旋转不变结构,分别估计各个部分,使得波达角(Direction of arrival)和 极化参数仅需一维谱峰搜索就可以估计得到,且无需参数匹配。最后,仿真实验验证了所提算法的有效性。     

A Cramér Rao bounds based analysis of 3D antenna array geometries made from ULA branches

In the context of passive sources localization using antenna array, the estimation accuracy of elevation, and azimuth are related not only to the kind of estimator which is used, but also to the geometry of the considered antenna array. Although there are several available results on the linear array, and also for planar arrays, other geometries existing in the literature, such as 3D arrays, have been less studied. In this paper, we study the impact of the geometry of a family of 3D models of antenna array on the estimation performance of elevation, and azimuth. The Cramér-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration. In particular, we give closed-form expressions of CRB for a 3D antenna array under both conditional, and unconditional observation models. Thanks to these explicit expressions, the impact of the third dimension to the estimation performance is analyzed. Particularly, we give criterions to design an isotropic 3D array depending on the considered observation model. Several 3D particular geometry antennas made from uniform linear array (ULA) are analyzed, and compared with 2D antenna arrays. The isotropy condition of such arrays is analyzed. The presented framework can be used for further studies of other types of arrays.     

Efficient 2-D DOA and frequency estimation for L-shaped array via RD-PM

This paper addresses the issue of joint two-dimensional direction of arrival (2-D DOA) and frequency estimation via reduced-dimensional propagator method (RD-PM) with L-shaped array. The proposed algorithm has no need for eigenvalue decomposition of the sample covariance matrix and simplifies three-dimensional global spectral search within the three-dimensional propagator method (3-D PM) to one-dimensional local search, which greatly reduces computational complexity. Furthermore, the proposed algorithm can work under both uniform and non-uniform L-shaped array and can achieve paired 2-D DOA and frequency estimates automatically. In addition, the 2-D DOA and frequency estimation performance for the proposed method is approximate 3-D PM algorithm and parallel factor (PARAFAC) method but exceeds the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and improved PM algorithm. The detailed derivation of Cram´er-Rao bound (CRB) is provided and the simulation results demonstrate the effectiveness and superiority of the proposed approach.     

Computationally Efficient Maximum Likelihood Approach to DOA Estimation of a Scattered Source

The problem of Direction-Of-Arrival (DOA)estimation in the presence of local scatterers using a uniform linear array(ULA) of sensors is addressed. We consider two models depending on whether theform of the azimuthal power distribution is explicitly known or not. For bothmodels, the block-diagonal structure of the associated Fisher InformationMatrix (FIM) is exploited to decouple the estimation of the DOA from that ofthe other model parameters. An asymptotically efficient Maximum Likelihood(ML)DOA estimator is derived which entails solving a 1-D minimization problemonly.Furthermore, the 1-D criterion can be expressed as a simple Fourier Transform.A numerical comparison with the Cramér-Rao Bound (CRB) illustrates thefactthat our computationally very simple DOA estimators are statisticallyefficientfor a wide range of scenarios.     

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.     

DOD and DOA estimation in bistatic MIMO radar for nested and coprime array with closed-form DOF

It is well known that sparse array can offer better angle resolution than that of uniform linear array (ULA) in the same number of physical sensors. But in bistatic minimum redundancy sparse array multi-input multi-output (MIMO) radar, it cannot offer closed-form degree of freedom (DOF) for the arbitrary number of sensors with direction of departure and direction of arrival estimation. Therefore, this article introduces a nested array and coprime array into sparse array to solve the problem. First, construct no holes difference-coarray by extracting specified covariance matrix elements. Then, transform the difference-coarray into ULA within bistatic MIMO radar through some mathematical operations. As a result, many angle estimation methods for traditional ULA can be applied to the sparse bistatic MIMO array radar. The proposed algorithm offers closed-form DOFs for sparse array and the array aperture is much larger than that of ULA with identical number of sensors. The usefulness of the proposed methods is verified through computer simulations.     

基于压缩感知DOA估计的稀疏阵列设计

根据格拉姆(Gram)矩阵优化测量矩阵的方法,给出了一种基于压缩感知波达方向(DOA)估计的均匀线阵的稀疏阵列设计方法.该方法不需要对阵列的输出数据进行压缩采样,直接利用稀疏阵列的输出数据,然后利用稀疏恢复算法求解DOA估计信息.实验仿真证明,相比于原均匀线阵,所提方法在阵元数目较少且信噪比较低的情况下具有更好的DOA估计性能.     

BER performance of a uniform circular array versus a uniform linear array in a mobile radio environment

In this letter, we present a comparison between the bit error rate (BER) performance of a uniform circular array (UCA) and a uniform linear array (ULA) assuming quadrature phase-shift keying (QPSK) and maximal-ratio-combining (MRC) in a mobile radio communication environment. The results are based on analysis, assuming a flat Rayleigh fading channel with omni-directional antennnas and considering the azimuthal plane only. The analytical BER is derived as a function of the spatial fading correlation for both types of antenna arrays. Results show that for similar aperture sizes the UCA outperforms the ULA when considering all angles-of-arrival. However, there is considerable variability over central angle-of-arrival (AOA) for low-to-moderate angle spreads. For angles-of-arrival concentrated near the broadside of the linear array, the ULA typically performs as well as or better than the UCA. A truncated Gaussian AOA (AOA) distribution is assumed to model spatial correlation and the numerical results focus on four element arrays.     

基于非均匀阵列的特征波束发射分集方案

在发射端将特征波束形成与空时分集技术相结合,在保持分集阶数的同时可以获得阵列增益.通过对该混合系统误码率性能的分析,提出了基于非均匀阵的技术方案.它可以在弱相关信道中保持较高的阵列增益,在强相关环境下使分集支路的平衡度得到改善.仿真结果表明,在相关度不同的多种信道环境中,采用非均匀阵可获得比均匀阵更好的误码率性能.     

MIMO雷达非均匀布阵的性能分析

多输入多输出（MIMO）雷达是一种新体制雷达,它在发射端发射正交信号,从而产生虚拟阵元,扩大阵列孔径,在DOA估计、参数识别等方面的性能较相控阵雷达有很大提高。而目前有关MIMO雷达中虚拟阵元的讨论都以均匀线阵（ULA）为基础,并与相控阵雷达的性能进行比较。丈中在ULA的基础上,研究了非均匀线阵（NLA）,研究结果表明,非均匀线阵产生了更多的有效虚拟阵元,与相控阵雷达和ULA布阵MIMO雷达相比．具有更多的空间自由度、更好的克拉关·罗界和更好的DOA性能。     

Cramer-Rao bounds for estimating range, velocity, and directionwith an active array

We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional (3-D) array with isotropic sensors in spatially white noise and show that it is a function of the array geometry only through the “moments of inertia” of the array. The volume of the confidence region for the target's location is proposed as a measure of accuracy. For this measure, we show that the highest (and lowest) target location accuracy is achieved if the target lies along one of the principal axes of inertia of the array. Finally, we compare the location accuracies of several array geometries     

均匀天线阵列的空间相关性函数分析

推导了均匀圆形阵列与均匀线形阵列的空间相关性函数精确表达式和近似表达式。表达式由天线间距、阵列形状以及到达角分布构成。利用均匀角能量分布,分析均匀圆形阵列与均匀线形阵列的空间相关性精确模型和近似模型,并利用Matlab进行仿真。仿真结果表明,近似分析在一定的条件下可替代精确分析,并可减少74%的运算时间。     

互耦效应对四元方阵天线阵列信道容量的影响

针对目前广泛研究的直线型排布阵列在来波平均到达角较大时信道容量会急剧下降的事实,提出并重点研究一种具空域对称结构的正方形排列四元天线阵列模型。在首先基于天线理论导出阵元耦合阻抗表达式的基础上,详细分析了引入阵列互耦效应后,阵元接收信号空域相关性及多输入多输出（MIMO）信道容量可能会受到的影响,并在来波角谱均匀分布情形下与传统四元直线阵的容量性能作仿真对比。理论分析和计算机数值仿真皆表明：由于空间对称的阵列排布结构导致四元方阵阵元间具有良好的互补性,因此,这种方阵阵列模型具有非常稳定的信道容量,更适合在实际通信环境中使用。     

基于L型阵列的方位估计及互耦自校正算法研究

 针对L型阵,提出了一种互耦自校正算法（SAL: self-calibration algorithm for L-shaped array）。该算法利用L型阵列特殊的互耦特性,实现了对信源信息（DOA）和阵列互耦系数的解耦合,从而无需任何校正源就可以实现两类参数的估计。与基于循环迭代最小化技术的传统自校正算法相比,该算法先通过搜索谱峰估计信源信息（DOA）,再估计互耦系数,从而避免了多维搜索带来的庞大运算量和迭代中的全局收敛性问题。仿真结果表明本文提出的自校正算法具有精度高、计算量小的特点。     

Beamspace Root-MUSIC for minimum redundancy linear arrays

Beamspace Root-MUSIC, a computationally efficient beamspace implementation of Root-MUSIC developed recently for use in conjunction with a uniformly spaced linear array (ULA), is discussed. Computationally efficient methods for using beamspace Root-MUSIC in conjunction with a minimum redundancy linear array (MRLA) for both the narrowband and wideband cases are developed. The MRLA is attractive in that it offers enhanced detection performance and enhanced resolution capability relative to a ULA having the same number of elements     

Benefit of Pattern Diversity via 2-Element Array of Circular Path Antennas in Indoor Clustered MIMO Channels

In this paper, we analyze a MIMO array consisting of two circular microstrip antennas, designed to exploit pattern diversity. We analytically derive the spatial correlation coefficients of this array as a function of the mode excited for realistic clustered MIMO channel models. We compare the performance of the circular patch array (CPA) against an array of two space dipoles. In particular, we compute a theoretical tradeoff to predict when the pattern diversity provided by the CPA is more effective than space diversity from the uniform linear array (ULA), based on the eigenvalues of the spatial correlation matrix. Through simulations, we show that CPAs yield better performance or satisfy more restrictive size constraints than ULAs in clustered MIMO channels, depending on the element spacing of the ULA, These results make the CPA an attractive solution for miniaturized MIMO arrays for portable devices or access points.