Wavefield modeling and array processing .I. Spatial sampling

We introduce the concept of wavefield modeling and study its relationship to array professing and direction finding. We show how the output of an array can be written as the product of a wavefield independent sampling matrix and an array independent coefficient vector. Using this decomposition, we derive the conditions under which the array output may be linearly interpolated to give the array output of a different array, within a desired accuracy. We proceed to show under what conditions the array output may be linearly interpolated to give the value of the wavefield over a continuous manifold. As a result, we also derive conditions under which the array manifold may be linearly transformed between frequencies. Finally, we treat the case where the sources are known to be limited to specific, possibly disjoint angular sectors of arbitrary shape, and show how the sampling matrix can in this case be replaced by a modified sampling matrix of lower rank. This result yields a straightforward extension of the formalism presented in this paper to the Ease of limited angular sectors. In two companion papers, we use wavefield modeling to derive practical algorithms and bounds on the performance of arrays     

VAE/MPM/GA Technique for DoA Estimation Using Optimized Antenna Arrays

Many algorithms have been proposed to estimate the direction of arrival for the targets, but through using a large number of snapshots. In real time applications such as automotive radar, this is unacceptable as it causes delay and heavy processing. Instead, if only a small number of snapshots or, optimally, a single snapshot is available for DoA estimation, it will be fast and efficient. Single snapshot algorithms have a drawback as they require a large number of antenna elements, which considered a limiting factor. In this paper, a single snapshot DoA estimation technique is introduced by using optimized antenna arrays. The proposed algorithm is based on utilization of virtual array extension, matrix pencil method, and the genetic algorithm. The use of virtual array extension greatly improves the MPM performance. Furthermore, it exhibits a high DoA estimation accuracy by using a reduced number of antenna elements. The genetic algorithm is employed to determine the minimum number of antenna elements, which are required to estimate the DoAs with minimal root mean square error.

     

Direction of Arrival Estimation in the Presence of Noise Coupling in Antenna Arrays

The direction of arrival (DOA) estimation problem in the presence of signal and noise coupling in antenna arrays is addressed. In many applications, such as smart antenna, radar and navigation systems, the noise coupling between different antenna array elements is often neglected in the antenna modeling and thus, may significantly degrade the system performance. Utilizing the exact noise covariance matrix enables to achieve high-performance source localization by taking into account the colored properties of the array noise. The noise covariance matrix of the antenna array consists of both the external noise sources from sky, ground and interference, and the internal noise sources from amplifiers and loads. Computation of the internal noise covariance matrix is implemented using the theory of noisy linear networks combined with the method of moments (MoM). Based on this noise statistical analysis, a new four-port antenna element consisting of two orthogonal loops is proposed with enhanced source localization performance. The maximum likelihood (ML) estimator and the Cramer-Rao lower bound (CRLB) for DOA estimation in the presence of noise coupling is derived. Simulation results show that the noise coupling in antenna arrays may substantially alter the source localization performance. The performance of a mismatched ML estimator based on a model which ignores the noise coupling shows significant performance degradation due to noise coupling. These results demonstrate the importance of the noise coupling modeling in the DOA estimation algorithms.     

Wavefield modeling and array processing .II. Algorithms

For pt.I see ibid. vol.42, no.10, p.2549, 1994. We present several novel algorithms for array processing, as well as extensions of existing methods based on this approach. We first consider the problem of localization of wideband sources via coherent processing, and show how wavefield modeling enables us to derive expressions for the frequency transformation (focusing) matrices. This method is extended to three dimensions and to sector processing. We then develop computationally efficient implementations of MUSIC and Root-MUSIC for the narrowband and the coherent and incoherent wideband cases, as well as a natural extension of Root-MUSIC to any 2-D array. In addition, wavefield modeling allows us for the first time to extend Root-MUSIC to 3-D arrays and wavefields. We also present a low complexity variant of Root-MUSIC for direction finding within a limited angular sector. Finally, we derive a low-dimensional sufficient statistic and reduced rank processing schemes for the case of oversampled arrays and/or limited angular sector scenarios     

A multiple antenna wireless testbed for the validation of DoA estimation algorithms

In this paper, a wireless testbed with a multiple antenna receiver is described. It comprises a rotating four-element antenna array connected to a quad radio frequency (RF) front-end, and a channel acquisition board equipped with a field programmable gate array (FPGA). The algorithms can be implemented directly on the FPGA, but they can also be tested via simulation, e.g., with Matlab, since the acquired data can be transferred from the board memory to a personal computer (PC). Moreover, the algorithm implementation on the FPGA can be done by exploiting the System Generator for DSP Xilinx tool that allows the algorithm synthesis from a Simulink block diagram. These features make the testbed useful for rapid prototyping. In particular, the presence of the rotating antenna array enables the analysis of direction of arrival (DoA) estimation techniques. We report the main results from the experimental measures conducted to characterize the hardware non idealities. We then describe a DoA estimation algorithm that has been used to compare real and simulated results. It is shown that the results are in good agreement with the simulations, also when the effect of non isotropic antenna gains and/or phase noise originated from non co-phased RF front-ends becomes considerable.     

基于MIMO雷达虚拟阵列的近场目标定位

提出了一种基于MIMO雷达虚拟阵列的近场目标定位新算法。该算法通过MIMO雷达形成的虚拟阵列的互协方差矩阵来构造一个新的二阶统计量矩阵,利用其相应的特征值及特征向量估计出近场目标的三维参数。由于不同虚拟阵列的噪声是不相关的,所以该算法可适用于任意的加性高斯噪声环境。与现有的无源阵列近场源定位算法相比,该算法的参数估计结果能自动配对,无需参数配对过程,且不存在接收阵列孔径损失的问题。计算机仿真结果证明了本文算法的正确性和有效性。     

Beamspace Transform for UCA: Error Analysis and Bias Reduction

In this paper, we analyze the error caused by the beamspace transform (BT) when it is applied to uniform circular array (UCA) configuration. Several algorithms for direction of arrival (DoA) estimation exploit this modal transform because it allows using computationally efficient techniques such as polynomial rooting and dealing with coherent sources. The BT is based on the phase-mode excitation principle. The performance of such DoA estimators is degraded if the array has a small number of elements. We introduce a modified beamspace transform (MBT) that performs mapping from element-space to beamspace domain taking into account the error caused by the transform. Justification of the difference in the statistical performances of MUSIC and root-MUSIC algorithms for UCA is also given. Moreover, we show that there is a significant difference in the performance of the UCA root-MUSIC technique depending on whether an even or odd number of elements is used. We derive an expression approximating the bias in the DoA estimates that is caused by the beamspace transform. Some design guidelines are provided for choosing the key UCA configuration parameters such as number of sensors, array radius, and interelement spacing in order to reduce the error. Finally, we propose a novel technique for bias removal. It allows practically bias-free DoA estimation.     

Spectral self-coherence restoral: a new approach to blind adaptivesignal extraction using antenna arrays

A new approach to blind adaptive signal extraction using narrowband antenna arrays is presented. The approach has the capability to extract communication signals from cochannel interference environments using only known spectral correlation properties of those signals, i.e. without using knowledge of the content or direction of arrival of the transmitted signal, or the array manifold or background noise covariance of the receiver, to train the antenna array. The class of spectral self-coherence restoral (SCORE) objective functions is introduced, and algorithms for adapting antenna arrays to optimize these objective functions are developed. Using the theory of spectral correlation, it is shown by analysis and simulation that these algorithms maximize the signal-to-interference-and-noise ratio at the output of the narrowband antenna array when a single communication signal with spectral self-coherence at a known value of frequency separation, along with an arbitrary number of interferers without spectral self-coherence at that frequency separation, are impinging on the array     

阵列幅度/相位误差的有源校正新方法

实际应用中的阵列存在幅度/相位响应误差,往往导致阵列高分辨算法性能的下降。对此本文给出一种阵列幅度/相位响应误差的有源校正新方法,它基于子空间正交理论,通过对误差建模,将阵列校正问题转换成误差参数估计问题,并利用经典的Lagrange乘子法方便地得到最优解。另外,此方法只需要一个已知方位的校正源,计算简便,无需迭代,可用于阵元位置已知的任意形状的阵列,因此更适用于实际阵列安装应用前的校正。通过半消声室实验对16-元圆环形声阵列进行了测试和校正,数据处理结果表明,本文所提的校正方法能够准确地估计出各阵元幅度/相位误差,且校正前后MVDR (Minimum Variance Distortionless Response) 波束形成的性能得到明显提高。      

Array Calibration for CDMA Smart Antenna Systems

In this paper, we investigate array calibration algorithms to derive a further improved version for correcting antenna array errors and RF transceiver errors in CDMA smart antenna systems. The structure of a multi‐channel RF transceiver with a digital calibration apparatus and its calibration techniques are presented, where we propose a new RF receiver calibration scheme to minimize interference of the calibration signal on the user signals. The calibration signal is injected into a multichannel receiver through a calibration signal injector whose array response vector is controlled in order to have a low correlation with the antenna response vector of the receive signals. We suggest a model‐based antenna array calibration to remove the antenna array errors including mutual coupling errors or to predict the element patterns from the array manifold measured at a small number of angles. Computer simulations and experiment results are shown to verify the calibration algorithms.     

Self-survey calibration of meteor radar antenna arrays

This paper presents the self-surveying technique for calibrating the antenna spacing, orientation, and phase errors in multiple receiver radar antenna arrays. Utilizing a set of source transmitters placed at known locations in the far-field of the array and measurements of the phase present at each antenna, the array's relative antenna locations and phase errors can be determined. The advantage of this technique is that the radar is used in its normal operating mode, providing an end-to-end calibration under true operational conditions. A self-survey calibration was performed with a meteor radar located at Sondre Stromfjord, Greenland, successfully mapping the array. The antenna positions were relatively close the expected locations, although the baselines were rotated approximately 5° from the true cardinal directions. The majority of the phase error was introduced by the receivers     

2-D DOA estimation in case of unknown mutual coupling for multipath signals

In this paper, two dimensional (2-D) direction-of-arrival (DOA) estimation problem in case of unknown mutual coupling and multipath signals is investigated for antenna arrays. A new technique is proposed which uses a special array structure consisting of parallel uniform linear array (PULA). PULA structure is complemented with auxiliary antennas in order to have a structured mutual coupling matrix (MCM). MCM has a symmetric banded Toeplitz structure which allows the application of the ESPRIT algorithm for 2-D paired DOA estimation. The advantage of the PULA structure is exploited by dividing it into overlapping linear sub-arrays (triplets) and spatial smoothing is employed to mitigate multipath signals. Closed form expressions are presented for search-free, paired and unambiguous 2-D DOA estimation. Two algorithms PULA-1 and PULA-2 are proposed to effectively solve the problem. Several simulations are done and the accuracy of the proposed solution is shown.     

An External Calibration Scheme for DBF Antenna Arrays

A novel calibration scheme is presented that is especially suited for complex digital beamforming (DBF) antenna arrays at millimeter-wave frequencies. Calibration data is extracted by sampling the field of each radiator at certain locations near the array by fixed probe antennas. A scalable calibration model for evaluation of the measured data is described. First tests are performed on a small passive array representing a unit cell of larger arrays. The calibration scheme is subsequently applied to and tested on a 64 element DBF transmit antenna array.      

Multiple-input-multiple-output measurements and modeling in Manhattan

Narrowband multiple-input-multiple-output (MIMO) measurements using 16 transmitters and 16 receivers at 2.11 GHz were carried out in Manhattan. High capacities were found for full, as well as smaller array configurations, all within 80% of the fully scattering channel capacity. Correlation model parameters are derived from data. Spatial MIMO channel capacity statistics are found to be well represented by the separate transmitter and receiver correlation matrices, with a median relative error in capacity of 3%, in contrast with the 18% median relative error observed by assuming the antennas to be uncorrelated. A reduced parameter model, consisting of 4 parameters, has been developed to statistically represent the channel correlation matrices. These correlation matrices are, in turn, used to generate H matrices with capacities that are consistent within a few percent of those measured in New York. The spatial channel model reported allows simulations of H matrices for arbitrary antenna configurations. These channel matrices may be used to test receiver algorithms in system performance studies. These results may also be used for antenna array design, as the decay of mobile antenna correlation with antenna separation has been reported here. An important finding for the base transmitter array was that the antennas were largely uncorrelated even at antenna separations as small as two wavelengths.     

On Clutter Rank Observed by Arbitrary Arrays

This paper analyzes the rank and eigenspectrum of the clutter covariance matrix observed by space-time radar systems with arbitrarily configured arrays and varying look geometry. Motivated by recent applications that suggest use of nonuniform antenna arrays, a generalized theory of clutter rank is derived and demonstrated. First, a one-dimensional effective random process is defined by projecting the measurements obtained by an arbitrary space-time radar system into an equivalent one-dimensional sampling structure. Then, this projection and the Karhunen-Loeve representation of random processes are used to predict clutter rank based on effective aperture-bandwidth product. Simulated results are used to confirm the theory over a wide range of scenarios, and along the way, the well-known Brennan's rule for clutter rank is shown to be a special case of the proposed aperture-bandwidth product     

基于共形天线阵的免搜索来波方向估计算法研究

运算量大,受阵列拓扑结构限制是传统基于子空间分解的来波方向(DOA)估计算法的主要问题,这些问题大大限制了其在实际工程中的应用。针对共形天线阵的特殊性,结合实际的共形阵,研究了几种可以应用于任意阵列结构的免搜索DOA估计算法,并比较了这些算法在共形阵上的性能。理论分析和数值仿真表明:在一定条件下这些算法均可在共形阵上取得较优的估计性能。     

基于酉变换-矩阵束的稀布线阵方向图综合

该文提出一种非迭代的稀布线阵方向图综合方法。该方法首先对方向图采样数据进行centro-Hermit化处理,然后通过酉变换构造等价实矩阵束,得到非均匀单元位置与新矩阵束广义特征值的关系。在此基础上,对实矩阵奇异值分解,并舍弃非主要奇异值以获得低阶左奇异向量矩阵,进而求得稀布阵列的阵元位置和相应激励。相比于其他方法,该方法能够直接得到阵元位置的实数解,奇异值分解和特征值分解均在实数域进行,提高逼近程度的同时有效降低了计算量,仿真验证了该方法利用少量阵元即可高效实现线阵的方向图综合。     

Basic array theory

Basic antenna array theory is outlined with major emphasis on pattern analysis and synthesis for periodic linear and planar arrays, phased arrays, and conformal arrays. Extension is made to synthesis techniques which use computer algorithms. These include arbitrary sidelobe control, shaped beams, and phase-only null steering. The subjects of random errors and phased array quantization errors are outlined     

Applications of cumulants to array processing .I. Apertureextension and array calibration

An interpretation for the use of cumulants in narrowband array processing problems is proposed. It is shown how fourth-order cumulants of multichannel observations increase the directional information compared with second-order statistics. Based on the interpretation, it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array. The amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far-field sources is also investigated. It is proven that the presence of a doublet and use of fourth-order cumulants is sufficient to accomplish this task. The proposed approach is computationally efficient and more general than covariance-based algorithms that have addressed the calibration problem under constraints. A class of beamforming techniques is proposed to recover the source waveforms. Proposed estimation procedures are based on cumulants, which bring insensitivity to the spatial correlation structure of additive Gaussian measurement noise. Simulations are provided to illustrate the use of the proposed algorithms     

Direction of Arrival (DoA) Estimation Under Array Sensor Failures Using a Minimal Resource Allocation Neural Network

This paper presents the use of a minimal resource allocation network (MRAN) for the direction of arrival (DoA) estimation under array sensor failure in a noisy environment. MRAN is a sequential learning algorithm in which the number of hidden neurons are added or removed based on the input data and produces a compact network. The training for MRAN is done under no failure and no noise case and the trained network is then used when there is a failure. Thus, the need for knowing the element and the time of its failure, as required in other methods is eliminated. MRAN's performance is compared with the conventional MUSIC algorithm and also the radial basis function neural network scheme developed by A. H. El Zooghby under normal and failed cases. In normal case, different antenna effects like mutual coupling, nonuniform array and unequal source power have been studied under different signal to noise ratio (SNR) values. Results indicate the superior performance of MRAN based DoA estimation scheme under different antenna effects, failure conditions and noise levels