High-resolution Direction Finding Research Articles

4D Automotive Radar Sensing for Autonomous Vehicles: A Sparsity-Oriented Approach

We propose a high-resolution imaging radar system to enable high-fidelity four-dimensional (4D) sensing for autonomous driving, i.e., range, Doppler, azimuth, and elevation, through a joint sparsity design in frequency spectrum and array configurations. To accommodate a high number of automotive radars operating at the same frequency band while avoiding mutual interference, random sparse step-frequency waveform (RSSFW) is proposed to synthesize a large effective bandwidth to achieve high range resolution profiles. To mitigate high range sidelobes in RSSFW radars, optimal weights are designed to minimize the peak sidelobe level such that targets with a relatively small radar cross section are detectable without introducing high probability of false alarm. We extend the RSSFW concept to multi-input multi-output (MIMO) radar by applying phase codes along slow time to synthesize a two-dimensional (2D) sparse array with hundreds of virtual array elements to enable high-resolution direction finding in both azimuth and elevation. The 2D sparse array acts as a sub-Nyquist sampler of the corresponding uniform rectangular array (URA) with half-wavelength interelement spacing, and the corresponding URA response is recovered by completing a low-rank block Hankel matrix. Consequently, the high sidelobes in the azimuth and elevation spectra are greatly suppressed so that weak targets can be reliably detected. The proposed imaging radar provides point clouds with a resolution comparable to LiDAR but with a much lower cost. Numerical simulations are conducted to demonstrate the performance of the proposed 4D imaging radar system with joint sparsity in frequency spectrum and antenna arrays.

Vehicle wheel detection using micro doppler effect

With the advent of autonomous driving, safety have become the top priority. To adhere vehicle safety standard for autonomous vehicle, the sensors play the primary role in sensing the environment. With high frequency resolution radar, micro motions of the vehicle wheel can be detected. Time-Frequency distribution is used to detect the frequency changes with respect to time. MUSIC is a high resolution direction finding algorithm, which can estimate the direction of arrival of echo signals. Micro Doppler effect provides the vehicle wheel information related to the number of spokes and its spoke size. With this information, it is possible to detect the exact position of the wheels in the vehicle.

Antenna Array Manifolds for High-Resolution Direction Finding

The antenna array manifold is central to high-resolution direction finding. The analytic manifold is defined here as the mathematical model of the array response calculated by solving the electromagnetic equations for the waves impinging on the array. Array manifolds commonly used in the array signal processing literature are approximations of the analytic manifold. This paper describes the characteristics of the analytic manifold and compares it with commonly used approximate manifolds. The impact of these approximations on the performance of direction-of-arrival estimation in challenging superresolution scenarios is evaluated by selected numerical examples.

Compressive spectral estimation methods using a noise reference

Compressive beamforming methods have shown promise for use in high resolution direction finding and source localization. However, these methods often fail in scenarios with low SNR, particularly if only a few snapshots are available. The Spectral Estimation Method (SEM) (Blacodon and Elias, 2004, J. Aircraft 41 (6), 1360–1369) provides a means of source localization and source power estimation by minimizing the mean squares error between cross-spectral-density matrices of a measured signal and modeled signals at each location of interest. SEM With Additive Noise (SEMWAN) (Blacodon, 2011, Applied Acoustics, 72, 11–21) does the same but also utilizes the cross-spectral-density matrix of one or more noise references. In this presentation, the performance of a compressive version of SEMWAN is assessed for use in low SNR scenarios when the solution is sparse and a noise reference is available. Compressive SEMWAN is analyzed first using far-field, free-space simulations with varying SNR and multiple sources. Compressive SEMWAN is then applied to laboratory measurements taken with real noise sources at varying SNR and including some multipath propagation. The performance in each scenario is compared directly to conventional beamforming, a standard compressive beamforming method, and traditional SEMWAN. [Sponsored by NAVSEA through the NEEC.]

Higher order direction finding from rectangular cumulant matrices: The rectangular [formula omitted]-MUSIC algorithms

Fourth-order (FO) high resolution direction finding methods such as 4-MUSIC have been developed for more than two decades for non-Gaussian sources mainly to overcome the limitations of second order (SO) high resolution methods such as MUSIC. In order to increase the performance of 4-MUSIC in the context of multiple sources, the MUSIC method has recently been extended to an arbitrary even order 2q (q≥2), for square arrangements of the 2qth-order data statistics, giving rise to the 2q-MUSIC algorithm. To further improve the performance of 2q-MUSIC, the purpose of this paper is to extend the latter to rectangular arrangements of the data statistics, giving rise to rectangular 2q-MUSIC algorithms. Two kinds of rectangular arrangements, corresponding to redundant and non-redundant arrangements are considered. In particular, it is shown that rectangular arrangements of the higher order (HO) data statistics achieve a trade-off between performance and maximal number of sources to be estimated. These rectangular arrangements also lead to a complexity reduction for a given level of performance, which is still increased by non-redundant arrangements of the statistics. These results, completely new, open new perspectives in HO array processing.

A Sub-Wavelength RF Source Tracking System for GPS-Denied Environments

A sub-wavelength source tracking system utilizing highly miniaturized antennas in the HF range for applications in GPS-denied environments including indoor and urban scenarios is proposed. A technique that combines a high resolution direction finding and radio triangulation utilizing a compact transmit (Tx) and receive (Rx) antenna system is pursued. Numerical models are used to investigate wave propagation and scattering in complex indoor scenarios as a function of frequency. We choose HF band to minimize attenuation through walls and multipath in indoor environments. In order to achieve a compact system, a low-profile and highly miniaturized antenna ( λ/300 height and λ/100 lateral dimensions at 20 MHz) having omnidirectional, vertically polarized field is designed. At such low frequencies, accurate measurement of the phase difference between the signals at the Rx antennas having very small baseline is challenging. To address this issue, a biomimetic circuit that mimics the hearing mechanism of a fly (Ormia Ochracea) is utilized. With this circuit, very small phase differences are amplified to measurable values. The numerical simulations are used to analyze direction of arrival retrieval and source localization in highly cluttered environments. A compact system prototype is also realized and source tracking in complex indoor scenarios is successfully demonstrated.

High-resolution direction finding of non-stationary signals using matching pursuit

One of the main goals of time–frequency (TF) signal representations in non-stationary array processing is to equip multi-antenna receivers with the ability to separate sources in the TF domain prior to direction finding. This permits high-resolution direction-of-arrival (DOA) estimation of individual sources and of more sources than sensors. In this paper, we use linear decomposition of sensor data based on matching pursuit (MP). The leading atoms of the MP, which capture most of the source TF signatures, can be different for different sources and, as such, provide the desired source discrimination. The MP coefficients with high signal-to-noise ratio (SNR) and corresponding to the leading decomposition atoms are used to develop the MP-MUSIC DOA estimation for non-stationary source signals. We demonstrate the source discriminatory capability of the proposed technique using linear FM, nonlinear FM, and other non-stationary signals. Further, we compare MP-MUSIC performance with conventional MUSIC and the time–frequency MUSIC, which incorporates bilinear transforms.

High-resolution direction finding without coherent signals number based on multibeam system

Multibeam acoustic imaging systems are widely utilized for both large- and small-scale underwater investigations, especially for detecting underwater target. Processing backscattered echoes from the targets, the system can plot an acoustic image of target, and then estimate the parameters, such as direction and range. The backscattered echoes of target are coherent signals, and can be modeled as multiple highlights. Usually, the distance between the highlights is close, and the number of the highlights is unknown. Then, the directions cannot be directly estimated due to these highlights are not distinguished in the acoustic image. In this paper, an high-resolution method is proposed for estimating the directions of arrival (DOAs) of coherent highlight signals without signals number. The multibeam underwater acoustic imaging technology and the beamspace MUSIC algorithm are combined together. In this method, eigen-decomposition is skipped, so that coherent signals' DOA can be estimated by high-resolution MUSIC method under the situations with unknown signals number. Due to estimating the DOAs of coherent signals in beamspace, the precision of DOA estimation is enhanced, and the computation complexity is less than the element-space MUSIC method. The method's feasibility and robustness are analyzed and verified by the simulation data.

Sequential High-Resolution Direction Finding From Higher Order Statistics

The classical higher order MUSIC-like methods based on a simultaneous search for all directions of arrival (DOA's) show: i) a capacity for processing underdetermined mixtures of sources; ii) a high robustness with respect to both a Gaussian noise with unknown spatial coherence and modeling errors; and iii) a better resolution than algorithms based on second order statistics. However, these methods have some limits: for a finite number of samples, they show poor performance for sources exhibiting quasi-colinear DOA's. In order to overcome this drawback, two new sequential MUSIC-like algorithms are proposed in this paper, namely the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2q</i> -D-MUSIC and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2q</i> -RAP-MUSIC <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(q</i> ≥ 2) algorithms. These methods are based on a sequential optimization of proposed generalized noise and signal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2q</i> -MUSIC metrics, respectively. That allows us to learn and then to take into account the level of correlation between sources. A comparative study, both in terms of performance and numerical complexity, is performed showing the interest of the proposed techniques when some sources are angularly close. Eventually, an upper bound of the maximum number of sources which can be processed by the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2q</i> -MUSIC-like techniques is given for all <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> . This improves recent work on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2q</i> th-order virtual arrays.

Robust Adaptive Trimming for High-Resolution Direction Finding

The presence of impulsive noise can severely degrade the accuracy performance of conventional direction of arrival (DOA) estimation algorithms, such as MUSIC and ESPIRIT. We propose a two-stage robust adaptive trimming approach. We first apply Shapiro-Wilk's goodness-of-fit <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> test for Gaussianity, as a preprocessing stage. We then robustly estimate the covariance matrix in order to minimize the impact of impulsive noise on conventional DOA estimation algorithms. Numerical simulations are presented to illustrate the efficacy of the proposed approach for high resolution direction finding in highly-impulsive environments.

High-Resolution Through-the-Wall Radar Imaging Using Beamspace MUSIC

The MUSIC algorithm is a high-resolution direction finding technique which has been successfully applied to enhance radar imaging in inverse synthetic aperture radar (ISAR). Although this signal subspace-based method has proven effective when dealing with point targets and high signal-to-noise ratio (SNR), it may fail to work when directly applied to extended targets or target returns of low SNR. The Beamspace MUSIC (BS-MUSIC), in which the MUSIC algorithm is applied to multiple beams, is capable of locating spatially extended targets in low SNR environments. In this paper, we consider BS-MUSIC as an image formation method for indoor radar imaging problems and sensing through-the-wall applications. We compare BS-MUSIC performance to conventional beamforming and element-space MUSIC. Imaging results, using both synthesized and real data, demonstrate the advantages of the proposed algorithm in depicting targets behind walls.

Fast Direction Finding Using Modified Pseudocovariance Matrix

A modified pseudocovariance matrix is described which can improve the performance of Kim 's (Fast DOA estimation algorithm using pseudocovariance IEEE Trans. Antennas Propagat., vol. 53, no. 4, pp. 1346-1351, Apr. 2005) algorithm to realize the fast direction finding with single snapshot in coherent or uncorrelated case. By adding the backwards formulation of pseudocovariance matrix, the rank of pseudocovariance matrix is enhanced. Then a set of pseudocovariance matrices are constructed by circularly shifting the matrix. By weighted averaging, a modified pseudocovariance matrix is reconstructed whose noise is reduced. The proposed matrix has less array element loss than that of the original matrix. Moreover, this algorithm can be applied in the lower signal-noise-ratio (SNR) through noise preprocessing. The new matrix has expanded the application of high-resolution direction finding to nonuniform linear array (NLA), since traditional methods usually assume the array is uniform linear when handling coherent sources. Simulations are conducted to compare the performance of the modified method and the original method. The results illustrate that the high performance of DOA estimate could be obtained rapidly

High-Resolution Direction Finding From Higher Order Statistics: The$2rm q$-MUSIC Algorithm

From the beginning of the 1980s, many second-order (SO) high-resolution direction-finding methods, such as the MUSIC method (or 2-MUSIC), have been developed mainly to process efficiently the multisource environments. Despite of their great interests, these methods suffer from serious drawbacks such as a weak robustness to both modeling errors and the presence of a strong colored background noise whose spatial coherence is unknown, poor performance in the presence of several poorly angularly separated sources from a limited duration observation and a maximum of N-1 sources to be processed from an array of N sensors. Mainly to overcome these limitations and in particular to increase both the resolution and the number of sources to be processed from an array of N sensors, fourth-order (FO) high-resolution direction-finding methods have been developed, from the end of the 1980s, to process non-Gaussian sources, omnipresent in radio communications, among which the 4-MUSIC method is the most popular. To increase even more the resolution, the robustness to modeling errors, and the number of sources to be processed from a given array of sensors, and thus to minimize the number of sensors in operational contexts, we propose in this paper an extension of the MUSIC method to an arbitrary even order 2q (qges1), giving rise to the 2q-MUSIC methods. The performance analysis of these new methods show off new important results for direction-finding applications and in particular the best performances, with respect to 2-MUSIC and 4-MUSIC, of 2q-MUSIC methods with q>2, despite their higher variance, when some resolution is required

Estimating angle of arrival with non‐uniformly spaced array

AbstractThe present direction‐finding equipment has insufficient accuracy and resolution, so that accurate evaluation of the direction of arrival and the position cannot be carried out. Although each radar signal has a narrow bandwidth, the entire bandwidth for various radars used exceeds four octaves. In order to search all of these, equipment for each bandwidth is used at present so that the entire frequency range is covered. However, it is more effective from the standpoint of equipment size and cost to cover the entire spectrum with a single kind of equipment. It is desirable to realize high‐accuracy high‐resolution direction finding over a broad bandwidth. In realization, broadband antennas are used, and high‐gain antennas are also needed in a low‐S/N environment. Since the dimensions of high‐gain and broadband antennas are large, an array configuration with a half‐wave spacing may not physically be possible. Thus, the array spacing becomes more than a half‐wavelength. If the range of direction estimation is −90 to +90°, the phase difference exceeds 360° so that ambiguity occurs. As a method to resolve this ambiguity problem, a nonuniformly spaced array is effective. In this paper, the array conditions for a nonuniformly spaced array are determined in the case of one arriving wave. Next, the case of several arriving waves is discussed and the array conditions for several arriving waves are derived. © 2001 Scripta Technica, Electron Comm Jpn Pt 1, 85(3): 1–8, 2002

High-resolution direction finding: the missing data case

This paper considers the problem of estimating the direction-of-arrival (DOA) of one or more signals using an array of sensors, where some of the sensors fail to work before the measurement is completed. Methods for estimating the array output covariance matrix are discussed. In particular, the maximum-likelihood (ML) estimate of this covariance matrix and its asymptotic accuracy are derived and discussed. Different covariance matrix estimates are used for DOA estimation together with the MUSIC algorithm and with a covariance matching technique. In contrast to MUSIC, the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix, and it is demonstrated that this yields a significant performance gain.

Direction Finding Based on Spatial Time-Frequency Distribution Matrices

Amin, Moeness G., and Zhang, Yimin, Direction Finding Based on Spatial Time-Frequency Distribution Matrices, Digital Signal Processing10 (2000), 325–339.Spatial time-frequency distributions (STFDs) have been recently introduced as the natural means to deal with source signals that are localizable in the time-frequency domain. It has been shown that improved estimates of the signal and noise subspaces are achieved by constructing the subspaces from the time-frequency signatures of the signal arrivals rather than from the data covariance matrices, which are commonly used in conventional subspace estimation methods. This paper discusses the application of STFD to high-resolution direction finding. We focus on both the role and the effect of crossterms in angle estimation when multiple time-frequency points are incorporated. Simulation examples are presented to compare the performance of joint block-diagonalization and time-frequency averaging techniques for incorporating multiple autoterm and crossterm points in subspace estimation.

DOA estimation of wide-band signals based on time-frequency analysis

A numerical study on an approach based on the time-frequency analysis is performed for the high-resolution direction finding applications of wide-band signals. In this method, the direction of arrival (DOA) is estimated using a subband of the incoming signal instead of the whole signal spectrum. This treatment forces the DOA of the wide-band signals to be similar to that of the DOA of the narrow-band signals. The reason behind this can be thought of as the after effects of reducing the signal bandwidth, which constrains the signal subspace. An empirical analysis of the performance of the DOA estimator Is also investigated. This is done to compare the correct and estimated angles of separation between the targets, and it is demonstrated that there is a good agreement which implies that the use of prefiltering does not affect the resolution of the DOA estimator.

High resolution wideband direction finding arraysbased onoptimum symmetrical number system encoding

A new interferometer direction finding (DF) array architecture based on the optimum symmetrical number system (OSNS) is presented. OSNS arrays are capable of unambiguous high resolution DF over a wide bandwidth and field of view with as few as three elements, with multiple baseline options. A three-element array was designed, fabricated and tested at 8.5 GHz to verify the OSNS concepts experimentally.

Parallel and adaptive high-resolution direction finding

Recently the new class of so-called subspace methods for high-resolution direction finding has received a great deal of attention in the literature. When a real-time implementation is aimed at, the computational complexity involved is known to represent a serious impediment. In this paper, an ESPRIT-type algorithm is developed, which is fully adaptive and therefore particularly suited for real-time processing. Furthermore, a systolic array is described, which allows the processing of incoming data at a rate which is independent of the problem size. The algorithm is based on orthogonal transformations only. Estimates are computed for the angles of arrival, as well as for the source signals. Our aim is not so much to develop yet another ESPRIT-type algorithm but rather to show that it is indeed possible to develop an algorithm that is fully parallel and adaptive. This is something that has not been done before. >

Azimuth and elevation computation in high resolution DOA estimation

A number of high-resolution direction finding methods for determining the two-dimensional DOA (directions of arrival) of a number of plane waves impinging on a sensor array are discussed. The array consists of triplets of sensors that are identical, as an extension of the one-dimensional ESPRIT scenario to two dimensions. Algorithms that yield the correct parameter pairs while avoiding an extensive search over the two separate one-dimensional parameter sets are devised.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>