Array Manifold Research Articles

Covariance differencing‐based angle estimation method for bistatic multiple‐input–multiple‐output radar in unknown coloured noise

A new angle estimation method is developed for bistatic multiple-input–multiple-output radar in the presence of unknown coloured noise. By utilising covariance differencing, the proposed method can eliminate influence of coloured noise effectively. Then, the angles are determined from the subspace estimate with the help of reduced-dimension multiple signal classification (MUSIC) method. The proposed method does not incur virtual aperture loss, and it is suitable for arbitrary array manifold. Numerical simulations verify the effectiveness of the authors’ method.

Diagonal rejection-based minimum variance distortionless response for fiber underwater acoustic array

The high mounting precision of the fiber underwater acoustic array leads to an array manifold without perturbation. Besides, the targets are either static or slowly moving in azimuth in underwater acoustic array signal processing. Therefore, the covariance matrix can be estimated accurately by prolonging the observation time. However, this processing is limited to poor bearing resolution due to small aperture, low SNR and strong interferences. In this paper, diagonal rejection (DR) technology for Minimum Variance Distortionless Response (MVDR) was developed to enhance the resolution performance. The core idea of DR is rejecting the main diagonal elements of the covariance matrix to improve the output signal to interference and noise ratio (SINR). The definition of SINR here implicitly assumes independence between the spatial filter and the received observations at which the SINR is measured. The power of noise converges on the diagonal line in the covariance matrix and then it is integrated into the output beams. With the diagonal noise rejected by a factor smaller than 1, the array weights of MVDR will concentrate on interference suppression, leading to a better resolution capability. The algorithm was theoretically proved with optimal rejecting coefficient derived under both infinite and finite snapshots scenarios. Numerical simulations were conducted with an example of a linear array with eight elements half-wavelength spaced. Both resolution and Direction-of-Arrival (DOA) performances of MVDR and DR-based MVDR (DR–MVDR) were compared under different SNR and snapshot numbers. A conclusion can be drawn that with the covariance matrix accurately estimated, DR–MVDR can provide a lower sidelobe output level and a better bearing resolution capacity than MVDR without harming the DOA performance.

Two-Dimensional DOA Estimation for Coherently Distributed Sources with Symmetric Properties in Crossed Arrays.

In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.

2-D DOA Estimation for L-Shaped Array With Array Aperture and Snapshots Extension Techniques

A two-dimensional (2-D) direction of arrival estimation method for L-shaped array with automatic pairing is proposed. It exploits the conjugate symmetry property of the array manifold matrix to increase the effective array aperture and the number of virtual snapshots simultaneously, and then applies the principle of MUSIC to construct an angle cost function and transforms the conventional 2-D search into 1-D via a Rayleigh quotient, which can greatly reduce the computation complexity. Finally, the azimuth and elevation angles are estimated without pair matching. Simulation results show that the proposed method has a better performance and can resolve more sources than some existing computationally efficient methods.

Robust Adaptive Beamforming With Precise Main Beam Control

Many efforts have been recently devoted to robust adaptive beamforming with main beam control such that sufficient robustness against large look direction mismatches can be achieved by flexibly adjusting the beamwidth and response ripple. However, most of the existing approaches inherently rely on assuming an exactly known array manifold, but have not yet addressed the issue of robust beamforming with precise main beam control in the presence of arbitrary steering vector uncertainties. This motivates us to develop a robust beamforming approach that is capable of accurately controlling the array main beam. Unlike the conventional methods, steering vector uncertainties are taken into account in the magnitude response constraints of the adaptive beamformer. This allows us to control the main beam as prescribed. As the resultant nonconvex problem has a more complicated formulation than that of the existing methods, techniques developed for solving the problem of robust beamforming with magnitude response constraints cannot be employed directly. To tackle this problem, the lower and upper norm bounds of the beamformer weight vector are derived. The semidefinite relaxation technique is then employed as approximate solver, ending up with iterative, grid search, and linearization solutions. Simulation results show that the proposed methods are able to precisely control the main beam magnitude response in the presence of steering vector uncertainties.

Enhanced, blind and robust far-field audio acquisition for portable devices

In this paper, a bilinear Wiener filtering method is proposed for multichannel audio acquisition without knowing the array configurations and frequency responses. Compared with mainstream algorithms, the proposed method has two important features: blindness and robustness. For the first feature, the method does not require any prior knowledge about the array manifold. The “blindness” is very attractive to the industry because even microphones picked from the same batch of the same manufacturer can be inconsistent. For the second feature, even in the presence of strong sensor noise, the method can yield a good performance in suppressing directional interferences. This helps bring better “robustness” to the method and make it more practical for real environments. In the method, a rectangular window is adopted to slide continuously over the parallel multichannel audio streams and then bilinear Wiener filtering is performed on the matrix denoting windowed parallel audio streams. Experiments in a recording studio show the method can suppress directional interferences well. Besides, it converges rapidly and is an appealing choice for consumer electronics.

Computational Efficient Two-Dimension DOA Estimation for Incoherently Distributed Noncircular Sources With Automatic Pairing

In this paper, the problem of two-dimensional (2-D) direction-of-arrival (DOA) estimation for incoherently distributed (ID) noncircular sources is addressed. A low-complexity estimator with automatic pairing in the three-parallel uniform linear arrays (ULAs) is proposed. First, the signal non-circularity is applied to establish an extended generalized array manifold (GAM) model based on one-order Taylor series approximation. Resorting to such model, the generalized rotational invariance relationships are identified among the extended GAM matrices of the three ULAs. Thereafter, a modified propagator method is utilized to estimate the central elevation and azimuth DOAs. Without any spectrum searching, estimation or eigenvalue decomposition of the sample covariance matrix, the proposed approach is capable of considerably reducing the calculation cost in comparison with the existing methods. In addition, it can automatically pair the estimated central azimuth and central elevation DOAs. We also derive the Cramer-Rao lower bound regarding the 2-D DOA estimation of the ID noncircular source and conduct the computational complexity analysis. Numerical results demonstrate that the proposed method achieves better estimation performance than the existing methods. Furthermore, it can be applied in the multi-source scenario where different sources may have different angular distribution shapes.

Direction-of-Arrival Estimation and Sensor Array Error Calibration Based on Blind Signal Separation

We consider estimating the direction-of-arrival (DOA) in the presence of sensor array error. In the proposed method, a blind signal separation method, the joint approximation and diagonalization of eigenmatrices algorithm, is implemented to separate the signal vector and the mixing matrix consisting of the array manifold matrix and the sensor array error matrix. Based on a new mixing matrix and the reconstruction of the array output vector of each individual signal, we propose a novel DOA estimation and sensor array error calibration procedure. This method is independent of array phase errors and performs well against difference of SNR of signals. Numerical simulations verify the effectiveness of the proposed method.

Sound source localization method in an environment with flow based on Amiet–IMACS

A sound source localization method is proposed to localize and analyze the sound source in an environment with airflow. It combines the improved mapping of acoustic correlated sources (IMACS) method and Amiet's method, and is called Amiet–IMACS. It can localize uncorrelated and correlated sound sources with airflow. To implement this approach, Amiet's method is used to correct the sound propagation path in 3D, which improves the accuracy of the array manifold matrix and decreases the position error of the localized source. Then, the mapping of acoustic correlated sources (MACS) method, which is as a high-resolution sound source localization algorithm, is improved by self-adjusting the constraint parameter at each irritation process to increase convergence speed. A sound source localization experiment using a pair of loud speakers in an anechoic wind tunnel under different flow speeds is conducted. The experiment exhibits the advantage of Amiet–IMACS in localizing a more accurate sound source position compared with implementing IMACS alone in an environment with flow. Moreover, the aerodynamic noise produced by a NASA EPPLER 862 STRUT airfoil model in airflow with a velocity of 80m/s is localized using the proposed method, which further proves its effectiveness in a flow environment. Finally, the relationship between the source position of this airfoil model and its frequency, along with its generation mechanism, is determined and interpreted.

A Modified MUSIC Algorithm for Direction of Arrival Estimation in the Presence of Antenna Array Manifold Mismatch

We introduce a modified multiple signal classification (MUSIC) algorithm to estimate the directions of arrival (DOAs) of multiple radio frequency signals. We specifically consider an antenna array with an imperfectly calibrated array response. The modified MUSIC algorithm estimates the DOA of each signal individually after attempting to null the other signals that are present. We compare the new approach to the conventional MUSIC algorithm in simulations, and show that the new approach leads to improved performance. The new approach converges quickly and produces DOA estimates with smaller mean error and standard deviation than MUSIC over a range of incident signal separations. We recommend our approach for systems with challenging antenna placements, a time varying host platform, and limited processing capabilities.

2D DOA Estimation for Coherent Signals with Acoustic Vector-Sensor Array

In this paper, a fast ESPRIT algorithm is presented for two-dimensional (2D) direction-of-arrival (DOA) estimation of coherent signals with a linear acoustic vector-sensor array. Conventional space smoothing ESPRIT (SS-ESPRIT) algorithm for acoustic vector-sensor array has two obvious weak points: (1) eigenvalue decomposition (EVD) of high-order covariance matrix; (2) frequently occurring parameters mismatch which leads to failed 2D DOA estimation. The proposed algorithm can remove the two shortcomings. Firstly, we use two selection matrices to separate received data and form a low-order cross-covariance matrix. Then, ESPRIT algorithm is used to estimate the elevation angles of incident signals. At last, using the estimated elevation angles, a modified array manifold matching method is used to estimate the azimuth angles of coherent signals. During the estimation process of azimuth angles, the proposed method is not required to perform any peak search or EVD. Moreover, azimuth angles are automatically matched with the estimated elevation angles. Compared with the conventional SS-ESPRIT algorithm, the proposed algorithm has lower complexity. However, the estimation accuracy of proposed method almost is the same as the conventional SS-ESPRIT algorithm and far better than PM algorithm. Numerical simulations are presented to demonstrate the performance of the proposed algorithm.

Enhanced knowledge-aided space–time adaptive processing exploiting inaccurate prior knowledge of the array manifold

The accuracy of the prior knowledge of the clutter environments is critical to the clutter suppression performance of knowledge-aided space–time adaptive processing (KA-STAP) algorithms in airborne radar applications. In this paper, we propose an enhanced KA-STAP algorithm to estimate the clutter covariance matrix considering inaccurate prior knowledge of the array manifold for airborne radar systems. The core idea of this algorithm is to incorporate prior knowledge about the range of the measured platform velocity and the crab angle, and other radar parameters into the assumed clutter model to obtain increased robustness against inaccuracies of the data. It first over-samples the space–time subspace using prior knowledge about the range values of parameters and the inaccurate array manifold. By selecting the important clutter space–time steering vectors from the over-sampled candidates and computing the corresponding eigenvectors and eigenvalues of the assumed clutter model, we can obtain a more accurate clutter covariance matrix estimate than directly using the prior knowledge of the array manifold. Some extensions of the proposed algorithm with existing techniques are presented and a complexity analysis is conducted. Simulation results illustrate that the proposed algorithms can obtain good clutter suppression performance, even using just one snapshot, and outperform existing KA-STAP algorithms in presence of the errors in the prior knowledge of the array manifold.

Investigations on antenna array calibration algorithms for direction-of-arrival estimation

Abstract. Direction-of-arrival (DOA) estimation algorithms deliver very precise results based on good and extensive antenna array calibration. The better the array manifold including all disturbances is known, the better the DOA estimation result. A simplification or ideally an omission of the calibration procedure has been a long pursued goal in the history of array signal processing. This paper investigates the practicability of some well known calibration algorithms and gives a deeper insight into existing obstacles. Further analysis on the validity of the common used data model is presented. A new effect in modeling errors is revealed and simulation results substantiate this theory.

An Angular Parameter Estimation Method for Incoherently Distributed Sources Via Generalized Shift Invariance

This paper proposes a new algorithm to estimate the nominal direction-of-arrival (DOA) and the angular spread of multiple incoherently distributed (ID) sources. With the general array manifold (GAM) model, the nominal DOAs are first separated from the original array manifold. Then, a generalized shift invariance property inside the array manifold is identified, based on which the nominal DOAs are obtained when the rank of a trickily formulated matrix drops. Next, the angular spreads are estimated from the central moments of the angular distribution. We also derive a polynomial rooting based search-free method for nominal DOA estimation. This method can greatly reduce the computational complexity. As compared with the popular ESPRIT-ID algorithm, the proposed algorithm can achieve higher accuracy, can handle more sources, and applies to a more general array structure. Extensive simulations are provided to demonstrate the superior performance of the proposed algorithm over the existing works.

Wind speed and direction measurement based on arc ultrasonic sensor array signal processing algorithm

This article investigates a kind of method to measure the wind speed and the wind direction, which is based on arc ultrasonic sensor array and combined with array signal processing algorithm. In the proposed method, a new arc ultrasonic array structure is introduced and the array manifold is derived firstly. On this basis, the measurement of the wind speed and the wind direction is analyzed and discussed by means of the basic idea of the classic MUSIC (Multiple Signal Classification) algorithm, which achieves the measurements of the 360° wind direction with resolution of 1° and 0–60m/s wind speed with resolution of 0.1m/s. The implementation of the proposed method is elaborated through the theoretical derivation and corresponding discussion. Besides, the simulation experiments are presented to show the feasibility of the proposed method. The theoretical analysis and simulation results indicate that the proposed method has superiority on anti-noise performance and improves the wind measurement accuracy.

A Sparse-Based Approach for DOA Estimation and Array Calibration in Uniform Linear Array

This paper aims at achieving a joint estimation of direction-of-arrival (DOA) and array perturbations, such as gain and phase uncertainty, mutual coupling, and sensor location error, which deteriorate the performance of the DOA estimation if not carefully handled. To that end, in this paper, the array perturbations represented by a perturbation matrix as multiplicative noise to the array manifold are then reformulated to facilitate the perturbation compensations. One great finding on the perturbation matrix is that it is a sparse matrix, which contains a lot of zero elements and only few nonzero elements. With this reformulation, the perturbation compensation problems turn into sparse matrix completion problems. Then, by utilizing the sparsity of both the DOAs and perturbation matrix, a joint estimation of DOAs and array perturbations is proposed under a unified optimization framework. In addition, numerical studies are presented to demonstrate the effectiveness of the joint estimation.

Near-field/far-field array manifold of an acoustic vector-sensor near a reflecting boundary.

The acoustic vector-sensor (a.k.a. the vector hydrophone) is a practical and versatile sound-measurement device, with applications in-room, open-air, or underwater. It consists of three identical uni-axial velocity-sensors in orthogonal orientations, plus a pressure-sensor-all in spatial collocation. Its far-field array manifold [Nehorai and Paldi (1994). IEEE Trans. Signal Process. 42, 2481-2491; Hawkes and Nehorai (2000). IEEE Trans. Signal Process. 48, 2981-2993] has been introduced into the technical field of signal processing about 2 decades ago, and many direction-finding algorithms have since been developed for this acoustic vector-sensor. The above array manifold is subsequently generalized for outside the far field in Wu, Wong, and Lau [(2010). IEEE Trans. Signal Process. 58, 3946-3951], but only if no reflection-boundary is to lie near the acoustic vector-sensor. As for the near-boundary array manifold for the general case of an emitter in the geometric near field, the far field, or anywhere in between-this paper derives and presents that array manifold in terms of signal-processing mathematics. Also derived here is the corresponding Cramér-Rao bound for azimuth-elevation-distance localization of an incident emitter, with the reflected wave shown to play a critical role on account of its constructive or destructive summation with the line-of-sight wave. The implications on source localization are explored, especially with respect to measurement model mismatch in maximum-likelihood direction finding and with regard to the spatial resolution between coexisting emitters.

Iterative Methods for Subspace and DOA Estimation in Nonuniform Noise

Usually, direction-of-arrival (DOA) estimators are derived under the assumption of uniform white noise, whose covariance matrix is a scaled identity matrix. However, in practice, the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix. In this situation, the performance of DOA estimators may be deteriorated considerably if the noise nonuniformity is ignored. To tackle this problem, iterative approaches to subspace estimation are developed and the corresponding subspace-based DOA estimators are addressed. In our proposed methods, the signal subspace and noise covariance matrix are first determined by maximizing the log-likelihood (LL) function or solving a least-squares (LS) minimization problem, both of which are accomplished in an iterative manner. Then, the DOAs are determined from the subspace estimate and/or noise covariance matrix estimate with the help of traditional DOA estimators. As the signal subspace and noise covariance matrix can be computed in closed-form in each iteration, the proposals are computationally attractive. Furthermore, the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold, enabling us to handle array uncertainties by incorporating conventional subspace-based calibration algorithms. Simulations and experimental results are included to demonstrate the superiority of the proposed approaches.

Sensor Gain-Phase Errors Estimation Using Disjoint Sources in Unknown Directions

Sensor gain-phase error estimation is necessary for equipment using sensor array, such as radar, sonar, and mobile communication before they come into service. Due to this requirement, we propose an offline calibration algorithm for sensor gain-phase errors using two auxiliary sources, which appear independently of both space and time, named disjoint sources. The significant superiority of this algorithm lies in the use of calibration sources in unknown directions. First, based on the data covariance matrix, the sensor phase errors are obtained, and the relation between phase error matrix and array manifold is established. Second, the directions of two disjoint sources are obtained by the way of 2D search based on eigen-structure subspace method. Third, we provide two methods to realize the algorithm. The proposed algorithm performs independently of phase errors. Moreover, the accurate direction measurement of calibration sources is not necessary. Computer simulations are shown to verify the efficacy of the proposed algorithm.

High‐resolution DOA estimation for cooperation networks using space‐time hopping

Since the traditional direction-of-arrival (DOA) estimation algorithm is passive and non-cooperation, its performance degrades with respect to the large number of terminals and closely spaced sources in multi-nodes networks. A cooperated space-time hopping algorithm to estimate the DOA of all users simultaneously is presented. The signal will be adjusted by the pre-assigned hopping weights during each symbol time. The change of the weights is equivalent to the change of array manifolds, thus enriching differences between uses’ channels. This algorithm is able to estimate more number of signals and separate some closely spaced sources. Simulations demonstrate the effectiveness of the algorithm.