Direction of arrival estimation for nonuniform linear antenna

This paper deals with the problem of the Direction Of Arrival (DOA) estimation with nonuniform linear arrays. The proposed method is based on the Expectation Maximization method where ESPRIT is used in the maximization step. The key idea is to iteratively interpolate the data to a virtual uniform linear array in order to apply ESPRIT to estimate the DOA. The iterative approach allows one to improve the interpolation using the previously estimated DOA. One of this method’s novelties lies in its capacity of dealing with any nonuniform array geometry. This technique manifests significant performance and computational advantages over previous algorithms such as Spectral MUSIC, EM-IQML and the method based on manifold separation technique. EM-ESPRIT is shown to be more robust to additive noise. Furthermore, EM-ESPRIT fully exploits the advantages of using a nonuniform array over a uniform array: simulations show that for the same aperture and with a smaller number of sensors, the nonuniform array presents almost identical performance as the equivalent uniform array.

The performance of wideband array signal processing algorithms is dependant on the noise level in the system. In this thesis, a method is proposed for reducing the level of white noise in wideband arrays via a judiciously designed spatial transformation followed by a bank of high-pass filters. The method is initially introduced for uniform linear arrays (ULAs) and analysed in detail. The spectrum of the signal and noise after being processed by the proposed noise reduction method is analysed, and the correlation matrix of the processed noise is derived. The reduced noise level leads to a higher signal-to-noise ratio (SNR) for the system, which can have a significant effect on the performance improvement of various beamforming methods and other array signal processing applications such as direction of arrival (DOA) estimation. The performance of two well-known beamformers, the reference signal based (RSB) beamformer and the linearly constrained minimum variance (LCMV) beamformer is reviewed. Then, the theoretical effect of applying the proposed noise reduction method as a pre-processing step on the performance enhancement of RSB and LCMV beamformers is studied. The theoretical results are then confirmed by simulation. As a representative example of wideband DOA estimation application, a compressive sensing-based DOA estimation method is employed to demonstrate the improved estimation by applying the pre-processing noise reduction method, which is confirmed by simulation. Next, the idea is extended to wideband non-uniform linear arrays (NLAs). Since, NLA does not have a uniform spacing, the beam response of the row vectors of the transformation is distorted. Therefore, the transformation is re-designed using the least squares method to satisfy the band-pass requirements of the transformation. Simulation results show a satisfactory improvement in the the performance of RSB and LCMV beamformers for the NLA structure. The idea is further extended to uniform rectangular arrays (URAs) and uniform circular arrays (UCAs), as two major types of the planar arrays. Two methods are proposed for reducing the effect of white noise in wideband URAs and for each one, a different transformation is designed. The first one is based on a two-dimensional (2D) transformation and the second one is an adaptation of the method developed for the ULA case. The developed method for the UCA structure is based on a one-dimensional (1D) transformation, with modified modulation for the transformation to satisfy the required band-pass characteristics of the transformation. Same as linear array structures, the RSB and LCMV beamformers are used to demonstrate the performance enhancement of the method for planar arrays.

In automotive millimeter-wave (MMW) radar systems, achieving high-precision direction of arrival (DOA) estimation with a limited number of array elements is a crucial research focus. Compressive sensing (CS) techniques have been demonstrated to offer superior performance in DOA estimation compared to spectral estimation methods. However, traditional CS methods suffer from an off-grid effect, which causes their reconstruction results to deviate from the actual positions of the signal sources, thereby reducing the accuracy. Currently, as a gridless method, atomic norm minimization (ANM) has shown effectiveness in DOA estimation for uniform linear arrays (ULAs). However, the performance of ANM is suboptimal in non-uniform linear arrays (NULAs), and their computational efficiency is not satisfactory. In this paper, we propose a novel algorithm for DOA estimation in NULA, drawing inspiration from the alternating descent conditional gradient algorithm framework. First, we construct an atomic set based on the observation scene and select the atoms with the highest correlation to the residuals as potential signal sources for global estimation. Then, we construct a mapping function for the signal sources in the continuous domain and perform conditional gradient descent in the neighborhood of each signal source, addressing the bias introduced by the off-grid effect. We compared the proposed algorithm with ANM, Iterative Shrinkage Thresholding (IST), and Multiple Signal Classification (MUSIC) algorithms. Simulation experiments validate that the proposed algorithm effectively addresses the off-grid effect and is applicable to DOA estimation in coprime and random arrays. Furthermore, real data experiments confirm the effectiveness of the proposed algorithm.

This paper concerns direction of arrival (DOA) estimation based on a sparse Bayesian learning (SBL) approach. We address two inherent problems of this class of DOA estimation methods: (i) a predefined dictionary can generate off-grid problems to a SBL DOA estimator; (ii) a parametric prior generally enforces the solution to be sparse, but the existence of noise can greatly affect the sparsity of the solution. Both of these issues may have a negative impact on the estimation accuracy. In this paper, we propose an improved root SBL (IRSBL) method for off-grid DOA estimation that adopts a coarse grid to generate an initial dictionary. To reduce the bias caused by dictionary mismatch, we integrate the polynomial rooting approach into the SBL method to refine the spatial angle grid. Then, we integrate a constant false alarm rate rule in the SBL framework to enforce sparsity and improve computational efficiency. Finally, we generalize the IRSBL method to the case of non-uniform linear arrays. Numerical analysis demonstrates that the proposed IRSBL method provides improved performance in terms of both estimation accuracy and computational complexity over the most relevant existing method.

We focus on developing an effective Direction Of Arrival (DOA) estimation method for wideband sources based on the super-resolution concept. In this letter, we represent the data model of a wideband DOA estimation problem in a new form. Then, using this model, we propose an atomic norm minimization problem that leads to an accurate wideband DOA estimation method with no need for any focusing matrices. Moreover, this method requires no initial estimate and can be implemented by non-uniform linear arrays. Numerical simulations show that in comparison to some well-known techniques, the proposed method generates outstanding accuracy and higher robustness to noise. The effectiveness of the method is also verified in presence of close adjacent sources.

We consider the problem of direction of arrival (DOA) estimation based on a nonuniform linear nested array, which is known to provide $O(N^2)$ degrees of freedom (DOFs) using only $N$ sensors. Both subspace-based and sparsity-based algorithms require certain modeling assumptions, e.g., exactly known array geometry, including sensor gain and phase. In practice, however, the actual sensor gain and phase are often perturbed from their nominal values, which disrupts the existing DOA estimation algorithms. In this paper, we investigate the self-calibration problem for perturbed nested arrays, proposing corresponding robust algorithms to estimate both the model errors and the DOAs. The partial Toeplitz structure of the covariance matrix is employed to estimate the gain errors, and the sparse total least squares (STLS) is used to deal with the phase error issue. In addition, we provide the Cramer-Rao bound (CRB) to analyze the robustness of the estimation performance of the proposed approaches. Furthermore, we extend the calibration strategies to general nonuniform linear arrays. Numerical examples are provided to verify the effectiveness of the proposed strategies.

Direction of arrival (DOA) estimation under impulsive noise has always been an important research area in array signal processing. The traditional methods under impulsive noise mostly rely on prior parameters and have high computational complexity. Based on the filtering theory, we present an effective pretreatment filtering technology to cut out the impulse mixed in the array received data and employ the nonuniform linear array to improve the estimation performance further. First, according to the amplitude characteristics of impulse noise, the pretreatment filtering technology is proposed to cut out the impulse based on the median filter and sliding average filter, which is valid for both strong and weak impulsive noise. Second, the minimum redundant array is adopted to carry out array virtual expansion so that the array aperture can be increased and the estimation performance can be improved. Finally, based on the idea of matrix reconstruction, we propose the improved estimation of signal parameters via rotational invariance techniques algorithm and an improved root multiple signal classification algorithm for DOA estimation. Theoretical analysis and simulation results show that the proposed method has a simple processing process, small calculation load, good array expansion ability, and excellent noise adaptability. Moreover, the proposed methods greatly improve the direction-finding performance under the condition of low signal-to-noise ratio and strong impulsive noise.

In this study, isotropic V-shaped uniform and nonuniform arrays are considered. An isotropic array has the same value for the Cramer-Rao bound (CRB) for all direction of arrival (DOA) angles. The conditions for isotropic V-shaped arrays are presented and closed form expressions for V-shaped uniform and nonuniform arrays are found. These expressions return the V-angle for the array. Therefore, given the number of sensors and sensor displacements, isotropic performance V-angle can be found easily. V-shaped arrays are compared with circular arrays and it is also shown that both uniform and nonuniform V-shaped arrays have certain advantages.

DOA (Direction of Arrival) estimation is a major problem in array signal processing applications. Recently, compressive sensing algorithms, including convex relaxation algorithms and greedy algorithms, have been recognized as a kind of novel DOA estimation algorithm. However, the success of these algorithms is limited by the RIP (Restricted Isometry Property) condition or the mutual coherence of measurement matrix. In the DOA estimation problem, the columns of measurement matrix are steering vectors corresponding to different DOAs. Thus, it violates the mutual coherence condition. The situation gets worse when there are two sources from two adjacent DOAs. In this paper, an algorithm based on OMP (Orthogonal Matching Pursuit), called ILS-OMP (Iterative Local Searching-Orthogonal Matching Pursuit), is proposed to improve DOA resolution by Iterative Local Searching. Firstly, the conventional OMP algorithm is used to obtain initial estimated DOAs. Then, in each iteration, a local searching process for every estimated DOA is utilized to find a new DOA in a given DOA set to further decrease the residual. Additionally, the estimated DOAs are updated by substituting the initial DOA with the new one. The simulation results demonstrate the advantages of the proposed algorithm.

Direction Of Arrival (DOA) estimation is a well known problem that has been studied through a wide range of different approaches and methods. Most of these methods make use of several snapshots in the array to provide an accurate result but their performance is commonly degraded when only a single snapshot is available. In a scenario where not only the DOAs are unknown but also the frequencies of the signals need to be estimated with a single snapshot is where heuristics show their potential. This communication presents the use of Particle Swarm Optimization (PSO) to estimate the DOA and the frequency of the incoming signals with a single snapshot. This enhanced methodology, applicable to both uniform and non-uniform arrays, can handle incoming signals with different complex amplitudes. Numerical results that show the validity of the approach are provided.

The paper deals with the optimization of the sparse planar antenna array for direction of arrival (DOA) estimation in two dimensions (azimuth and elevation). The optimization algorithm was proposed on the basis of the peak sidelobe level (SLL) and half-power beamwidth (HPBW) parameters. In empirical validation, we have set up a measurement system to test the efficiency of an optimized array configuration. The array was configured using the patch antennas with frequency band 2.4 GHz. In comparison with several popular array configurations, the experimental results show that the proposed antenna array was optimized, and it provided higher accuracy and resolution in two-dimensional (2D) DOA estimation.

Due to the existence of dense subarray, nested array (NA) is susceptible to mutual coupling, which seriously degrades the parameter estimation performance. To deal with this problem, we propose an improved scheme to obtain direction of arrival (DOA) and mutual coupling estimation in this paper. Specifically, a new sparse subarray can be formed by moving specific sensors of the nested array, which enables well-performed estimation free from severe mutual coupling effect. Subsequently, the contaminated steering vector of the whole non-uniform sparse array is constructed and a quadratic optimization problem is established to simultaneously eliminate DOA estimation ambiguity and estimate mutual coupling coefficients (MCCs). Numerical simulations demonstrate the superiority of the proposed scheme in terms of estimation accuracy and computation complexity.

gold-MUSIC based DOA estimation using ULA antenna of DS-CDMA sources with propagation delay diversity

In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

Uniform linear array (ULA) geometry does not perform well for direction of arrival (DOA) estimation at directions close to the array endfires. Shirvani and Akbari solved this problem by displacing two elements from both ends of the ULA to the top and/or bottom of the array axis. Shirvani-Akbari array (SAA) presents a considerable improvement in the DOA estimation of narrowband sources arriving at endfire directions in terms of DOA estimation accuracy and angular resolution. In this paper, all new proposed SAA configurations are modelled and also examined, numerically. In this paper, two well-known DOA estimation algorithms, multiple signal classification (MUSIC) and minimum variance distortionless response (MVDR), are used to evaluate the effectiveness of proposed arrays using total root mean square error (RMSE) criterion. In addition, two new scenarios are proposed which divide angular search to two parts, directions close to array endfires as well as middle angles. For middle angles, which belong to (−70∘≤𝜃≤70∘), ULA is considered, and for endfire angles, the angles which belong to (−90∘≤𝜃≤−70∘) and (70∘≤𝜃≤90∘), SAA is considered. Simulation results of new proposed scenarios for DOA estimation of narrowband signals show the better performance with lower computational load.