Unknown Nonuniform Noise Research Articles

Source Number Estimation in 2D Uniform Circular and L-Shaped Arrays With Unknown Nonuniform Noise

Source Number Estimation in 2D Uniform Circular and L-Shaped Arrays With Unknown Nonuniform Noise

Expectation-maximization type algorithms for direction of arrival estimation in unknown nonuniform noise

The expectation–maximization (EM) algorithm updates all of the parameter estimates simultaneously, which is not applicable to direction of arrival (DOA) estimation in unknown nonuniform noise. In this work, we present several computationally efficient EM-type algorithms, which update the parameter estimates sequentially, for solving both the deterministic and stochastic maximum–likelihood (ML) direction finding problems in unknown nonuniform noise. Specifically, we design a generalized EM (GEM) algorithm and a space-alternating generalized EM (SAGE) algorithm for computing the deterministic ML estimator. Simulation results show that the SAGE algorithm outperforms the GEM algorithm. Moreover, we design two SAGE algorithms for computing the stochastic ML estimator, in which the first updates the DOA estimates simultaneously while the second updates the DOA estimates sequentially. Simulation results show that the second SAGE algorithm outperforms the first one.

Attention based DOA estimation in the presence of unknown nonuniform noise

To solve the problem of performance degradation of the direction-of-arrival (DOA) estimate in non-uniform noise environment, we propose a novel attention mechanism using deep learning technology, namely array covariance attention (ACA). Specifically, to design the ACA, according to the structural characteristics of the covariance matrix, the pooling operation is removed, and one-dimensional convolution kernels are used to aggregate correlation characteristics in two spatial directions. With fully connected layers and non-linear activation layers, the characteristics are then coded into the perceptual attention matrix to improve useful information of the covariance matrix. Furthermore, to achieve a better performance, the integration position of the attention mechanism is also discussed in the network. Finally, a new deep-learning network is created for DOA estimation in the presence of non-uniform noise. The experimental results demonstrate the efficiency and superiority of the proposed network.

Stochastic Maximum Likelihood Direction Finding in the Presence of Nonuniform Noise Fields

The maximum likelihood (ML) technique plays an important role in direction-of-arrival (DOA) estimation. In this paper, we employ and design the expectation–conditional maximization either (ECME) algorithm, a generalization of the expectation–maximization algorithm, for solving the ML direction finding problem of stochastic sources, which may be correlated, in unknown nonuniform noise. Unlike alternating maximization, the ECME algorithm updates both the source and noise covariance matrix estimates by explicit formulas, and can guarantee that both estimates are positive semi-definite and definite, respectively. Thus, the ECME algorithm is computationally efficient and operationally stable. Simulation results confirm that the ECME algorithm can efficiently obtain the ML based DOA estimate of each stochastic source.

Mixed source localization considering mutual coupling and unknown nonuniform noise under exact spatial geometry

A mixed far-field (FF) and near-field (NF) source localization method in the presence of unknown mutual coupling and nonuniform noise is proposed in this paper, where the exact spatial geometry considering propagation attenuation is adopted. First, the nonuniform noise covariance and FF direction of arrival (DOA) are estimated by the iterative least-squares subspace (ILSS) technique and the principle of rank reduction (RARE), respectively. Then, the NF source components are extracted by applying the oblique projection technique. Finally, by choosing three relative sensor positions and constructing four special cumulant matrices properly, NF DOA and range information are obtained in closed-form expressions, where a scheme to avoid ambiguity is exploited. Simulation result show that the proposed method can yield an improved performance in comparison with existing state-of-the-art methods.

A gridless method for direction finding with sparse arrays in nonuniform noise

The performance of direction finding methods would deteriorate due to unknown nonuniform noise. To cope with this problem, we propose a novel gridless direction finding method based on atomic norm minimization exploiting sparse linear array in nonuniform noise. Specifically, after eliminating the concentrated nonuniform noise related term in coarray signal, the concept of array interpolation is used to recover both the noiseless counterpart of the removed term as well as the holes in coarray. Thus, the effect of nonuniform noise is removed. Besides, we impose a new constraint based on the estimation error distribution of the noise independent terms in the coarray signal. The regularization parameter can thus be selected directly from the Chi-square distribution probability table. In the proposed method, the tedious selection of regularization parameter and the effect of grid mismatch are avoided. Moreover, we derive the corresponding semidefinite programming (SDP) form. With its optimal solution, eigen-decomposition with high complexity is avoided for subsequent DOA estimation. Different from the traditional SDP form, it has an additional transformation matrix composed of the estimation error. Simulations show that the proposed method owns the highest estimation accuracy than previous algorithms in the nonuniform noise.

Underdetermined DOA estimation for moving array with reduced mutual coupling in unknown nonuniform noise environment

In practice, direction of arrival (DOA) estimation methods will suffer from significant performance degradation due to limited physical sensors, mutual coupling effect and unknown nonuniform noise. To improve the performance of underdetermined DOA estimation in the case, this paper proposes a moving sparse uniform linear array (ULA) for more degrees of freedom (DOF) and lower mutual coupling, and then provides an estimation algorithm with unknown nonuniform noise mitigation. There is a systematic procedure to determine the inter-sensor spacing of the original array and number of shifted arrays for the synthetic ULA, for achieving increased DOF. The construction and analysis of mutual coupling matrix are exploited to show the reduced mutual coupling in the synthetic array. A procedure of nonuniform noise suppression for the synthetic array is given by averaging the noise power from the original array, and then root-MUSIC is employed for DOA estimation with low-complexity. Simulation results are given to demonstrate the superiority of the proposed array and algorithm in terms of DOF enhancement, mutual coupling reduction and nonuniform noise mitigation.

Direction-of-Arrival Estimation of Coherent Signals for Uniform Linear Antenna Arrays With Mutual Coupling in Unknown Nonuniform Noise

We recently proposed a direction-of-arrival (DOA) estimation method for the coexistence of uncorrelated and coherent signals, which is related to the uniform linear antenna arrays with mutual coupling (MC) in the presence of unknown nonuniform noise. This technique, however, relies on the assumption of mixed signals and is not suitable for scenarios with purely coherent signals. This paper extends the mixed signal scenario to the purely coherent signals one on one hand, and on the other hand, allows us to directly adopt the ESPPRIT algorithm to perform DOA estimation in MC environments. To be specific, with the help of the least squares (LS) criterion, the nonuniform noise is first eliminated, and the traditional middle subarray scheme can then be employed to be immune to the influence of MC. Unlike the former operation, following a different line of attack the latter can make full use of the whole array and provide a larger array antenna aperture. Furthermore, we derive a new strategy to directly determine the DOAs without taking MC into account and performing spectral search. This brings substantial benefits to the DOA estimation accuracy and computational cost. The superiority of the proposed approaches is verified by numerical examples.

DOA Estimations With Limited Snapshots Based on Improved Rank-One Correlation Model in Unknown Nonuniform Noise

It is well known that classic direction-of-arrival (DOA) estimation techniques yield unsatisfactory performance with limited snapshots in unknown nonuniform noise. In this article, a sparse reconstruction (SR) DOA estimation method combining vectorized and reduced signal covariance matrix (SCM) is proposed. The new approach is based on an improved rank-one correlation model for denoising. With an extended virtual aperture array, this technique is able to provide a high-resolution DOA estimation with limited snapshots and is robust to nonuniform noise. In addition, two effective algorithms are also derived to obtain noise-free SCMs. One is to obtain diagonal entries of the noise-free SCM from the off-diagonal entries based on the fact that diagonal entries of SCM across the array are identical. The other is based on matrix completion (MC) theory which uses the low rank property of the SCM. Numerical results demonstrate that the new approaches yield superior performance than existing techniques in DOA estimations for multiple and compactly placed sources.

RxCV-based unitary SBL algorithm for off-grid DOA estimation with MIMO radar in unknown non-uniform noise

As an indispensable part of array signal processing, direction-of-arrival (DOA) estimation has been well investigated over the past few decades, and many excellent DOA estimation methods have been proposed. In this paper, a receiving domain covariance vector (RxCV) based unitary SBL algorithm is proposed for the off-grid DOA estimation of monostatic multiple-input multiple-output (MIMO) radar in unknown non-uniform noise environment. In the proposed algorithm, the data received by MIMO radar is firstly transformed into receiving domain by a reshape operation. Then the RxCV-based unitary off-grid sparse model without non-uniform noise is constructed through unitary transformation and first-order linear approximation, where the unknown non-uniform noise is got rid off by a linear transformation. Based on the RxCV-based unitary off-grid sparse model, the sparse Bayesian learning (SBL) criterion is adopted to estimate the parameters, where signal variance and off-gird error are estimated by using expectation-maximization (EM) strategy. The DOA estimation is ultimately realized through 1-dimensional spectrum search of the received data. Results of the simulation experiments have provided the evidence of that the proposed algorithm is robustness against nonuniform noise and off-grid error, and it can maintain superior DOA estimation performance compared with other reported sparse signal representation based methods.

Iterative methods for DOA estimation of correlated sources in spatially colored noise fields

Direction of arrival (DOA) estimation in the presence of correlated sources and unknown spatially colored noise field is concerned in this paper. We develop two iterative approaches to jointly estimate the angle parameters and unknown nonuniform noise covariance matrix from multi-snapshot sensor array data. Specifically, we show that both methods allow to obtain the estimates by explicit formulas: i) By concentrating the ML estimation problem with regard to all nuisance parameters, the proposed method provides a concise derivation of the concentrated likelihood function; ii) compact expressions of the estimates of the parameters of interest from sparse Bayesian learning (SBL) principle are also presented. This technique can be deemed as an alternative to ML estimation, and it provides better accuracy often at a lower computational cost. In spatially colored noise fields, the proposals are free of any further structural constraints that are usually imposed on the received signals in most existing direction finding approaches. Extensive simulations and experimental results are presented to demonstrate the satisfying performance of the proposed methods.

Direction Finding by Covariance Matrix Sparse Representation With Sensor Gain and Phase Uncertainties in Unknown Non-Uniform Noise

The perfectly partly calibrated antenna array is a frequently assumption in most of the existing array gain/phase calibration methods. In practice, however, the partly calibrated array is usually not available. In this letter, a tail optimization method for direction finding with unknown gains and phases in the presence of spatially non-uniform noise is proposed. Specifically, the unknown gain/phase entry is firstly merged into the signal power by using the sparse representation. Subsequently, a tail optimization method that can significantly suppress the occurrence of pseudo-peaks is designed to determine the signal DOAs without a priori information of unknown sensor gain and phase errors. In addition, the spatially non-uniform noise can be removed by a linear transformation to improve the robustness against the noise. Numerical simulations examples are presented to demonstrate the effectiveness and superior performance of the proposed approach over the other existing counterparts.

Stokes parameters and DOA estimation for nested polarization sensitive array in unknown nonuniform noise environment

To obtain a large aperture for improving parameter estimation performance, this paper introduces a novel polarization sensitive array composed of augmented and optimally nested subarrays with differently oriented antennas, and then proposes an algorithm for direction of arrival (DOA) and Stokes parameter estimation of completely and partially polarized signals, in unknown nonuniform noise environment and without source number knowledge. The aperture of the proposed array significantly increases since the difference co-array of the optimally nested subarray can obtain the maximum degrees of freedom. There is a systematic procedure to determine the numbers of antennas in the two subarrays in order to obtain similar apertures for the two subarrays. Unfortunately, both the difference co-arrays of the optimally nested subarray and between the two subarrays have holes, which degrades performance of parameter estimation. By using oblique projection operators, the proposed algorithm first fills the holes and suppresses the nonuniform noise to obtain hole-free and noiseless difference co-arrays, and then the difference co-arrays are employed to form a block-sparsity model. Finally, based on the model, block orthogonal matching pursuit algorithm is used for parameter estimation. The Cramér-Rao bound and its existence condition are derived. Simulation results are given to demonstrate the superior performance of the proposed array and method.

Reweighted Covariance Fitting Based on Nonconvex Schatten-p Minimization for Gridless Direction of Arrival Estimation

In this paper, we reformulate the gridless direction of arrival (DoA) estimation problem in a novel reweighted covariance fitting (CF) method. The proposed method promotes joint sparsity among different snapshots by means of nonconvex Schatten-p quasi-norm penalty. Furthermore, for more tractable and scalable optimization problem, we apply the unified surrogate for Schatten-p quasi-norm with two-factor matrix norms. Then, a locally convergent iterative reweighted minimization method is derived and solved efficiently via a semidefinite program using the optimization toolbox. Finally, numerical simulations are carried out in the background of unknown nonuniform noise and under the consideration of coprime array (CPA) structure. The results illustrate the superiority of the proposed method in terms of resolution, robustness against nonuniform noise, and correlations of sources, in addition to its applicability in a limited number of snapshots.

Parametric Sparse Bayesian Dictionary Learning for Multiple Sources Localization With Propagation Parameters Uncertainty

Received signal strength (RSS) based source localization method is popular due to its simplicity and low cost. However, this method is highly dependent on the propagation model which is not easy to be captured in practice. Moreover, most existing works only consider the single source and the identical measurement noise scenario, while in practice multiple co-channel sources may transmit simultaneously, and the measurement noise tends to be nonuniform. In this paper, we study the multiple co-channel sources localization (MSL) problem under unknown nonuniform noise, while jointly estimating the parametric propagation model. Specifically, we model the MSL problem as being parameterized by the unknown source locations and propagation parameters, and then reformulate it as a joint parametric sparsifying dictionary learning (PSDL) and sparse signal recovery (SSR) problem which is solved under the framework of sparse Bayesian learning with iterative parametric dictionary approximation. Furthermore, multiple snapshot measurements are utilized to improve the localization accuracy, and the Cramer-Rao lower bound (CRLB) is derived to analyze the theoretical estimation error bound. Comparing with the state-of-the-art sparsity-based MSL algorithms as well as CRLB, extensive simulations show the importance of jointly inferring the propagation parameters,and highlight the effectiveness and superiority of the proposed method.

Underdetermined DOA Estimation via Covariance Matrix Completion for Nested Sparse Circular Array in Nonuniform Noise

This paper proposes a covariance matrix completion based algorithm for underdetermined direction of arrival (DOA) estimation in the presence of unknown nonuniform noise using nested sparse circular array (NSCA) with only N sensors. The proposed algorithm provides a systematic procedure to complete a covariance matrix for a virtual uniform circular array (UCA) with M sensors (M > N). Compared with the covariance matrix of the NSCA, the completed covariance matrix is capable of increasing degrees of freedom (DOFs), and is noise-free to mitigate the effect of nonuniform noise. The elements of the completed covariance matrix are from three steps: (1) elements from covariance matrix of the NSCA; (2) elements generated from the properties of the UCA; (3) elements produced from output of oblique projection operator based on initial DOAs. Then compressive sensing (CS) method is used to estimate DOAs based on the completed covariance matrix for better performance. The computational complexity of the proposed algorithm, and CRB are also given. Simulation results demonstrate that the proposed algorithm outperforms the state-of-the-art methods in estimation accuracy.

Covariance Matrix Reconstruction for Direction Finding with Nested Arrays Using Iterative Reweighted Nuclear Norm Minimization

In this paper, we address the direction finding problem in the background of unknown nonuniform noise with nested array. A novel gridless direction finding method is proposed via the low-rank covariance matrix approximation, which is based on a reweighted nuclear norm optimization. In the proposed method, we first eliminate the noise variance variable by linear transform and utilize the covariance fitting criteria to determine the regularization parameter for insuring robustness. And then we reconstruct the low-rank covariance matrix by iteratively reweighted nuclear norm optimization that imposes the nonconvex penalty. Finally, we exploit the search-free DoA estimation method to perform the parameter estimation. Numerical simulations are carried out to verify the effectiveness of the proposed method. Moreover, results indicate that the proposed method has more accurate DoA estimation in the nonuniform noise and off-grid cases compared with the state-of-the-art DoA estimation algorithm.

Unitary Matrix Completion-Based DOA Estimation of Noncircular Signals in Nonuniform Noise

In this paper, a novel direction-of-arrival (DOA) estimation algorithm is proposed for noncircular signals with nonuniform noise by using the unitary matrix completion (UMC) technique. First, the proposed method utilizes the noncircular property of signals to design a virtual array for approximately doubling the array aperture. Then, the virtual complex-valued covariance matrix with the unknown nonuniform noise is transformed into the real-valued one by utilizing the unitary transformation to improve the computational efficiency. Next, a novel UMC method is formulated for the DOA estimation to remove the influence of nonuniform noise. Finally, the DOA without the influence of the unknown noncircularity phase is obtained by using the modified estimation of signal parameters via rotational invariance technique (ESPRIT). Especially, for handling the coherent sources, the forward–backward spatial smoothing technique is utilized to reconstruct a full-rank covariance matrix so that the signal subspace and the noise subspace can be correctly separated. Due to utilizing the extended array aperture and the unitary transformation, the proposed method can identify more sources than the number of physical sensors and provides higher angular resolution and better estimation performance. Compared with the existing DOA estimation algorithms for noncircular signals, the proposed one can effectively suppress the influence of the nonuniform noise. The simulation results are provided to verify the effectiveness and superiority of the proposed method.

Underdetermined Direction-of-Arrival Estimation Using Difference Coarray in the Presence of Unknown Nonuniform Noise

The coarray techniques, e.g., nested and coprime arrays, can significantly improve degrees of freedom (DOFs) via constructing a so-called difference coarray, which enables underdetermined direction-of-arrival (DOA) estimation within reach in the presence of unknown nonuniform noise. There are repeated lags in the difference coarray, which also contain useful statistical information. In this paper, the repeated lags are properly used for DOA estimation algorithm design in unknown nonuniform noise environments. Specifically, the number of repeated lags in the difference coarray is rigorously given. Then these repeated lags and unique lags are judiciously rearranged to form a pseudo data set, which is composed of linearly independent vectors. Based on the pseudo data set, we propose two algorithms for DOA estimation in the presence of unknown nonuniform noise. One is a searching algorithm without source number knowledge (SASNK), and the other is a multi-snapshot compressive sensing method (MSCS) with better DOA estimation performance. The MSCS also does not require source number information. Numerical results are included to showcase the effectiveness of the proposed algorithms.

A De-Noising 2-D-DOA Estimation Method for Uniform Rectangle Array

This letter tackles the problem of 2-D direction-of-arrival (2-D-DOA) estimation for uniform rectangle array (URA) in the presence of unknown nonuniform noise. By exploiting the diagonal characteristic of the noise covariance matrix, a reduced covariance tensor is formulated, which links the 2-D-DOA estimation problem to the quadrilinear decomposition model, and an alternating least squares strategy is developed to obtain the 2-D-DOA estimates. Furthermore, the stochastic Cramer–Rao bound of 2-D-DOA estimation for URA is derived. The proposed method does not require eigendecomposition and can achieve automatically paired 2-D-DOA estimates. Numerical experiments demonstrate the effectiveness of the proposed method.