Robust wavelet denoising based DOA estimation with mutual coupling compensation

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.

To effectively find the direction of non-circular signals received by a uniform linear array (ULA) in the presence of non-negligible perturbations between array elements, i.e., mutual coupling, in colored noise, a direction of arrival (DOA) estimation approach in the context of high order statistics is proposed in this correspondence. Exploiting the non-circularity hidden behind a certain class of wireless communication signals to build up an augmented cumulant matrix, and carrying out a reformulation of the distorted steering vector to extract the angular information from the unknown mutual coupling, by exploiting the characteristic of mutual coupling, i.e., a limited operating range and an inverse relation of coupling effects to interspace, we develop a MUSIC-like estimator based on the rank-reduction (RARE) technique to directly determine directions of incident signals without mutual coupling compensation. Besides, we provide a solution to the problem of coherency between signals and mutual coupling between sensors co-existing, by selecting a middle sub-array to mitigate the undesirable effects and exploiting the rotation-invariant property to blindly separate the coherent signals into different groups to enhance the degrees of freedom. Compared with the existing robust DOA methods to the unknown mutual coupling under the framework of fourth-order cumulants (FOC), our work takes advantage of the larger virtual array and is able to resolve more signals due to greater degrees of freedom. Additionally, as the effective aperture is virtually extended, the developed estimator can achieve better performance under scenarios with high degree of mutual coupling between two sensors. Simulation results demonstrate the validity and efficiency of the proposed method.

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.

Performance degradation due to the mutual coupling effect of antenna arrays in direction-of-arrival (DOA) estimations has been well known, and many mutual coupling compensation methods have been proposed throughout the years. In particular, the mutual coupling effect becomes significant when the antenna elements are closely spaced, which is difficult to compensate. In this paper, a new, accurate method is introduced to determine the receiving mutual impedances of antenna arrays with closely spaced omni-directional antenna elements. This new method uses a number of plane wave sources coming from different directions to determine the receiving mutual impedances of a particular antenna element with all other antenna elements in the array in a single step. This step is repeated for all the antenna elements in the array, and the full mutual impedance matrix of the array is thus obtained. Using the Matrix Pencil Method (MPM), DOA estimations using eight-element arrays were used to demonstrate the validity and accuracy of this new method.

Direction of arrival (DOA) estimation is a classic problem in array processing. It has wide applications in wireless communications, radar, acoustics, and smart antennas, to name just a few. In this paper, we present a novel comparative study of six array geometries and their impact on mutual coupling and DOA estimation performance. Two scenarios are presented: with and without mutual coupling. A numerical software package was used to simulate the array geometries with dipole antennas. The mutual coupling matrix was calculated from the S‐parameters of the simulated arrays at the operating frequency based on specific sensor locations. The MUSIC algorithm was used to resolve the source location using the difference coarray technique. A well‐known smoothing technique was used to improve the rank of the covariance matrix, allowing MUSIC to compute the DOA using the sparse arrays. Several properties of each array are described, such as the physical sensor location, difference coarray, weight function, and coupling matrix. The sparse array HFCA and UACA achieved an RMSE below 2 degrees (for both 9 and 16 sources and the whole SNR range) and 0.5 degrees (for both 9 and 16 sources and SNR equals to 30 dB), respectively. The performance of the DOA estimation was compared using RMSE as a metric, considering the environment configuration with different number of sources and SNR conditions.

A structured least square (LS) method for simultaneous estimation of the mutual coupling matrix (MCM) and directions of arrival (DOAs) of signal sources for uniform linear array (ULA) and uniform circular array (UCA) is presented. The DOAs and MCM can be simultaneously estimated by the proposed method when observations of at least two different DOAs are available. This method significantly simplifies the procedure of mutual coupling compensation and it can also be applied for the calibration of ULA and UCA. Simulation results demonstrate the efficiency and accuracy of the proposed method.

A new mutual coupling compensation method based on a new mutual impedance matrix, as well as its application to dipole arrays, are proposed. This new mutual impedance matrix is deduced by electromotive force (EMF) method, based on the current distribution obtained by the characteristic basis function method. It appears in a concise and explicit formulation that facilitates the numerical calculation. The compensation performance is demonstrated and evaluated through its application in direction of arrival (DOA) estimation. Numerical results show that the proposed method exhibits excellent compensation performance compared with conventional mutual impedance matrix approaches.

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.

Distributed subarray antennas (DSAs), which are sparse arrays consisting of two or more far separated subarrays, have many advantages over uniform linear array, especially for direction of arrival (DOA) estimation. However, they are subject to manifold ambiguity, which has significant influence on DOA estimation. In order to solve the manifold ambiguity of uncorrelated sources for DSA, a novel method based on estimation of signal parameters via rotational invariance technique by utilizing optimal subarray partition is proposed in this paper. In the proposed method, an optimized reference estimation is obtained by the rotational invariance between the new subarrays with optimal partition of DSA. The high accuracy and unambiguous DOA estimations are then disambiguated easily according to the optimized reference estimation. In this way, the performance of disambiguated DOA estimation can be enhanced in cases of the low signal-to-noise ratio and the large spacing between the subarrays. Moreover, the ambiguity threshold effect of DOA estimation for DSA is analyzed by means of the maximum a posteriori estimator. Computer simulation results show good performance of the proposed method and the effectiveness of the ambiguity threshold for DSA.

Strong interference will affect direction of arrival (DOA) estimation of weak desired signal and even cause DOA estimation failure. This paper investigates the weak signal DOA estimation for an antenna array under strong interference signals, and proposed a novel DOA estimation method for strong interference source suppression and weighted l1-norm sparse representation. A parallel adaptive beamforming algorithm based on power inversion is used to suppress strong interference and form new array data. To reduce spurious peaks in the spectrum under strong interference, a weighted matrix is determined by the optimized subspace algorithm for the subspace projection. Then, the DOA estimation, which is calculated by weighted l1-norm sparse representation, is formed by the weighted matrix and new array data. In this paper, the superiority of the proposed algorithm is illustrated by an example of unmanned aerial vehicle (UAV) video signal DOA estimation under strong interference signals. The simulated results of an orthogonal frequency division multiplexing signal indicate that the proposed algorithm shows merits of fewer snapshots, a sharper main lobe, a lower average noise spectrum value, higher DOA estimation accuracy and success rate. For validation, an outdoor experiment was conducted which demonstrated that the proposed algorithm is superior to other algorithms and can be used for DOA estimation of UAV video signals under strong WiFi interference. Both the simulations and experiments verify that the proposed algorithm can effectively suppress strong interference and achieve better DOA estimation performance for weak signals.

Recently, popular machine learning algorithms have successfully been applied to the direction of arrival (DOA) estimation. An implementation of determination of DOA estimation is presented based on deep neural networks (DNNs) to reduce the computational complexity of traditional superresolution DOA estimation methods. The classical DOA estimation algorithms have limitations due to unforeseen effects, such as array perturbations. Instead of computing an inverse mapping based on the incomplete forward mapping that relates the signal directions to the array outputs, the DOA problem is approached as a mapping, which can be approximated using a suitable DNN trained with input output pairs. The neural network architecture is based on a multilayer perception and a group of parallel DNNs to perform detection and DOA estimation, respectively. Simulation results are performed to investigate the effect of network parameters on estimation accuracy so that they can be roughly determined in the case of one signal scenario. Based on a set of simulations and experimental measurements, the performance of the optimum network is also assessed and compared to that of the classical DOA estimation methods for multiple signals. It has been shown that the proposed method can not only achieve reasonably high DOA estimation accuracy, but also dramatically reduce the computational complexity and the memory space.

FOMP algorithm for Direction of Arrival estimation

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

Recently developed super nested array families have drawn much attention owing to their merits on keeping the benefits of the standard nested arrays while further mitigating coupling in dense subarray portions. In this communication, a new mutual coupling model for nested arrays is constructed. Analyzing the structure of the newly formed mutual coupling matrix, a transformation of the distorted steering vector to separate angular information from the mutual coupling coefficients is revealed. By this property, direction of arrival (DOA) estimates can be determined via a grid search for the minimum of a determinant function of DOA, which is induced by the rank reduction property. We also extend the robust DOA estimation method to accommodate the unknown mutual coupling and gain-phase mismatches in the nested array. Compared with the schemes of super nested array families on reducing the mutual coupling effects, the solutions presented in this paper has two advantages: (a) It is applicable to the standard nested arrays without rearranging the configuration to increase the inter-element spacing, alleviating the cross talk in dense uniform linear arrays (ULAs) as well as gain-phase errors in sparse ULA parts; (b) Perturbations in nested arrays are estimated in colored noise, which is significant but rarely discussed before. Simulations results corroborate the superiority of the proposed methods using fourth-order cumulants.

For direction of arrival (DoA) estimation, the data-driven deep-learning method has an advantage over the model-based methods since it is more robust against model imperfections. Conventionally, networks are based singly on regression or classification and may lead to unstable training and limited resolution. Alternatively, this paper proposes a two-branch neural network (TB-Net) that combines classification and regression in parallel. The grid-based classification branch is optimized by binary cross-entropy (BCE) loss and provides a mask that indicates the existence of the DoAs at predefined grids. The regression branch refines the DoA estimates by predicting the deviations from the grids. At the output layer, the outputs of the two branches are combined to obtain final DoA estimates. To achieve a lightweight model, only convolutional layers are used in the proposed TB-Net. The simulation results demonstrated that compared with the model-based and existing deep-learning methods, the proposed method can achieve higher DoA estimation accuracy in the presence of model imperfections and only has a size of 1.8 MB.