DOA Estimation Based on Golden Ratio-Inspired Coprime Array

Sparse Bayesian learning (SBL) is applied to the coprime array for underdetermined wideband direction of arrival (DOA) estimation. Using the augmented covariance matrix, the coprime array can achieve a higher number of degrees of freedom (DOFs) to resolve more sources than the number of physical sensors. The sparse-based DOA estimation can deteriorate the detection and estimation performance because the sources may be off the search grid no matter how fine the grid is. This dictionary mismatch problem can be well resolved by the SBL using fixed point updates. The SBL can automatically choose sparsity and approximately resolve the non-convex optimizaton problem. Numerical simulations are conducted to validate the effectiveness of the underdetermined wideband DOA estimation via SBL based on coprime array. It is clear that SBL can obtain good performance in detection and estimation compared to least absolute shrinkage and selection operator (LASSO), simultaneous orthogonal matching pursuit least squares (SOMP-LS) , simultaneous orthogonal matching pursuit total least squares (SOMP-TLS) and off-grid sparse Bayesian inference (OGSBI).

The limited space of a conformal array may lead to a serious mutual coupling effect, which will significantly affect the performance of direction of arrival (DOA) estimation algorithms. In this paper, an efficient 2-D direction finding method is developed in the presence of unknown mutual coupling for the uniform cylindrical conformal array (CCA). To avoid the time-consuming two-dimensional spectral peak searching, the 2-D DOA estimation is decoupled and divided into two 1-D DOA estimations. Elevation is first estimated based on a subarray estimation of signal parameters via rotation invariant technique (ESPRIT), and then azimuth is estimated based on the rank reduction (RARE) method by using the elevation estimation result. Consequently, the mutual coupling coefficients can be estimated after getting the DOA estimates. The proposed method can well calibrate the mutual coupling effect of a cylindrical array with a low computational complexity. The final simulation results corroborate our analysis.

Many direction-of-arrival (DOA) estimation algorithms have been proposed recently. However, the effect of mutual coupling among antenna elements has not been taken into consideration. In this paper, a novel DOA and mutual coupling coefficient estimation algorithm is proposed in intelligent transportation systems (ITS) via conformal array. By constructing the spectial mutual coupling matrix (MCM), the effect of mutual coupling can be eliminated via instrumental element method. Then the DOA of incident signals can be estimated based on parallel factor (PARAFAC) theory. The PARAFAC model is constructed in cumulant domain using covariance matrices. The mutual coupling coefficients are estimated based on the former DOA estimation and the matrix transformation between MCM and the steering vector. Finally, due to the drawback of the parameter pairing method in Wan et al., 2014, a novel method is given to improve the performance of parameter pairing. The computer simulation verifies the effectiveness of the proposed algorithm.

Recently, structured sparse arrays have been developed for improving direction-of-arrival (DOA) estimation performance on moving platforms. By employing synthetic aperture processing technology, these sparse arrays can yield a synthetic difference coarray with lots of contiguous lags, resulting in a high number of uniform degrees of freedom (DOFs). In this paper, we devise an improved open-box array (IOBA) configuration for two-dimensional (2D) DOA estimation on moving platforms. The proposed array configuration is devised by rearranging the sensors in the standard open-box array (OBA). More specifically, the IOBA is derived by placing sparsely the sensors of the OBA within a rectangular region. Under the fixed number of sensors, the IOBA configuration is uniquely determined by a closed-form expression and its number of uniform DOFs can also be analytically expressed. By exploiting array motion, the IOBA can generate more contiguous coarray lags, and thus it provides a high number of uniform DOFs than the existing sparse planar arrays. Moreover, the IOBA suffers less mutual coupling effects than the existing sparse planar arrays. Numerical results demonstrate the superiority of the proposed array over several existing sparse planar arrays.

This paper addresses the degradation in direction of departure (DOD) and direction of arrival (DOA) estimation performance caused by array mutual coupling in bistatic MIMO sonar systems. A joint DOD-DOA estimation algorithm based on smoothed Atomic Norm Minimization (ANM) is proposed. The method mitigates the effects of array mutual coupling by applying a decoupling smoothing matrix to preprocess the received signals. The processed signals exhibit a structure resembling line spectral signals, which allows for the formulation of an ANM optimization problem. By exploiting the inherent sparsity of the signals, the proposed algorithm effectively reconstructs a high signal-to-noise ratio (SNR) covariance matrix, even with a limited number of snapshots, enabling accurate estimation of DOD and DOA. Simulation results validate the algorithm’s performance under mutual coupling conditions in MIMO sonar transmit and receive arrays. The algorithm maintains high estimation accuracy even with a limited number of received snapshots, making it suitable for rapid target localization in real underwater detection applications. Compared to existing gridless sparse recovery methods for covariance matrix estimation, the proposed algorithm achieves lower computational dimensions and faster execution. Additional simulation experiments further demonstrate the effectiveness and superiority of the proposed method under varying SNR and target angle separation conditions.

A coprime array is capable of achieving more degrees-of-freedom for direction-of-arrival (DOA) estimation than a uniform linear array when utilizing the same number of sensors. However, existing algorithms exploiting coprime array usually adopt predefined spatial sampling grids for optimization problem design or include spectrum peak search process for DOA estimation, resulting in the contradiction between estimation performance and computational complexity. To address this problem, we introduce the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) to the coprime coarray domain, and propose a novel coarray ESPRIT-based DOA estimation algorithm to efficiently retrieve the off-grid DOAs. Specifically, the coprime coarray statistics are derived according to the received signals from a coprime array to ensure the degrees-of-freedom (DOF) superiority, where a pair of shift invariant uniform linear subarrays is extracted. The rotational invariance of the signal subspaces corresponding to the underlying subarrays is then investigated based on the coprime coarray covariance matrix, and the incorporation of ESPRIT in the coarray domain makes it feasible to formulate the closed-form solution for DOA estimation. Theoretical analyses and simulation results verify the efficiency and the effectiveness of the proposed DOA estimation algorithm.

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.

To obtain an antenna array with isotropic radiation, spherical antenna array (SAA) is the right array configuration. The challenges of locating signals transmitted within the proximity of antenna array have been investigated considerably in the literature. However, near‐field (NF) source localization of signals has hitherto not been investigated effectively using SAA in the presence of mutual coupling (MC). MC is another critical problem in antenna arrays. This paper presents an NF range and direction‐of‐arrival (DoA) estimation technique via the direction‐independent and signal invariant spherical harmonics (SH) characteristics in the presence of mutual coupling. The energy of electromagnetic (EM) signal on the surface of SAA is captured successfully using a proposed pressure interpolation approach. The DoA estimation within the NF region is then calculated via the distribution of pressure. The direction‐independent and signal invariant characteristics, which are SH features, are obtained using the DoA estimates in the NF region. We equally proposed a learning scheme that uses the source activity detection and convolutional neural network (CNN) to estimate the range of the NF source via the direction‐independent and signal invariant features. Considering the MC problem and using the DoA estimates, an accurate spectrum peak in the multipath situation in conjunction with MC and a sharper spectrum peak from a unique MC structure and smoothing algorithms are obtained. For ground truth performance evaluation of the SH features within the context of NF localization, a numerical experiment is conducted and measured data were used for analysis to incorporate the MC and consequently computed the root mean square error (RMSE) of the source range and NF DoA estimate. The results obtained from numerical experiments and measured data indicate the validity and effectiveness of the proposed approach. In addition, these results are motivating enough for the deployment of the proposed method in practical applications.

A novel high degree of freedom sparse array with displaced multistage cascade subarrays

A special coprime array configuration for increased degrees of freedom

The performance of an antenna array is considerably affected by mutual coupling effects between antenna elements. When a large number of antenna elements are located close to each other, mutual coupling becomes more significant. In this study, by using a new mutual impedance matrix, a decoupling methodology for compensating mutual coupling effects in a practical very high frequency (VHF)/ultra high frequency (UHF) Yagi‐Uda antenna array is introduced. No previous publications have studied VHF/UHF Yagi‐Uda antenna arrays in this context. In the proposed scheme, extreme care has been taken to account for both self‐ and mutual impedance related to mutual coupling effects. Experimental and simulation results show that using the proposed method, a perfect decoupling is achieved. The application of high‐resolution direction of arrival (DOA) estimation algorithms in decoupled experimental data leads to excellent performance of DOA estimation, in terms of accuracy and resolution. In addition, it is concluded (from experimental and simulation results) that mutual coupling effects between array elements as well as the root‐mean‐square error of estimated parameters depend on the direction of arrival. It is also deduced that in the presence of mutual coupling, estimation of signal parameter via rotation invariance techniques algorithm performs better than other subspace‐based algorithms.

In this proposed work, a subspace based method of Direction of Arrival (DOA) estimation with Mutual Coupling (MC) compensation and wavelet denoising for Uniform Linear Array (ULA) is addressed. A preprocessing technique of denoising by Wavelet Transform (WT) is accomplished and followed by Mutual Coupling compensation algorithm to improve DOA estimation. A complex symmetric Toeplitz matrix is modeled and based on this matrix, mutual coupling between sensors is compensated. By denoising and mutual coupling compensation, this method accomplishes a satisfactory performance for weak signals in DOA estimation without array calibration. The effectiveness of the proposed method is studied through simulations.

Machine learning-assisted simulated annealing for deciphering multi-factor coupling mechanisms in complex wastewater adsorption systems with experimental validation.

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.

Errors in the representation of the drop size distribution are a major source of uncertainty in rainfall estimation, since both radar reflectivity and microwave attenuation depend nonlinearly on precipitation microphysics. These uncertainties propagate directly into the specific attenuation–rain rate (k–R) relationship through the interaction between electromagnetic waves and hydrometeors, leading to systematic biases when globally fixed coefficients are used. In standard practice, the k–R relationship is expressed as a power law of the form k=aRb, where the coefficients a and b are typically taken from the International Telecommunication Union (ITU) recommendations and assumed to be globally applicable. The use of the ITU coefficients implicitly assumes stationary rainfall microphysics, which is physically inconsistent under varying cloud and rain regimes. This highlights the need for stratified parameterizations in which the coefficients are optimized for different microphysical conditions. In this context, cloud phase information from geostationary satellites provides a physically meaningful basis for clustering the k–R relationship, as different cloud phases are associated with distinct precipitation formation processes and drop size distributions.The objective of this study is to derive cloud phase dependent k–R parameterizations and to assess their performance across a large disdrometer network. A global disdrometer dataset (Ghiggi et al., 2021, DISDRODB) covering multiple climatic regions is used to simulate k–R relationships across a wide frequency range from 5 to 100 GHz using the T-matrix scattering method. SEVIRI MSG observations are used as input to the Cloud Physical Properties (CPP) product provided by the EUMETSAT Climate Monitoring Satellite Application Facility (CM SAF), from which cloud phase is classified into water, supercooled water, mixed phase, deep convective, cirrus, and opaque ice categories. Frequency dependent k–R coefficients are derived separately for each cloud type. The framework is evaluated across more than 100 independent disdrometer sites, primarily concentrated in Europe.Relative to the ITU recommended model (ITU-R P.838-3), the cloud phase adaptive parameterization substantially reduces root mean square error (RMSE), with the strongest improvements observed at 5 to 8 GHz. At these frequencies, more than 90 percent of sites show lower RMSE, with average reductions reaching up to 1.5 mm.h-1. More moderate improvements are found at higher frequencies from 60 to 100 GHz, where around 60 percent of sites show RMSE reductions, with average improvements below 0.5 mm.h-1.These results show that cloud phase informed k–R parameterizations can significantly improve rainfall estimation from commercial microwave links and indicate potential applicability to radar systems.Reference:Ghiggi, G., Billault-Roux, A. C., Candolfi, K., Pillac-Mage, L., Unal, C., Schleiss, M., Uijlenhoet, R., Raupach, T., and Berne, A.: DISDRODB – A global disdrometer archive of raindrop size distribution observations, PrePEP 2025, Karlsruhe, Germany, 10–12 March 2025, https://indico.kit.edu/event/4015/contributions/18545/, 2025. This work was supported by the Czech Science Foundation (GACR), Czech Republic, under Grant No. 24-13677L (MERGOSAT).