Critical Review of Basic Methods on DoA Estimation of EM Waves Impinging a Spherical Antenna Array

Direction-of-arrival (DoA) estimation of electromagnetic (EM) waves impinging on a spherical antenna array in short time windows is examined in this paper. Reflected EM signals due to non-line-of-sight propagation measured with a spherical antenna array can be coherent and/or highly correlated in a snapshot. This makes spectral-based methods inefficient. Spectral methods, such as maximum likelihood (ML) methods, multiple signal classification (MUSIC), and beamforming methods, are theoretically and systematically investigated in this study. MUSIC is an approach used for frequency estimation and radio direction finding, ML is a technique used for estimating the parameters of an assumed probability distribution for given observed data, and PWD applies a Fourier transform to the capture response and produces them in the frequency domain. Although they have been previously adapted and used to estimate DoA of EM signals impinging on linear and planar antenna array configurations, this paper investigates their suitability and effectiveness for a spherical antenna array. Various computer simulations were conducted, and plots of root-mean-square error (RMSE) against the square root of the Cramér–Rao lower bound (CRLB) were generated and used to evaluate the performance of each method. Numerical experiments and results from measured data show the degree of appropriateness and efficiency of each method. For instance, the techniques exhibit identical performance to that in the wideband scenario when the frequency f = 8 GHz, f = 16 GHz, and f = 32 GHz, but f = 16 GHz performs best. This indicates that the difference between the covariance matrix of the signal is coherent and that the steering vectors of signals impinging from that angle are small. MUSIC and PWD share the same problems in the single-frequency scenario as in the wideband scenario when the delay sample d = 0. Consequently, the DoA estimation obtained with ML techniques is more suitable, less biased, and more robust against noise than beamforming and MUSIC techniques. In addition, deterministic ML (DML) and weighted subspace fitting (WSF) techniques show better DoA estimation performance than the stochastic ML (SML) technique. For a large number of snapshots, WSF is a better choice because it is more computationally efficient than DML. Finally, the results obtained indicate that WSF and ML methods perform better than MUSIC and PWD for the coherent or partially correlated signals studied.

Source Localization of EM Waves in the Near-Field of Spherical Antenna Array in the Presence of Unknown Mutual Coupling

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.

Spherical Scanning 3-D Microwave Imaging of Near-field Scatterers Mutually Coupled With an Antenna Array

<div>*This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.<br></div><div><br></div>In this article, we propose a 3-D synthetic aperture imaging method with spherical antenna scanning to identify scatterers located close to an antenna array, such as fixtures or support of the antenna. Previous studies have shown that 2-D and 3-D synthetic aperture imaging techniques with planar, circular, and cylindrical scanning can successfully reconstruct spatial images of near-field scatterers. The spherical scanning approach considered in this article is expected to improve the 3-D image resolution because more angular diversity can be achieved in the elevation direction. However, as we show in this study, simple extension of the previous techniques to the spherical case results in undesired blur artifacts in the reconstructed image. To overcome this problem, we introduce a correction factor in the image reconstruction. The proposed imaging algorithm is validated by numerical electromagnetic simulation based on the method of moments.

Spherical Scanning 3-D Microwave Imaging of Near-field Scatterers Mutually Coupled With an Antenna Array

<div>*This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.<br></div><div><br></div>In this article, we propose a 3-D synthetic aperture imaging method with spherical antenna scanning to identify scatterers located close to an antenna array, such as fixtures or support of the antenna. Previous studies have shown that 2-D and 3-D synthetic aperture imaging techniques with planar, circular, and cylindrical scanning can successfully reconstruct spatial images of near-field scatterers. The spherical scanning approach considered in this article is expected to improve the 3-D image resolution because more angular diversity can be achieved in the elevation direction. However, as we show in this study, simple extension of the previous techniques to the spherical case results in undesired blur artifacts in the reconstructed image. To overcome this problem, we introduce a correction factor in the image reconstruction. The proposed imaging algorithm is validated by numerical electromagnetic simulation based on the method of moments.

Excitation of a homogeneous dielectric sphere by a point electric dipole

Electrically small dielectric antennas are of great interest for modern technologies, since they can significantly reduce the physical size of electronic devices for processing and transmitting information. We investigate the influence of the resonance conditions of an electrically small dielectric spherical antenna with a high refractive index on its directivity and analyze the dependence of these resonances on the effectively excited modes of the dielectric sphere.

Direction-of-Arrival Estimation of Electromagnetic Wave Impinging on Spherical Antenna Array in the Presence of Mutual Coupling Using a Multiple Signal Classification Method

A spherical antenna array (SAA) is the configuration of choice in obtaining an antenna array with isotropic characteristics. An SAA has the capacity to receive an electromagnetic wave (EM) with equal intensity irrespective of the direction-of-arrival (DoA) and polarization. Therefore, the DoA estimation of electromagnetic (EM) waves impinging on an SAA with unknown mutual coupling needs to be considered. In the spherical domain, the traditional multiple signal classification algorithm (SH-MUSIC) is faced with a computational complexity problem. This paper presents a one-dimensional MUSIC method (1D-MUSIC) for the estimation of the azimuth and elevation angles. An intermediate mapping matrix that exists between Fourier series and the spherical harmonic function is designed, and the Fourier series Vandermonde structure is used for the realization of the polynomial rooting technique. This mapping matrix can be computed prior to the DoA estimation, and it is only a function of the array configuration. Based on the mapping matrix, the 2-D angle search is transformed into two 1-D angle findings. Employing the features of the Fourier series, two root polynomials are designed for the estimation of the elevation and azimuth angles, spontaneously. The developed method avoids the 2-D spectral search, and angles are paired in automation. Both numerical simulation results, and results from experimental measured data (i.e., with mutual coupling effect incorporated), show the validity, potency, and potential practical application of the developed algorithm.