Machine–learning-enabled metasurface for direction of arrival estimation

Metasurfaces, interacted with artificial intelligence, have now been motivating many contemporary research studies to revisit established fields, e.g., direction of arrival (DOA) estimation. Conventional DOA estimation techniques typically necessitate bulky-sized beam-scanning equipment for signal acquisition or complicated reconstruction algorithms for data postprocessing, making them ineffective for in-situ detection. In this article, we propose a machine-learning-enabled metasurface for DOA estimation. For certain incident signals, a tunable metasurface is controlled in sequence, generating a series of field intensities at the single receiving probe. The perceived data are subsequently processed by a pretrained random forest model to access the incident angle. As an illustrative example, we experimentally demonstrate a high-accuracy intelligent DOA estimation approach for a wide range of incident angles and achieve more than 95% accuracy with an error of less than 0.5 ° $0.5{\degree}$ . The reported strategy opens a feasible route for intelligent DOA detection in full space and wide band. Moreover, it will provide breakthrough inspiration for traditional applications incorporating time-saving and equipment-simplified majorization.

TB-NET: A Two-Branch Neural Network for Direction of Arrival Estimation under Model Imperfections

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.

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.

Accurate Direction-of-Arrival Estimation Method based on Space-Time Modulated Metasurface

In this paper, we present a metasurface-based Direction of Arrival (DoA) estimation method that exploits the properties of space-time modulated reflecting metasurfaces to estimate in real-time the impinging angle of an illuminating monochromatic plane wave. The approach makes use of the amplitude unbalance of the received fields at broadside at the frequencies of the two first-order harmonics generated by the interaction between the incident plane wave and the modulated metasurface. Here, we first describe analytically how to generate the desired higher-order harmonics in the reflected spectrum and how to realize the breaking of the spatial symmetry of each order harmonic scattering pattern. Then, the one dimensional (1D) omnidirectional incident angle can be analytically computed using +1st and -1st order harmonics. The approach is also extended to 2D DoA estimation by using two orthogonally arranged 1D DoA modulation arrays. The accuracy of 1D DoA estimation is verified through full-wave numerical simulations. Compared to conventional DoA estimation methods, the proposed approach simplifies the computation and hardware complexity, ensuring at the same time estimation accuracy. The proposed method may have potential applications in wireless communications, target recognition, and identification.

Accurate Direction-of-Arrival Estimation Method based on Space-Time Modulated Metasurface

In this paper, we present a metasurface-based Direction of Arrival (DoA) estimation method that exploits the properties of space-time modulated reflecting metasurfaces to estimate in real-time the impinging angle of an illuminating monochromatic plane wave. The approach makes use of the amplitude unbalance of the received fields at broadside at the frequencies of the two first-order harmonics generated by the interaction between the incident plane wave and the modulated metasurface. Here, we first describe analytically how to generate the desired higher-order harmonics in the reflected spectrum and how to realize the breaking of the spatial symmetry of each order harmonic scattering pattern. Then, the one dimensional (1D) omnidirectional incident angle can be analytically computed using +1st and -1st order harmonics. The approach is also extended to 2D DoA estimation by using two orthogonally arranged 1D DoA modulation arrays. The accuracy of 1D DoA estimation is verified through full-wave numerical simulations. Compared to conventional DoA estimation methods, the proposed approach simplifies the computation and hardware complexity, ensuring at the same time estimation accuracy. The proposed method may have potential applications in wireless communications, target recognition, and identification.