High-resolution Direction Of Arrival Research Articles

Gridless DOA Estimation Method for Arbitrary Array Geometries Based on Complex-Valued Deep Neural Networks

Gridless direction of arrival (DOA) estimation methods have garnered significant attention due to their ability to avoid grid mismatch errors, which can adversely affect the performance of high-resolution DOA estimation algorithms. However, most existing gridless methods are primarily restricted to applications involving uniform linear arrays or sparse linear arrays. In this paper, we derive the relationship between the element-domain covariance matrix and the angular-domain covariance matrix for arbitrary array geometries by expanding the steering vector using a Fourier series. Then, a deep neural network is designed to reconstruct the angular-domain covariance matrix from the sample covariance matrix and the gridless DOA estimation can be obtained by Root-MUSIC. Simulation results on arbitrary array geometries demonstrate that the proposed method outperforms existing methods like MUSIC, SPICE, and SBL in terms of resolution probability and DOA estimation accuracy, especially when the angular separation between targets is small. Additionally, the proposed method does not require any hyperparameter tuning, is robust to varying snapshot numbers, and has a lower computational complexity. Finally, real hydrophone data from the SWellEx-96 ocean experiment validates the effectiveness of the proposed method in practical underwater acoustic environments.

High-Resolution and Robust One-Bit Direct-of-Arrival Estimation via Reweighted Atomic Norm Estimation.

In recent years, one-bit quantization has attracted widespread attention in the field of direction-of-arrival (DOA) estimation as a low-cost and low-power solution. Many researchers have proposed various estimation algorithms for one-bit DOA estimation, among which atomic norm minimization algorithms exhibit particularly attractive performance as gridless estimation algorithms. However, current one-bit DOA algorithms with atomic norm minimization typically rely on approximating the trace function, which is not the optimal approximation and introduces errors, along with resolution limitations. To date, there have been few studies on how to enhance resolution under the framework of one-bit DOA estimation. This paper aims to improve the resolution constraints of one-bit DOA estimation. The log-det heuristic is applied to approximate and solve the atomic norm minimization problem. In particular, a reweighted binary atomic norm minimization with noise assumption constraints is proposed to achieve high-resolution and robust one-bit DOA estimation. Finally, the alternating direction method of multipliers algorithm is employed to solve the established optimization problem. Simulations are conducted to demonstrate that the proposed algorithm can effectively enhance the resolution.

A high-resolution DOA estimation via random forest virtual array extension

In sonar detection, underwater recognition, and similar fields, the challenge of using small-scale arrays is frequently encountered. With small-scale arrays, the degrees of freedom (DOFs) and accuracy of direction of arrival (DOA) estimation decrease significantly. Moreover, existing algorithms are less robust in complex environments and typically require substantial computing resources to ensure accurate estimation. To overcome these problems, this paper proposes a high-resolution DOA estimation via Random Forest virtual array extension (RFVAE). The algorithm first trains the random forest (RF) network using real array element data, and thus proposes a virtual covariance reconstruction technique. This technique allows for a substantial increase in the number of virtual array elements. Then, based on the virtual covariance reconstruction technique, a high resolution estimation network technique is proposed, which can increase the accuracy and DOFs of DOA estimation. Experimental results show that the proposed algorithm reduces error by 30% to 80% compared to recent technologies and can provide up to twice as many virtual elements. Additionally, the estimation speed can be increased by 3 to 1000 times, and it has significantly stronger robustness, functioning normally at signal-to-noise ratios 10 dB lower than the conditions under which other algorithms fail.

Frequency-difference beamforming and sparse processing

Frequency-difference processing enables the estimation of the direction of arrival (DOA) for sources beyond the spatial aliasing frequency. The beamforming method takes advantage of the frequency difference between multiple frequencies, enabling processing at a lower frequency than the aliasing frequency. During this process, the number of DOAs we need to estimate becomes squared, and we require a high-resolution DOA estimator. Sparse processing has demonstrated high-resolution capabilities in DOA estimation, resulting in beamforming spectra with sharp peaks and enhancing resolution for accuracy. This presentation proposes the utilization of both frequency-difference processing and sparse processing. The suggested method is an aliasing-free beamformer for high-frequency sources using frequency-difference processing and achieves high-resolution capability using sparse processing.

Broadband high-resolution direction of arrival estimation using the generalized weighted Radon transform

Traditional direction of arrival (DOA) estimation algorithms typically have poor spatial resolution and robustness. In this paper, we propose a broadband high-resolution DOA estimation method based on the generalized weighted Radon transform (GWRT). The array signal can be converted into the frequency-wavenumber (f-k) domain using the conditional wavenumber spectrum function (CWSF). Then, a linear integral mathematical model for high-resolution DOA estimation is derived by transforming the f-k domain into the azimuth-energy domain using the GWRT. Computer simulation and sea trials were conducted to validate the feasibility and performance of the proposed method. The results obtained indicate that the proposed method yields a lower sidelobe level and can more effectively suppress the output energy in the non-target direction when compared to the conventional beamforming (CBF), steered minimum variance (STMV), and deconvolution (DCV) methods. Further, the proposed method provides improved spatial resolution and robustness in a multi-target environment.

High-resolution DOA estimation in the hydrophone array shape with uncertainty based on dynamic compressed sensing

Compressed sensing (CS) technology is a popular method for the direction of arrival (DOA) estimation of underwater acoustic radiation noise due to its high resolution. However, in practical applications such as buried arrays and other arrays, uncertainty in the hydrophone array shape can lead to model mismatch which significantly reduces DOA estimation accuracy. This paper focuses on high-resolution wideband DOA estimation in the radiated noise from underwater targets of interest using dynamic compressed sensing. The study introduces phase error into the signal model to simulate the model mismatch, and improves DOA estimation accuracy by jointly estimating both the DOA and phase error. Simulation results demonstrate that the proposed algorithm is effective in improving the accuracy of DOA estimation.

Deep learning-based DOA estimation for hybrid massive MIMO receive array with overlapped subarrays

As massive MIMO is a key technology in the future sixth generation (6G), the large-scale antenna arrays are widely considered in direction-of-arrival (DOA) estimation for they can provide larger aperture and higher estimation resolution. However, the conventional fully digital architecture requires one radio-frequency (RF) chain per antenna, and this is challenging for the high hardware costs and much more power consumption caused by the large number of RF chains. Therefore, an overlapped subarray (OSA) architecture-based hybrid massive MIMO array is proposed to reduce the hardware costs, and it can also have better DOA estimation accuracy compared to non-overlapped subarray (NOSA) architecture. The simulation results also show that the accuracy of the proposed OSA architecture has 6^{circ } advantage over the NOSA architecture with signal-to-noise ratio (SNR) at 10 dB. In addition, to improve the DOA estimation resolution, a deep learning (DL)-based estimator is proposed by combining convolution denoise autoencoder (CDAE) and deep neural network (DNN), where CDAE can remove the approximation error of sample covariance matrix (SCM) and DNN is used to perform high-resolution DOA estimation. From the simulation results, CDAE-DNN can achieve the accuracy lower bound at textrm{SNR}=-8 dB and the number of snapshots N=100, this means it has better performance in poor communication situation and can save more software resources compared to conventional estimators.

High-resolution DOA estimation achieved by a single acoustic vector sensor under anisotropic noise

The acoustic vector sensor (AVS) has a wide application in the direction of arrival (DOA) estimation of sound sources including aircraft, underwater or on-land vehicles, search-and-rescue efforts, etc. The performance of only one acoustic vector sensor can compare favorably with a traditional acoustic array in DOA estimation. The anisotropic noise problem of the vector sensor has had a severe affective on the estimation accuracy and has caused little attention until now. In this paper, an AVS measurement system is designed, and an Anisotropic Sparse Bayesian Learning (SBL) method (the A-SBL method) is proposed to model and estimate the anisotropic noise of the AVS system. A high-resolution DOA estimation method is also introduced based on the noise estimation algorithm. The experimental results exhibit the necessity of modeling the anisotropic noise, and the estimation accuracy of the proposed A-SBL method based on the noise model is verified. The comparison of DOA methods shows the superiority of the proposed method, in which the DOA estimation error is not more than 1°. The proposed method’s utility may be found in applications for localization or tracking of targets with prominent acoustic characteristics when the environment is complicated.

Fast Sparse Non-Negative Least Squares via ADMM for High Resolution DOA Estimation

High-resolution and low-complexity direction of arrival (DOA) estimation deserves a warm welcome in a real radar sensor. However, achieving this goal is nontrivial. For the DOA estimation of the uniform linear array (ULA), we offer an efficient approach to reach a good compromise between complexity, resolution and accuracy. Under the covariance fitting framework, we construct a sparse non-negative least squares (NNLS) that is solved by the alternating direction method of multipliers (ADMM) at a low-computational complexity. The regularization item involved in the ADMM procedure yields an inherent improvement on robustness. Moreover, a large-scale matrix inversion that is a computationally expensive operation in the ADMM procedure is recursively computed by exploiting the diagonal matrix property of the regularization item, resulting in a reduction on complexity. In addition, the pre-estimation of the noise variance further reduces the scale of the sparse NNLS problem and alleviates the ill-conditioning effect to some extent. Compared to several sparse covariance fitting methods, both the simulation data and the 77 GHz radar-measured data demonstrate that the proposed algorithm has the good resolution, robustness, and accuracy performance with lower computationally cost.

Flexible extended nested arrays for DOA estimation: Degrees of freedom perspective

Recently, the design of sparse arrays for direction-of-arrival (DOA) estimation has gained considerable attention due to their ability to yield a sizeable virtual aperture, enhanced degrees-of-freedom (DOF), and high-resolution DOA estimation. This paper presents a flexible extended nested array with multiple subarrays (f-ENAMS), whereby the sensors from the dense uniform subarray of a nested array (NA) are further distributed, and the NA’s DOF is thus improved. Essentially, the dense subarray of NA is split into four sections and distributed equally on either side of NA’s sparse subarray to array aperture while maintaining a hole-free difference co-array (DCA). In this regard, this paper proposes a new extended nested array structure named f-ENAMS, which achieves the same higher DOF capacity as the two-sided extended nested array (TS-ENA). Moreover, an improved f-ENAMS is proposed by relocating further sensors from the dense subarrays of f-ENAMS. As a result, the improved f-ENAMS possess more DOF than other existing extended NAs. For simplicity, the former is called f-ENAMS-I, and the latter is f-ENAMS-II. Both f-ENAMS arrays have closed-form expressions for sensor positions and a hole-free DCA. Numerical examples verify the superiority of the f-ENAMS arrays in terms of achievable DOF, weight functions, and DOA estimation performance.

High resolution DOA estimation of acoustic plane waves: An innovative comparison among Cuckoo search heuristics and subspace based algorithms

SONAR signal processing plays an indispensable role when it comes to parameter estimation of Direction of Arrival (DOA) of acoustic plane waves for closely spaced target exclusively under severe noisy environments. Resolution performance of classical MUSIC and ESPRIT algorithms and other subspace-based algorithms decreases under scenarios like low SNR, smaller number of snapshots and closely spaced targets. In this study, optimization strength of swarm intelligence of Cuckoo Search Algorithm (CSA) is accomplished for viable DOA estimation in different scenarios of underwater environment using a Uniform Linear Array (ULA). Higher resolution for closely spaced targets is achieved using smaller number of snapshots viably with CSA by investigating global minima of the highly nonlinear cost function of ULA. Performance analysis of CSA for different number of targets employing estimation accuracy, higher resolution, variance analysis, frequency distribution of RMSE over the monte Carlo runs and robustness against noise in the presence of additive-white Gaussian measurement noise is achieved. Comparative studies of CSA with Root MUSIC and ESPRIT along with Crammer Rao Bound analysis witnesses better results for estimating DOA parameters which are further endorsed from the results of Monte Carlo simulations.

Gridless sparse covariance-based beamforming via alternating projections including co-prime arrays.

This paper presents gridless sparse processing for direction-of-arrival (DOA) estimation. The method solves a gridless version of sparse covariance-based estimation using alternating projections. Gridless sparse DOA estimation is represented by the reconstruction of Toeplitz-structured low-rank matrices, which our method recovers by alternatively projecting a solution matrix. Compared to the existing gridless sparse methods, our method improves speed and accuracy and considers non-uniformly configured linear arrays. High-resolution and reliable DOA estimation are achieved even with single-snapshot data, coherent sources, and non-uniform arrays. Simulation results demonstrate performance improvements compared to the existing DOA estimators, including gridless sparse methods. The method is illustrated using experimental data from a real ocean experiment.

A low‐computational‐cost alternating switches algorithm for real‐valued spatial covariance matrix reconstruction

The application of the emerging hybrid analog–digital architecture for future millimeter-wave communications has attracted significant attention. Although this architecture can reduce the hardware cost and power consumption considerably, the high-resolution direction of arrival (DOA) estimation in the architecture based on switches is still a challenge. As a solution, an alternating switches algorithm (ASA) is proposed in this paper. By appropriately adjusting the switch connected to each antenna, the real-valued spatial covariance matrix (SCM) is reconstructed with low-dimensional vector-to-vector multiplication. Subsequently, the DOA angle of each signal is estimated based on a split subspace extracted from the real-valued SCM. Finally, a set of simulation experiments are performed to verify the performance of the proposed algorithm. The results indicate that the ASA can reconstruct the real-valued SCM and realize high-resolution DOA estimation with a substantially low computational cost.

Robust high-resolution direction-of-arrival estimation method using DenseBlock-based U-net.

Direction-of-arrival (DOA) estimation is widely used in underwater detection and localization. To address the high-resolution DOA estimation problem, a DenseBlock-based U-net structure is proposed in this paper. U-net is a U-shaped fully convolutional neural network, which yields a two-dimensional image. DenseBlock is a more efficient structure than typical convolutional layers. The proposed network replaces the concatenated convolutional layers in the original U-net with DenseBlocks. Through training, the network can remove the interference of sidelobes and noise in a conventional beam forming bearing-time record (BTR) and get a clean BTR; hence, this method has narrow beam width and few sidelobes. In addition, the network can be trained by simulation data and applied in actual data when the simulated and actual data are similar in BTR features, so the method has high generalization. For a multi-target problem, the network does not need to be trained on all cases with different target quantities and therefore can reduce the training set size. As a data-driven method, it does not rely on prior assumptions of the array model and possesses better robustness to array imperfections than typical model-based DOA algorithms. Simulations and experiments verify the advantages of the proposed method.

A Covariance Matrix Reconstruction Approach for Single Snapshot Direction of Arrival Estimation.

Achieving accurate single snapshot direction of arrival (DOA) information significantly improves communication performance. This paper investigates an accurate and high-resolution DOA estimation technique by enabling single snapshot data collection and enhancing DOA estimation results compared to multiple snapshot methods. This is carried out by manipulating the incoming signal covariance matrix while suppressing undesired additive white Gaussian noise (AWGN) by actively updating and estimating the antenna array manifold vector. We demonstrated the estimation performance in simulation that our proposed technique supersedes the estimation performance of existing state-of-the-art techniques in various signal-to-noise ratio (SNR) scenarios and single snapshot sampling environments. Our proposed covariance-based single snapshot (CbSS) technique yields the lowest root-mean-squared error (RMSE) against the true DOA compared to root-MUSIC and the partial relaxation (PR) approach for multiple snapshots and a single signal source environment. In addition, our proposed technique presents the lowest DOA estimation performance degradation in a multiple uncorrelated and coherent signal source environment by up to 25.5% with nearly negligible bias. Lastly, our proposed CbSS technique presents the best DOA estimation results for a single snapshot and single-source scenario with an RMSE of against the true DOA compared to root-MUSIC and the PR approach with nearly negligible bias as well. A potential application for CbSS would be in a scenario where accurate DOA estimation with a small antenna array form factor is a limitation, such as in the intelligent transportation system industry and wireless communication.

An Optimal Subspace Deconvolution Algorithm for Robust and High-Resolution Beamforming.

Utilizing the difference in phase and power spectrum between signals and noise, the estimation of direction of arrival (DOA) can be transferred to a spatial sample classification problem. The power ratio, namely signal-to-noise ratio (SNR), is highly required in most high-resolution beamforming methods so that high resolution and robustness are incompatible in a noisy background. Therefore, this paper proposes a Subspaces Deconvolution Vector (SDV) beamforming method to improve the robustness of a high-resolution DOA estimation. In a noisy environment, to handle the difficulty in separating signals from noise, we intend to initial beamforming value presets by incoherent eigenvalue in the frequency domain. The high resolution in the frequency domain guarantees the stability of the beamforming. By combining the robustness of conventional beamforming, the proposed method makes use of the subspace deconvolution vector to build a high-resolution beamforming process. The SDV method is aimed to obtain unitary frequency matrixes more stably and improve the accuracy of signal subspaces. The results of simulations and experiments show that when the input SNR is less than −27 dB, signals of decomposition differ unremarkably in the subspace while the SDV method can still obtain clear angles. In a marine background, this method works well in separating the noise and recruiting the characteristics of the signal into the DOA for subsequent processing.

DOA estimation based on cyclostationary feature extraction: An adaptive high-resolution algorithm

The quality of direction of arrival (DOA) estimation is affected by factors such as noise and interferences in wireless communication and other systems. By employing the benefits of cyclostationary signal analysis, which includes immunity to noise and interferences, in this paper, a simple high-resolution DOA estimation method is proposed. Most of the cyclostationary-based DOA estimation methods depend on the statistical properties of the received signals (e.g., the cyclic correlation matrix). Unlike them, in the proposed method, the received signal directly enters a DOA estimation loop containing a normalized least mean square (NLMS) adaptive algorithm. The method has high resolution and performance and low computational complexity in comparison with its counterparts. Moreover, it is befitting for signals in the presence of noise (Gaussian and impulsive) and interferences. Simulation results validate the efficiency of the proposed method from different aspects in comparison with other related studies.

Novel Multiplexing Scheme for Resolving the Velocity Ambiguity Problem in MIMO FMCW Radar Using MPSK Code

For the high-resolution DoA (Direction of Arrival) estimation, various multiplexing schemes are considered for the multi-input multi-output (MIMO) fast chirp frequency-modulated continuous-wave (FMCW) radar. However, current schemes such as time-division multiplexing (TDM) and binary-phase modulation (BPM) may reduce the maximum detectable velocity, which causes the velocity ambiguity problem. As an extension of the BPM scheme to mitigate this issue, we propose a novel multiplexing scheme using M phase-shift keying (MPSK) code which duplicates shifted target peaks at unequal intervals over the velocity domain. The proposed scheme finds the true peaks to resolve the velocity ambiguity problem by the inversion of the circulant matrix with low additional computation. In addition, the successful implementation of the proposed scheme is conducted with 4 by 8 MIMO uniform linear array (ULA) antennas through the state-of-the-art FMCW radar. Finally, the proposed scheme is compared to the conventional TDM based MIMO scheme regarding signal to noise ratio (SNR) and phase calibration issues for moving targets. The proposed scheme is to estimate the accurate 4D information of targets while resolving the velocity ambiguity problem in the MIMO FMCW radar systems.

High-Resolution and Low-Complexity Direction of Arrival Estimation for Hybrid Array of Subarrays

In this paper, the problem of direction-of-arrival (DoA) estimation for a hybrid array of subarrays is considered in millimeter-wave communication systems. Unlike much prior work using the outputs from the analog subarrays with symbol-wise processing, the proposed framework jointly exploits multiple outputs in time domain for high-resolution DoA estimation. With block-wise processing, the proposed method designs an optimal hybrid combiner maximizing beamforming gain, while reducing a receiver complexity based on fast Fourier transform filtering for each blocked signal. The performance of the proposed method is analyzed, including estimation performance with a limited training signal, training overhead, and computational complexity. An extension of the proposed method to a uniform planar array case is also discussed. Numerical results show the effectiveness of the proposed algorithm.

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.