Accurate DOA Estimation for Large-Scale Uniform Circular Array Using a Single Snapshot

© 1997-2012 IEEE. A large-scale antenna array is an enabling technique for millimeter-wave communications. Uniform circular arrays (UCAs) have the spatial invariance property, ensuring the same beamforming performance in the whole angular region. However, the direction-of-arrival (DOA) estimation in UCAs is challenging since the array response of a UCA does not conform to a Vandermonde structure as that of a uniform linear array. This letter proposes an accurate and low-complexity DOA estimation approach by exploiting the good correlation property of the array response of the UCA. The DOA estimates are first obtained from a circular convolution between a single snapshot and the designed coefficient vector. Then, by searching for the best initial phase of the coefficient vector, the DOA estimates can be refined to a configurable accuracy. The simulation results demonstrate that the proposed approach outperforms the state of the art by orders of magnitude in estimation accuracy

Interpretable and Efficient Beamforming-Based Deep Learning for Single Snapshot DOA Estimation

We introduce an interpretable deep learning approach for direction of arrival (DOA) estimation with a single snapshot. Classical subspace-based methods like MUSIC and ESPRIT use spatial smoothing on uniform linear arrays for single snapshot DOA estimation but face drawbacks in reduced array aperture and inapplicability to sparse arrays. Single-snapshot methods such as compressive sensing and iterative adaptation approach (IAA) encounter challenges with high computational costs and slow convergence, hampering real-time use. Recent deep learning DOA methods offer promising accuracy and speed. However, the practical deployment of deep networks is hindered by their black-box nature. To address this, we propose a deep-MPDR network translating minimum power distortionless response (MPDR)-type beamformer into deep learning, enhancing generalization and efficiency. Comprehensive experiments conducted using both simulated and real-world datasets substantiate its dominance in terms of inference time and accuracy in comparison to conventional methods. Moreover, it excels in terms of efficiency, generalizability, and interpretability when contrasted with other deep learning DOA estimation networks.Comment: 10 pages, 10 figure

Direction of Arrival Estimation Using Hybrid Spatial Cross-Cumulants and Root-MUSIC

This paper presents a novel Direction of Arrival (DOA) estimation technique called Cross Cumulant-MUSIC (CC-MUSIC) which jointly employs higher order cumulant statistics and the root-MUSIC algorithm to perform high-resolution DOA estimation in low Signal-to-Noise Ratio (SNR) scenarios. From the simulation results based out of a 4 element uniform linear array and a far-field narrowband signal source, CC-MUSIC outperforms second-order DOA estimation techniques such as root-MUSIC and ESPRIT with a minimum average of10.99% to 46.33% depending on the snapshot values at SNR of <15dB for a single signal source scenario and 39.1% to 83.8% for a multi-signal source scenario respectively when contaminated with an Additive White Gaussian Noise (AWGN). The work presented here has implications of future studies for optimization and real-world application where SNR environment is noisy while requiring accurate DOA estimation

Gridless Two-dimensional DOA Estimation With L-shaped Array Based on the Cross-covariance Matrix

The atomic norm minimization (ANM) has been successfully incorporated into the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for super-resolution. However, its computational workload might be unaffordable when the number of snapshots is large. In this paper, we propose two gridless methods for 2-D DOA estimation with L-shaped array based on the atomic norm to improve the computational efficiency. Firstly, by exploiting the cross-covariance matrix an ANM-based model has been proposed. We then prove that this model can be efficiently solved as a semi-definite programming (SDP). Secondly, a modified model has been presented to improve the estimation accuracy. It is shown that our proposed methods can be applied to both uniform and sparse L-shaped arrays and do not require any knowledge of the number of sources. Furthermore, since our methods greatly reduce the model size as compared to the conventional ANM method, and thus are much more efficient. Simulations results are provided to demonstrate the advantage of our methods

Grid-free compressive beamforming

The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve high-resolution imaging. On a discrete angular grid, the CS reconstruction degrades due to basis mismatch when the DOAs do not coincide with the angular directions on the grid. To overcome this limitation, a continuous formulation of the DOA problem is employed and an optimization procedure is introduced, which promotes sparsity on a continuous optimization variable. The DOA estimation problem with infinitely many unknowns, i.e., source locations and amplitudes, is solved over a few optimization variables with semidefinite programming. The grid-free CS reconstruction provides high-resolution imaging even with non-uniform arrays, single-snapshot data and under noisy conditions as demonstrated on experimental towed array data.Comment: 14 pages, 8 figures, journal pape

Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrade when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1-D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators

Multiple and single snapshot compressive beamforming

For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an $\ell_1$-norm constraint renders the problem solvable with convex optimization, and promoting sparsity gives high-resolution DOA maps. Here, the sparse source distribution is derived using maximum a posteriori (MAP) estimates for both single and multiple snapshots. CS does not require inversion of the data covariance matrix and thus works well even for a single snapshot where it gives higher resolution than conventional beamforming. For multiple snapshots, CS outperforms conventional high-resolution methods, even with coherent arrivals and at low signal-to-noise ratio. The superior resolution of CS is demonstrated with vertical array data from the SWellEx96 experiment for coherent multi-paths.Comment: In press Journal of Acoustical Society of Americ