Performance Evaluation of DOA Estimation using MATLAB

This paper presents the performance analysis of directions of arrival estimation techniques, Subspace and the Non-Subspace methods. In this paper, exploring the analysis category of high resolution and super resolution algorithms, presentation of description, comparison and the performance and resolution analyses of these algorithms are made. Sensitivity to various perturbations and the effect of parameters related to the design of the sensor array itself such as the number of array elements and their spacing are also investigated

Joint DOA and Polarization Estimation with Sparsely Distributed and Spatially Non-Collocating Dipole/Loop Triads

This paper introduces an ESPRIT-based algorithm to estimate the directions-of-arrival and polarizations for multiple sources. The investigated algorithm is based on new sparse array geometries, which are composed of three non-collocating dipole triads or three non-collocating loop triads. Both the inter-triad spacings and the inter-sensor spacings in the same triad can be far larger than a half-wavelength of the incident sources. By adopting the ESPRIT algorithm, the eigenvalues of the data-correlation matrix offer the fine but ambiguous estimates of the direction-cosines for each source, and the eigenvectors provide the estimates of each source's steering vector. Based on the constrained array geometries, the fine and unambiguous estimates of directions-of-arrival and polarizations are obtained. Simulation results verify the efficacy of the investigated approach and also verify the aperture extension property of the proposed array geometries.Comment: 17 pages, 5 figure

Bayesian inference for PCA and MUSIC algorithms with unknown number of sources

Principal component analysis (PCA) is a popular method for projecting data onto uncorrelated components in lower dimension, although the optimal number of components is not specified. Likewise, multiple signal classification (MUSIC) algorithm is a popular PCA-based method for estimating directions of arrival (DOAs) of sinusoidal sources, yet it requires the number of sources to be known a priori. The accurate estimation of the number of sources is hence a crucial issue for performance of these algorithms. In this paper, we will show that both PCA and MUSIC actually return the exact joint maximum-a-posteriori (MAP) estimate for uncorrelated steering vectors, although they can only compute this MAP estimate approximately in correlated case. We then use Bayesian method to, for the first time, compute the MAP estimate for the number of sources in PCA and MUSIC algorithms. Intuitively, this MAP estimate corresponds to the highest probability that signal-plus-noise's variance still dominates projected noise's variance on signal subspace. In simulations of overlapping multi-tone sources for linear sensor array, our exact MAP estimate is far superior to the asymptotic Akaike information criterion (AIC), which is a popular method for estimating the number of components in PCA and MUSIC algorithms.Comment: IEEE Transactions on Signal Processin

Direction Finding Algorithms with Joint Iterative Subspace Optimization

In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output power with respect to each scanning angle. Subspace algorithms to estimate the rank-reduction matrix and the auxiliary vector are proposed. Simulations are performed to show that the proposed algorithms achieve an enhanced performance over existing algorithms in the studied scenarios.Comment: 11 figures, 4 tables. IEEE Transactions on Aerospace and Electronic Systems, 201

Coherent Sources Direction Finding and Polarization Estimation with Various Compositions of Spatially Spread Polarized Antenna Arrays

Various compositions of sparsely polarized antenna arrays are proposed in this paper to estimate the direction-of-arrivals (DOAs) and polarizations of multiple coherent sources. These polarized antenna arrays are composed of one of the following five sparsely-spread sub-array geometries: 1) four spatially-spread dipoles with three orthogonal orientations, 2) four spatially-spread loops with three orthogonal orientations, 3) three spatially-spread dipoles and three spatially-spread loops with orthogonal orientations, 4) three collocated dipole-loop pairs with orthogonal orientations, and 5) a collocated dipole-triad and a collocated loop-triad. All the dipoles/loops/pairs/triads in each sub-array can also be sparsely spaced with the inter-antenna spacing far larger than a half-wavelength. Only one dimensional spatial-smoothing is used in the proposed algorithm to derive the two-dimensional DOAs and polarizations of multiple cross-correlated signals. From the simulation results, the sparse array composed of dipole-triads and loop-triads is recommended to construct a large aperture array, while the sparse arrays composed of only dipoles or only loops are recommended to efficiently reduce the mutual coupling across the antennas. Practical applications include distributed arrays and passive radar systems.Comment: 40 pages, 18 figures, to appear in Signal Processin

Reduced-Rank DOA Estimation based on Joint Iterative Subspace Optimization and Grid Search

In this paper, we propose a novel reduced-rank algorithm for direction of arrival (DOA) estimation based on the minimum variance (MV) power spectral evaluation. It is suitable to DOA estimation with large arrays and can be applied to arbitrary array geometries. The proposed DOA estimation algorithm is formulated as a joint optimization of a subspace projection matrix and an auxiliary reduced-rank parameter vector with respect to the MV and grid search. A constrained least squares method is employed to solve this joint optimization problem for the output power over the grid. The proposed algorithm is described for problems of large number of users' direction finding with or without exact information of the number of sources, and does not require the singular value decomposition (SVD). The spatial smoothing (SS) technique is also employed in the proposed algorithm for dealing with correlated sources problem. Simulations are conducted with comparisons against existent algorithms to show the improved performance of the proposed algorithm in different scenarios.Comment: 3 figure

One-Bit MUSIC

In this letter, we consider the problem of direction-of-arrival (DOA) estimation with one-bit quantized array measurements. With analysis, it is shown that, under mild conditions the one-bit covariance matrix can be approximated by the sum of a scaled unquantized covariance matrix and a scaled identity matrix. Although the scaling parameters unknown because of the extreme quantization, they do not affect the subspace-based DOA estimators. Specifically, the signal and noise subspaces can be straightforwardly determined through the eigendecomposition of the one-bit covariance matrix, without pre-processing such as unquantized covariance matrix reconstruction. With so-obtained subspaces, the most classical multiple signal classification (MUSIC) technique can be applied to determine the signal DOAs. The resulting method is thus termed as one-bit MUSIC. Thanks to the simplicity of this method, it can be very easily implemented in practical applications, whereas the DOA estimation performance is comparable to the case with unquantized covariance matrix reconstruction, as demonstrated by various simulations.Comment: 5 pages, 6 figures, submitted to IEEE Signal Processing Letter

Gridless Quadrature Compressive Sampling with Interpolated Array Technique

Quadrature compressive sampling (QuadCS) is a sub-Nyquist sampling scheme for acquiring in-phase and quadrature (I/Q) components in radar. In this scheme, the received intermediate frequency (IF) signals are expressed as a linear combination of time-delayed and scaled replicas of the transmitted waveforms. For sparse IF signals on discrete grids of time-delay space, the QuadCS can efficiently reconstruct the I/Q components from sub-Nyquist samples. In practice, the signals are characterized by a set of unknown time-delay parameters in a continuous space. Then conventional sparse signal reconstruction will deteriorate the QuadCS reconstruction performance. This paper focuses on the reconstruction of the I/Q components with continuous delay parameters. A parametric spectrum-matched dictionary is defined, which sparsely describes the IF signals in the frequency domain by delay parameters and gain coefficients, and the QuadCS system is reexamined under the new dictionary. With the inherent structure of the QuadCS system, it is found that the estimation of delay parameters can be decoupled from that of sparse gain coefficients, yielding a beamspace direction-of-arrival (DOA) estimation formulation with a time-varying beamforming matrix. Then an interpolated beamspace DOA method is developed to perform the DOA estimation. An optimal interpolated array is established and sufficient conditions to guarantee the successful estimation of the delay parameters are derived. With the estimated delays, the gain coefficients can be conveniently determined by solving a linear least-squares problem. Extensive simulations demonstrate the superior performance of the proposed algorithm in reconstructing the sparse signals with continuous delay parameters.Comment: 34 pages, 11 figure

Direct Localization of Multiple Sources by Partly Calibrated Arrays

We present novel solutions to the problem of direct localization of multiple narrow-band and arbitrarily correlated sources by partly calibrated arrays, i.e., arrays composed of fully calibrated sub-arrays yet lacking inter-array calibration. The solutions presented vary in their performance and computational complexity. We present first a relaxed maximum likelihood solution whose concentrated likelihood involves only the unknown locations of the sources and requires an eigen-decomposition of the array covariance matrix at every potential location. To reduce the computational load, we introduce an approximation which eliminates the need for such an eigen-decomposition at every potential location. To further reduce the computational load, novel MUSIC-like and MVDR-like solutions are presented which are computationally much simpler than the existing solutions. The performance of these solutions is evaluated and compared via simulations

Cross Correlation-based Direct Positioning for Wideband Sources using Phased Arrays

Recent developments in Phased Array direct positioning methods have improved accuracy for passively geo-locating multiple radio frequency-emitting signal sources. However, the number of geo-localisable signal sources is still limited by the number of antenna elements at each node. This is the limitation for methods based on MUSIC, otherwise known as signal subspace identification. This paper attempts to exploit properties of wideband signal sources to compartmentalise signals into their respective Time Differences of Arrival. By performing direct positioning after the compartmentalisation process, we will show that geolocation of a large number of sources can be achieved by our proposed method at accuracies that exceed all existing methods, especially under low signal-to-noise ratio conditions.Comment: 9 pages, 4 figures, submitted to IEEE Transactions on Signal Processin