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

Deterministic Performance Analysis of Subspace Methods for Cisoid Parameter Estimation

Performance analyses of subspace algorithms for cisoid parameter estimation available in the literature are predominantly of statistical nature with a focus on asymptotic$-$either in the sample size or the SNR$-$statements. This paper presents a deterministic, finite sample size, and finite-SNR performance analysis of the ESPRIT algorithm and the matrix pencil method. Our results are based, inter alia, on a new upper bound on the condition number of Vandermonde matrices with nodes inside the unit disk. This bound is obtained through a generalization of Hilbert's inequality frequently used in large sieve theory.Comment: IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain, July 201

Clustering of Series via Dynamic Mode Decomposition and the Matrix Pencil Method

In this paper, a new algorithm for extracting features from sequences of multidimensional observations is presented. The independently developed Dynamic Mode Decomposition and Matrix Pencil methods provide a least-squares model-based approach for estimating complex frequencies present in signals as well as their corresponding amplitudes. Unlike other feature extraction methods such as Fourier Transform or Autoregression which have to be computed for each sequence individually, the least-squares approach considers the whole dataset at once. It invokes order reduction methods to extract a small number of features best describing all given data, and indicate which frequencies correspond to which sequences. As an illustrative example, the new method is applied to regions of different grain orientation in a Transmission Electron Microscopy image

Transmit Array Interpolation for DOA Estimation via Tensor Decomposition in 2D MIMO Radar

In this paper, we propose a two-dimensional (2D) joint transmit array interpolation and beamspace design for planar array mono-static multiple-input-multiple-output (MIMO) radar for direction-of-arrival (DOA) estimation via tensor modeling. Our underlying idea is to map the transmit array to a desired array and suppress the transmit power outside the spatial sector of interest. In doing so, the signal-tonoise ratio is improved at the receive array. Then, we fold the received data along each dimension into a tensorial structure and apply tensor-based methods to obtain DOA estimates. In addition, we derive a close-form expression for DOA estimation bias caused by interpolation errors and argue for using a specially designed look-up table to compensate the bias. The corresponding Cramer-Rao Bound (CRB) is also derived. Simulation results are provided to show the performance of the proposed method and compare its performance to CRB.Comment: 37 pages, 13 figures, Submitted to the IEEE Trans. Signal Processing in December 201

Modal Analysis Using Sparse and Co-prime Arrays

Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system identification, and direction of arrival estimation. Our results differ from standard results of modal analysis to the extent that we consider sparse and co-prime samplings in space, or equivalently sparse and co-prime samplings in time. Our main result is a characterization of the orthogonal subspace. This is the subspace that is orthogonal to the signal subspace spanned by the columns of the generalized Vandermonde matrix of modes in sparse or co-prime arrays. This characterization is derived in a form that allows us to adapt modern methods of linear prediction and approximate least squares, such as iterative quadratic maximum likelihood (IQML), for estimating mode parameters. Several numerical examples are presented to demonstrate the validity of the proposed modal estimation methods, and to compare the fidelity of modal estimation with sparse and co-prime arrays, versus SNR. Our calculations of Cram\'{e}r-Rao bounds allow us to analyze the loss in performance sustained by sparse and co-prime arrays that are compressions of uniform linear arrays.Comment: 22 page

MCA Learning Algorithm for Incident Signals Estimation: A Review

Recently there has been many works on adaptive subspace filtering in the signal processing literature. Most of them are concerned with tracking the signal subspace spanned by the eigenvectors corresponding to the eigenvalues of the covariance matrix of the signal plus noise data. Minor Component Analysis (MCA) is important tool and has a wide application in telecommunications, antenna array processing, statistical parametric estimation, etc. As an important feature extraction technique, MCA is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix. In this paper, we will present a MCA learning algorithm to extract minor component from input signals, and the learning rate parameter is also presented, which ensures fast convergence of the algorithm, because it has direct effect on the convergence of the weight vector and the error level is affected by this value. MCA is performed to determine the estimated DOA. Simulation results will be furnished to illustrate the theoretical results achieved.Comment: 5 pages,8 figures, 1 table. International Journal of Computer Trends and Technology (IJCTT),Feb 201

An original Propagator for large array

In this paper, we demonstrate that when the ratio $n$ of the number of antenna elements $N$ to the number $P$ of radiating sources is superior or equal to $2$, then it is possible to choose a propagator from a set of $n(n+1)/2-1$ operators to compute the Angles of Arrival (AoA) of the narrowband incoming waves. This new non eigenbased approach is efficient when the Signal to Noise Ratio (SNR) is moderate, and gives multitude of possibilities, that are dependent of the random data, to construct the complex sets whose columns are orthogonal to the signal subspace generated by the radiating sources. Elementary examples are given for $n=3$, $n=4$ and $n=6$. The simulation results are presented to illustrate the performance of the proposed computational methods.Comment: Fourteen pages and four figure

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

Least-squares based iterative multipath super-resolution technique

In this paper, we study the problem of multipath channel estimation for direct sequence spread spectrum signals. To resolve multipath components arriving within a short interval, we propose a new algorithm called the least-squares based iterative multipath super-resolution (LIMS). Compared to conventional super-resolution techniques, such as the multiple signal classification (MUSIC) and the estimation of signal parameters via rotation invariance techniques (ESPRIT), our algorithm has several appealing features. In particular, even in critical situations where the conventional super-resolution techniques are not very powerful due to limited data or the correlation between path coefficients, the LIMS algorithm can produce successful results. In addition, due to its iterative nature, the LIMS algorithm is suitable for recursive multipath tracking, whereas the conventional super-resolution techniques may not be. Through numerical simulations, we show that the LIMS algorithm can resolve the first arrival path among closely arriving independently faded multipaths with a much lower mean square error than can conventional early-late discriminator based techniques.Comment: 13 pages, 7 figure