A Unified Approach to Sparse Signal Processing

A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common benefits of significant reduction in sampling rate and processing manipulations are revealed. The key applications of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding in finite/real Galois fields is then related to sampling with similar reconstruction algorithms. The methods of Prony, Pisarenko, and MUSIC are next discussed for sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter and Error Locator Polynomials in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method. Such spectral estimation methods is then related to multi-source location and DOA estimation in array processing. The notions of sparse array beamforming and sparse sensor networks are also introduced. Sparsity in unobservable source signals is also shown to facilitate source separation in SCA; the algorithms developed in this area are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate OFDM channels.Comment: 43 pages, 40 figures, 15 table

Joint DOA Estimation and Array Calibration Using Multiple Parametric Dictionary Learning

This letter proposes a multiple parametric dictionary learning algorithm for direction of arrival (DOA) estimation in presence of array gain-phase error and mutual coupling. It jointly solves both the DOA estimation and array imperfection problems to yield a robust DOA estimation in presence of array imperfection errors and off-grid. In the proposed method, a multiple parametric dictionary learning-based algorithm with an steepest-descent iteration is used for learning the parametric perturbation matrices and the steering matrix simultaneously. It also exploits the multiple snapshots information to enhance the performance of DOA estimation. Simulation results show the efficiency of the proposed algorithm when both off-grid problem and array imperfection exist

A Unified Performance Analysis of Subspace-Based DOA Estimation Algorithms in Array Signal Processing

In the last decade, the subspace approach has found prominence in the problem of estimating directions of arrival using an array of sensors. Many subspace methods have been proposed and improved; the most attractive ones among these are MUSIC, Min-Norm, State-Space Realization (TAM) and ESPRIT. However, performance analyses are required for justifying and comparing these methods before applying them. Early performance justifications and comparisons were based on simulations. In recent years, many excellent analytical studies have been reported, but these studies have one or more of the following restrictions: (i) assume asymptotic measurements, (ii) analyze some specific parameter perturbation directly instead of through the perturbation of the appropriate subspace, (iii) evaluate individual algorithms using different approximations (so it is hard to compare the analyses of different methods), (iv) involve complicated mathematics and statistics which result in difficult expressions. In our attempt to obtain a unified, nonasymptotic analysis to subspace processing algorithms in a greatly simplified and self-contained fashion, we classify these algorithms into category by the subspace they use - orthogonalsubspace processing and signal-subspace processing. We then derive expressions for the first-order perturbation of the signal and orthogonal subspaces using a matrix approximation technique. These formulas provides a common foundation for our analysis of all the DOA estimation algorithms mentioned above. define three approaches by the numerical procedure these algorithms exploit - extrema-searching, polynomial-rooting approach, matrix-shifting approach. We establish a common model for each approach and analyze these common models (instead of individual algorithms), and specialize the results for each algorithm. provide a first-order relationship between subspace perturbations and direction-of-arrival perturbations. use the perturbation formulas to derive variance expressions for DOA estimates for all the algorithms. We make the comparisons and discussions among these algorithms and approaches with our theoretical prediction and numerical simulations. The tractable formulas derived in this analysis provide insight into the performance of the algorithms. Simulations verify the analysis

A Simplified Sub-Nyquist Receiver Architecture for Joint DOA and Frequency Estimation

Joint estimation of carrier frequency and direction of arrival (DOA) for multiple signals has been found in many practical applications such as Cognitive Radio (CR). However, Nyquist sampling mechanism is costly or implemented due to wide spectrum range. Taking advantage of sub-Nyquist sampling technology, some array receiver architectures are proposed to realize joint estimation of carrier frequency and DOA. To further decrease equivalent sampling rate and hardware complexity, we propose a simplifying receiver architecture based on our previous work. We come up with joint DOA and frequency estimation algorithms for the novel architecture. The simulations demonstrate that the receiver architecture and the proposed approaches are feasible.Comment: arXiv admin note: text overlap with arXiv:1604.0503

Sparse Bayesian learning with uncertainty models and multiple dictionaries

Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed point updates. It provides comparable performance and is significantly faster than convex optimization techniques used in sparse processing. We propose a signal model which accounts for dictionary mismatch and the presence of errors in the weight vector at low signal-to-noise ratios. A fixed point update equation is derived which incorporates the statistics of mismatch and weight errors. We also process observations from multiple dictionaries. Noise variances are estimated using stochastic maximum likelihood. The derived update equations are studied quantitatively using beamforming simulations applied to direction-of-arrival (DoA). Performance of SBL using single- and multi-frequency observations, and in the presence of aliasing, is evaluated. SwellEx-96 experimental data demonstrates qualitatively the advantages of SBL.Comment: 11 pages, 8 figure

Coarrays, MUSIC, and the Cram\'er Rao Bound

Sparse linear arrays, such as co-prime arrays and nested arrays, have the attractive capability of providing enhanced degrees of freedom. By exploiting the coarray structure, an augmented sample covariance matrix can be constructed and MUSIC (MUtiple SIgnal Classification) can be applied to identify more sources than the number of sensors. While such a MUSIC algorithm works quite well, its performance has not been theoretically analyzed. In this paper, we derive a simplified asymptotic mean square error (MSE) expression for the MUSIC algorithm applied to the coarray model, which is applicable even if the source number exceeds the sensor number. We show that the directly augmented sample covariance matrix and the spatial smoothed sample covariance matrix yield the same asymptotic MSE for MUSIC. We also show that when there are more sources than the number of sensors, the MSE converges to a positive value instead of zero when the signal-to-noise ratio (SNR) goes to infinity. This finding explains the "saturation" behavior of the coarray-based MUSIC algorithms in the high SNR region observed in previous studies. Finally, we derive the Cram\'er-Rao bound (CRB) for sparse linear arrays, and conduct a numerical study of the statistical efficiency of the coarray-based estimator. Experimental results verify theoretical derivations and reveal the complex efficiency pattern of coarray-based MUSIC algorithms.Comment: Revised Corollary 2. Added Fig.

Joint DOA and Frequency Estimation with Sub-Nyquist Sampling

In this paper, to jointly estimate the frequency and the direction-of-arrival(DOA) of the narrowband far-field signals, a novel array receiver architecture is presented by the concept of the sub-Nyquist sampling techniques. In particular, our contribution is threefold. i) First, we propose a time-space union signal reception model for receiving array signals, where the sub-Nyquist sampling techniques and arbitrary array geometries are employed to decrease the time-domain sampling rate and improve the DOA estimation accuracy. A better joint estimation is obtained in the higher time-space union space. ii) Second, two joint estimation algorithms are proposed for the receiving model. One is based on a trilinear decomposition from the third-order tensor theory and the other is based on subspace decomposition. iii) Third, we derive the corresponding Cram\'er\text{-}Rao Bound (CRB) for frequency and DOA estimates. In the case of the branch number of our architecture is equal to the reduction factor of the sampling rate, it is observed that the CRB is robust in terms of the number of signals, while the CRB based on the Nyquist sampling scheme will increase with respect to the number of signals. In addition, the new steer vectors of the union time-space model are completely uncorrelated under the limited number of sensors, which improves the estimation performance. Furthermore, the simulation results demonstrate that our estimates via the receiver architecture associated with the proposed algorithms closely match the CRB according to the noise levels, the branch number and the source number as well

A DoA Estimation Based Robust Beam Forming Method for UAV-BS Communication

High data rate communication with Unmanned Aerial Vehicles (UAV) is of growing demand among industrial and commercial applications since the last decade. In this paper, we investigate enhancing beam forming performance based on signal Direction of Arrival (DoA) estimation to support UAV-cellular network communication. We first study UAV fast moving scenario where we found that drone's mobility cause degradation of beam forming algorithm performance. Then, we propose a DoA estimation algorithm and a steering vector adaptive receiving beam forming method. The DoA estimation algorithm is of high precision with low computational complexity. Also it enables a beam former to timely adjust steering vector value in calculating beam forming weight. Simulation results show higher SINR performance and more stability of proposed method than traditional method based on Multiple Signal Classification (MUSIC) DoA estimation algorithm.Comment: We would like to make some variations to the simulation result

Source Localization and Tracking for Dynamic Radio Cartography using Directional Antennas

Utilization of directional antennas is a promising solution for efficient spectrum sensing and accurate source localization and tracking. Spectrum sensors equipped with directional antennas should constantly scan the space in order to track emitting sources and discover new activities in the area of interest. In this paper, we propose a new formulation that unifies received-signal-strength (RSS) and direction of arrival (DoA) in a compressive sensing (CS) framework. The underlying CS measurement matrix is a function of beamforming vectors of sensors and is referred to as the propagation matrix. Comparing to the omni-directional antenna case, our employed propagation matrix provides more incoherent projections, an essential factor in the compressive sensing theory. Based on the new formulation, we optimize the antenna beams, enhance spectrum sensing efficiency, track active primary users accurately and monitor spectrum activities in an area of interest. In many practical scenarios there is no fusion center to integrate received data from spectrum sensors. We propose the distributed version of our algorithm for such cases. Experimental results show a significant improvement in source localization accuracy, compared with the scenario when sensors are equipped with omni-directional antennas. Applicability of the proposed framework for dynamic radio cartography is shown. Moreover, comparing the estimated dynamic RF map over time with the ground truth demonstrates the effectiveness of our proposed method for accurate signal estimation and recovery.Comment: SECON 2019 workshop on Edge Computing for Cyber Physical System

Iterative Sparse Asymptotic Minimum Variance Based Approaches for Array Processing

This paper presents a series of user parameter-free iterative Sparse Asymptotic Minimum Variance (SAMV) approaches for array processing applications based on the asymptotically minimum variance (AMV) criterion. With the assumption of abundant snapshots in the direction-of-arrival (DOA) estimation problem, the signal powers and noise variance are jointly estimated by the proposed iterative AMV approach, which is later proved to coincide with the Maximum Likelihood (ML) estimator. We then propose a series of power-based iterative SAMV approaches, which are robust against insufficient snapshots, coherent sources and arbitrary array geometries. Moreover, to overcome the direction grid limitation on the estimation accuracy, the SAMV-Stochastic ML (SAMV-SML) approaches are derived by explicitly minimizing a closed form stochastic ML cost function with respect to one scalar parameter, eliminating the need of any additional grid refinement techniques. To assist the performance evaluation, approximate solutions to the SAMV approaches are also provided at high signal-to-noise ratio (SNR) and low SNR, respectively. Finally, numerical examples are generated to compare the performance of the proposed approaches with existing approaches.Comment: Abeida Habti, Qilin Zhang, Jian Li, and Nadjim Merabtine. "Iterative sparse asymptotic minimum variance based approaches for array processing." IEEE Transactions on Signal Processing 61, no. 4 (2013): 933-94