Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size

Classical methods of DOA estimation such as the MUSIC algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix. For a small number of samples, such methods are exposed to performance breakdown, as the sample covariance matrix can largely deviate from the true covariance matrix. In this paper, the problem of DOA estimation performance breakdown is investigated. We consider the structure of the sample covariance matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, the subspace leakage is theoretically derived. We also propose a two-step method which improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced. Furthermore, we introduce a phenomenon named as root-swap which occurs in the root-MUSIC algorithm in the low sample size region and degrades the performance of the DOA estimation. A new method is then proposed to alleviate this problem. Numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods. Moreover, the proposed algorithms are combined with the pseudo-noise resampling method to further improve the performance.Comment: 37 pages, 10 figures, Submitted to the IEEE Transactions on Signal Processing in July 201

Three more Decades in Array Signal Processing Research: An Optimization and Structure Exploitation Perspective

The signal processing community currently witnesses the emergence of sensor array processing and Direction-of-Arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and availability of powerful and affordable multi-antenna hardware platforms. The history of advances in super resolution DoA estimation techniques is long, starting from the early parametric multi-source methods such as the computationally expensive maximum likelihood (ML) techniques to the early subspace-based techniques such as Pisarenko and MUSIC. Inspired by the seminal review paper Two Decades of Array Signal Processing Research: The Parametric Approach by Krim and Viberg published in the IEEE Signal Processing Magazine, we are looking back at another three decades in Array Signal Processing Research under the classical narrowband array processing model based on second order statistics. We revisit major trends in the field and retell the story of array signal processing from a modern optimization and structure exploitation perspective. In our overview, through prominent examples, we illustrate how different DoA estimation methods can be cast as optimization problems with side constraints originating from prior knowledge regarding the structure of the measurement system. Due to space limitations, our review of the DoA estimation research in the past three decades is by no means complete. For didactic reasons, we mainly focus on developments in the field that easily relate the traditional multi-source estimation criteria and choose simple illustrative examples.Comment: 16 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Incremental and Adaptive L1-Norm Principal Component Analysis: Novel Algorithms and Applications

L1-norm Principal-Component Analysis (L1-PCA) is known to attain remarkable resistance against faulty/corrupted points among the processed data. However, computing L1-PCA of “big data” with large number of measurements and/or dimensions may be computationally impractical. This work proposes new algorithmic solutions for incremental and adaptive L1-PCA. The first algorithm computes L1-PCA incrementally, processing one measurement at a time, with very low computational and memory requirements; thus, it is appropriate for big data and big streaming data applications. The second algorithm combines the merits of the first one with additional ability to track changes in the nominal signal subspace by revising the computed L1-PCA as new measurements arrive, demonstrating both robustness against outliers and adaptivity to signal-subspace changes. The proposed algorithms are evaluated in an array of experimental studies on subspace estimation, video surveillance (foreground/background separation), image conditioning, and direction-of-arrival (DoA) estimation

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

Design and Implementation of System Components for Radio Frequency Based Asset Tracking Devices to Enhance Location Based Services. Study of angle of arrival techniques, effects of mutual coupling, design of an angle of arrival algorithm, design of a novel miniature reconfigurable antenna optimised for wireless communication systems

The angle of arrival estimation of multiple sources plays a vital role in the field of array signal processing as MIMO systems can be employed at both the transmitter and the receiver end and the system capacity, reliability and throughput can be significantly increased by using array signal processing. Almost all applications require accurate direction of arrival (DOA) estimation to localize the sources of the signals. Another important parameter of localization systems is the array geometry and sensor design which can be application specific and is used to estimate the DOA. In this work, various array geometries and arrival estimation algorithms are studied and then a new scheme for multiple source estimation is proposed and evaluated based on the performance of subspace and non-subspace decomposition methods. The proposed scheme has shown to outperform the conventional Multiple Signal Classification (MUSIC) estimation and Bartlett estimation techniques. The new scheme has a better performance advantage at low and high signal to noise ratio values (SNRs). The research work also studies different array geometries for both single and multiple incident sources and proposes a geometry which is cost effective and efficient for 3, 4, and 5 antenna array elements. This research also considers the shape of the ground plane and its effects on the angle of arrival estimation and in addition it shows how the mutual couplings between the elements effect the overall estimation and how this error can be minimised by using a decoupling matrix. At the end, a novel miniaturised multi element reconfigurable antenna to represent the receiver base station is designed and tested. The antenna radiation patterns in the azimuth angle are almost omni-directional with linear polarisation. The antenna geometry is uniplanar printed logspiral with striplines feeding network and biased components to improve the impedance bandwidth. The antenna provides the benefit of small size, and re-configurability and is very well suited for the asset tracking applications

Array and multichannel signal processing using nonparametric statistics

In array signal processing a group of sensors located at distinct spatial locations is deployed to measure a propagating wavefield. The multichannel output is then processed to provide information about parameters of interest. Application areas include smart antennas in communications, radar, sonar and biomedicine. When deriving array signal processing algorithms the noise is typically modeled as a white Gaussian random process. A shortcoming of the estimation procedures derived under Gaussian assumption is that they are extremely sensitive to deviations from the assumed model, i.e. they are not robust. In real-world applications the assumption of white Gaussian noise is not always valid. Consequently, there has been a growing interest in estimation methods which work reliably in both Gaussian and non-Gaussian noise. In this thesis, new statistical procedures for array and multichannel signal processing are developed. In the area of array signal processing, the work concentrates on high-resolution subspace-based Direction Of Arrival (DOA) estimation and estimation of the number of source signals. Robust methods for DOA estimation and estimation of the number of source signals are derived. Spatial-smoothing based extensions of the techniques to deal with coherent signals are also derived. The methods developed are based on multivariate nonparametric statistics, in particular sign and rank covariance matrices. It is shown that these statistics may be used to obtain convergent estimates of the signal and noise subspaces for a large family of symmetric noise distributions. Simulations reveal that the techniques developed exhibit near-optimal performance when the noise distribution is Gaussian and are highly reliable if the noise is non-Gaussian. Multivariate nonparametric statistics are also applied to frequency estimation and estimation of the eigenvectors of the covariance matrix. Theoretical justification for the techniques is shown and their robust performance is illustrated in simulations.reviewe

Wideband DOA Estimation via Sparse Bayesian Learning over a Khatri-Rao Dictionary

This paper deals with the wideband direction-of-arrival (DOA) estimation by exploiting the multiple measurement vectors (MMV) based sparse Bayesian learning (SBL) framework. First, the array covariance matrices at different frequency bins are focused to the reference frequency by the conventional focusing technique and then transformed into the vector form. Then a matrix called the Khatri-Rao dictionary is constructed by using the Khatri-Rao product and the multiple focused array covariance vectors are set as the new observations. DOA estimation is to find the sparsest representations of the new observations over the Khatri-Rao dictionary via SBL. The performance of the proposed method is compared with other well-known focusing based wideband algorithms and the Cramer-Rao lower bound (CRLB). The results show that it achieves higher resolution and accuracy and can reach the CRLB under relative demanding conditions. Moreover, the method imposes no restriction on the pattern of signal power spectral density and due to the increased number of rows of the dictionary, it can resolve more sources than sensors