R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6 figure

Approches tomographiques structurelles pour l'analyse du milieu urbain par tomographie SAR THR : TomoSAR

SAR tomography consists in exploiting multiple images from the same area acquired from a slightly different angle to retrieve the 3-D distribution of the complex reflectivity on the ground. As the transmitted waves are coherent, the desired spatial information (along with the vertical axis) is coded in the phase of the pixels. Many methods have been proposed to retrieve this information in the past years. However, the natural redundancies of the scene are generally not exploited to improve the tomographic estimation step. This Ph.D. presents new approaches to regularize the estimated reflectivity density obtained through SAR tomography by exploiting the urban geometrical structures.La tomographie SAR exploite plusieurs acquisitions d'une même zone acquises d'un point de vue légerement différent pour reconstruire la densité complexe de réflectivité au sol. Cette technique d'imagerie s'appuyant sur l'émission et la réception d'ondes électromagnétiques cohérentes, les données analysées sont complexes et l'information spatiale manquante (selon la verticale) est codée dans la phase. De nombreuse méthodes ont pu être proposées pour retrouver cette information. L'utilisation des redondances naturelles à certains milieux n'est toutefois généralement pas exploitée pour améliorer l'estimation tomographique. Cette thèse propose d'utiliser l'information structurelle propre aux structures urbaines pour régulariser les densités de réflecteurs obtenues par cette technique

Efficient Beamspace Eigen-Based Direction of Arrival Estimation schemes

The Multiple SIgnal Classification (MUSIC) algorithm developed in the late 70\u27s was the first vector subspace approach used to accurately determine the arrival angles of signal wavefronts impinging upon an array of sensors. As facilitated by the geometry associated with the common uniform linear array of sensors, a root-based formulation was developed to replace the computationally intensive spectral search process and was found to offer an enhanced resolution capability in the presence of two closely-spaced signals. Operation in beamspace, where sectors of space are individually probed via a pre-processor operating on the sensor data, was found to offer both a performance benefit and a reduced computationa1 complexi ty resulting from the reduced data dimension associated with beamspace processing. Little progress, however, has been made in the development of a computationally efficient Root-MUSIC algorithm in a beamspace setting. Two approaches of efficiently arriving at a Root-MUSIC formulation in beamspace are developed and analyzed in this Thesis. In the first approach, a structura1 constraint is placed on the beamforming vectors that can be exploited to yield a reduced order polynomial whose roots provide information on the signal arrival angles. The second approach is considerably more general, and hence, applicable to any vector subspace angle estimation algorithm. In this approach, classical multirate digital signal processing is applied to effectively reduce the dimension of the vectors that span the signal subspace, leading to an efficient beamspace Root-MUSIC (or ESPRIT) algorithm. An auxiliaay, yet important, observation is shown to allow a real-valued eigenanalysis of the beamspace sample covariance matrix to provide a computational savings as well as a performance benefit, particularly in the case of correlated signal scenes. A rigorous theoretical analysis, based upon derived large-sample statistics of the signal subspace eigenvectors, is included to provide insight into the operation of the two algorithmic methodologies employing the real-valued processing enhancement. Numerous simulations are presented to validate the theoretical angle bias and variance expressions as well as to assess the merit of the two beamspace approaches

Array imperfection calibration for wireless channel multipath characterisation

As one of the fastest growing technologies in modern telecommunications, wireless networking has become a very important and indispensable part in our life. A good understanding of the wireless channel and its key physical parameters are extremely useful when we want to apply them into practical applications. In wireless communications, the wireless channel refers to the propagation of electromagnetic radiation from a transmitter to a receiver. The estimation of multipath channel parameters, such as angle of depature (AoD), angle of arrival (AoA), and time difference of arrival (TDoA), is an active research problem and its typical applications are radar, communication, vehicle navigation and localization in the indoor environment where the GPS service is impractical. However, the performance of the parameter estimation deteriorates significantly in the presence of array imperfections, which include the mutual coupling, antenna location error, phase uncertainty and so on. These array imperfections are hardly to be calibrated completely via antenna design. In this thesis, we experimentally evaluate an B matrix method to cope with these array imperfection, our results shows a great improvement of AoA estimation results

Enhanced High-Resolution Imaging through Multiple-Frequency Coarray Augmentation

In imaging, much attention is paid to increasing the resolution capabilities of a system. Increasing resolution allows for high-accuracy source location and the ability to discriminate between two closely-spaced objects. In conventional narrowband techniques, resolution is fundamentally limited by the size of the aperture. For apertures consisting of individual elements, direction-of-arrival techniques allow for high-resolution images of point sources. The main limiting factor on conventional high-resolution imaging is the number of elements in the aperture. For both passive and active imaging, to resolve K point sources/targets, there must be at least K+1 elements receiving radiation. In active imaging, when these targets reflect coherently - the more difficult case in imaging - an additional constraint is that at least K of the elements must also be transmitting radiation to illuminate the targets. For small arrays consisting of only a few elements, this constraint can be problematic. In this dissertation, we focus on improving resolution by using multiple frequencies in both passive and active imaging, especially for small arrays. Using multiple frequencies increases the size of the coarray, which is the true limiting factor for resolution of an imaging system when virtual arrays are considered. For passive imaging, we show that the number of sources that can be resolved is limited only by the bandwidth available for certain types of sources. In active imaging, we develop a frequency-averaging method that permits resolution of K coherent point targets with fewer than K transmitting and receiving elements. These methods are investigated primarily for linear arrays, but planar arrays are also briefly examined. Another resolution improvement method researched in this work is a retransmission scheme for active imaging using classical beamforming techniques. In this method, the coarray is extended not by using multiple frequencies, but by retransmitting the received data back into the scene as a second transmission and processing the returns. It is known that when this method is used to image multiple targets, the resulting image is contaminated by crossterms. We investigate methods to reduce the crossterms

Improving Range Estimation of a 3D FLASH LADAR via Blind Deconvolution

The purpose of this research effort is to improve and characterize range estimation in a three-dimensional FLASH LAser Detection And Ranging (3D FLASH LADAR) by investigating spatial dimension blurring effects. The myriad of emerging applications for 3D FLASH LADAR both as primary and supplemental sensor necessitate superior performance including accurate range estimates. Along with range information, this sensor also provides an imaging or laser vision capability. Consequently, accurate range estimates would also greatly aid in image quality of a target or remote scene under interrogation. Unlike previous efforts, this research accounts for pixel coupling by defining the range image mathematical model as a convolution between the system spatial impulse response and the object (target or remote scene) at a particular range slice. Using this model, improved range estimation is possible by object restoration from the data observations. Object estimation is principally performed by deriving a blind deconvolution Generalized Expectation Maximization (GEM) algorithm with the range determined from the estimated object by a normalized correlation method. Theoretical derivations and simulation results are verified with experimental data of a bar target taken from a 3D FLASH LADAR system in a laboratory environment. Additionally, among other factors, range separation estimation variance is a function of two LADAR design parameters (range sampling interval and transmitted pulse-width), which can be optimized using the expected range resolution between two point sources. Using both CRB theory and an unbiased estimator, an investigation is accomplished that finds the optimal pulse-width for several range sampling scenarios using a range resolution metric