Identification of Parametric Underspread Linear Systems and Super-Resolution Radar

Identification of time-varying linear systems, which introduce both time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task in many engineering applications. This paper studies the problem of identification of underspread linear systems (ULSs), whose responses lie within a unit-area region in the delay Doppler space, by probing them with a known input signal. It is shown that sufficiently-underspread parametric linear systems, described by a finite set of delays and Doppler-shifts, are identifiable from a single observation as long as the time bandwidth product of the input signal is proportional to the square of the total number of delay Doppler pairs in the system. In addition, an algorithm is developed that enables identification of parametric ULSs from an input train of pulses in polynomial time by exploiting recent results on sub-Nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials. Finally, application of these results to super-resolution target detection using radar is discussed. Specifically, it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay Doppler space, resulting in a resolution that substantially exceeds that of standard matched-filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing-based radar methods.Comment: Revised version of a journal paper submitted to IEEE Trans. Signal Processing: 30 pages, 17 figure

Adaptive MIMO Radar for Target Detection, Estimation, and Tracking

We develop and analyze signal processing algorithms to detect, estimate, and track targets using multiple-input multiple-output: MIMO) radar systems. MIMO radar systems have attracted much attention in the recent past due to the additional degrees of freedom they offer. They are commonly used in two different antenna configurations: widely-separated: distributed) and colocated. Distributed MIMO radar exploits spatial diversity by utilizing multiple uncorrelated looks at the target. Colocated MIMO radar systems offer performance improvement by exploiting waveform diversity. Each antenna has the freedom to transmit a waveform that is different from the waveforms of the other transmitters. First, we propose a radar system that combines the advantages of distributed MIMO radar and fully polarimetric radar. We develop the signal model for this system and analyze the performance of the optimal Neyman-Pearson detector by obtaining approximate expressions for the probabilities of detection and false alarm. Using these expressions, we adaptively design the transmit waveform polarizations that optimize the target detection performance. Conventional radar design approaches do not consider the goal of the target itself, which always tries to reduce its detectability. We propose to incorporate this knowledge about the goal of the target while solving the polarimetric MIMO radar design problem by formulating it as a game between the target and the radar design engineer. Unlike conventional methods, this game-theoretic design does not require target parameter estimation from large amounts of training data. Our approach is generic and can be applied to other radar design problems also. Next, we propose a distributed MIMO radar system that employs monopulse processing, and develop an algorithm for tracking a moving target using this system. We electronically generate two beams at each receiver and use them for computing the local estimates. Later, we efficiently combine the information present in these local estimates, using the instantaneous signal energies at each receiver to keep track of the target. Finally, we develop multiple-target estimation algorithms for both distributed and colocated MIMO radar by exploiting the inherent sparsity on the delay-Doppler plane. We propose a new performance metric that naturally fits into this multiple target scenario and develop an adaptive optimal energy allocation mechanism. We employ compressive sensing to perform accurate estimation from far fewer samples than the Nyquist rate. For colocated MIMO radar, we transmit frequency-hopping codes to exploit the frequency diversity. We derive an analytical expression for the block coherence measure of the dictionary matrix and design an optimal code matrix using this expression. Additionally, we also transmit ultra wideband noise waveforms that improve the system resolution and provide a low probability of intercept: LPI)

Waveform Diversity and Range-Coupled Adaptive Radar Signal Processing

Waveform diversity may offer several benefits to radar systems though often at the cost of reduced sensitivity. Multi-dimensional processing schemes are known to offer many degrees of freedom, which can be exploited to suppress the ambiguity inherent to pulse compression, array processing, and Doppler frequency estimation. Spatial waveform diversity can be achieved by transmitting different but correlated waveforms from each element of an antenna array. A simple yet effective scheme is employed to transmit different waveforms in different spatial directions. A new reiterative minimum mean squared error approach entitled Space-Range Adaptive Processing, which adapts simultaneously in range and angle, is derived and shown in simulation to offer enhanced performance when spatial waveform diversity is employed relative to both conventional matched filtering and sequentially adapting in angle and then range. The same mathematical framework is utilized to develop Time-Range Adaptive Processing (TRAP) algorithm which is capable of simultaneously adapting in Doppler frequency and range. TRAP is useful when pulse-to-pulse changing of the center frequency or waveform coding is used to achieve enhanced range resolution or unambiguous ranging, respectively. The inherent computational complexity of the new multi-dimensional algorithms is addressed by segmenting the full-dimension cost functions, yielding a reduced-dimensional variants of each. Finally, a non-adaptive approach based on the multi-dimensional TRAP signal model is utilized to develop an efficient clutter cancellation technique capable of suppressing multiple range intervals of clutter when waveform diversity is applied to pulse-Doppler radar

Joint Design of Overlaid Communication Systems and Pulsed Radars

The focus of this paper is on co-existence between a communication system and a pulsed radar sharing the same bandwidth. Based on the fact that the interference generated by the radar onto the communication receiver is intermittent and depends on the density of scattering objects (such as, e.g., targets), we first show that the communication system is equivalent to a set of independent parallel channels, whereby pre-coding on each channel can be introduced as a new degree of freedom. We introduce a new figure of merit, named the {\em compound rate}, which is a convex combination of rates with and without interference, to be optimized under constraints concerning the signal-to-interference-plus-noise ratio (including {\em signal-dependent} interference due to clutter) experienced by the radar and obviously the powers emitted by the two systems: the degrees of freedom are the radar waveform and the afore-mentioned encoding matrix for the communication symbols. We provide closed-form solutions for the optimum transmit policies for both systems under two basic models for the scattering produced by the radar onto the communication receiver, and account for possible correlation of the signal-independent fraction of the interference impinging on the radar. We also discuss the region of the achievable communication rates with and without interference. A thorough performance assessment shows the potentials and the limitations of the proposed co-existing architecture

Portable Ultrasound Imaging

This PhD project investigates hardware strategies and imaging methods for hand-held ultrasound systems. The overall idea is to use a wireless ultrasound probe linked to general-purpose mobile devices for the processing and visualization. The approach has the potential to reduce the upfront costs of the ultrasound system and, consequently, to allow for a wide-scale utilization of diagnostic ultrasound in any medical specialties and out of the radiology department. The first part of the contribution deals with the study of hardware solutions for the reduction of the system complexity. Analog and digital beamforming strategies are simulated from a system-level perspective. The quality of the B-mode image is evaluated and the minimum specifications are derived for the design of a portable probe with integrated electronics in-handle. The system is based on a synthetic aperture sequential beamforming approach that allows to significantly reduce the data rate between the probe and processing unit. The second part investigates the feasibility of vector flow imaging in a hand-held ultrasound system. Vector flow imaging overcomes the limitations of conventional imaging methods in terms of flow angle compensation. Furthermore, high frame rate can be obtained by using synthetic aperture focusing techniques. A method is developed combining synthetic aperture sequential beamforming and directional transverse oscillation to achieve the wireless transmission of the data along with a relatively inexpensive 2-D velocity estimation. The performance of the method is thoroughly assessed through simulations and measurements, and in vivo investigations are carried out to show its potential in presence of complex flow dynamics. A sufficient frame rate is achieved to allow for the visualization of vortices in the carotid bifurcation. Furthermore, the method is implemented on a commercially available tablet to evaluate the real-time processing performance in the built-in GPU with concurrent wireless transmission of the data. Based on the demonstrations in this thesis, a flexible framework can be implemented with performance that can be scaled to the needs of the user and according to the computing resources available. The integration of high-frame-rate vector flow imaging in a hand-held ultrasound scanner, in addition, has the potential to improve the operator’s workflow and opens the way to new possibilities in the clinical practice

Ultrafast Echocardiography

Grâce à son accessibilité, sa polyvalence et sa sécurité, l'échocardiographie est devenue la technique d'imagerie la plus utilisée pour évaluer la fonction cardiaque. Au vu du succès de l'échographie ultrarapide par ondes planes des techniques similaires pour augmenter la résolution temporelle en échocardiographie ont été mise en oeuvre. L’augmentation de la résolution temporelle de l’échographie cardiaque au-delà des valeurs actuellement atteignables (~ 60 à 80 images par secondes), pourrait être utilisé pour améliorer d’autres caractéristiques de l'échocardiographie, comme par exemple élargir la plage de vitesses détectables en imagerie Doppler couleur limitées par la valeur de Nyquist. Nous avons étudié l'échocardiographie ultrarapide en utilisant des fronts d’ondes ultrasonores divergentes. La résolution temporelle atteinte par la méthode d'ondes divergentes a permis d’améliorer les capacités des modes d’échocardiographie en mode B et en Doppler couleur. La résolution temporelle de la méthode mode B a été augmentée jusqu'à 633 images par secondes, tout en gardant une qualité d'image comparable à celle de la méthode d’échocardiographie conventionnelle. La vitesse de Nyquist de la méthode Doppler couleur a été multipliée jusqu'à 6 fois au delà de la limite conventionnelle en utilisant une technique inspirée de l’imagerie radar; l’implémentation de cette méthode n’aurait pas été possible sans l’utilisation de fronts d’ondes divergentes. Les performances avantageuses de la méthode d'échocardiographie ultrarapide sont supportées par plusieurs résultats in vitro et in vivo inclus dans ce manuscrit.Because of its low cost, versatility and safety, echocardiography has become the most common imaging technique to assess the cardiac function. The recent success of ultrafast ultrasound plane wave imaging has prompted the implementation of similar approaches to enhance the echocardiography temporal resolution. The ability to enhance the echocardiography frame rate beyond conventional values (~60 to 80 fps) would positively impact other echocardiography features, e.g. broaden the color Doppler unambiguous velocity range. We investigated the ultrafast echocardiography imaging approach using ultrasound diverging waves. The high frame rate offered by the diverging wave method was used to enhance the capabilities of both B-mode and color Doppler echocardiography. The B-mode temporal resolution was increased to 633 fps whilst the image quality was kept almost unchanged with reference to the conventional echocardiography technique. The color Doppler Nyquist velocity range was extended to up to 6 times the conventional limit using a weather radar imaging approach; such an approach could not have been implemented without using the ultrafast diverging wave imaging technique. The advantageous performance of the ultrafast diverging wave echocardiography approach is supported by multiple in vitro and in vivo results included in this manuscript

Spaceborne synthetic-aperture imaging radars: Applications, techniques, and technology

In the last four years, the first two Earth-orbiting, space-borne, synthetic-aperture imaging radars (SAR) were successfully developed and operated. This was a major achievement in the development of spaceborne radar sensors and ground processors. The data acquired with these sensors extended the capability of Earth resources and ocean-surface observation into a new region of the electromagnetic spectrum. This paper is a review of the different aspects of spaceborne imaging radars. It includes a review of: 1) the unique characteristics of space-borne SAR systems; 2) the state of the art in spaceborne SAR hardware and SAR optical and digital processors; 3) the different data-handling techniques; and 4) the different applications of spaceborne SAR data