Cramer-Rao Bound for Target Localization for Widely Separated MIMO Radar

In this paper, we derive the Cramer-Rao Bounds (CRBs) for the 2-dimensional (2D) target localization and velocity estimations for widely separated Multiple-Input Multiple-Output (MIMO) radar. The transmitters emit signals with different frequencies and the receivers receive these signals with amplitude fluctuations and with Doppler shifts due to the target motion. The received signal model is constructed using the Swerling target fluctuations to take into account the undesired effects of target amplitude and phase fluctuations. Moreover, the time delays and the Doppler frequencies are included in the signal model to get a more realistic model. Then, the Cramer-Rao Bounds are derived for the proposed signal model for the target position and velocity estimations. Contrary to known models of CRBs, we derived the CRBs jointly and using the Swerling target fluctuations

Investigation of Non-coherent Discrete Target Range Estimation Techniques for High-precision Location

Ranging is an essential and crucial task for radar systems. How to solve the range-detection problem effectively and precisely is massively important. Meanwhile, unambiguity and high resolution are the points of interest as well. Coherent and non-coherent techniques can be applied to achieve range estimation, and both of them have advantages and disadvantages. Coherent estimates offer higher precision but are more vulnerable to noise and clutter and phase wrap errors, particularly in a complex or harsh environment, while the non-coherent approaches are simpler but provide lower precision. With the purpose of mitigating inaccuracy and perturbation in range estimation, miscellaneous techniques are employed to achieve optimally precise detection. Numerous elegant processing solutions stemming from non-coherent estimate are now introduced into the coherent realm, and vice versa. This thesis describes two non-coherent ranging estimate techniques with novel algorithms to mitigate the instinct deficit of non-coherent ranging approaches. One technique is based on peak detection and realised by Kth-order Polynomial Interpolation, while another is based on Z-transform and realised by Most-likelihood Chirp Z-transform. A two-stage approach for the fine ranging estimate is applied to the Discrete Fourier transform domain of both algorithms. An N-point Discrete Fourier transform is implemented to attain a coarse estimation; an accurate process around the point of interest determined in the first stage is conducted. For KPI technique, it interpolates around the peak of Discrete Fourier transform profiles of the chirp signal to achieve accurate interpolation and optimum precision. For Most-likelihood Chirp Z-transform technique, the Chirp Z-transform accurately implements the periodogram where only a narrow band spectrum is processed. Furthermore, the concept of most-likelihood estimator is introduced to combine with Chirp Z-transform to acquire better ranging performance. Cramer-Rao lower bound is presented to evaluate the performance of these two techniques from the perspective of statistical signal processing. Mathematical derivation, simulation modelling, theoretical analysis and experimental validation are conducted to assess technique performance. Further research will be pushed forward to algorithm optimisation and system development of a location system using non-coherent techniques and make a comparison to a coherent approach

OFDM Waveform Optimisation for Joint Communications and Sensing

Radar systems are radios to sense objects in their surrounding environment. These operate at a defined set of frequency ranges. Communication systems are used to transfer information between two points. In the present day, proliferation of mobile devices and the advancement of technology have led to communication systems being ubiquitous. This has made these systems to operate at the frequency bands already used by the radar systems. Thus, the communication signal interferes a radar receiver and vice versa, degrading performance of both systems. Different methods have been proposed to combat this phenomenon. One of the novel topics in this is the RF convergence, where a given bandwidth is used jointly by both systems. A differentiation criterion must be adopted between the two systems so that a receiver is able to separately extract radar and communication signals. The hardware convergence due to the emergence of software-defined radios also motivated a single system be used for both radar and communication. A joint waveform is adopted for both radar and communication systems, as the transmit signal. As orthogonal frequency-division multiplexing (OFDM) waveform is the most prominent in mobile communications, it is selected as the joint waveform. Considering practical cellular communication systems adopting OFDM, there often exist unused subcarriers within OFDM symbols. These can be filled up with arbitrary data to improve the performance of the radar system. This is the approach used, where the filling up is performed through an optimisation algorithm. The filled subcarriers are termed as radar subcarriers while the rest as communication subcarriers, throughout the thesis. The optimisation problem minimises the Cramer--Rao lower bounds of the delay and Doppler estimates made by the radar system subject to a set of constraints. It also outputs the indices of the radar and communication subcarriers within an OFDM symbol, which minimise the lower bounds. The first constraint allocates power between radar and communication subcarriers depending on their subcarrier ratio in an OFDM symbol. The second constraint ensures the peak-to-average power ratio (PAPR) of the joint waveform has an acceptable level of PAPR. The results show that the optimised waveform provides significant improvement in the Cramer--Rao lower bounds compared with the unoptimised waveform. In compensation for this, the power allocated to the communication subcarriers needs to be reduced. Thus, improving the performances of the radar and communication systems are a trade-off. It is also observed that for the minimum lower bounds, radar subcarriers need to be placed at the two edges of an OFDM symbol. Optimisation is also seen to improve the estimation performance of a maximum likelihood estimator, concluding that optimising the subcarriers to minimise a theoretical bound enables to achieve improvement for practical systems

Improvement of ECM Techniques through Implementation of a Genetic Algorithm

This research effective effort develops the necessary interfaces between the radar signal processing components and an optimization routine, such as genetic algorithms, to develop Electronic Countermeasure (ECM) waveforms under a Hardware-in-the-Loop (HILS) architecture. The various ECM waveforms are stored in an ECM library, where an operator selects the desired function to use against a particular system. This optimization works with modular components, compared to previous research that embedded a genetic algorithm into the Range Gate Pull-off (RGPO) waveform optimization loop, which can be interchanged based upon the operator\u27s desired hardware/ software testing setup. The ECM library\u27s first entries contain the RGPO and Velocity Gate Pull-off (VGPO) signals, developed mathematically for multiple polynomial profiles representing realistic moving false targets. The Lab-Volt™ training system and jammer pod provided a validation medium for the developed RGPO and VGPO waveforms. These waveforms were optimized using a Simulink model of the Lab-Volt™ radar system and the MATLAB® Genetic Algorithm (GA) and Direct Search toolbox, contained in Version 7.4 (R2007a), using a defined parameter set, specified for the RGPO waveform. Integration of MATLAB® code with Simulink models provides the necessary interfaces to later transition from software radar models to actual system hardware. Results from GA optimization illuminate the necessity to specifically define the necessary constrains, both linear and nonlinear, imposed upon the environmental conditions. Given defined constraints relative to the Lab-Volt™ training system, the HILS architecture produced multiple constant velocity range profiles with walk-off ranges and maximum velocities similar to the Lab-Volt™ Jammer Pod

The effect of clustering on the uncertainty of differential reflectivity measurements

One of the most important avenues of recent meteorological radar research is the application of polarization techniques to improve radar rainfall estimation. A keystone in many of these methods is the so-called differential reflectivity ZDR, the ratio of the reflectivity factor ZH at horizontal polarization backscattered from a horizontally polarized transmission to that corresponding to a vertically polarized transmission ZV. For such quantitative applications, it is important to understand the statistical accuracy of observations of ZDR. The underlying assumption of all past estimations of meteorological radar uncertainties is that the signals obey Rayleigh statistics. It is now evident, however, that as a radar scans, the meteorological conditions no longer always satisfy the requirements for Rayleigh statistics. In this work, ZDR is reconsidered, but this time within the new framework of non-Rayleigh signal statistics. Using Monte Carlo experiments, it is found that clustering of the scatterers multiplies the standard deviation of ZDR beyond what is always calculated assuming Rayleigh statistics. The magnitude of this enhancement depends on the magnitudes of the clustering index and of the cross correlation between ZHand ZV. Also, it does not depend upon the number of independent samples in an ensemble estimate. An example using real radar data in convective showers suggests that non-Rayleigh signal statistics should be taken into account in future implementations of polarization radar rainfall estimation techniques using ZDR. At the very least, it is time to begin to document the prevalence and magnitude of the clustering index in a wide variety of meteorological conditions

Detection and motion parameters estimation techniques in Forward Scatter Radar

Forward scatter Radar systems designed to take advantage of the greater radar cross section, that is robust to Radar Absorbing Material and other stealth technology, and of the long integration times, due to the little phase and amplitude fluctuations, are attractive for a variety of applications. Many of which fit well with the needs of augmentation of the surveillance capabilities of low-observable targets that may have a small backscatter RCS when observed with the conventional radar systems. This thesis reports on research into this field of radar systems with additional contributions to target detection and motion parameters estimation. Particularly, the first part of the thesis deals with the detection of moving targets that follow a linear trajectory in a single node FSR configuration. The detection scheme based on a square-law detector followed by an appropriate matched filter, here addressed as Crystal Video Detector (CVD) following the traditional terminology (Crystal Video Receiver), has already been put forward in the literature. Performance prediction and FSR system design were key motivator to analytically characterize the detection performance of CVD in terms of both, probability of false alarm and probability of detection. The derived closed-form expressions were validate from Monte Carlo simulations under different geometrical conditions and from experimental data acquired by a passive FSR based on FM signals. Furthermore, new detection schemes based on the CVD ensuring the constant false alarm rate (CFAR) condition were devised and analytically characterized. The performance analysis showed quite small losses of the CFAR-CVD detectors compared to the fixed threshold CVD. The second part of the thesis still handles the problem of target detection through the derivation of innovative detection schemes based on the Generalized Likelihood Ratio Test (GLRT). A comparison with the detection performance of the CVD has proven the better performance of the GLRT-based detectors. In most cases the improvement has an upper bound of 3 dB. However, there are specific circumstances where the standard FSR detector shows significant losses while the GLRT schemes suffer a much smaller degradation. Moreover the possibility to have a set of secondary data assumed target free, drove to the devising of new GLRT schemes. The results demonstrated a non-negligible further improvement over the previous GLRT schemes when the operation conditions get close to the near field transition point. The detection performance of the derived detectors without and with secondary data were analytically characterized. This analytical performance allowed to derive simplified equivalent SNR expressions that relate the GLRT detection performance to the main system and target parameters. These expressions showed to be useful for the design of effective FSR geometries that guarantee desired detection performance for specific targets. In the third part of the thesis the focus is moved to the motion parameters estimation through both, a single baseline and a dual baseline FSR configuration. Accordingly, the Doppler signature extracted from the Crystal Video based scheme is exploited. Following motion parameters estimation approaches already introduced in the literature, a two dimensional filter bank technique was proposed. The main target parameters encoding Doppler rate, main lobe width and crossing time instant were estimated from such technique. The accuracy of the proposed technique was investigated from a theoretical point of view through the derivation of simplified closed-form expression of the Cramer Rao Lower Bound (CRLB). The analysis proved that unbiased estimates of the desired target parameters can be obtained that approach the derived CRLB in the high SNR region. After the dependence of the kinematic parameters on the parameters estimated from the bank was exploited. The cross baseline velocity in a single baseline configuration was estimated under the assumption that the baseline crossing point is known. Meanwhile the dual baseline configuration ensures the possibility to estimate also the baseline crossing point without a priori knowledge on the other target kinematic parameters. Once more, the CRLB of the target motion parameters for both reference scenarios was derived. The analysis proved that unbiased estimates of the target motion parameters can be obtained with high accuracy even for low SNR conditions. The effectiveness of the proposed approach was also shown from experimental data acquired by a passive FSR based on FM signals

Estimation of the Degree of Polarization in Polarimetric SAR Imagery : Principles and Applications

Les radars à synthèse d’ouverture (RSO) polarimétriques sont devenus incontournables dans le domaine de la télédétection, grâce à leur zone de couverture étendue, ainsi que leur capacité à acquérir des données dans n’importe quelles conditions atmosphériques de jour comme de nuit. Au cours des trois dernières décennies, plusieurs RSO polarimétriques ont été utilisés portant une variété de modes d’imagerie, tels que la polarisation unique, la polarisation double et également des modes dits pleinement polarimétriques. Grâce aux recherches récentes, d’autres modes alternatifs, tels que la polarisation hybride et compacte, ont été proposés pour les futures missions RSOs. Toutefois, un débat anime la communauté de la télédétection quant à l’utilité des modes alternatifs et quant au compromis entre la polarimétrie double et la polarimétrie totale. Cette thèse contribue à ce débat en analysant et comparant ces différents modes d’imagerie RSO dans une variété d’applications, avec un accent particulier sur la surveillance maritime (la détection des navires et de marées noires). Pour nos comparaisons, nous considérons un paramètre fondamental, appelé le degré de polarisation (DoP). Ce paramètre scalaire a été reconnu comme l’un des paramètres les plus pertinents pour caractériser les ondes électromagnétiques partiellement polarisées. A l’aide d’une analyse statistique détaillée sur les images polarimétriques RSO, nous proposons des estimateurs efficaces du DoP pour les systèmes d’imagerie cohérente et incohérente. Ainsi, nous étendons la notion de DoP aux différents modes d’imagerie polarimétrique hybride et compacte. Cette étude comparative réalisée dans différents contextes d’application dégage des propriétés permettant de guider le choix parmi les différents modes polarimétriques. Les expériences sont effectuées sur les données polarimétriques provenant du satellite Canadian RADARSAT-2 et le RSO aéroporté Américain AirSAR, couvrant divers types de terrains tels que l’urbain, la végétation et l’océan. Par ailleurs nous réalisons une étude détaillée sur les potentiels du DoP pour la détection et la reconnaissance des marées noires basée sur les acquisitions récentes d’UAVSAR, couvrant la catastrophe de Deepwater Horizon dans le golfe du Mexique. ABSTRACT : Polarimetric Synthetic Aperture Radar (SAR) systems have become highly fruitful thanks to their wide area coverage and day and night all-weather capabilities. Several polarimetric SARs have been flown over the last few decades with a variety of polarimetric SAR imaging modes; traditional ones are linear singleand dual-pol modes. More sophisticated ones are full-pol modes. Other alternative modes, such as hybrid and compact dual-pol, have also been recently proposed for future SAR missions. The discussion is vivid across the remote sensing society about both the utility of such alternative modes, and also the trade-off between dual and full polarimetry. This thesis contributes to that discussion by analyzing and comparing different polarimetric SAR modes in a variety of geoscience applications, with a particular focus on maritime monitoring and surveillance. For our comparisons, we make use of a fundamental, physically related discriminator called the Degree of Polarization (DoP). This scalar parameter has been recognized as one of the most important parameters characterizing a partially polarized electromagnetic wave. Based on a detailed statistical analysis of polarimetric SAR images, we propose efficient estimators of the DoP for both coherent and in-coherent SAR systems. We extend the DoP concept to different hybrid and compact SAR modes and compare the achieved performance with different full-pol methods. We perform a detailed study of vessel detection and oil-spill recognition, based on linear and hybrid/compact dual-pol DoP, using recent data from the Deepwater Horizon oil-spill, acquired by the National Aeronautics and Space Administration (NASA)/Jet Propulsion Laboratory (JPL) Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR). Extensive experiments are also performed over various terrain types, such as urban, vegetation, and ocean, using the data acquired by the Canadian RADARSAT-2 and the NASA/JPL Airborne SAR (AirSAR) system

Cognitive radar network design and applications

PhD ThesisIn recent years, several emerging technologies in modern radar system design are attracting the attention of radar researchers and practitioners alike, noteworthy among which are multiple-input multiple-output (MIMO), ultra wideband (UWB) and joint communication-radar technologies. This thesis, in particular focuses upon a cognitive approach to design these modern radars. In the existing literature, these technologies have been implemented on a traditional platform in which the transmitter and receiver subsystems are discrete and do not exchange vital radar scene information. Although such radar architectures benefit from these mentioned technological advances, their performance remains sub-optimal due to the lack of exchange of dynamic radar scene information between the subsystems. Consequently, such systems are not capable to adapt their operational parameters “on the fly”, which is in accordance with the dynamic radar environment. This thesis explores the research gap of evaluating cognitive mechanisms, which could enable modern radars to adapt their operational parameters like waveform, power and spectrum by continually learning about the radar scene through constant interactions with the environment and exchanging this information between the radar transmitter and receiver. The cognitive feedback between the receiver and transmitter subsystems is the facilitator of intelligence for this type of architecture. In this thesis, the cognitive architecture is fused together with modern radar systems like MIMO, UWB and joint communication-radar designs to achieve significant performance improvement in terms of target parameter extraction. Specifically, in the context of MIMO radar, a novel cognitive waveform optimization approach has been developed which facilitates enhanced target signature extraction. In terms of UWB radar system design, a novel cognitive illumination and target tracking algorithm for target parameter extraction in indoor scenarios has been developed. A cognitive system architecture and waveform design algorithm has been proposed for joint communication-radar systems. This thesis also explores the development of cognitive dynamic systems that allows the fusion of cognitive radar and cognitive radio paradigms for optimal resources allocation in wireless networks. In summary, the thesis provides a theoretical framework for implementing cognitive mechanisms in modern radar system design. Through such a novel approach, intelligent illumination strategies could be devised, which enable the adaptation of radar operational modes in accordance with the target scene variations in real time. This leads to the development of radar systems which are better aware of their surroundings and are able to quickly adapt to the target scene variations in real time.Newcastle University, Newcastle upon Tyne: University of Greenwich

Deterministic Algorithms for Four-Dimensional Imaging in Colocated MIMO OFDM-Based Radar Systems

In this manuscript, the problem of detecting multiple targets and jointly estimating their spatial coordinates (namely, the range, the Doppler and the direction of arrival of their electromagnetic echoes) in a colocated multiple-input multiple-output radar system employing orthogonal frequency division multiplexing is investigated. It is well known its optimal solution, namely the joint maximum likelihood estimator of an unknown number of targets, is unfeasible because of its huge computational complexity. Moreover, until now, sub-optimal solutions have not been proposed in the technical literature. In this manuscript a novel approach to the development of reduced complexity solutions is illustrated. It is based on the idea of separating angle estimation from range-Doppler estimation, and of exploiting known algorithms for solving these two sub-problems. A detailed analysis of the accuracy and complexity of various detection and estimation methods based on this approach is provided. Our numerical results evidence that one of these methods is able to approach optimal performance in the maximum likelihood sense with a limited computational effort in different scenarios

Realization Limits of Impulse-Radio UWB Indoor Localization Systems

In this work, the realization limits of an impulse-based Ultra-Wideband (UWB) localization system for indoor applications have been thoroughly investigated and verified by measurements. The analysis spans from the position calculation algorithms, through hardware realization and modeling, up to the localization experiments conducted in realistic scenarios. The main focus was put on identification and characterization of limiting factors as well as developing methods to overcome them