Adaptive OFDM Radar for Target Detection and Tracking

We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing: OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar\u27s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the $ell_1$-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose an tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter

Selección óptima del factor de ajuste CA-CFAR para clutter marino de potencia K estadísticamente variable

The presence of the sea clutter interfering signal sets limitations on the quality of radar detection in coastal and ocean environments. The CA-CFAR processor is the classic solution for detecting radar targets. It usually operates keeping constant its adjustment factor during the entire operation period. As a consequence, the scheme does not take into account the slow statistical variations of the background signal when performing the clutter discrimination. To solve this problem, the authors conducted an intensive processing of 40 million computer generated clutter power samples in MATLAB. As a result, they found the optimal adjustment factor values to be applied in 40 possible clutter statistical states, suggesting thus the use of the CA-CFAR architecture with a variable adjustment factor. In addition, a curve fitting procedure was performed, obtaining mathematical expressions that generalize the results for the whole addressed range of clutter statistical states. The experiments were executed with a 64 cells CA-CFAR and found the adjustment factor values for three common false alarms probabilities. The K distribution was used as clutter model, thanks to its wide popularity. This paper facilitates the handling of the K power distribution avoiding the use of Gamma and Bessel functions, commonly found in developments related to the K model. Moreover, requirements for building an adaptive clutter detector in K power clutter with a priori knowledge of the shape parameter were fulfill. Also, several recommendations are given to continue the development of a more overall solution which will also include the estimation of the shape parameter.La presencia de la señal interferente de clutter marino establece limitaciones en la calidad de la detección de radar en ambientes costeros y de alta mar. El procesador CA-CFAR es la solución clásica para detectar blancos de radar. Usualmente mantiene su factor de ajuste constante todo el período de operación. Como consecuencia, el esquema no toma en consideración las variaciones estadísticas de la señal de fondo cuando realiza la discriminación del clutter. Para resolver este problema, los autores realizaron un procesamiento intensivo de 40 millones de muestras de clutter de intensidad, generadas en computadora a través de MATLAB. Como resultado, encontraron los valores óptimos del factor de ajuste a ser aplicados para 40 posibles estados estadísticos del clutter, sugiriendo el uso de la arquitectura CA-CFAR con un factor de ajuste variable. Adicionalmente, fue llevado a cabo un ajuste de curvas, obteniéndose expresiones matemáticas que generalizan los resultados en todo el intervalo de considerado de estados estadísticos del clutter. Los experimentos se ejecutaron con un CA-CFAR de 64 celdas y apuntaron a encontrar los valores del factor de ajuste para tres probabilidades de falsa alarma comunes. La distribución K fue elegida como el modelo usado para el clutter, gracias a su amplia popularidad. Este artículo facilita el manejo de la distribución K de intensidad, evitando el uso de funciones Gamma y Bessel, comúnmente encontradas en desarrollos relacionados con el modelo K. Además, fueron cumplidos los requerimientos necesarios para construir un detector adaptativo en clutter de potencia K con conocimiento previo del parámetro de forma. Al mismo tiempo, fueron dadas varias recomendaciones para continuar el desarrollo de una solución más general que también incluirá la estimación del parámetro de forma

Mathematical optimization and game theoretic methods for radar networks

Radar systems are undoubtedly included in the hall of the most momentous discoveries of the previous century. Although radars were initially used for ship and aircraft detection, nowadays these systems are used in highly diverse fields, expanding from civil aviation, marine navigation and air-defence to ocean surveillance, meteorology and medicine. Recent advances in signal processing and the constant development of computational capabilities led to radar systems with impressive surveillance and tracking characteristics but on the other hand the continuous growth of distributed networks made them susceptible to multisource interference. This thesis aims at addressing vulnerabilities of modern radar networks and further improving their characteristics through the design of signal processing algorithms and by utilizing convex optimization and game theoretic methods. In particular, the problems of beamforming, power allocation, jammer avoidance and uncertainty within the context of multiple-input multiple-output (MIMO) radar networks are addressed. In order to improve the beamforming performance of phased-array and MIMO radars employing two-dimensional arrays of antennas, a hybrid two-dimensional Phased-MIMO radar with fully overlapped subarrays is proposed. The work considers both adaptive (convex optimization, CAPON beamformer) and non-adaptive (conventional) beamforming techniques. The transmit, receive and overall beampatterns of the Phased-MIMO model are compared with the respective beampatterns of the phased-array and the MIMO schemes, proving that the hybrid model provides superior capabilities in beamforming. By incorporating game theoretic techniques in the radar field, various vulnerabilities and problems can be investigated. Hence, a game theoretic power allocation scheme is proposed and a Nash equilibrium analysis for a multistatic MIMO network is performed. A network of radars is considered, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since no communication between the clusters is assumed, non-cooperative game theoretic techniques and convex optimization methods are utilized to tackle the power adaptation problem. During the proof of the existence and the uniqueness of the solution, which is also presented, important contributions on the SINR performance and the transmission power of the radars have been derived. Game theory can also been applied to mitigate jammer interference in a radar network. Hence, a competitive power allocation problem for a MIMO radar system in the presence of multiple jammers is investigated. The main objective of the radar network is to minimize the total power emitted by the radars while achieving a specific detection criterion for each of the targets-jammers, while the intelligent jammers have the ability to observe the radar transmission power and consequently decide its jamming power to maximize the interference to the radar system. In this context, convex optimization methods, noncooperative game theoretic techniques and hypothesis testing are incorporated to identify the jammers and to determine the optimal power allocation. Furthermore, a proof of the existence and the uniqueness of the solution is presented. Apart from resource allocation applications, game theory can also address distributed beamforming problems. More specifically, a distributed beamforming and power allocation technique for a radar system in the presence of multiple targets is considered. The primary goal of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Initially, a strategic noncooperative game (SNG) is used, where there is no communication between the various radars of the system. Subsequently, a more coordinated game theoretic approach incorporating a pricing mechanism is adopted. Furthermore, a Stackelberg game is formulated by adding a surveillance radar to the system model, which will play the role of the leader, and thus the remaining radars will be the followers. For each one of these games, a proof of the existence and uniqueness of the solution is presented. In the aforementioned game theoretic applications, the radars are considered to know the exact radar cross section (RCS) parameters of the targets and thus the exact channel gains of all players, which may not be feasible in a real system. Therefore, in the last part of this thesis, uncertainty regarding the channel gains among the radars and the targets is introduced, which originates from the RCS fluctuations of the targets. Bayesian game theory provides a framework to address such problems of incomplete information. Hence, a Bayesian game is proposed, where each radar egotistically maximizes its SINR, under a predefined power constraint

New Findings on GLRT Radar Detection of Nonfluctuating Targets via Phased Arrays

This paper addresses the standard generalized likelihood ratio test (GLRT) detection problem of weak signals in background noise. In so doing, we consider a nonfluctuating target embedded in complex white Gaussian noise (CWGN), in which the amplitude of the target echo and the noise power are assumed to be unknown. Important works have analyzed the performance for the referred scenario and proposed GLRT-based detectors. Such detectors are projected at an early stage (i.e., prior to the formation of a post-beamforming scalar waveform), thereby imposing high demands on hardware, processing, and data storage. From a hardware perspective, most radar systems fail to meet these strong requirements. In fact, due to hardware and computational constraints, most radars use a combination of analog and digital beamformers (sums) before any estimation or further pre-processing. The rationale behind this study is to derive a GLRT detector that meets the hardware and system requirements. In this work, we design and analyze a more practical and easy-to-implement GLRT detector, which is projected after the analog beamforming. The performance of the proposed detector is analyzed and the probabilities of detection (PD) and false alarm (PFA) are derived in closed form. Moreover, we show that in the low signal-to-noise ratio (SNR) regime, the post-beamforming GLRT detector performs better than both the classic pre-beamforming GLRT detector and the square-law detector. This finding suggests that if the signals are weak, instead of processing the signals separately, we first must to reinforce the overall signal and then assembling the system's detection statistic. At last, the SNR losses are quantified, in which the superiority of the post-beamforming GLRT detector was evidenced as the number of antennas and samples increase.Comment: 13 pages, 12 figures, 1 tabl

On the sum of random samples with bounded Pareto distribution

Heavy-tailed random samples, as well as their sum or average, are encountered in a number of signal pro-cessing applications in radar, communications, finance, and natural sciences. Modeling such data through the Pareto distribution is particularly attractive due to its simple analytical form, but may lead to infinite variance and/or mean, which is not physically plausible: in fact, samples are always bounded in practice, namely because of clipping during the signal acquisition or deliberate censoring or trimming (truncation) at the processing stage. Based on this motivation, the paper derives and analyzes the distribution of the sum of right-censored Pareto Type-II variables, which generalizes the conventional Pareto (Type-I) and Lomax distributions. The distribution of the sum of truncated Pareto is also obtained, and an analytical connection is drawn with the unbounded case. A numerical analysis illustrates the findings, providing insights on several aspects, including the intimate mixture structure of the obtained expressions. An il-lustrative application to the analysis of real radar data is also provided. (c) 2021 Elsevier B.V. All rights reserved

Game theoretic analysis for MIMO radars with multiple targets

This paper considers a distributed beamforming and resource allocation technique for a radar system in the presence of multiple targets. The primary objective of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Therefore, we use convex optimization methods together with noncooperative and partially cooperative game theoretic approaches. Initially, we consider a strategic noncooperative game (SNG), where there is no communication between the various radars of the system. Hence each radar selfishly determines its optimal beamforming and power allocation. Subsequently, we assume a more coordinated game theoretic approach incorporating a pricing mechanism. Introducing a price in the utility function of each radar/player, enforces beamformers to minimize the interference induced to other radars and to increase the social fairness of the system. Furthermore, we formulate a Stackelberg game by adding a surveillance radar to the system model, which will play the role of the leader, and hence the remaining radars will be the followers. The leader applies a pricing policy of interference charged to the followers aiming at maximizing his profit while keeping the incoming interference under a certain threshold. We also present a proof of the existence and uniqueness of the Nash Equilibrium (NE) in both the partially cooperative and noncooperative games. Finally, the simulation results confirm the convergence of the algorithm in all three cases

Robust CFAR Detector Based on Truncated Statistics for Polarimetric Synthetic Aperture Radar

Constant false alarm rate (CFAR) algorithms using a local training window are widely used for ship detection with synthetic aperture radar (SAR) imagery. However, when the density of the targets is high, such as in busy shipping lines and crowded harbors, the background statistics may be contaminated by the presence of nearby targets in the training window. Recently, a robust CFAR detector based on truncated statistics (TS) was proposed. However, the truncation of data in the format of polarimetric covariance matrices is much more complicated with respect to the truncation of intensity (single polarization) data. In this article, a polarimetric whitening filter TS CFAR (PWF-TS-CFAR) is proposed to estimate the background parameters accurately in the contaminated sea clutter for PolSAR imagery. The CFAR detector uses a polarimetric whitening filter (PWF) to turn the multidimensional problem to a 1-D case. It uses truncation to exclude possible statistically interfering outliers and uses TS to model the remaining background samples. The algorithm does not require prior knowledge of the interfering targets, and it is performed iteratively and adaptively to derive better estimates of the polarimetric covariance matrix (although this is computationally expensive). The PWF-TS-CFAR detector provides accurate background clutter modeling, a stable false alarm property, and improves the detection performance in high-target-density situations. RadarSat2 data are used to verify our derivations, and the results are in line with the theory

Signal Processing for Non-Gaussian Statistics: Clutter Distribution Identification and Adaptive Threshold Estimation

We examine the problem of determining a decision threshold for the binary hypothesis test that naturally arises when a radar system must decide if there is a target present in a range cell under test. Modern radar systems require predictable, low, constant rates of false alarm (i.e. when unwanted noise and clutter returns are mistaken for a target). Measured clutter returns have often been fitted to heavy tailed, non-Gaussian distributions. The heavy tails on these distributions cause an unacceptable rise in the number of false alarms. We use the class of spherically invariant random vectors (SIRVs) to model clutter returns. SIRVs arise from a phenomenological consideration of the radar sensing problem, and include both the Gaussian distribution and most commonly reported non-Gaussian clutter distributions (e.g. K distribution, Weibull distribution). We propose an extension of a prior technique called the Ozturk algorithm. The Ozturk algorithm generates a graphical library of points corresponding to known SIRV distributions. These points are generated from linked vectors whose magnitude is derived from the order statistics of the SIRV distributions. Measured data is then compared to the library and a distribution is chosen that best approximates the measured data. Our extension introduces a framework of weighting functions and examines both a distribution classification technique as well as a method of determining an adaptive threshold in data that may or may not belong to a known distribution. The extensions are then compared to neural networking techniques. Special attention is paid to producing a robust, adaptive estimation of the detection threshold. Finally, divergence measures of SIRVs are examined

Adaptive Beamsteering Cognitive Radar with Integrated Search-and-Track of Swarm Targets

The article of record as published may be found at http://dx.doi.org/10.1109/ACCESS.2021.3069350, IEEE AccessAdaptive beamsteering cognitive radar (AB-CRr) systems seek to improve detection and tracking performance by formulating a beam placement strategy adapted to their environment. AB-CRr builds a probabilistic model of the target environment that enables it to more efficiently employ its limited resources to locate and track targets. In this work, we investigate methods for adapting the AB- CRr framework to detect and track large target swarms. This is achieved by integrating the properties of correlated-motion swarms into both the radar tracking model and AB-CRr’s underlying dynamic probability model. As a result, a list of newly CRr-integrated contributions are enumerated: a) improved uncertainty function design, b) incorporates Mahalanobis nearest neighbors multi-target association methodology into AB-CRr, c) introduces a novel Kalman-based consolidated swarm tracking methodology with a common velocity state vector that frames targets as a correlated collection of swarm members, d) introduces an improved uncertainty growth model for updating environment probability map, e) introduces a method for incorporating estimated swarm structure and behavior into the uncertainty update model referred to as "track hinting", and f) introduces new metrics for swarm search/detection and tracking called swarm centroid track error and swarm tracking dwell ratio. The results demonstrate that AB-CRr is capable of adapting its beamsteering strategy to efficiently perform resource balancing between target search and swarm tracking applications, while taking advantage of group structure and intra-swarm target correlation to resist large swarms overloading available resources.Approved for public release; distribution is unlimited