In this work we study PhD in general transport properties of and quasi particles-energy particles in one-dimensional systems. We study various models and, through different techniques, we obtained a long spectrum of new results. We did a quick study in a ternary d-1 with electronic distribution site built from a stochastic process known by Ornstein-Uhlenbeck (or). Through exact diagonalizacão we calculate the optical absorption spectrum and distribution of spacing between n ´ levels for this ternary model. Overall, we demonstrated that ´ and can control the position of the absorption peaks by regulating the ternary distribution. In a second moment, we present the results obtained for systems with electronic Dynamics coupled to's vibrations. In this sense, we conducted three separate works: at first, we study the dynamics of an electron in a anarmônica in the presence of electron-interaction network. This anarmônica network was built using the formalism of Fermi-Pasta-Ulam with cubic potential. We made also use of the tight-binding approach to treat the electronic transport, and a classical formalism to describe the longitudinal vibrations. In our studies, electron-interaction network was considered such that the integral of transfer between the neighboring atoms ´ is dependent on the effective distance between neighboring atoms ´ (SuSchrieffer-approach model J. Heeger SSH). Our results suggest a kind of solitônico mode control on electronic Dynamics along the nonlinear network adopted. And, therefore, a kind of State electron moving soliton along the chain. This apparent mobility of electron pair-soliton shown with seemingly constant speed and can be a crucial ingredient in the transport of loads in non-linear chains. In our second approach we investigate the dynamics of electronic State moving in a DNA chain containing N bases, in what we consider beyond the DNA intrinsic disorder distribution, the effect of the vibrations of the DNA. Again, the term electron network was considered such that the electronic hopping energy could depend on the effective distance between the nearest DNA bases. The main results obtained show that the electron-Phonon coupling can transpose the location of Anderson, promoting the emergence of a dynamic sub-difusiva to long. In our work, verificamos also played the role of Atomic coupling type (for 1st gear one cas ˆ nicas, cu ´ Bamford or interac ¸ ' Morse type) within the context of electronic transport in the presence of electron-Phonon coupling. Another point which we investigated was the interaction with acoustic waves pumped throughout the network (an simplificada way to consider acu waves ´ sticas ´ also surface in calls from SAW or Surface Acoustic Waves). In a context we conducted a research on the magnetic dynamics of a magnon in Heisenberg ferromagnetic systems in presence of interactions magnon-fo non ˆ. Our results show that the propagation of spin wave follows a super-difusivo scheme for all values of intensity of magnon-coupling network considered. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho de doutorado estudamos em linhas gerais propriedades de transporte de energia, partículas e quasi-partículas em sistemas unidimensionais. Estudamos diversos modelos e, através de técnicas distintas, obtivemos um longo espectro de novos resultados. Fizemos um rápido estudo em uma cadeia eletrônica ternária 1-d com distribuição on-site construída a partir de um processo estocástico conhecido por Ornstein-Uhlenbeck (OU). Através de diagonalizacão exata calculamos o espectro de absorção ótica e a distribuição de espaçamentos entre n´níveis para este modelo ternário. De modo geral, demonstramos que ´e possível controlar a posição dos picos de absorção regulando a distribuição ternária. Em um segundo momento, apresentamos os resultados obtidos para sistemas com a dinâmica eletrônica acoplada a`s vibrações da rede. Neste sentido, realizamos três trabalhos distintos: a princípio, estudamos a dinâmica de um elétron em uma cadeia anarmônica na presença da interação elétron-rede. Esta rede anarmônica foi construída utilizando o formalismo de Fermi-Pasta-Ulam com o potencial cúbico. Fizemos uso também da aproximação tight-binding para tratar o transporte eletrônico, e um formalismo clássico para descrever as vibrações longitudinais. Em nossos estudos, a interação elétron-rede foi considerada de tal forma que a integral de transferência entre os ´átomos vizinhos seja dependente da distância efetiva entre os ´átomos vizinhos (modelo de aproximação SuSchrieffer-Heeger SSH). Nossos resultados sugerem um tipo de controle do modo solitônico sobre a dinâmica eletrônica ao longo da rede não-linear adotada. Indicando, portanto, um tipo de estado elétron-sóliton se movendo ao longo da cadeia. Esta aparente mobilidade do par elétron-sóliton se mostra com velocidade aparentemente constante e pode ser um ingrediente crucial no transporte de cargas em cadeias não-lineares. Em nossa segunda abordagem investigamos a dinâmica de um estado eletrônico se movendo em uma cadeia de DNA contendo N bases, em que consideramos além da distribuição de desordem DNA intrínseca, o efeito das vibrações do DNA. Novamente, o termo elétron-rede foi considerado de tal forma que a energia de hopping eletrônica pudesse depender da distância efetiva entre as bases mais próximas do DNA. Os principais resultados obtidos revelam que o acoplamento elétron-fônon pode transpor a localização de Anderson, promovendo o aparecimento de uma dinâmica sub-difusiva para tempos longos. Em nosso trabalho, verificamos também o papel do tipo de acoplamento atômico (for¸cas harmoˆnicas, cu´bicas ou interac¸˜ao tipo Morse) dentro do contexto do transporte eletrônico na presença de acoplamento elétron-fônon. Outro ponto que investigamos foi a interação com ondas acústicas bombeadas ao longo da rede (uma maneira simplificada de considerar ondas acu´sticas de superfície tamb´em chamadas de SAW ou Surface Acoustic Waves). Em um contexto magnético realizamos uma investigacão sobre a dinâmica de um magnon em sistemas ferromagnéticos de Heisenberg na presença de interações magnon-foˆnon. Nossos resultados apontam que a propagação da onda de spin segue um regime super-difusivo para todos os valores de intensidade de acoplamento magnon-rede considerados.

abstract: Tracking targets in the presence of clutter is inevitable, and presents many challenges. Additionally, rapid, drastic changes in clutter density between different environments or scenarios can make it even more difficult for tracking algorithms to adapt. A novel approach to target tracking in such dynamic clutter environments is proposed using a particle filter (PF) integrated with Interacting Multiple Models (IMMs) to compensate and adapt to the transition between different clutter densities. This model was implemented for the case of a monostatic sensor tracking a single target moving with constant velocity along a two-dimensional trajectory, which crossed between regions of drastically different clutter densities. Multiple combinations of clutter density transitions were considered, using up to three different clutter densities. It was shown that the integrated IMM PF algorithm outperforms traditional approaches such as the PF in terms of tracking results and performance. The minimal additional computational expense of including the IMM more than warrants the benefits of having it supplement and amplify the advantages of the PF. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2015

Le sujet de cette thèse est l'étude d'idéaux monomiaux de l'anneau de polynômes S qui ont une résolution linéaire. D'après un résultat remarquable de Bayer et Stilman et en utilisant la polarisation, la classification des idéaux monomiaux ayant une résolution linéaire est équivalente à la classification des idéaux monomiaux libres de carrés ayant une résolution linéaire. Pour cette raison dans cette thèse nous considérons seulement le cas d'idéaux monomiaux libres de carrés. De plus, le théorème de Eagon-Reiner établit une dualité entre les idéaux monomiaux libres de carrés ayant une résolution linéaire et les idéaux monomiaux libres de carrés Cohen-Macaulay, ce qui montre que le problème de classification des idéaux monomiaux libres de carrés ayant une résolution linéaire est très difficile. Nous rappelons que les idéaux monomiaux libres de carrés sont en correspondance biunivoque avec les complexes simpliciaux d'une part, et d'autre part avec les clutters. Ces correspondances nous motivent pour utiliser les propriétés combinatoires des complexes simpliciaux et des clutters pour obtenir des résultats algébriques. La classification des idéaux monomiaux libres de carrés ayant une résolution linéaire engendrés en degré 2 a été faite par Froberg en 1990. Froberg a observé que l'idéal des circuits d'un graphe G a une résolution 2-linéaire si et seulement si G est un graphe de cordes, i.e. il n'a pas de cycles minimaux de longueur plus grande que 4. Dans [Em, ThVt, VtV, W] les auteurs ont partiellement généralisé les résultats de Froberg à des idéaux engendrés en degré >2. Ils ont introduit plusieurs définitions de clutters de cordes et démontré que les idéaux de circuits correspondant ont une résolution linéaire. Nous pouvons voir les cycles du point de vue topologique, comme la triangulation d'une courbe fermée, dans cette thèse nous utiliserons cette idée pour étudier des clutters associés à des triangulation de pseudo-manifolds en vue d'obtenir une généralisation partielle des résultats de Froberg à des idéaux engendrés en degré >2. Nous comparons notre travail à ceux de [Em, ThVt, VtV, W]. Nous présentons nos résultats dans le chapitres 4 et 5. / In this thesis, we study square-free monomial ideals of the polynomial ring S which have a linear resolution. By remarkable result of Bayer and Stilman [BS] and the technique of polarization, classification of ideals with linear resolution is equivalent to classification of square-free monomial ideals with linear resolution. For this reason, we consider only square-free monomial ideals in S. However, classification of square-free monomial ideals with linear resolution seems to be so difficult because by Eagon-Reiner Theorem [ER], this is equivalent to classification of Cohen-Macaulay ideals. It is worth to note that, square-free monomial ideals in S are in one-to-one correspondence to Stanley-Reisener ideals of simplicial complexes on one hand and the circuit ideal of clutters from another hand. This correspondence motivated mathematicians to use the combinatorial and geometrical properties of these objects in order to get the desired algebraic results. Classification of square-free monomial ideals with 2-linear resolution, was successfully done by Froberg [Fr] in 1990. Froberg observed that the circuit ideal of a graph G has a 2-linear resolution if and only if G is chordal, that is, G does not have an induced cycle of length > 3. In [Em, ThVt, VtV, W] the authors have partially generalized the Fr¨oberg's theorem for degree greater than 2. They have introduced several definitions of chordal clutters and proved that, their corresponding circuit ideals have linear resolutions. Viewing cycles as geometrical objects (triangulation of closed curves), in this thesis we try to generalize the concept of cycles to triangulation of pseudo-manifolds and get a partial generalization of Froberg's theorem for higher dimensional hypergraphs. All the results in Chapters 4 and 5 and some results in Chapter 3 are devoted to be the original results.

Shape-Based matching (SBM) is a known method for 2D object recognition that is rather robust against illumination variations, noise, clutter and partial occlusion. The objects to be recognized can be translated, rotated and scaled. The translation of an object is determined by evaluating a similarity measure for all possible positions (similar to cross correlation). The similarity measure is based on dot products between normalized gradient directions in edges. Rotation and scale is determined by evaluating all possible combinations, spanning a huge search space. A resolution pyramid is used to form a heuristic for the search that then gains real-time performance. For SBM, a model consisting of normalized edge gradient directions, are constructed for all possible combinations of rotation and scale. We have avoided this by using (bilinear) interpolation in the search gradient map, which greatly reduces the amount of storage required. SBM is highly parallelizable by nature and with our suggested improvements it becomes much suited for running on a GPU. This have been implemented and tested, and the results clearly outperform those of our reference CPU implementation (with magnitudes of hundreds). It is also very scalable and easily benefits from future devices without effort. An extensive evaluation material and tools for evaluating object recognition algorithms have been developed and the implementation is evaluated and compared to two commercial 2D object recognition solutions. The results show that the method is very powerful when dealing with the distortions listed above and competes well with its opponents.

A Wireless Sensor Network (WSN) is a dense network of autonomous devices (or motes) with sensors that cooperatively monitor some physical or environmental conditions. These devices are resource constrained -limited memory, power and computational resources. Thus, any algorithm developed for WSN should be deigned such that the algorithm consumes the resources as minimal as possible. The problem addressed in this thesis is developing a low-complexity algorithm for intrusion detection in the presence of clutter arising from moving vegetation, using Passive Infra-Red (PIR) sensors. The algorithm is based on a combination of Haar Transform (HT) and Support-Vector-Machine (SVM) based training. The spectral signature of the waveforms is used to separate between the intruder and clutter waveforms. The spectral signature is computed using HT and this is fed to SVM which returns an optimal hyperplane that separates the intruder and clutter signatures. This hyperplane obtained by offline training is used online in the mote for surveillance. The algorithm is field-tested in the Indian Institute of Science campus. Based on experimental observations about the PIR sensor and the lens system, an analytical model for the waveform generated by an intruder moving along a straight line with uniform velocity in the vicinity of the sensor is developed. Analysis on how this model can be exploited to track the intruder path by optimally positioning multiple sensor nodes is provided. Algorithm for tracking the intruder path using features of the waveform from three sensors mounted on a single mote is also developed.

Cette thèse présente un ensemble de travaux qui s'inscrivent dans le domaine du génie biomédical pour des applications cliniques. L'objectif principal de ce travail est de fournir aux cliniciens un mode d'imagerie ultrasonore pour extraire simultanément la vitesse du flux et le mouvement de la paroi à des cadences d'imagerie élevées dans les artères. Les pathologies cardiovasculaires sont une cause majeure de décès et d'invalidité dans le monde. Bien que l'origine de ces maladies ne soit pas encore entièrement comprise, il semble que certains marqueurs pathologiques de la paroi et du flux pourraient permettre une détection plus précoce. Parce que les tissus artériels sont sujets à des phénomènes rapides et complexes, une modalité d'imagerie à haute cadence semble très pertinente pour étudier les pathologies du système cardiovasculaire. Malheureusement, aucune technique n'est actuellement utilisée cliniquement ni même approuvée pour l'extraction de marqueurs pathologiques du sang et de la paroi à des cadences d'imagerie élevées. C'est pourquoi, dans cette thèse, je propose de concevoir une séquence et un algorithme ultrasonore permettant d'extraire ces deux aspects, à des cadences d'imagerie élevées sur les artères, pour une application clinique potentielle. Trois contributions scientifiques principales sont présentées cette thèse : i) la conception de la séquence ultrasonore avec un estimateur de mouvement 2D, ii) une nouvelle approche adaptative de filtrage de paroi, et iii) un essai clinique. La séquence d'imagerie ultrasonore est basée sur la transmission d'ondes planes permettant d'obtenir des cadences d'imagerie allant jusqu'à 10 000 Hz sur la carotide. La méthode d'estimation de mouvement est basée sur une approche introduisant une oscillation latérale virtuelle dans les images qui, couplée à un estimateur de phase 2D basé sur des travaux antérieurs de la littérature, permet d'extraire des champs vectoriels de vitesses. Les validations pour l'estimation des vitesses du flux et du mouvement des parois ont été effectuées à l'aide d'un fantôme d'écoulement Doppler commercial et d'un fantôme de carotide réaliste conçu pour les expériences. Une technique de filtrage adaptatif de paroi a été développée et validée sur des volontaires à l'aide des estimations de vitesses tissulaires, ce qui permet d'éliminer précisément le signal du tissu des signaux du sang. Enfin, l'essai clinique a été réalisé à l'hôpital avec un groupe de volontaires et un groupe de patients. La séquence ultrasonore, l'algorithme d'estimation de mouvement et les approches adaptatives de filtrage de paroi ont été validés dans la thèse. La méthode permet d'extraire les vitesses du flux et de la paroi à haute cadence d'imagerie, avec de faibles erreurs et écarts-types. L'approche adaptative du filtrage de paroi permet de mieux extraire le flux par rapport à d'autres approches standard. Cette amélioration est particulièrement perceptible à proximité de la paroi, ce qui permettrait des mesures précises de l'écoulement et des contraintes le long des parois artérielles où les plaques peuvent se former et se développer. Pour conclure, l'essai clinique a démontré la faisabilité de notre approche dans un environnement clinique avec l'extraction des mouvements tissulaires, du flux et de paramètres artériels qui ont montré des différences entre et au sein des groupes. Cette thèse est donc un pas en avant vers l'utilisation clinique de l'imagerie ultrasonore à haute cadence pour la quantification du mouvement tissulaire et du flux pour la détection et le diagnostic des maladies cardiovasculaires / This thesis is focused on biomedical engineering for clinical applications. The main goal of this work is to provide to clinicians an ultrasound mode to simultaneously extract wall motion and flow at high frame rates in arteries. Cardiovascular pathologies are a major cause of death and disability worldwide. Although the formation of such diseases is still not fully understood, it appears that some pathological markers from both wall and flow could allow an earlier detection. Because tissues are subject to fast and complex phenomena in the arteries, a high frame rate imaging modality seems highly relevant to extract as much information as possible on the condition of the cardiovascular system. Unfortunately, no technique is currently clinically used or even approved for the extraction of both flow and wall pathological markers at high frame rates. Therefore, in this thesis, I propose to design an ultrasound sequence and algorithm permitting to extract both aspects, at high frame rates on arteries, for a potential clinical application. There are three main scientific contributions in this thesis: i) the design of the ultrasound sequence with a 2D motion estimator, ii) a new adaptive clutter filtering approach, and iii) a clinical trial. The ultrasound sequence is based on plane wave acquisition permitting to yield frame rates up to 10 000 Hz in the carotid. The pipeline used an approach introducing a virtual lateral oscillation in ultrasound images which, coupled with a 2D phase-based estimator based on previous works from the literature, allows to extract vectorial velocity fields. Validations for both flow and wall motion estimation were performed on a commercial Doppler flow phantom and an in-house realistic carotid phantom was designed for the experiments. An adaptive clutter filtering technique was also developed and validated on volunteers based on tissue estimates, which permit to precisely remove tissue clutter from flow signals. Finally, the clinical trial was performed at the hospital with a group of volunteers and a group of patients. The ultrasound sequence, motion estimation algorithm, and adaptive clutter filtering approaches were well validated in the thesis. The method can provide both wall motion and flow estimates at high frame rates, with low errors and standard deviations. The adaptive clutter filtering approach permits to better extract the flow compared to other standard approaches. This improvement is especially noticeable close to the wall, which would allow accurate flow and stress measurements along arterial walls where plaques can form and develop. To conclude, the clinical trial has demonstrated the feasibility in a clinical environment with the extraction of wall motion, flow, and arterial parameters that showed differences between and within groups. This thesis is then a step toward clinical use of high frame rate ultrasound imaging for quantification of both wall motion and flow for pathological detection of cardiovascular diseases

Due to recent improvements, robots are more applicable in factories and various production lines where smoke, fog, dust, and steam are inevitable. Despite their advantages, robots introduce new safety requirements when combined with humans. Radars can play a crucial role in this context by providing safe zones where robots are operating in the absence of humans. The goal of this Master’s thesis is to investigate different clutter suppression methods for single radar sensor reflection data via digital signal processing. This was done in collaboration with ABB Jokab AB, Sweden. The calculations and implementation of the digital signal processing algorithms are made with Octave. A critical problem is false detection that could possibly cause irreparable damage. Therefore, a safety system with an extremely low false alarm rate is desired to reduce costs and damages. In this project, we have studied four different digital low pass filters: moving average, multiple-pass moving average, Butterworth, and window-based filters. The results are compared, and it is ascertained that all the results are logically compatible, broadly comparable, and usable in this context.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第20034号 / 情博第629号 / 新制||情||109(附属図書館) / 33130 / 京都大学大学院情報学研究科通信情報システム専攻 / (主査)教授 佐藤 亨, 教授 守倉 正博, 教授 山本 衛 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Game engines are well known for their use in the gaming industry but are starting to have an impact in other areas as well. Architecture, automotive, and the defence industry are today using these engines to visualise and, to some extent, test their products. In this thesis, we have examined how the game engine Unity could be used for simulating a radar with the purpose of detecting and measuring sea clutter. Following a pre-study examining different implementation approaches, it was decided to use ray tracing. The radar itself is simulated by using the camera to emit rays and having a plane object directly behind it act as a receiver. Rays are then individually traced for each pixel, propagating throughout the scene and saving information such as hit coordinates, distance travelled, and direction. By using the total travel distance of each ray that returned to the receiver, the phase of each ray is calculated. This is then used to compute the total amplitude, which represents the returned signal strength. Using a compute shader, most of the computations are done in parallel on the GPU, enabling millions of rays to be traced. As measuring sea clutter was an objective of the study, tests measuring the ocean were carried out. These used ocean surfaces with two different sea states, using the Phillips spectrum to generate realistic waves. A ship object was then tested in free space and on two different ocean surfaces. The calculated amplitude and the number of rays returned were used to determine the signal strength returned and the RCS of the object. The purpose of this was to compare with other results of sea clutter studied, observed both in the real world and in simulated scenarios, and determine if our approach could be a valid choice for the industry. Some results matched the findings of a similar study that used a professional radar simulation tool called OKTAL. Other results of sea clutter were found to not be realistic due to certain limitations. The current main limitation of our implementation is not being able to trace a large enough ocean surface with the finer details needed for realistic results. However, this could be solved by creating a better implementation. These findings suggest that simulating radar and sea clutter in Unity is a feasible approach worth continuing to explore. / Spelmotorer är välkända för sin användning inom spelindustrin men har också fått genomslag inom andra områden. Arkitektur, fordonsindustrin och försvarsindustrin använder idag dessa verktyg för att visualisera och till viss mån, även testa sina produkter. I detta examensarbete har vi undersökt hur spelmotorn Unity kan användas för att simulera en radar i syfte att detektera och mäta sjöklotter. Efter en förstudie där olika implementeringsmetoder undersöktes, beslutades det att använda strålspårning (eng. ray tracing). Själva radarn simuleras genom att använda kameraobjektet i Unity för att sända ut strålar. Bakom kameran finns ett planobjekt som fungerar som mottagare. Strålar spåras sedan individuellt för varje pixel och sprider sig genom en given scen. Samtidigt sparas information såsom träffkoordinater, den totala färdsträckan samt riktning. Genom att använda det totala färdavståndet för varje stråle som återvänt till mottagaren kan fasen för varje stråle beräknas. Detta kan sedan användas för att beräkna den totala returnerade amplituden, vilket motsvarar den returnerade signalstyrkan. Med hjälp av en "compute shader" kan databeräkningarna göras parallellt av GPU:n vilket underlättar när så många strålar ska spåras. Eftersom syftet med uppsatsen var mätning av simulerat sjöklotter, genomfördes tester för att mäta på ett simulerat hav. Havsytorna hade två olika sjöstadier, vilka genererades med Phillips-spektrumet för att få realistiska vågor. Ett fartygsobjekt testades sedan i frirymd och sedan även i de två olika havsytorna. Amplituden och mängden strålar som returnerades användes för att bestämma den totala returnerade signalstyrkan och "Radar Cross Section" (RCS) för objektet. Syftet med detta var att kunna jämföra med andra studier gällande sjöklotter, både simulerade som verklighetsbaserade och avgöra om vårt tillvägagångssätt kunde resultera i ett användbart verktyg för branschen. De olika amplituder och antalet strålar som vi fick tillbaka varierade beroende på vilka vinklar och havsytor som användes.Vissa resultat var inte realistiska jämfört med verkliga mätningar av sjöklotter. Det beror främst på våra nuvarande begränsningar i att inte kunna spåra en tillräckligt stor och tillräckligt detaljerad havsyta, vilket behövs för att mätningarna ska vara mer realistiska. Däremot matchade vi några resultat med de från en liknande studie, där verktyget OKTAL, som är ett professionellt radarsimuleringsverktyg, användes. Detta i kombination med möjligheterna för en förbättrad implementation tyder på att användningen av en spelmotor som Unity är ett intressant verktyg värd att vidareutforska radarsimuleringar med.

Advances in digital signal processing (DSP) and computing technology have resulted in the emergence of increasingly adaptive radar systems. It is clear that the Electronic Attack (EA), or jamming, of such radar systems is expected to become a more difficult task. The reason for this research was to address the issue of jamming adaptive radar systems. This required consideration of adaptive jamming systems and the development of a methodology for outlining the features of such a system is proposed as the key contribution of this thesis. For the first time, game-based optimization methods have been applied to a maritime counter-surveillance/counter-targeting scenario involving conventional, as well as so-called ‘smart’ noise jamming.Conventional noise jamming methods feature prominently in the origins of radar electronic warfare, and are still widely implemented. They have been well studied, and are important for comparisons with coherent jamming techniques.Moreover, noise jamming is more readily applied with limited information support and is therefore germane to the problem of jamming adaptive radars; during theearly stages when the jammer tries to learn about the radar’s parameters and its own optimal actions.A radar and a jammer were considered as informed opponents ‘playing’ in a non-cooperative two-player, zero-sum game. The effects of jamming on the target detection performance of a radar using Constant False Alarm Rate (CFAR)processing were analyzed using a game theoretic approach for three cases: (1) Ungated Range Noise (URN), (2) Range-Gated Noise (RGN) and (3) False-Target (FT) jamming.Assuming a Swerling type II target in the presence of Rayleigh-distributed clutter, utility functions were described for Cell-Averaging (CA) and Order Statistic (OS) CFAR processors and the three cases of jamming. The analyses included optimizations of these utility functions, subject to certain constraints, with respectto control variables (strategies) in the jammer, such as jammer power and spatial extent of jamming, and control variables in the radar, such as threshold parameter and reference window size. The utility functions were evaluated over the players’ strategy sets and the resulting matrix-form games were solved for the optimal or ‘best response’ strategies of both the jammer and the radar.