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

Time-Range FDA Beampattern Characteristics

Current literature show that frequency diverse arrays (FDAs) are able of producing range-angle-dependent and time-variant transmit beampatterns, but the resulting time and range dependencies and their characteristics are still not well understood. This paper examines the FDA transmission model and the model for the FDA array factor, considering their time-range relationship. We develop two novel FDA transmit beampatterns, both yielding the auto-scanning capability of the FDA transmit beams. The scan speed, scan volume, and initial mainlobe direction of the beams are also analyzed. In addition, the equivalent conditions for the FDA integral transmit beampattern and the multiple-input multiple-output (MIMO) beampattern are investigated. Various numerical simulations illustrate the auto-scanning property of the FDA beampattern and the proposed equivalent relationship with the MIMO beampattern, providing the basis for an improved understanding and design of the FDA transmit beampattern.Comment: 10 pages, 9 figure

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance

SPS phase control system performance via analytical simulation

A solar power satellite transmission system which incorporates automatic beam forming, steering, and phase control is discussed. The phase control concept centers around the notation of an active retrodirective phased array as a means of pointing the beam to the appropriate spot on Earth. The transmitting antenna (spacetenna) directs the high power beam so that it focuses on the ground-based receiving antenna (rectenna). A combination of analysis and computerized simulation was conducted to determine the far field performance of the reference distribution system, and the beam forming and microwave power generating systems

Theory and Applications of Aperiodic (Random) Phased Arrays

A need for network centric topologies using mobile wireless communications makes it important to investigate new distributed beamforming techniques. Platforms such as micro air vehicles (MAVs), unattended ground sensors (UGSs), and unpiloted aerial vehicles (UAVs) can all benefit from advances in this area utilizing advantages in stealth, enhanced survivability and maximum maneuverability. Moreover, in this dissertation, electromagnetic radiation is investigated such that the signal power of each element is coherently added in the far-field region of a specified target direction with net destructive interference occurring in all other regions to suppress sidelobe behavior. This provides superior range and resolution characteristics for a variety of applications including; early warning radar, ballistic missile defense and search and rescue efforts. A wide variety of topologies can be used to confine geometrically these mobile random arrays for analysis. The distribution function for these topologies must be able to generalize the randomness within the geometry. By this means it is feasible to assume the random element distribution of a very large volumetric space will yield either a normal or Gaussian distribution. Therefore the underlying assumption stands that the statistically averaged beam pattern develops from an arrangement of uniformly or Gaussian distrusted elements; both confined to a variety of geometry of radius A and is further generalized using a simple theory based upon the Fourier Transform. Hence, this theory will be derived and serve as the foundation for advanced performance characteristics of these arrays such as its ability for sidelobe tapering, adaptive nulling and multi beam control. In addition it will be shown that for the most ideal of conditions a steerable beam pattern free of sidelobe behavior (better known as a Gaussian distribution) is quite possible. As well these random array structures will be shown to provide superior bandwidth capability over tradiational array structures since they are frequency independent. Last of all a summary of the random array analysis and its results concludes this dissertation

Deployable antenna phase A study

Applications for large deployable antennas were re-examined, flight demonstration objectives were defined, the flight article (antenna) was preliminarily designed, and the flight program and ground development program, including the support equipment, were defined for a proposed space transportation system flight experiment to demonstrate a large (50 to 200 meter) deployable antenna system. Tasks described include: (1) performance requirements analysis; (2) system design and definition; (3) orbital operations analysis; and (4) programmatic analysis