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

Frequency Diverse Array Radar: Signal Characterization and Measurement Accuracy

Radar systems provide an important remote sensing capability, and are crucial to the layered sensing vision; a concept of operation that aims to apply the right number of the right types of sensors, in the right places, at the right times for superior battle space situational awareness. The layered sensing vision poses a range of technical challenges, including radar, that are yet to be addressed. To address the radar-specific design challenges, the research community responded with waveform diversity; a relatively new field of study which aims reduce the cost of remote sensing while improving performance. Early work suggests that the frequency diverse array radar may be able to perform several remote sensing missions simultaneously without sacrificing performance. With few techniques available for modeling and characterizing the frequency diverse array, this research aims to specify, validate and characterize a waveform diverse signal model that can be used to model a variety of traditional and contemporary radar configurations, including frequency diverse array radars. To meet the aim of the research, a generalized radar array signal model is specified. A representative hardware system is built to generate the arbitrary radar signals, then the measured and simulated signals are compared to validate the model. Using the generalized model, expressions for the average transmit signal power, angular resolution, and the ambiguity function are also derived. The range, velocity and direction-of-arrival measurement accuracies for a set of signal configurations are evaluated to determine whether the configuration improves fundamental measurement accuracy

Design and Optimization of Physical Waveform-Diverse and Spatially-Diverse Radar Emissions

With the advancement of arbitrary waveform generation techniques, new radar transmission modes can be designed via precise control of the waveform's time-domain signal structure. The finer degree of emission control for a waveform (or multiple waveforms via a digital array) presents an opportunity to reduce ambiguities in the estimation of parameters within the radar backscatter. While this freedom opens the door to new emission capabilities, one must still consider the practical attributes for radar waveform design. Constraints such as constant amplitude (to maintain sufficient power efficiency) and continuous phase (for spectral containment) are still considered prerequisites for high-powered radar waveforms. These criteria are also applicable to the design of multiple waveforms emitted from an antenna array in a multiple-input multiple-output (MIMO) mode. In this work, three spatially-diverse radar emission design methods are introduced that provide constant amplitude, spectrally-contained waveforms implemented via a digital array radar (DAR). The first design method, denoted as spatial modulation, designs the radar waveforms via a polyphase-coded frequency-modulated (PCFM) framework to steer the coherent mainbeam of the emission within a pulse. The second design method is an iterative scheme to generate waveforms that achieve a desired wideband and/or widebeam radar emission. However, a wideband and widebeam emission can place a portion of the emitted energy into what is known as the `invisible' space of the array, which is related to the storage of reactive power that can damage a radar transmitter. The proposed design method purposefully avoids this space and a quantity denoted as the Fractional Reactive Power (FRP) is defined to assess the quality of the result. The third design method produces simultaneous radar and communications beams in separate spatial directions while maintaining constant modulus by leveraging the orthogonal complement of the emitted directions. This orthogonal energy defines a trade-space between power efficiency gained from constraining waveforms to be constant amplitude and power efficiency lost by emitting energy in undesired directions. The design of FM waveforms via traditional gradient-based optimization methods is also considered. A waveform model is proposed that is a generalization of the PCFM implementation, denoted as coded-FM (CFM), which defines the phase of the waveform via a summation of weighted, predefined basis functions. Therefore, gradient-based methods can be used to minimize a given cost function with respect to a finite set of optimizable parameters. A generalized integrated sidelobe level (GISL) metric is used as the optimization cost function to minimize the correlation range sidelobes of the radar waveform. System specific waveform optimization is explored by incorporating the linear models of three different loopback configurations into the GISL metric to match the optimized waveforms to the particular systems

Coherent FDA Receiver and Joint Range-Space-Time Processing

When a target is masked by mainlobe clutter with the same Doppler frequency, it is difficult for conventional airborne radars to determine whether a target is present in a given observation using regular space-time adaptive processing techniques. Different from phased-array and multiple-input multiple-output (MIMO) arrays, frequency diverse arrays (FDAs) employ frequency offsets across the array elements, delivering additional range-controllable degrees of freedom, potentially enabling suppression for this kind of clutter. However, the reception of coherent FDA systems employing small frequency offsets and achieving high transmit gain can be further improved. To this end, this work proposes an coherent airborne FDA radar receiver that explores the orthogonality of echo signals in the Doppler domain, allowing a joint space-time processing module to be deployed to separate the aliased returns. The resulting range-space-time adaptive processing allows for a preferable detection performance for coherent airborne FDA radars as compared to current alternative techniques.Comment: 11 pages, 9 figure

Generating Pictures from Waves: Aspects of Image Formation

Thesis Supervisor: Gregory W. Wornell Title: Professor of Electrical Engineering and Computer ScienceThe research communities, technologies, and tools for image formation are diverse. On the one hand, computer vision and graphics researchers analyze incoherent light using coarse geometric approximations from optics. On the other hand, array signal processing and acoustics researchers analyze coherent sound waves using stochastic estimation theory and diffraction formulas from physics. The ability to inexpensively fabricate analog circuitry and digital logic for millimeter-wave radar and ultrasound creates opportunities in comparing diverse perspectives on image formation, and presents challenges in implementing imaging systems that scale in size. We present algorithms, architectures, and abstractions for image formation that relate the different communities, technologies, and tools. We address practical technical challenges in operating millimeter-wave radar and ultrasound systems in the presence of phase noise and scattering. We model a broad class of physical phenomena with isotropic point sources. We show that the optimal source location estimator for coherent waves reduces to processing an image produced by a conventional camera, provided the sources are wellseparated relative to the system resolution, and in the limit of small wavelength and globally incoherent light. We introduce quasi light fields to generalize the incoherent image formation process to coherent waves, offering resolution tradeoffs that surpass the traditional Fourier uncertainty principle by leveraging time-frequency distributions. We show that the number of sensors in a coherent imaging array defines a stable operating point relative to the phase noise. We introduce a digital phase tightening algorithm to reduce phase noise. We present a system identification framework for multiple-input multiple-output (MIMO) ultrasound imaging that generalizes existing approaches with time-varying filters. Our theoretical results enable the application of traditional techniques in incoherent imaging to coherent imaging, and vice versa. Our practical results suggest a methodology for designing millimeter-wave imaging systems. Our conclusions reinforce architectural principles governing transmitter and receiver design, the role of analog and digital circuity, and the tradeoff between data rate and data precision.Microsoft Research, MIT Lincoln Laboratory, and the C2S2 Focus Center, one of six research centers funded under the Focus Center Research Program (FCRP), a Semiconductor Research Corporation entity

Generating pictures from waves : aspects of image formation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 171-177).The research communities, technologies, and tools for image formation are diverse. On the one hand, computer vision and graphics researchers analyze incoherent light using coarse geometric approximations from optics. On the other hand, array signal processing and acoustics researchers analyze coherent sound waves using stochastic estimation theory and diffraction formulas from physics. The ability to inexpensively fabricate analog circuitry and digital logic for millimeter-wave radar and ultrasound creates opportunities in comparing diverse perspectives on image formation, and presents challenges in implementing imaging systems that scale in size. We present algorithms, architectures, and abstractions for image formation that relate the different communities, technologies, and tools. We address practical technical challenges in operating millimeter-wave radar and ultrasound systems in the presence of phase noise and scattering. We model a broad class of physical phenomena with isotropic point sources. We show that the optimal source location estimator for coherent waves reduces to processing an image produced by a conventional camera, provided the sources are well separated relative to the system resolution, and in the limit of small wavelength and globally incoherent light. We introduce quasi light fields to generalize the incoherent image formation process to coherent waves, offering resolution tradeoffs that surpass the traditional Fourier uncertainty principle by leveraging time-frequency distributions. We show that the number of sensors in a coherent imaging array defines a stable operating point relative to the phase noise. We introduce a digital phase tightening algorithm to reduce phase noise. We present a system identification framework for multiple-input multiple-output (MIMO) ultrasound imaging that generalizes existing approaches with time-varying filters. Our theoretical results enable the application of traditional techniques in incoherent imaging to coherent imaging, and vice versa. Our practical results suggest a methodology for designing millimeter-wave imaging systems. Our conclusions reinforce architectural principles governing transmitter and receiver design, the role of analog and digital circuity, and the tradeoff between data rate and data precision.by Anthony Accardi.Ph.D