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

Design and Implementation of a FPGA and DSP Based MIMO Radar Imaging System

The work presented in this paper is aimed at the implementation of a real-time multiple-input multiple-output (MIMO) imaging radar used for area surveillance. In this radar, the equivalent virtual array method and time-division technique are applied to make 16 virtual elements synthesized from the MIMO antenna array. The chirp signal generater is based on a combination of direct digital synthesizer (DDS) and phase locked loop (PLL). A signal conditioning circuit is used to deal with the coupling effect within the array. The signal processing platform is based on an efficient field programmable gates array (FPGA) and digital signal processor (DSP) pipeline where a robust beamforming imaging algorithm is running on. The radar system was evaluated through a real field experiment. Imaging capability and real-time performance shown in the results demonstrate the practical feasibility of the implementation

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

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

Transmit Signal Design for MIMO Radar and Massive MIMO Channel Estimation

The widespread availability of antenna arrays and the capability to independently control signal emissions from each antenna make transmit signal design increasingly important for radar and wireless communication systems. In the rst part of this work, we develop the framework for a MIMO radar transmit scheme which trades o waveform diversity for beampattern directivity. Time-division beamforming consists of a linear precoder that provides direct control of the transmit beampattern and is able to form multiple transmit beams in a single pulse. The MIMO receive ambiguity function, which incorporates the receiver structure, reveals a space and delay-Doppler separability that emphasizes the importance of the transmit-receive beampattern and single-input single-output (SISO) ambiguity function. The second part of this work focuses on channel estimation for massive MIMO systems. As the size of arrays increase, conventional channel estimation techniques no longer remain practical. In current systems, training sequences probe wireless channels in orthogonal directions to obtain channel state information for block fading channels. The training overhead becomes signicant as the number of transmit antennas increases, thereby creating a need for alternative channel estimation techniques. In this work, we relax the orthogonal restriction on the sounding vectors and introduce a feedback channel to enable closed-loop sounding vector design. A probability of misalignment framework is introduced, which provides a measure to sequentially design sounding vectors

Three-Dimensional Target Localization and Cramér-Rao Bound for Two-Dimensional OFDM-MIMO Radar

Target localization using a frequency diversity multiple-input multiple-output (MIMO) system is one of the hottest research directions in the radar society. In this paper, three-dimensional (3D) target localization is considered for two-dimensional MIMO radar with orthogonal frequency division multiplexing linear frequency modulated (OFDM-LFM) waveforms. To realize joint estimation for range and angle in azimuth and elevation, the range-angle-dependent beam pattern with high range resolution is produced by the OFDM-LFM waveform. Then, the 3D target localization proposal is presented and the corresponding closed-form expressions of Cramér-Rao bound (CRB) are derived. Furthermore, for mitigating the coupling of angle and range and further improving the estimation precision, a CRB optimization method is proposed. Different from the existing methods of FDA-based radar, the proposed method can provide higher range estimation because of multiple transmitted frequency bands. Numerical simulation results are provided to demonstrate the effectiveness of the proposed approach and its improved performance of target localization

Joint DOA and DOD Estimation in Bistatic MIMO Radar without Estimating the Number of Targets

Existing subspace-based direction finding methods for multiple-input multiple-output (MIMO) radar assume perfect knowledge about the dimension of the signal or noise subspace, which is hard to be established without prior knowledge of the signal environment. In this paper, an efficient method for joint DOA and DOD estimation in bistatic MIMO radar without estimating the number of targets is presented. The proposed method computes an estimate of the noise subspace using the power of R (POR) technique. Then the two-dimensional (2D) direction finding problem is decoupled into two successive one-dimensional (1D) angle estimation problems by employing the rank reduction (RARE) estimator

Spatiotemporal arrayed MIMO radar

In the last decade, Multiple Input Multiple Output (MIMO) radar has emerged as a leading candidate for stimulating major new advancement in radar theory. A fundamental challenge in MIMO radar is to identify a theoretical framework within which the radar system may be represented and analysed. In the relatively well-established field of Single Input Multiple Output (SIMO) array signal processing, this task has already been achieved using the array manifold (which is a geometric object that completely characterises the array system). A central objective of this thesis is therefore to bridge the gap between SIMO and MIMO by developing a manifold representation of the MIMO radar system. A new differential geometric framework, based on the complex Cartan matrix, is exploited in this thesis for characterising array manifold curves. New formulas are presented for recursively calculating the strictly orthonormal moving frame, U(s), and corresponding complex Cartan Matrix, C(s), for arbitrary array geometries. The circular approximation of the array manifold is derived under this new framework and compact closed-form expressions are provided for the popular uniform linear array geometry. Based on a number of approximations derived using the circular approximation of the array manifold, the performance capabilites of various popular detection and parameter estimation algorithms are investigated. The figure of merit "C" is then used to place these capabilities into the context of the theoretically ideal algorithm. The concept of a virtual SIMO array system is used as a basis for characterising the full MIMO radar configuration using a single equivalent response vector. By tracing out this response vector across the whole parameter space, a manifold is formed that fully characterises the MIMO radar system. In the important case of orthogonal transmit waveforms, the fundamental performance bounds of the MIMO radar system are studied. A space-time receiver architecture is proposed which exploits the virtual SIMO structure as part of a subspace-based joint Doppler, delay and direction of arrival (DOA) estimation framework. Due to the great computational burden of an exhaustive 3-parameter search, the joint Doppler-delay-DOA estimation is partitioned into an equivalent two-stage algorithm. The proposed approach is evaluated via computer simulation studies and shown to outperform existing methods.Open Acces