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

Joint Route Optimization and Multidimensional Resource Management Scheme for Airborne Radar Network in Target Tracking Application

In this article, we investigate the problem of joint route optimization and multidimensional resource management (JRO-MDRM) for an airborne radar network in target tracking application. The mechanism of the proposed JRO-MDRM scheme is to adopt the optimization technique to collaboratively design the flight route, transmit power, dwell time, waveform bandwidth, and pulselength of each airborne radar node subject to the system kinematic limitations and several resource budgets, with the aim of simultaneously enhancing the target tracking accuracy and low probability of intercept (LPI) performance of the overall system. The predicted Bayesian Cramér–Rao lower bound and the probability of intercept are calculated and employed as the metrics to gauge the target tracking performance and LPI performance, respectively. It is shown that the resulting optimization problem is nonlinear and nonconvex, and the corresponding working parameters are coupled in both objective functions, which is generally intractable. By incorporating the particle swarm optimization and cyclic minimization approaches, an efficient four-step solution algorithm is proposed to deal with the above problem. Extensive numerical results are provided to demonstrate the correctness and advantages of our developed scheme compared with other existing benchmarks

Joint waveform and guidance control optimisation for target rendezvous

The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimising a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the Linear Quadratic Gaussian (LQG) control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimisation and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control

Joint Transmit Resource Management and Waveform Selection Strategy for Target Tracking in Distributed Phased Array Radar Network

In this paper, a joint transmit resource management and waveform selection (JTRMWS) strategy is put forward for target tracking in distributed phased array radar network. We establish the problem of joint transmit resource and waveform optimization as a dual-objective optimization model. The key idea of the proposed JTRMWS scheme is to utilize the optimization technique to collaboratively coordinate the transmit power, dwell time, waveform bandwidth, and pulse length of each radar node in order to improve the target tracking accuracy and low probability of intercept (LPI) performance of distributed phased array radar network, subject to the illumination resource budgets and waveform library limitation. The analytical expressions for the predicted Bayesian Cram\'{e}r-Rao lower bound (BCRLB) and the probability of intercept are calculated and subsequently adopted as the metric functions to evaluate the target tracking accuracy and LPI performance, respectively. It is shown that the JTRMWS problem is a non-linear and non-convex optimization problem, where the above four adaptable parameters are all coupled in the objective functions and constraints. Combined with the particle swarm optimization (PSO) algorithm, an efficient and fast three-stage-based solution technique is developed to deal with the resulting problem. Simulation results are provided to verify the effectiveness and superiority of the proposed JTRMWS algorithm compared with other state-of-the-art benchmarks

3D Localization and Tracking Methods for Multi-Platform Radar Networks

Multi-platform radar networks (MPRNs) are an emerging sensing technology due to their ability to provide improved surveillance capabilities over plain monostatic and bistatic systems. The design of advanced detection, localization, and tracking algorithms for efficient fusion of information obtained through multiple receivers has attracted much attention. However, considerable challenges remain. This article provides an overview on recent unconstrained and constrained localization techniques as well as multitarget tracking (MTT) algorithms tailored to MPRNs. In particular, two data-processing methods are illustrated and explored in detail, one aimed at accomplishing localization tasks the other tracking functions. As to the former, assuming a MPRN with one transmitter and multiple receivers, the angular and range constrained estimator (ARCE) algorithm capitalizes on the knowledge of the transmitter antenna beamwidth. As to the latter, the scalable sum-product algorithm (SPA) based MTT technique is presented. Additionally, a solution to combine ARCE and SPA-based MTT is investigated in order to boost the accuracy of the overall surveillance system. Simulated experiments show the benefit of the combined algorithm in comparison with the conventional baseline SPA-based MTT and the stand-alone ARCE localization, in a 3D sensing scenario