554 research outputs found
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
Game-theoretic power allocation and the Nash equilibrium analysis for a multistatic MIMO radar network
CCBY We investigate a game-theoretic power allocation scheme and perform a Nash equilibrium analysis for a multistatic multiple-input multiple-output (MIMO) radar network. We consider a network of radars, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since there is no communication between the distributed clusters, we incorporate convex optimization methods and noncooperative game-theoretic techniques based on the estimate of the signal to interference plus noise ratio (SINR) to tackle the power adaptation problem. Therefore, each cluster egotistically determines its optimal power allocation in a distributed scheme. Furthermore, we prove that the best response function of each cluster regarding this generalized Nash game (GNG) belongs to the framework of standard functions. The standard function property together with the proof of the existence of solution for the game guarantees the uniqueness of the Nash equilibrium. The mathematical analysis based on Karush-Kuhn-Tucker conditions reveal some interesting results in terms of number of active radars and the number of radars that over satisfy the desired SINRs. Finally, the simulation results confirm the convergence of the algorithm to the unique solution and demonstrate the distributed nature of the system
Joint Beacon Power and Beacon Rate Control Based on Game Theoretic Approach in Vehicular Ad Hoc Networks
In vehicular ad hoc networks (VANETs), each vehicle broadcasts its information periodically in its beacons to create awareness for surrounding vehicles aware of their presence. But, the wireless channel is congested by the increase beacons number, packet collision lost a lot of beacons. This paper tackles the problem of joint beaconing power and a beaconing rate in VANETs. A joint utilitybased beacon power and beacon rate game are formulated as a non-cooperative game and a cooperative game. A three distributed and iterative algorithm (Nash Seeking Algorithm, Best Response Algorithm, Cooperative Bargaining Algorithm) for computing the desired equilibrium is introduced, where the optimal values of each vehicle beaconing power and beaconing rate are
simultaneously updated at the same step. Extensive simulations show the convergence of a proposed algorithm to the equilibrium and give some insights on how the game parameters may vary the game outcome. It is demonstrated that the Cooperative Bargaining Algorithm is a fast algorithm that converges the equilibrium
Collaborative Trajectory Planning and Resource Allocation for Multi-Target Tracking in Airborne Radar Networks under Spectral Coexistence
This paper develops a collaborative trajectory planning and resource allocation (CTPRA) strategy for multi-target tracking (MTT) in a spectral coexistence environment utilizing airborne radar networks. The key mechanism of the proposed strategy is to jointly design the flight trajectory and optimize the radar assignment, transmit power, dwell time, and signal effective bandwidth allocation of multiple airborne radars, aiming to enhance the MTT performance under the constraints of the tolerable threshold of interference energy, platform kinematic limitations, and given illumination resource budgets. The closed-form expression for the Bayesian Cramér–Rao lower bound (BCRLB) under the consideration of spectral coexistence is calculated and adopted as the optimization criterion of the CTPRA strategy. It is shown that the formulated CTPRA problem is a mixed-integer programming, non-linear, non-convex optimization model owing to its highly coupled Boolean and continuous parameters. By incorporating semi-definite programming (SDP), particle swarm optimization (PSO), and the cyclic minimization technique, an iterative four-stage solution methodology is proposed to tackle the formulated optimization problem efficiently. The numerical results validate the effectiveness and the MTT performance improvement of the proposed CTPRA strategy in comparison with other benchmarks
Spectrum sensing for cognitive radio and radar systems
The use of the radio frequency spectrum is increasing at a rapid rate. Reliable and efficient operation in a crowded radio spectrum requires innovative solutions and techniques. Future wireless communication and radar systems should be aware of their surrounding radio environment in order to have the ability to adapt their operation to the effective situation. Spectrum sensing techniques such as detection, waveform recognition, and specific emitter identification are key sources of information for characterizing the surrounding radio environment and extracting valuable information, and consequently adjusting transceiver parameters for facilitating flexible, efficient, and reliable operation.
In this thesis, spectrum sensing algorithms for cognitive radios and radar intercept receivers are proposed. Single-user and collaborative cyclostationarity-based detection algorithms are proposed: Multicycle detectors and robust nonparametric spatial sign cyclic correlation based fixed sample size and sequential detectors are proposed. Asymptotic distributions of the test statistics under the null hypothesis are established. A censoring scheme in which only informative test statistics are transmitted to the fusion center is proposed for collaborative detection. The proposed detectors and methods have the following benefits: employing cyclostationarity enables distinction among different systems, collaboration mitigates the effects of shadowing and multipath fading, using multiple strong cyclic frequencies improves the performance, robust detection provides reliable performance in heavy-tailed non-Gaussian noise, sequential detection reduces the average detection time, and censoring improves energy efficiency.
In addition, a radar waveform recognition system for classifying common pulse compression waveforms is developed. The proposed supervised classification system classifies an intercepted radar pulse to one of eight different classes based on the pulse compression waveform: linear frequency modulation, Costas frequency codes, binary codes, as well as Frank, P1, P2, P3, and P4 polyphase codes.
A robust M-estimation based method for radar emitter identification is proposed as well. A common modulation profile from a group of intercepted pulses is estimated and used for identifying the radar emitter. The M-estimation based approach provides robustness against preprocessing errors and deviations from the assumed noise model
Electronic Warfare Receiver Resource Management and Optimization
Optimization of electronic warfare (EW) receiver scan strategies is critical to improving the probability of surviving military missions in hostile environments. The problem is that the limited understanding of how dynamic variations in radar and EW receiver characteristics has influenced the response time to detect enemy threats. The dependent variable was the EW receiver response time and the 4 independent variables were EW receiver revisit interval, EW receiver dwell time, radar scan time, and radar illumination time. Previous researchers have not explained how dynamic variations of independent variables affected response time. The purpose of this experimental study was to develop a model to understand how dynamic variations of the independent variables influenced response time. Queuing theory provided the theoretical foundation for the study using Little\u27s formula to determine the ideal EW receiver revisit interval as it states the mathematical relationship among the variables. Findings from a simulation that produced 17,000 data points indicated that Little\u27s formula was valid for use in EW receivers. Findings also demonstrated that variation of the independent variables had a small but statistically significant effect on the average response time. The most significant finding was the sensitivity in the variance of response time given minor differences of the test conditions, which can lead to unexpectedly long response times. Military users and designers of EW systems benefit most from this study by optimizing system response time, thus improving survivability. Additionally, this research demonstrated a method that may improve EW product development times and reduce the cost to taxpayers through more efficient test and evaluation techniques
Air Vehicle Path Planning
This dissertation explores optimal path planning for air vehicles. An air vehicle exposed to illumination by a tracking radar is considered and the problem of determining an optimal planar trajectory connecting two prespecified points is addressed. An analytic solution yielding the trajectory minimizing the received radar energy reflected from the target is derived using the Calculus of Variations. Additionally, the related problem of an air vehicle tracked by a passive sensor is also solved. Using the insights gained from the single air vehicle radar exposure minimization problem, a hierarchical cooperative control law is formulated to determine the optimal trajectories that minimize the cumulative exposure of multiple air vehicles during a rendezvous maneuver. The problem of one air vehicle minimizing exposure to multiple radars is also addressed using a variational approach, as well as a sub-optimal minimax argument. Local and global optimality issues are explored. A novel decision criterion is developed determining the geometric conditions dictating when it is preferable to go between or around two radars. Lastly, an optimal minimum time control law is obtained for the search and target identification mission of an autonomous air vehicle. This work demonstrates that an awareness of the consequences of embracing sub-optimal and non-globally optimal solutions for optimization problems, such as air vehicle path planning, is essential
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