Game theoretic analysis for MIMO radars with multiple targets

This paper considers a distributed beamforming and resource allocation technique for a radar system in the presence of multiple targets. The primary objective 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. Therefore, we use convex optimization methods together with noncooperative and partially cooperative game theoretic approaches. Initially, we consider a strategic noncooperative game (SNG), where there is no communication between the various radars of the system. Hence each radar selfishly determines its optimal beamforming and power allocation. Subsequently, we assume a more coordinated game theoretic approach incorporating a pricing mechanism. Introducing a price in the utility function of each radar/player, enforces beamformers to minimize the interference induced to other radars and to increase the social fairness of the system. Furthermore, we formulate a Stackelberg game by adding a surveillance radar to the system model, which will play the role of the leader, and hence the remaining radars will be the followers. The leader applies a pricing policy of interference charged to the followers aiming at maximizing his profit while keeping the incoming interference under a certain threshold. We also present a proof of the existence and uniqueness of the Nash Equilibrium (NE) in both the partially cooperative and noncooperative games. Finally, the simulation results confirm the convergence of the algorithm in all three cases

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

Fundamental Limits on Performance for Cooperative Radar-Communications Coexistence

abstract: Spectral congestion is quickly becoming a problem for the telecommunications sector. In order to alleviate spectral congestion and achieve electromagnetic radio frequency (RF) convergence, communications and radar systems are increasingly encouraged to share bandwidth. In direct opposition to the traditional spectrum sharing approach between radar and communications systems of complete isolation (temporal, spectral or spatial), both systems can be jointly co-designed from the ground up to maximize their joint performance for mutual benefit. In order to properly characterize and understand cooperative spectrum sharing between radar and communications systems, the fundamental limits on performance of a cooperative radar-communications system are investigated. To facilitate this investigation, performance metrics are chosen in this dissertation that allow radar and communications to be compared on the same scale. To that effect, information is chosen as the performance metric and an information theoretic radar performance metric compatible with the communications data rate, the radar estimation rate, is developed. The estimation rate measures the amount of information learned by illuminating a target. With the development of the estimation rate, standard multi-user communications performance bounds are extended with joint radar-communications users to produce bounds on the performance of a joint radar-communications system. System performance for variations of the standard spectrum sharing problem defined in this dissertation are investigated, and inner bounds on performance are extended to account for the effect of continuous radar waveform optimization, multiple radar targets, clutter, phase noise, and radar detection. A detailed interpretation of the estimation rate and a brief discussion on how to use these performance bounds to select an optimal operating point and achieve RF convergence are provided.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

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

DVB-T Receiver Independent of Channel Allocation, with Frequency Offset Compensation for Improving Resolution in Low Cost Passive Radar.

In this article, a commercial low cost solution for increasing DVB-T based passive radar (also referred to as passive coherentlocation)robustnesswith respectto channel allocation and range resolution, is designed. IDEPAR demonstrator is updated to include a new recording system in charge of DVB-T channels reallocation. The use of commercial hardware introduces frequency mismatching between acquired channels that compromises system operation. To face channel frequency alignment, fulfilling the requirements imposed by the high Doppler resolution typical of passive radars, a novel compensation algorithm is proposed, based on the minimization of signal dispersion in the Cross-Ambiguity Function domain. The well-known cyclic prefix van de Beek method is used as reference. Results show an increase in target signal to interference ratio and detection performances, as well as a reduction of clutter dispersion when the novel proposed algorithm is applied. The low cost solution is also compared to a high performance one capable of acquiring a wide bandwidth of sparse DVB-T channels, and performing channel reallocation by digital signal processing. Results show that both systems reached similar performances in terms of range resolution and SNR improvement

Joint transmitter selection and resource management strategy based on low probability of intercept optimization for distributed radar networks

In this paper, a joint transmitter selection and resource management (JTSRM) strategy based on low probability of intercept (LPI) is proposed for target tracking in distributed radar network system. The basis of the JTSRM strategy is to utilize the optimization technique to control transmitting resources of radar networks in order to improve the LPI performance, while guaranteeing a specified target tracking accuracy. The weighted intercept probability and transmit power of radar networks is defined and subsequently employed as the optimization criterion for the JTSRM strategy. The resulting optimization problem is to minimize the LPI performance criterion of radar networks by optimizing the revisit interval, dwell time, transmitter selection, and transmit power subject to a desired target tracking performance and some resource constraints. An efficient and fast three‐step solution technique is also developed to solve this problem. The presented mechanism implements the optimal working parameters based on the feedback information in the tracking recursion cycle in order to improve the LPI performance for radar networks. Numerical simulations are provided to verify the superior performance of the proposed JTSRM strategy

Power minimization based robust OFDM radar waveform design for radar and communication systems in coexistence.

This paper considers the problem of power minimization based robust orthogonal frequency division multiplexing (OFDM) radar waveform design, in which the radar coexists with a communication system in the same frequency band. Recognizing that the precise characteristics of target spectra are impossible to capture in practice, it is assumed that the target spectra lie in uncertainty sets bounded by known upper and lower bounds. Based on this uncertainty model, three different power minimization based robust radar waveform design criteria are proposed to minimize the worst-case radar transmitted power by optimizing the OFDM radar waveform, which are constrained by a specified mutual information (MI) requirement for target characterization and a minimum capacity threshold for communication system. These criteria differ in the way the communication signals scattered off the target are considered: (i) as useful energy, (ii) as interference or (iii) ignored altogether at the radar receiver. Numerical simulations demonstrate that the radar transmitted power can be efficiently reduced by exploiting the communication signals scattered off the target at the radar receiver. It is also shown that the robust waveforms bound the worst-case power-saving performance of radar system for any target spectra in the uncertainty sets