Distributed power allocation for cognitive tracking based on non-cooperative game in decentralized netted radar

Abstract

The traditional centralized power allocation method for cognitive tracking in the netted radar can achieve the best resource utilization efficiency and target tracking performance. However, this method has poor robustness, low fault tolerance, and a high bandwidth requirement. In order to address this challenge, we propose a decentralized distributed power allocation method based on the non-cooperative game for multi-target tracking. Firstly, we model the power allocation problem for decentralized netted radar as a non-cooperative game problem and consider each radar node in the radar network as a player in the game. Then, we employ the determinant of Fisher information matrix to evaluate target tracking accuracy and use it to construct the utility function of the non-cooperative game based on the game rule. Finally, we propose an iterative distributed computing method to solve the Nash equilibrium. Meanwhile, we theoretically prove the Nash equilibrium solution's existence and uniqueness. Numerical simulation results show that the tracking performance of the proposed method is superior to the uniform and random power allocation method. Simultaneously, the tracking performance of the proposed method is close to the centralized power allocation method with a much lower computational load.

Introduction

The netted radar is a cooperative network composed of several independent distributed radar nodes [1], [2]. Each radar node interacts with the other nodes through the fusion types of data and signal levels [3]. The netted radar makes full use of the target scattering information obtained by each radar node from the different directions to achieve high-precision target positioning and tracking [4]. Meanwhile, the target state information processed by the data processor can be fed back to the transmitter of each radar node for the resources allocation [5], [6], [7], [8]. According to the changing external environment, the netted radar can establish a dynamic optimization model of system resources [9], [10]. The probe performance of the netted radar can be improved by the closed-loop of cognitive tracking from the receiver to the transmitter [11], [12], [13].

In general, the cognitive tracking of netted radar needs a powerful fusion control center. Each radar node transfers its data to the central fusion node for estimating the target state. Then, the central node makes a unified decision on the resource scheduling scheme according to the estimation result. In theory, this top-down centralized processing method can achieve the best target probe performance and resource utilization efficiency. However, the central node needs to obtain the global information of the network, and it takes on complex and heavy global data processing tasks. The requirement for the communication bandwidth is also very high. More importantly, the entire network system will paralyze once the central node fails.

All radar nodes have the data fusion function in the decentralized netted radar. Decentralized topology requires each node to complete tracking filtering independently to obtain the local estimation results of the target state. Then each node communicates with its adjacent nodes, exchanges the target state estimation information, and finally obtains a unified estimation result. Compared with the top-down centralized processing method, the distributed processing method has the advantages of low complexity, high fault tolerance, and strong robustness. Therefore, it is of great significance to research the distributed resource allocation for the cognitive tracking in decentralized netted radar [14], [15], [16], [17].

Game theory provides a valuable framework for analyzing the cooperation and competition between the radar nodes [18], [19]. It is an optimal decision-making theory based on behavior rules [20], suitable for distributed resource management [21], [22]. In recent years, many scholars have applied the game theory to the distributed resource management of netted radar. The problems they researched involve the selection of radar nodes [23], the selection of transmit waveforms [24], and the allocation of transmit power [25], [26]. The basic models of game theory mainly include the non-cooperative game (strategy game) [27], [28] and the cooperative game (coalition game) [29], [30], [31].

For the non-cooperative game, Reference [23] studied the target selection problem of a multi-functional radar network. In the non-cooperative game model, each radar node is considered as a player in the game. Each player's utility is described using a proper tracking accuracy criterion. The strategies of players are the selection of the observed targets. The scholars propose a distributed target selection algorithm considering the partial targets observability and node connectivity. Compared with the centralized method, this method significantly reduces the complexity of the target selection problem. Reference [24] has researched the problem of transmit waveform selection for multi-static radar networks. A potential game model is established to maximize each radar node's signal to clutter ratio. It is proved that the game model could converge to the Nash equilibrium solution. Reference [25] studied the problem of netted radar anti-interception based on the non-cooperative game. A novel low probability of intercept (LPI) performance-oriented utility function is defined as a metric to evaluate power control. The distributed power control problem is formulated as a non-cooperative game. The signal to interference noise ratio (SINR) threshold and the transmit power limit of each radar node are taken as constraints. Then, an iterative power control method is proposed. This method can also converge to the Nash equilibrium solution quickly.

The non-cooperative game pays more attention to the individual benefits of the participants than to the collective benefits. In contrast, the cooperative game will emphasize the overall detection performance of each radar node after forming a “coalition”. Reference [26] has studied the power allocation of distributed multiple-input multiple-output (MIMO) radar for the cooperative game. The signal model includes transmission loss, transmit power, and initial target density. Based on the signal model, the objective function is established to maximize Bayesian FIM's determinant based on the cooperative game. Then, a power allocation algorithm based on the Shapley value is proposed. This algorithm can significantly improve the overall tracking performance of the radar system.

The above works of literature prove that the game theory can effectively address the problem of distributed resource allocation. Inspired by that, we research the distributed power allocation based on the game theory for multi-target tracking in the cognitive netted radar. The main contributions of this work are as follows. 1) For the multi-target tracking scene, the distributed power allocation problem for netted radar is modeled as a non-cooperative game, and each radar node in the radar network is regarded as a player in the game. 2) The determinant of the FIM is derived to evaluate the target tracking accuracy. Based on the game rules, the utility function of the non-cooperative game is constructed by using the determinant of FIM. 3) An iterative distributed computing method is proposed, quickly converging to the Nash equilibrium solution. The existence and uniqueness of the Nash equilibrium solution are proved theoretically. The tracking performance of the proposed method is close to the centralized allocation method, and the computational cost is significantly reduced.

The main content of this paper is as follows. Section 2 introduces the target tracking model of netted radar and the calculation process of the determinant of FIM. In Section 3, a power allocation model based on the non-cooperative game is established, and an iterative method is proposed to solve the Nash equilibrium of the game model. Meanwhile, the existence and uniqueness of the Nash equilibrium solution are proved. In Section 4, the performance of the proposed algorithm is compared with other power allocation algorithms. Finally, concluding remarks are addressed in Section 5.