MI-Based Robust Waveform Design in Radar and Jammer Games

Hindawi Complexity Volume 2019, Article ID 4057849, 14 pages https://doi.org/10.1155/2019/4057849 Research Article MI-Based Robust Waveform Design in Radar and Jammer Games Bin Wang , Xu Chen, Fengming Xin , and Xin Song Northeastern University at Qinhuangdao, China Correspondence should be addressed to Bin Wang; Received 24 October 2018; Revised 2 February 2019; Accepted 28 February 2019; Published 26 March 2019 Guest Editor: Jose Garcia-Rodriguez Copyright © 2019 Bin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Due to the uncertainties of the radar target prior information in the actual scene, the waveform designed based on the radar target prior information cannot meet the needs of parameter estimation. To improve the performance of parameter estimation, a novel transmitted waveform design method under the hierarchical game model of radar and jammer, which maximizes the mutual information (MI) between the radar target echo and the random target spectrum response, is proposed. In the hierarchical game model of radar and jammer, the radar is in a leading position while the jammer is in a following position. The strategy of the jammer is optimized based on the radar transmitted waveform of previous moment, then the radar selects its own strategy based on the strategy of the jammer. It is generally assumed that the radar and the jammer have intercepted the real target spectrum and then the optimal jamming and the optimal transmitted waveform spectrum are obtained. However, the exact characteristic of the real target spectrum is hard to capture accurately in actual scenes. To simulate this, the real target spectrum is considered to be within an uncertainty range which is confined by known upper and lower bounds. Then, the minimax robust jamming and the maximin robust transmitted waveform are designed successively based on the MI criteria, which optimizes the performance under the most unfavorable condition of the radar and the jammer, respectively. Simulation results demonstrate that the robust transmitted waveform design method guarantees the parameter estimation performance effectively and provides useful guidance for waveform energy allocation. 1. Introduction Cognitive radar (CR) is a new radar system concept proposed in recent years. This system is inspired by the bat echolocation, which improves the system performance of the radar through using the feedback structure from the receiver to the transmitter to optimize the transmitted waveform based on the recognition of the target and the scene [1]. The transmitted waveform of the traditional radar is independent of the environment and each transmission repeats the same waveform. Therefore the research of the traditional radar is devoted to optimizing the receiver design through radar signal processing [2]. Different from the traditional radar, CR transmitter can adjust the transmitted waveform adaptively to achieve optimal matching with the environment according to the acquired information [3]. During the past decades, many adaptive waveform design methods for radar target parameter estimation have been developed by a lot of experts and scholars. MI is a useful information metric in information theory [4], which has been widely adopted in cognitive radar and other engineering fields [5, 6]. One important method for radar waveform design is to use information theory. Researchers such as Vaidyanathan applied information theory to the radar of the MIMO system [7]. Many radar experts are devoted to improving the parameter estimation performance by boosting MI [8–10]. The innovative study in [9] optimizes the transmitted waveform through maximizing the conditional MI between the radar target echo and the random target spectrum response. Kwon et al. studied multitarget detection at low SNR, using the maximum eigenvalue of the sample covariance matrix and the correlation coefficient between the transmitted signal and the echo signal to obtain a modified full correlation detector from the perspective of average mutual information [11]. Under certain assumptions, such as fully known noise PSD and white noise, better estimation performance can be obtained by maximizing MI, as shown in [12]. 2 However, the designed optimal waveforms under the environment of complex target model are not well known and do not consider the complex battlefield game environment, while in practice precise estimation of the real target spectrum is impossible and the game between radar and jammer is real existence in many cases. The mismatch of prior information of the real target and the ignorance of battlefield game environment might reduce the waveform performance transmitted by the radar transmitter. In this paper, a novel transmitted waveform design technique based on MI under the environment of complex battlefield game and complicated target model is presented. Minimax robust jamming and maximin robust waveform design methods are proposed successively to reduce the impact of insufficient prior information on the performance of the designed waveform. Our main contribution is that the imprecise estimation of target spectrum [12] is considered in the optimal jamming and the optimal transmitted waveform design strategies. In addition, we also establish a hierarchical game model of radar and jammer, which regards radar as the leader and jammer as the follower. The minimax robust jamming and maximin robust transmitted waveform techniques under the established hierarchical game model above based on the MI are developed successively. In summary, first of all, given that the real target spectrum is known, the optimal jamming and optimal transmitted waveform design methods for random target based on MI are proposed successively. Secondly, by considering the uncertainty of the target spectrum, the MI-based minimax robust jamming and maximin robust transmitted waveform techniques are proposed successively. In this paper, we consider the single target model and multitarget model, respectively; then the minimax robust jamming and maximin robust transmitted waveform techniques under the two different target models above based on MI are proposed, respectively. The minimax robust jamming and maximin robust transmitted waveform design methods optimize the performance under the most unfavorable condition of the jammer and the radar transmitter, respectively. Their behaviour with regard to the uncertainty of target spectrum is also analyzed. The MIbased robust jamming and robust waveform provide useful guidance for waveform energy allocation strategy. These two waveform design techniques are easy to implement in an intelligent jammer and a cognitive radar and will have important applications in electronic warfare. In the actual situation, the minimax and maximin robust waveform (...truncated)