Jamming in defence applications is increasingly difficult because of advanced signal processing countermeasures. The jamming power allocation techniques for MIMO radar are investigated based on two criteria, namely the minimum mean square error (MMSE) for target estimation and the mutual information (MI) between the radar echo and the target impulse response. Different jamming power allocation strategies are obtained using the two criteria, respectively. Furthermore, the robust jamming power allocation strategies are studied when the target, environment or waveform information are not perfectly known. The worst case performance is optimised considering two cases of uncertainty. The analysis indicates that the least favourable sets (LFSs) of the MMSE‐ and MI‐based robust jamming are different if the radar waveform power and the target power spectral density (PSD) lie in the uncertainty sets which are confined by known upper and lower bounds. The LFSs of the MMSE‐ and MI‐based robust jamming are the same if the target PSD and the noise PSD lie in the uncertainty sets. Results are useful for the implementation of cognitive jammer.

Jamming in defence applications is increasingly difficult because of advanced signal processing countermeasures. In this study, task‐dependent power‐constraint optimal jamming techniques are investigated. To prevent the target from being detected, a novel jamming technique is proposed to minimise the signal‐to‐interference‐plus‐noise ratio (SINR) of the radar for extended known and stochastic target. To impair the parameter estimation performance, another jamming technique is proposed which minimises the mutual information (MI) between the radar return and the stochastic target impulse response. The optimal jamming spectrum is obtained assuming that the jammer has intercepted the radar waveform generally. However, the precise characteristic of radar waveform is impossible to capture in practice. To model this, it is considered that the waveform spectrum lies in an uncertainty class confined by known upper and lower bounds. Then, the minimax robust jamming is designed based on the SINR and MI criteria, which optimises the worst‐case performance. Results demonstrate that the two criteria lead to different optimal jamming results but they have a close relationship from the Shannon's capacity equation which provides useful guidance on jamming power allocation for different jamming tasks. However, their behaviour with respect to the waveform uncertainty is the same.

Cognitive electronic warfare (CEW) has received increasing attention, and it is widely recognized that it will play a significant role. Cognitive jamming decision-making, as one of the critical technologies of CEW, dramatically impacts the global battlefield situation. In this paper, we introduce the A2C algorithm into cognitive jamming decision-making and propose a heuristic improved A2C algorithm. As a fusion algorithm of DQN and Policy Gradient, on the one hand, the Actor-Critic algorithm has the advantages of iterative updating of policies and high efficiency in complex spaces, compared to the DQN algorithm. On the other hand, compared with the Policy Gradient algorithm, it features fast convergence. But, it suffers from high variance, making convergence difficult. First, we establish a cognitive jamming decision-making model to address the above issues. Then, we develop an improved A2C algorithm by introducing a baseline and dueling networks. The baseline reduces the variance of the critic network, while dueling networks further decrease variance, enhancing the convergence of the A2C algorithm. Additionally, the improved A2C algorithm does not rely on prior information, and enhances the adaptive capability of the jammer when interacting with the target radar. We conducted numerical simulations based on the designed cognitive jamming decisionmaking model. The results demonstrated that compared with the four algorithms (DQN, Policy Gradient, Actor-Critic, A2C), the convergence speed of the improved A2C algorithm is improved by 50%, 57.8%, 34.5%, and 13.64%, respectively, and verified the excellent performance of the improved A2C. Finally, we introduce the heuristic reward function and propose the heuristic improved A2C algorithm. Compared with the improved A2C algorithm, the convergence speed of this algorithm is improved by 31.58%. The simulation results prove that the algorithm can greatly improve our advantage in electronic countermeasures

In this article, a novel R-convolution kernel, named the fast quantum walk kernel (FQWK), is proposed for unattributed graphs. In FQWK, the similarity of the neighborhood-pair substructure between two nodes is measured via the superposition amplitude of quantum walks between those nodes. The quantum interference in this kind of local substructures provides more information on the substructures so that FQWK can capture finer-grained local structural features of graphs. In addition, to efficiently compute the transition amplitudes of multistep discrete-time quantum walks, a fast recursive method is designed. Thus, compared with all the existing kernels based on the quantum walk, FQWK has the highest computation speed. Extensive experiments demonstrate that FQWK outperforms state-of-the-art graph kernels in terms of classification accuracy for unattributed graphs. Meanwhile, it can be applied to distinguish a larger family of graphs, including cospectral graphs, regular graphs, and even strong regular graphs, which are not distinguishable by classical walk-based methods.

In modern electronic warfare, both the radar and the jammer are capable of changing their waveforms to achieve better performance. The conflict relationship between the radar and jammer can be modeled as a non-cooperative game. In this paper, the optimal strategies of a monostatic radar and a jammer are investigated in terms of both Stackelberg game and symmetric game. Instead of using the widely used mutual information as the utility function, signal-to-jamming-plus-noise ratio (SJNR) is used in formulating the utility functions which is directly related to the target detection performance. In Stackelberg game, the Stackelberg equilibria solutions are derived when the leader is the radar and the jammer, respectively. In symmetric game, the existence of Nash equilibrium (NE) is investigated and the corresponding strategies are obtained when Nash equilibrium exists. If Nash equilibrium does not exist, the Stackelberg equilibria strategies are still useful as they can be regarded as the robust strategies which could optimize the worst case performance. The relationship between the mutual information utility function and the proposed SJNR utility function is investigated as well. Simulation results show the effectiveness of the radar and jammer strategies. The investigation in this paper can provide optimal waveform solutions for the monostatic radar and the jammer in the confrontation scenario.