Backward and Sequential Inductions for Anti-Jamming Equilibrium Strategy Generation of Frequency Agile Radar

Mainlobe jamming has emerged as a serious threat to the radar and the carrier frequency agility of the radar provides a promising way to address this challenge. In this paper, the electromagnetic confrontation between a smart mainlobe jammer and a frequency agile radar is investigated from a game theory perspective. The interaction process between them typically includes multiple pulses, in which the radar determines its carrier frequency sequence, and the jammer synchronously chooses the jamming mode. This bilateral process is modeled as a two-player zero-sum extensive-form game with simultaneous moves. To solve the game, the backward induction (BI) algorithm is introduced to find the subgame perfect Nash equilibrium. Although the BI algorithm can exactly find the SPNE, its computational cost grows exponentially with the number of pulses, making it impractical. Therefore, a fast algorithm called the sequential induction (SI) algorithm is proposed to obtain an approximation Nash equilibrium, whose computational complexity is linear with respect to the number of pulses. Additionally, the obtained radar's SEQ strategy with history-independent and reuse characteristics is reliable and efficient in a game with a changing number of stages. Simulation results demonstrate the effectiveness of the proposed SI algorithm for approximately finding the Nash equilibrium.