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Synthetic aperture radar (SAR) is a high-resolution imaging radar. With the deteriorating electromagnetic environment, SAR systems are susceptible to various forms of electromagnetic interference, including deception jamming. This jamming notably impacts SAR signal processing and subsequently worsens the quality of acquired images. Chaotic frequency modulation (CFM) signals could effectively counteract deception jamming. Nevertheless, due to the inadequate band-limited performance of CFM signals, higher oversampling factors are needed for achieving optimal low sidelobe levels, leading to increased system costs and excessively high data rates. Additionally, not all chaotic sentences meet the CFM signal requirements. In response, this paper proposes a novel signal modulation method called chaotic-nonlinear frequency modulation (C-NLFM) that enhances band-limited performance. The optimum parameters for C-NLFM signals are selected using the particle swarm optimization (PSO) algorithm. In this way, C-NLFM signals attain ideal low sidelobe levels even when faced with reduced oversampling factors. Meanwhile, this chaotic coding mode retains its capability to effectively suppress deception jamming. Moreover, C-NLFM signals demonstrate versatility in adapting to various chaotic sequences, thereby enhancing their flexibility to modify the signals as required. Through comprehensive simulations, data analysis, and a semi-physical experiment, the effectiveness and superiority of this proposed method have been confirmed. [ABSTRACT FROM AUTHOR]