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In this paper, in order to reduce the probability of the radar waveform intercepted by the passive detection system, the time-bandwidth product of the radar waveform is increased, and the detection probability of the radar waveform to the target is improved. This paper tackles the holographic RF stealth radar and proposes a joint coding waveform based on the linear frequency modulation (LFM) waveform. Joint coding uses complementary codes to perform phase-coding, and combines the codewords optimized by genetic algorithm in order to perform discrete frequency-coding waveform. The joint coding waveform model is theoretically analyzed, and the ambiguity function, pulse compression and target detection probability of the joint coding waveform are obtained by numerical simulation. In addition, the complexity of the algorithm and the low probability of intercept (LPI) characteristic of the joint coding waveform are analyzed. The results show that the joint coding waveform has an approximate "pushpin" ambiguity function, ultra-low sidelobe characteristics, better RF stealth and target detection performance. Finally, it has good application prospects in the current battlefield environment. [ABSTRACT FROM AUTHOR]