This paper focuses on the cognitive design of transmit waveform to improve target detection capability in the presence of signal-dependent modulated jamming (e.g., chopping and interleaving (C&I) jamming). In particular, we reasonably assume that the modulation mode of signal-dependent jamming is available based on cognitive paradigm. The first design criterion is to minimize the integrated crosscorrelation energy (ICE) between the transmit waveform and jamming signal. In this way, the received jamming signal can be suppressed after matched filter processing is performed using the optimized waveform. The second design criterion is to minimize the integrated auto-correlation sidelobe level (IASL) for maintaining good range compression property. The practical constant modulus constraint is imposed on the transmit waveform. Finally, to deal with the resulting non-convex problem, an iterative algorithm based on the majorization-minimization framework is developed. Numerical examples for specific signal-dependent modulated jammings are provided to demonstrate the effectiveness of the proposed methodology.