We propose a novel signal model by combining the sparse stepped frequency signals with chaotic signals, i.e. the sparse stepped chaotic signal (SSCS) model, as well as the corresponding compression algorithm based on compressed sensing. In SSCS, the chaotic signals are modulated to sparse stepped frequencies to compose a transmitting burst. When receiving, the echo signals are demodulated to the baseband and then can be sampled directly at a rate much lower than the Nyquist rate determined by the bandwidth of chaotic signal of each subpulse. Compared with radars using conventional stepped frequency waveforms, the SSCS radar can transmit fewer subpulses in a burst and directly use lower speed ADC next to the receiver. Both simulated and real radar data are processed to demonstrate the effectiveness of the proposed SSCS as well as the compression algorithm by which high resolution range profiles are very well reconstructed.
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