Wavelet-modulated pulse for compressive sensing in SAR

A new wavelet modulated pulse is proposed for synthetic aperture radar (SAR). Conventionally SAR image is constructed using chirp, i.e., FM in the range direction, and the Doppler effect in the azimuth direction. The proposed scheme is to physically modulate the amplitude of the radar pulse (AM) using wavelets. Such a radar pulse results in the shift of the wavelets in the temporal domain due to the range, while the Doppler effect causes variation of the scaling coefficient. In both directions, pulse compression can be achieved by taking advantage of the autocorrelation function of the compactly supported orthogonal wavelets and processing the echo signal in the two directions accordingly. Furthermore, by using wavelet modulated pulses, the echo signal is equivalent to the wavelet transform (WT) to the target area. Since WT has been proved more effective in image compression than conventional discrete cosine transform (DCT), wavelet-modulated pulse is equivalent to compression to the SAR image thus to achieve compressive sensing. Experiments have been performed using the latest embedded software defined radio (SDR) technology. Equipped with the most recent FPGA and digital signal processors along with high speed analog-to-digital and digital-to-analog converters, the SDR allows signal processing tasks commonly done by analog circuits to be performed digitally with high flexibility in algorithm design. Based on the developmental need of the user, the small form factor software defined radio (SFF SDR) can serve as a simple data collection device for waveform testing or it can be programmed into a real-time embedded radar system.