Closed-form mismatched filter synthesis for complementary range response

The combined response of a pair of complementary waveforms has zero range sidelobes and could significantly improve synthetic aperture radar (SAR) image quality by reducing multiplicative noise. However, complementary waveforms may not be practical for SAR imaging for reasons such as Doppler tolerance and unimodular waveform constraints. By using mismatched filters to achieve either a complementary or near-complementary response, two or more practical waveforms could be employed and SAR image quality improved. A closed-form approach was developed that calculates mismatched filters so that the coherent sum of the range responses from each waveform and its corresponding mismatched filter is complementary. A second approach reduced sidelobes while retaining a frequency response close to the waveforms’ frequency responses. Images processed using X-band radar data collected under the Air Force Gotcha program exhibited improvements in image quality over those processed using matched filters. The closed-form approach is presented for both complementary and reduced-sidelobe mismatched filters and image quality is quantified. The approach developed in this work offers improved image quality, is suitable for near real-time operation, and is independent of the waveforms.