CZT Algorithm for the Doppler Scale Signal Model of Multireceiver SAS Based on Shear Theorem

In multireceiver synthetic aperture sonars (SASs), the traditional non-stop-hop-stop model normally ignores the intrapulse motion of sonar platform. However, such intrapulse motion brings the Doppler scale effect (DSE) to the echo signal, which will lead to the change in carrier frequency (CF) and frequency modulation (FM) rate of echo signal and may eventually result in image defocus. In this article, considering the intrapulse motion, the time-varying time delay and range history of multireceiver SAS were derived by introducing the range time into the range history, and then the Doppler scale signal model was established. After approximating the derived time-varying range history, the 2-D spectrum was derived by using the shear theorem. When compared with the traditional 2-D spectrum, an interesting phenomenon was found that the change in FM rate has no effect on the 2-D spectrum. Actually, only two additional terms, i.e., range cell migration (ARCM) and azimuth modulation (AAM), were introduced into the new 2-D spectrum due to the change in CF. Besides, the condition of neglecting the ARCM was given by further analyzing the 2-D spectrum, while the AAM is usually small and can be easily compensated together with the ARCM correction. Finally, a chirp-z transform (CZT) algorithm for the Doppler scale signal model was proposed to correct the ARCM, which can simultaneously correct the ARCM and compensate the AAM (although not required) in the 2-D frequency domain by phase multiplication. The effectiveness of the signal model and the proposed algorithm is verified by simulations and field data.