2D optimal MMF design with a controllable maximum loss for Doppler signals

Mismatched filter (MMF) is a commonly used technique to suppress the masking effect of weak targets due to the range sidelobes of stronger targets. Although the existing design of MMFs is proved to have a good performance for radar, they cannot be directly applied to sonar, since the Doppler effect for sonar is far more severe than that for radar. In this study, the authors propose a novel two-dimensional (2D) optimal design of MMFs with a controllable maximum loss for sonar. First, they investigate the design of MMFs based on the 2D cross-correlation function when considering the Doppler effect. It is capable of improving the suppression performance of range sidelobes caused by Doppler signals. MMFs are extended to two dimensions. Then, the optimisation problems to minimise the integrated sidelobe level or the peak sidelobe level are established. It has the capability to flexibly control the maximum loss of signal-to-noise ratio and the 2D MMF characteristics by weighted functions. Finally, the constrained optimisation problems can be solved by transforming into the second-order cone programming problems. Simulations relative to multiple signals (P4 polyphase code, binary m-sequence and chirp signal) prove the validity of the design approach.