Area Preserving Linear Transformations and Spread Doppler Clutter Mitigation in Over-the-Horizon Radar

The use of recurrent waveforms in over the horizon radar (OTHR) necessitates techniques for ambiguity resolution and manipulation. In this paper, we elucidate methods for systematically transforming any given waveform, so that its ambiguity function is transformed by any desired area preserving linear transformation of delay-Doppler plane. Furthermore, given the desired delay-Doppler transformation, the corresponding waveform transformation can be explicitly constructed through the factorisation of $2\times 2$ matrices. Using this theory it is shown that the usual phase and frequency coding techniques used for range folded spread Doppler clutter mitigation, which induce an approximate Doppler shearing of delay-Doppler plane, can be replaced by chirp modulating the recurrent waveform. These non-recurrent chirped waveforms induce an exact Doppler shearing and lead to simpler and more robust signal processing of the returns.