Ambiguity and area preserving linear transformations in over-the-horizon radar

Abstract

The use of recurrent waveforms in over-the-horizon radar (OTHR) necessitates techniques for ambiguity resolution and manipulation. This paper provides a number of techniques for manipulating the shape of radar ambiguity functions. A new and simple characterisation of the radar ambiguity function is introduced in terms of twisted convolution. It is shown that the ambiguity function of any waveform can be transformed by any desired area preserving linear transformation of the 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. Among other applications of this theory, it is shown that the usual OTHR 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.