Exploring Group Theory for Optimal Cognitive Radar Waveform Design

We explore applying group theory principles in designing waveforms for a cognitive radar. By leveraging affine groups, we provide a mathematical framework for designing radar waveforms for a wideband multiple-input multiple-output (MIMO) radar. Prior works in this area have considered this approach for the narrowband or single-antenna radar systems. We first derive a general wideband ambiguity function of a MIMO radar by correlating the signal with its time-dilated, Doppler-shifted, and position-delayed replicas. The ambiguity function is essentially a coefficient function of the unitary representation of an affine group. We then construct complementary waveforms that minimize range sidelobes in the cross-ambiguity matrix, depending on the requirements of cognitive radar. Our numerical experiments demonstrate the effectiveness of group-theory-based complementary waveform designs.