Spectrally-efficient FM noise radar waveforms optimized in the logarithmic domain

It was recently experimentally demonstrated that spectrally-shaped FM noise waveforms can be designed that achieve very high time-bandwidth products and commensurately low sidelobes. While relatively good spectral containment can be obtained, increasing spectrum pressure may require that it be even better. To that end, here a logarithmic spectral shaping is performed by way of gradient-based optimization of a logarithmic frequency template error (Log-FTE) metric applied to a polyphase-coded FM (PCFM) waveform structure. Simulation and loopback experimental measurements show that this approach facilitates excellent spectral containment while still providing the high dimensionality and diversity benefits of FM noise waveforms.