Sparse frequency waveform analysis and design based on ambiguity function theory

This study presents new insights into sparse frequency waveform analysis and new waveform design methods. For a general radar waveform, the total ambiguity in its auto-correlation function (ACF) is equal to the total energy in its power spectral density (PSD) in the frequency domain. With this relationship, the total ambiguity in an ACF is found to be minimised when the corresponding PSD is uniformly distributed. This property is extended to the sparse frequency waveform by establishing the relationship between the optimal PSD and the minimum ambiguity in ACF. Based on this analysis, a new method of designing sparse frequency waveform with sidelobe constraint is proposed. The new method simultaneously optimises the sidelobe performance and the PSD performance through constrained non-linear optimisation. This is different from existing methods that compromise the performance of sidelobe to the performance of PSD in an ad-hoc manner by minimising the weighted sum of the total power in the stopbands and the total power in the sidelobe. The analysis and the design method have been extended to the case of multiple sparse frequency waveforms. Simulation studies are provided to demonstrate the effectiveness of the proposed new design methods.