Sparse frequency waveform analysis and design based on ambiguity function theory


This study presents new insights into sparse frequency waveform analysis and new waveform style methods. For a general radar waveform, the overall ambiguity in its auto-correlation operate (ACF) is equal to the whole energy in its power spectral density (PSD) in the frequency domain. With this relationship, the whole 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 connection between the optimal PSD and also the minimum ambiguity in ACF. Primarily based on this analysis, a brand new method of planning sparse frequency waveform with sidelobe constraint is proposed. The new methodology simultaneously optimises the sidelobe performance and the PSD performance through constrained non-linear optimisation. This is often totally different from existing methods that compromise the performance of sidelobe to the performance of PSD in an advertisement-hoc manner by minimising the weighted add of the total power in the stopbands and the whole power in the sidelobe. The analysis and the design methodology are extended to the case of multiple sparse frequency waveforms. Simulation studies are provided to demonstrate the effectiveness of the proposed new style ways.

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