Recurrent lobes reduction of stepped-frequency LFM pulse train using ambiguity function

Stepped-frequency linear frequency modulation (LFM) pulse train is one of the well-known waveforms employed in modern wideband radar to efficiently achieve good range and Doppler resolution without increasing requirements on overall system cost and complexity. Unfortunately, this waveform associates with a drawback of undesirable spikes, known as ‘recurrent lobes or grating lobes’ due to the fixed frequency step. We investigate a generic stepped-frequency LFM pulse train and analyze its significant characteristics by using ambiguity function in more details, especially for zero-Doppler cut and zero-delay cut. Then we propose a method that allows us to reduce grating lobes below a desired threshold level. Two special cases for reduction are discussed for the specific relationships among waveform parameters. Both the analytical and numerical methods for parameter design are given along with distinct examples, which show that selecting a certain larger overlap ratio makes no need to suppress these spikes.