Range sidelobe suppression in a desired Doppler interval

We present a novel method of constructing a Doppler resilient pulse train of Golay complementary waveforms, for which the range sidelobes of the pulse train ambiguity function vanish inside a desired Doppler interval. This is accomplished by coordinating the transmission of a Golay pair of phase coded waveforms in time according to the 1´s and -1´s in a biphase sequence. The magnitude of the range sidelobes of the pulse train ambiguity function is shown to be proportional to the magnitude spectrum of the biphase sequence. Range sidelobes inside a desired Doppler interval are suppressed by selecting a sequence whose spectrum has a high-order null at a Doppler frequency inside the desired interval. We show that the spectrum of the biphase sequence obtained by oversampling the length-2^M Prouhet-Thue-Morse (PTM) sequence by a factor m has an Mthorder null at all rational Doppler shifts thetas₀=2pil/m, where lne0 and mne1 are co-prime integers. This spectrum also has an (M-1)th-order null at zero Doppler and (M-h-1)thorder nulls at all Doppler shifts thetas₀=2pil/(2^hm), where lne0 and mne1 are again co-prime and 1leshlesM-1.