Doppler Resilient Golay Complementary Pairs for Radar

We present a systematic way of constructing a Doppler resilient sequence of Golay complementary waveforms for radar, for which the composite ambiguity function maintains ideal shape at small Doppler shifts. The idea is to determine a sequence of Golay pairs that annihilates the low-order terms of the Taylor expansion of the composite ambiguity function. The Prouhet-Thue-Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay pairs. We extend this construction to multiple dimensions. In particular, we consider radar polarimetry, where the dimensions are realized by two orthogonal polarizations. We determine a sequence of two-by-two Alamouti matrices, where the entries involve Golay pairs and for which the matrix-valued composite ambiguity function vanishes at small Doppler shifts.