  We describe a method of constructing a sequence of phase coded waveforms with
perfect autocorrelation in the presence of Doppler shift. The constituent
waveforms are Golay complementary pairs which have perfect autocorrelation at
zero Doppler but are sensitive to nonzero Doppler shifts. We extend this
construction to multiple dimensions, in particular to radar polarimetry, where
the two dimensions are realized by orthogonal polarizations. Here we determine
a sequence of two-by-two Alamouti matrices where the entries involve Golay
pairs and for which the sum of the matrix-valued ambiguity functions vanish at
small Doppler shifts. The Prouhet-Thue-Morse sequence plays a key role in the
construction of Doppler resilient sequences of Golay pairs.
