  We present a general method for constructing radar transmit pulse trains and
receive filters for which the radar point-spread function in delay and Doppler
(radar cross-ambiguity function) is essentially free of range sidelobes inside
a Doppler interval around the zero-Doppler axis. The transmit and receive pulse
trains are constructed by coordinating the transmission of a pair of Golay
complementary waveforms across time according to zeros and ones in a binary
sequence $P$. In the receive pulse train filter, each waveform is weighted
according to an element from another sequence $Q$. We show that the spectrum of
essentially the product of $P$ and $Q$ sequences controls the size of the range
sidelobes of the cross-ambiguity function. We annihilate the range sidelobes at
low Doppler by designing the $(P,Q)$ pairs such that their products have
high-order spectral nulls around zero Doppler. We specify the subspace, along
with a basis, for such sequences, thereby providing a general way of
constructing $(P,Q)$ pairs. At the same time, the signal-to-noise ratio (SNR)
at the receiver output, for a single point target in white noise, depends only
on the choice of $Q$. By jointly designing the transmit-receive sequences
$(P,Q)$, we can maximize the output SNR subject to achieving a given order of
the spectral null. The proposed $(P,Q)$ constructions can also be extended to
sequences consisting of more than two complementary waveforms; this is done
explicitly for a library of Golay complementary quads. Finally, we extend the
construction of $(P,Q)$ pairs to multiple-input-multiple-output (MIMO) radar,
by designing transmit-receive pairs of paraunitary waveform matrices whose
matrix-valued cross-ambiguity function is essentially free of range sidelobes
inside a Doppler interval around the zero-Doppler axis.
