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,
given by the cross-ambiguity function of the transmit pulse train and the pulse
train used in the receive filter, is essentially free of range sidelobes inside
a Doppler interval around the zero-Doppler axis. The transmit pulse train is
constructed by coordinating the transmission of a pair of Golay complementary
waveforms across time according to zeros and ones in a binary sequence P. The
pulse train used to filter the received signal is constructed in a similar way,
in terms of sequencing the Golay waveforms, but each waveform in the pulse
train is weighted by an element from another sequence Q. We show that a
spectrum jointly determined by P and Q sequences controls the size of the range
sidelobes of the cross-ambiguity function and by properly choosing P and Q we
can clear out the range sidelobes inside a Doppler interval around the zero-
Doppler axis. The joint design of P and Q enables a tradeoff between the order
of the spectral null for range sidelobe suppression and the signal-to-noise
ratio at the receiver output. We establish this trade-off and derive a
necessary and sufficient condition for the construction of P and Q sequences
that produce a null of a desired order
