  To relieve the interference caused by range-Doppler sidelobes in pulsed
radars, we propose a new method to construct Doppler resilient complementary
waveforms based on Golay codes. We design both the transmit pulse train and the
receive pulse weights, so that the similarity between the pulse weights and a
given window function is maximized and the constraints on Doppler null points
and energy are met. That is summarized as a two-way partitioning problem, and
then solved by semidefinite programming and randomization techniques. The novel
waveform thus obtained has its range sidelobe outright suppressed in multiple
and flexibly-adjustable Doppler zones, and performs well in Doppler sidelobe
suppression, Doppler resolution and SNR. It shows great promise in detecting
slightly-moving weak targets with the existence of dense interference.
