  While Doppler resilient complementary waveforms have previously been
considered to suppress range sidelobes within a Doppler interval of interest in
radar systems, their capability of Doppler resilience has not been fully
utilized. In this paper, a new construction of Doppler resilient complementary
waveforms based on a null space is proposed. With this new construction, one
can flexibly include a specified Doppler interval of interest or even an
overall Doppler interval into a term which results in range sidelobes. We can
force this term to zero, which can be solved to obtain a null space. From the
null space, the characteristic vector to control the transmission of basic
Golay waveforms, and the coefficients of the receiver filter for Golay
complementary waveform can be extracted. Besides, based on the derived null
space, two challenging non-convex optimization problems are formulated and
solved for maximizing the signal-to-noise ratio (SNR). Moreover, the
coefficients of the receiver filter and the characteristic vector can be
applied to fully polarimetric radar systems to achieve nearly perfect Doppler
resilient performance, and hence fully suppress the inter-antenna
interferences.
