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We present a general method for constructing radar transmit pulse trains andreceive filters for which the radar point-spread function in delay and Doppler(radar cross-ambiguity function) is essentially free of range sidelobes insidea Doppler interval around the zero-Doppler axis. The transmit and receive pulsetrains are constructed by coordinating the transmission of a pair of Golaycomplementary waveforms across time according to zeros and ones in a binarysequence $P$. In the receive pulse train filter, each waveform is weightedaccording to an element from another sequence $Q$. We show that the spectrum ofessentially the product of $P$ and $Q$ sequences controls the size of the rangesidelobes of the cross-ambiguity function. We annihilate the range sidelobes atlow Doppler by designing the $(P,Q)$ pairs such that their products havehigh-order spectral nulls around zero Doppler. We specify the subspace, alongwith a basis, for such sequences, thereby providing a general way ofconstructing $(P,Q)$ pairs. At the same time, the signal-to-noise ratio (SNR)at the receiver output, for a single point target in white noise, depends onlyon 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 ofthe spectral null. The proposed $(P,Q)$ constructions can also be extended tosequences consisting of more than two complementary waveforms; this is doneexplicitly for a library of Golay complementary quads. Finally, we extend theconstruction of $(P,Q)$ pairs to multiple-input-multiple-output (MIMO) radar,by designing transmit-receive pairs of paraunitary waveform matrices whosematrix-valued cross-ambiguity function is essentially free of range sidelobesinside a Doppler interval around the zero-Doppler axis.

Coordinating Complementary Waveforms for Suppressing Range Sidelobes in a Doppler Band