Coordinating Complementary Waveforms for Suppressing Range Sidelobes in a Doppler Band
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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.
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