In active sensing systems such as radar and sensor networks, one is interested in transmitting waveforms that
possess an ideal thumbtack shaped ambiguity function. However, the synthesis of waveforms with the desired
ambiguity function is a difficult problem in applied mathematics and more often than not, one needs to rely
on developing waveforms with an ambiguity function that is close to the desired ambiguity function in some
sense. Designing waveforms with ambiguity functions that possess certain desirable properties has been a well
researched problem in the field of signal analysis. In this paper, we present a methodology for designing multiantenna
adaptive waveforms with autocorrelation functions that allow perfect separation at the receiver. We
focus on the 4×4 case and derive the conditions that the four waveforms must satisfy in order to achieve perfect
separation. Using these conditions, we show that waveforms constructed using Golay complementary sequences,
barker codes and quarter-band signals through kronecker products satisfy these conditions and are therefore
seperable at the receiver. We also give examples of more general wavefom families that are matched to the
environment and also of waveforms that do not necessarily satisfy the conditions for perfect separation but still
have good delay-Doppler ambiguity functions making them suitable for sensing environments.
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