A Doppler statistic for zero autocorrelation waveforms

There are several natural constructions of constant amplitude zero autocorrelation (off the DC-component) waveforms. We adopt a construction for waveforms of length K, where K is a non-square-free integer. This property of K is used in the derivation of a frequency shifting (Doppler) detection algorithm which we derive. There are number theoretic properties which account for the properties of this algorithm, as well as for analogous but different properties in the square-free case. A variety of relevant examples is given along with the technical rationale for the algorithm.