Ambiguity Function and Frame-Theoretic Properties of Periodic Zero-Autocorrelation Waveforms

Periodic constant-amplitude zero-autocorrelation (CAZAC) waveforms u are analyzed in terms of the discrete periodic ambiguity function A(u). Elementary number-theoretic considerations illustrate that peaks in A(u) are not stable under small perturbations in its domain. Further, it is proved that the analysis of vector-valued CAZAC waveforms depends on methods from the theory of frames. Finally, techniques are introduced to characterize the structure of A(u) to compute u in terms of A(u) and to evaluate MSE for CAZAC waveforms.