The induced correlations of a pair of sequences are defined as the full-period correlations between the linear phase-shifting sequences of one of the given pair and the other one. This concept was introduced in the analysis of their partial-period correlations which are an important performance measurement of the employed communication system. In this paper, we investigate the induced correlations of Zadoff-Chu sequences in a transform approach. For a pair of Zadoff-Chu sequences, we first compute the spectrums of their induced correlations. By taking the inverse discrete Fourier transform (IDFT) on these spectrums, we then derive their induced correlations in a closed form. As a result, we show that their induced correlations can be viewed as expanded and scaled Zadoff-Chu sequences of a smaller period. Not only does our approach give the magnitudes of the induced correlations of Zadoff-Chu sequences, but it also gives the phase information which is applicable to computation of their partial-period correlations.

Partial-period correlations of sequences are an important performance measure of communication systems employing them, but are known to be notoriously difficult to analyze. In this paper, we present a systematic approach to partial-period correlations as a generalization of the Paterson-Lothian approach. For a pair of sequences (not necessarily distinct), we introduce the linear phase-shifting sequences of one of them and analyze their full-period correlations, called the induced correlations, with the other one. By exploiting the induced correlations, we obtain the partial-period correlation properties of the given pair. We then investigate Zadoff-Chu sequences, and give some theoretical results on their partial-period autocorrelations, including closed-form expressions, and the first and second moments. We also derive an upper bound on the magnitudes of the partial-period cross-correlations of Zadoff-Chu sequences. Finally, we explore generalized chirp-like discrete Fourier transform sequences and show that their partial-period cross-correlations have the same magnitudes as the partial-period autocorrelations of the employed Zadoff-Chu sequence up to permutation.

In this paper, we investigate the partial-period correlation of Zadoff-Chu sequences. For a pair of Zadoff-Chu sequences, we define the linear phase-shifting sequences of one of them and analyze their full-period correlation properties with the other one. By linking them to the partial-period correlation of the given pair, we derive an upper bound on the magnitude of the partial-period correlation of Zadoff-Chu sequences.