The Induced Correlations of Zadoff-Chu Sequences

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.