On large zero auto/cross correlation zone of Golay/QAM Golay sequences and their applications and related correlation properties

Golay sequences have been studied for more than five decades since Golay first discovered those sequences, which have found many applications in communications, especially, for peak average power ratio reduction in orthogonal frequency division multiple (OFDM) systems in recent cellular communication. However, the periodic auto- correlation of a single Golay sequence is unknown. In this talk, I will present our recent results on zero correlation zones of Golay sequences. First we show that there exists three different classes of Golay sequences with a zero auto- correlation zone (ZACZ) of length approximately an half, a quarter or one eighth of their period. Those zones can also be hold for zero crosscorrelation zone (ZCCZ). Furthermore, the large ZACZ or ZCCZ of Golay sequences can be inherited by QAM Golay sequences. Those new findings on Golay sequences can be explored during synchronization and detection at the receiver end and thus improve the performance of the communication system. As an example, we present the application of binary Golay sequences with ZACZ for intersymbol interference (ISI) channel estimation and show the comparisons of the performance of Golay- sequence-aided channel estimation with m-sequences and Frank-Zadoff-Chu sequences. Finally, we consider different measurements for correlation of sequences. We show that three classes of Golay/QAM Golay sequences have the same large zero correlation zones as above when it is measured by odd correlation. The content of the talk is taken from the series of joint work with Fei Hou and Yang Yang.