On the Perfect Cyclically Conjugated Even and Odd Periodic Autocorrelation Properties of Quaternary Golay Sequences

A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: generalized even and odd periodic autocorrelation, and generalized even and odd periodic cyclically conjugated autocorrelation. In particular, we study a special case of autocorrelation function called cyclically conjugated autocorrelation function. As a result, we present several classes of perfect cyclically conjugated even periodic and odd periodic autocorrelation of quaternary Golay sequences. We also considered such perfect property for 4q-QAM Golay sequences, q ≥ 2 being an integer. Those proposed sequences could be used for synchronization and detection if the time delay is known. Index Terms. Golay sequence, quadrature amplitude modulation (QAM), cyclically conjugated even periodic autocorrelation, cyclically conjugated odd periodic autocorrelation. 1