Design of Sequences with Low PAPR and Low Time-domain Cross-correlation Based on Complete Graphs

Sequences with low peak-to-average power ratio (PAPR) and low time-domain cross-correlation play a crucial role in the uplink of 4G LTE and 5G NR, serving as sounding reference signals for channel sounding and data demodulation. This paper, for the first time, transforms the time-domain cross-correlation problem into a characterization of sequence PAPR, thereby establishing a theoretical lower bound on the time-domain cross-correlation of sequences and defining Golay orthogonal sequence sets with low PAPR and low time-domain cross-correlation properties. Furthermore, by establishing a connection between mutually orthogonal Hamiltonian paths (H-paths) in the complete graph and generalized Boolean functions, this paper innovatively proposes a construction framework for designing Golay orthogonal sequence sets based on orthogonal H-paths. Simultaneously, this paper discusses the theoretical upper bound on the maximum number of orthogonal H-paths in the complete graph Kn, and proposes two specific construction schemes for orthogonal H-path sets for any odd number n. Based on this scheme, we designed two classes of Golay orthogonal sequence sets, which have better PAPR and time-domain cross-correlation performance compared to well-known Zadoff-Chu sequences used in 4G LTE and 5G NR.