Design and Analysis of Non-Binary Cyclic Permutation Sequences for Low-Correlation Multiuser Synchronization

This paper extends cyclic permutation coding, previously applied for error correction in power-line communications (PLC), to synchronization-oriented sequence design by introducing a novel class of Non-Binary Cyclic Permutation Sequences (NCPS) for low-correlation multiuser synchronization. Unlike conventional Zadoff–Chu (ZC) and constant-amplitude zero-autocorrelation (CAZAC) sequences that rely on complex-valued phase laws, NCPS employ discrete modular permutations mapped to complex exponentials. Autocorrelation properties were analytically derived where tractable, while general correlation behavior was characterized through structural analysis and confirmed via simulation. Results demonstrated that NCPS achieved near-orthogonal cyclic correlation performance comparable to ZC sequences while preserving optimal Hamming distance, beneficial for error correction, and offering reduced implementation complexity. These characteristics highlight the potential of NCPS as synchronization preambles in PLC systems and other low-complexity or quantized communication platforms, including Internet of Things networks.