Lower Bounds on the Correlation Property for OFDM Sequences with Spectral-Null Constraints

Sequences with specific autocorrelation (AC) and cross-correlation (CC) properties are crucial components in radar and wireless communications. In this paper, we derive the theoretical bounds on the AC and CC for OFDM sequences with constraints of spectral nulls, e.g., the mandatory nulls on the DC sub-carrier and guardbands in OFDM systems. The bounds and trade-off limits are provided for the properties of sequences, including the peak AC and CC levels, the cardinality of the sequence set, the sequence length, and the temporal length of the low correlation zone. We also investigate the trade-offs of correlations among sequence sets. The presented trade-off limits can serve as guidelines for applications where the performance measures or design criteria are related to the peak AC and CC levels.