Generalized bounds on partial aperiodic correlation of complex roots of unity sequences

Authors:
Lifang Feng;Pingzhi Fan
Affiliations:
Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China;Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China
Venue:
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Year:
2006

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Abstract

Partial correlation properties of sets of sequences are important in CDMA system as well as in ranging, channel estimation and synchronization applications. In general, it is desirable to have sequence sets with small absolute values of partial correlations. In this paper, generalized lower bounds on partial aperiodic correlation of complex roots of unity sequence sets with respect to family size, sequence length, subsequence length, maximum partial aperiodic autocorrelation sidelobe, maximum partial aperiodic crosscorrelation value and the zero or low correlation zone are derived. It is shown that the previous aperiodic sequence bounds such as Sarwate bounds, Welch bounds, Levenshtein bounds, Tang-Fan bounds and Peng-Fan bounds can be considered as special cases of the new partial aperiodic bounds derived.