A new lower bound is proposed in this article. Like Levenshtein bound, it relates to the maximum correlation value (autocorrelation and cross-correlation) a set of sequences can achieve. The novelty introduced here is that each sequence is associated with a mismatched filter. The proposed bound is inspired from Levenshtein's, holds for any set of unimodular sequences and can be applied in both aperiodic and periodic cases. It appears that the obtained expression does not deviate a lot from the (matched) Levenshtein, which indicates that the use of a mismatched filter will not guarantee much better sidelobe performance, as the number fo sequences is significant, contrary to the popular belief.

This paper deals with lower bounds on aperiodic correlation of sequences. It intends to solve two open questions. The first one is on the validity of the Levenshtein bound for a set of sequences other than binary sequences or those over the roots of unity. Although this result could be a priori extended to polyphase sequences, a formal demonstration is presented here, proving that it does actually hold for these sequences. The second open question is on the possibility to find a bound tighter than Welch's, in the case of a set consisting of two sequences M = 2. By including the specific structure of correlation sequences, a tighter lower bound is introduced for this case. Besides, this method also provides in the cases M = 3 and M = 4 a tighter bound than the up-to-now tightest bound provided by Liu et al.