Improved Lower Bound for Quasi-Complementary Sequence Set

The Welch bound for aperiodic correlation for binary sequence set was improved by Levenshtein by weighting the cyclic shifts of the sequence vectors. Taking Levenshtein's idea, a new lower bound for quasi-complementary sequence set (QCSS) over the complex roots-of-unity is derived in this paper. It is shown to be tighter than the Welch bound for QCSS in one of the following cases: 1) K = 4M - 1, M >= 2 and N > 2/1-1/M; 2) K >= 4M, M >= 2 and N >= 2. where K, M, N respectively denotes the set size, number of channels, elementary sequence length of QCSS