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.