A frequency-domain approach to tightening the generalized levenshtein bound

Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross-correlation sums. GLB is an indefinite fractional quadratic function of a “simplex” weight vector w and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic optimization for the tightening of the GLB. Our key idea is to apply the frequency-domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible (K, M) cases, where K, M denote the set size, the number of channels, of QCSS, respectively.