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Title: Asymptotically locally optimal weight vector design for a tighter correlation lower bound of quasi-complementary sequence sets
Authors: Liu, Zilong
Guan, Yong Liang
Mow, Wai Ho
Keywords: Correlation
Multicarrier Code Division Multiple Access
Engineering::Electrical and electronic engineering
Issue Date: 2017
Source: Liu, Z., Guan, Y. L., & Mow, W. H. (2017). Asymptotically locally optimal weight vector design for a tighter correlation lower bound of quasi-complementary sequence sets. IEEE Transactions on Signal Processing, 65(12), 3107-3119. doi:10.1109/TSP.2017.2684740
Series/Report no.: IEEE Transactions on Signal Processing
Abstract: A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low nontrivial aperiodic auto- and cross-correlation sums. For multicarrier code-division multiple-access applications, the availability of large QCSSs with low correlation sums is desirable. The generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of QCSSs. The bounding expression of GLB is a fractional quadratic function of a weight vector w and is expressed in terms of three additional parameters associated with QCSS: the set size K, the number of channels M, and the sequence length N. It is known that a tighter GLB (compared to the Welch bound) is possible only if the condition M ≥ 2 and K ≥ K̅ + 1, where K̅ is a certain function of M and N, is satisfied. A challenging research problem is to determine if there exists a weight vector that gives rise to a tighter GLB for all (not just some) K ≥ K̅ + 1 and M ≥ 2, especially for large N, i.e., the condition is asymptotically both necessary and sufficient. To achieve this, we analytically optimize the GLB which is (in general) nonconvex as the numerator term is an indefinite quadratic function of the weight vector. Our key idea is to apply the frequency domain decomposition of the circulant matrix (in the numerator term) to convert the nonconvex problem into a convex one. Following this optimization approach, we derive a new weight vector meeting the aforementioned objective and prove that it is a local minimizer of the GLB under certain conditions.
ISSN: 1053-587X
DOI: 10.1109/TSP.2017.2684740
Rights: © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
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