Liu, Zilong and Guan, Yong Liang and Mow, Wai Ho (2017) 'Asymptotically Locally Optimal Weight Vector Design for a Tighter Correlation Lower Bound of QuasiComplementary Sequence Sets.' IEEE Transactions on Signal Processing, 65 (12). 3107  3119. ISSN 1053587X

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Abstract
A quasicomplementary sequence set (QCSS) refers to a set of twodimensional matrices with low nontrivial aperiodic auto and crosscorrelation sums. For multicarrier codedivision multipleaccess 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.
Item Type:  Article 

Divisions:  Faculty of Science and Health > Computer Science and Electronic Engineering, School of 
Depositing User:  Elements 
Date Deposited:  05 Oct 2020 16:23 
Last Modified:  05 Oct 2020 16:23 
URI:  http://repository.essex.ac.uk/id/eprint/26512 
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