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Title: Perfect- and quasi- complementary sequences
Authors: Liu, Zilong
Keywords: DRNTU::Engineering::Electrical and electronic engineering::Wireless communication systems
Issue Date: 2014
Source: Liu, Z. (2014). Perfect- and quasi- complementary sequences. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: A perfect complementary sequence set (PCSS) refers to a set of two-dimensional matrices which have zero non-trivial aperiodic auto- and cross- correlation sums. A perfect complementary sequence (matrix) reduces to a Golay complementary pair (GCP) if it consists of two row sequences only. Owing to this correlation property, PCSSs have found a number of modern applications including the following two: interference-free asynchronous multicarrier code-division multiple-access (MC-CDMA) communications and code-keying orthogonal frequency-division multiplexing (OFDM) communications with low peak-to-mean envelope power ratio (PMEPR). The first practical problem considered is the high PMEPR problem existing in MC-CDMA systems using traditional PCSSs. Specifically, the PMEPR value of an MC-CDMA signal formed by using a traditional PCSS is equal to M (i.e., the number of subcarriers) which is unacceptable for large M. To solve this problem, a new family of complete complementary sequences with system PMEPR value of at most 2 is proposed. For practical asynchronous PCSS-MC-CDMA communications, the “fractional-delay” problem which prevents a PCSS-MC-CDMA system from achieving interference-free performance, is identified for the first time. Specifically, the “fractional-delay” problem occurs when any inter-user delay takes on a value which is a fraction (rather than an integer) of the half chip-duration. By exploiting the correlation property of a PCSS, we have proposed a fractional-delay-resilient receiver with interference-free achievability in strong interference case. Thirdly, the small set size (denoted by K) problem of PCSSs which limits the number of supportable CDMA users, is studied. Precisely, a PCSS-MC-CDMA with M subcarriers can support at most M users only. To enlarge the set size, quasi-complementary sequence sets (QCSSs), consisting of low correlation complementary sequence sets (LC-CSSs) and low correlation zone complementary sequence sets (LCZ-CSSs), are proposed. Correlation lower bounds of these two types of QCSSs are investigated. For LC-CSSs over complex roots of unity, a tighter generalized Levenshtein bound on aperiodic correlation sum (over the Welch bound for LC-CSSs) is derived. Also, a new weight vector which leads to a tighter Levenshtein bound for K ≥ 3, is proposed. This settles an open problem left by Levenshtein on tightening his correlation lower bound for K = 3. In addition, constructions of optimal and near-optimal periodic LC-CSSs (with respect to a derived lower bound) are proposed for the first time by applying linear-phase transform (modulated by Singer difference sets) to optimal quadriphase sequence sets. Since binary GCPs are known for certain even-lengths only, we investigate optimal odd-length binary pairs, each displaying the closest correlation property to a GCP. We show that every length-N optimal pair has maximum zero correlation zone (ZCZ) width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2. Systematic constructions of such optimal pairs are proposed by insertion and deletion of certain binary GCPs, which settle the Li-Fan-Tang-Tu open problem in 2011 on constructing odd-length binary pairs with ZCZ widths of (N + 1)/2. To enable high-rate code-keying OFDM communications using codebooks from Golay sequences, we have generalized the Case IV and Case V constructions (out of the existing known five constructions) of QAM Golay sequences from 64 to 4^q (q ≥ 3) using selected Gaussian integer pairs.
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