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New Class of Optimal Z-Complementary Code Sets | IEEE Journals & Magazine | IEEE Xplore

New Class of Optimal Z-Complementary Code Sets


Abstract:

Z-complementary code sets (ZCCSs) can support interference-free multi-carrier code-division multiple access (MC-CDMA) in quasi-synchronous channels due to their favourabl...Show More

Abstract:

Z-complementary code sets (ZCCSs) can support interference-free multi-carrier code-division multiple access (MC-CDMA) in quasi-synchronous channels due to their favourable correlation properties. In this letter, based on the existing optimal ZCCSs and CCCs, we propose new class of optimal ZCCSs using Kronecker product. The resultant sequence sets have enlarged set size and sequence lengths which have not been reported before.
Published in: IEEE Signal Processing Letters ( Volume: 29)
Page(s): 1477 - 1481
Date of Publication: 23 June 2022

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I. Introduction

M. J. Golay first proposed the Golay complementary pairs (GCPs) in 1951 while studying infrared multislit spectroscopy [1]. GCPs are a pair of sequences having zero aperiodic autocorrelation sums (AACSs) at each non-zero time shift. Because of its ideal correlation properties, GCPs have been found several applications in modern day communication systems [2] and radar [3]. However, the lengths of GCPs are very limited [4]. Specifically, binary GCPs are available only for lengths of the form , where are non-negative integers [4]. In 1972, Tseng and Liu extended the idea of GCPs to complementary sequence set (CSS), where each set contains multiple sequences, and have zero AACSs except at zero time shift [5]. In addition, the idea was further extended to a set of CSSs, which are mutually orthogonal to each other, known as mutually orthogonal complementary sequence sets (MOCSSs). A -MOCSS is a family of CSSs, where denotes the set size (i.e., the number of users), denotes the flock size (i.e., the number of sub-carriers) and denotes the sequence length [5]. In [6], the upper bound of the set size of the -MOCSS is given, i.e., . When the set size equals the flock size, MOCSS is called a complete complementary code (CCC). CCCs have been applied in multi-carrier code division multiple access (MC-CDMA) systems [7], MIMO channel estimation and suppressing the multiple access interference. However, a CCC has a limited number of users, which is upper bounded by its set size.

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References

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