Construction of spectrally-null-constrained zero-correlation zone sequences with flexible support

Nishant Kumar, Palash Sarkar, Sudhan Majhi
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Abstract

In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectrally-null-constrained (SNC) property to achieve a low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences are reduced to traditional ZCZ sequences when the support size is equal to the length of the sequence. To obtain ZCZ sequences, we first propose a construction of traditional/SNC-complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class, we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller (GRM) code and the proposed traditional ZCZ sequences is also established. The enumeration of traditional ZCZ sequences within a GRM code is also established. This enumeration is achieved by tallying the distinct second-order cosets of the first-order GRM code and quantifying the number of ZCZ sequences residing within a particular coset. Moreover, the Hamming distance of the proposed traditional ZCZ sequences is also computed.

构建具有灵活支持的谱空约束零相关区序列
近年来,由于零相关区(ZCZ)序列在准同步码分多址(QS-CDMA)系统和其他无线通信领域的重要应用,人们对其进行了研究。然而,在认知无线电(CR)网络中,设计具有频谱空受限(SNC)特性的 ZCZ 序列以实现低频谱密度曲线是可取的。本文的重点是构建具有灵活支持的 SNC-ZCZ 序列,其中支持指的是序列中与非零条目相对应的索引集合。当支持度大小等于序列长度时,所提出的 SNC-ZCZ 序列将简化为传统的 ZCZ 序列。为了获得 ZCZ 序列,我们首先利用一类扩展布尔函数(EBF)提出了传统/SNC-完整互补码(SNC-CCC)的构造。在该类函数的帮助下,我们提出了另一类 EBFs,该类 EBFs 可生成关于 Tang-Fan-Matsufuzi 约束的质幂长度渐近最优的传统/SNC-ZCZ 序列。此外,还建立了一阶广义里德-穆勒(GRM)码的二阶余集与所提出的传统 ZCZ 序列之间的关系。还建立了 GRM 码中传统 ZCZ 序列的枚举。这种枚举是通过统计一阶 GRM 码的不同二阶余集并量化特定余集中的 ZCZ 序列数量来实现的。此外,还计算了所提出的传统 ZCZ 序列的汉明距离。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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