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Frequency distance sequences for packet detection in physical-layer security

DESIGNS CODES AND CRYPTOGRAPHY 2025年第4期93卷 997-1020页

作者： Abubaker, Radi Gong, Guang Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

In this paper, we investigate how to construct the required sequences to be used as pilot signals for packet detection in physical-layer security. Our construction starts from the frequency domain, where a set of orthogonal frequencies cover an entire given bandwidth. The construction is a generalized construction from Milewski's construction, where it takes the inverse discrete Fourier transform of the given frequency domain sequences. In this paper, we call a set of the q sequences of length & ell;q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell q$$\end{document} with an equal distanced, nonzero frequency response in the frequency domain a frequency distance sequence set (FDSS) and a sequence interleaved from this set an FDSS interleaved sequence. By applying frequency and time domain relations, we show that such a set is mutually orthogonal, and is a complementary sequence set if and only if the seed sequence is perfect (i.e., zero autocorrelation at all out-of-phase shift). The FDSS interleaved sequence is perfect if and only if the seed sequence is perfect. We apply the proposed sequences to real world experiments as pilot sequences for coarse synchronization. In our experiments, we selected Frank-Zadoff-Chu sequences and Golay pair sequences in our construction for use with an ADALM-Pluto SDR from Analog Devices and simulations, and we show the pilot detection rate under different noisy channel conditions, when compared to alternative pilot selections. The false negative detection rate of our pilot decreases to zero when the SNR is 20 dB. In contrast, a general OFDM QPSK pilot has a false-negative detection rate near 70% at the same SNR. In general, our pilot sequence consistently has a lower false-negative rate to the OFDM QPSK pilot, which failed to detect most packets in th

关键词： Frequency distance sequence set DFT/IDFT Zero autocorrelation Mutually orthogonal complementary sequence set Pilot sequences Packet detection Physical layer security

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Constructions of complementary sequence sets and Complete complementary Codes by Ideal Two-Level Autocorrelation sequences and Permutation Polynomials

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第7期69卷 4723-4739页

作者： Wang, Zilong Gong, Guang Xidian Univ Sch Cyber Engn State Key Lab Integrated Serv Networks Xian 710071 Peoples R China Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

In this paper, we further investigate the constructions of complementary sequence sets (CSSs) and complete complementary codes (CCCs) by Butson-type Hadamard matrices. By taking the algebraic structure of Butson-type Hadamard (BH) matrices into consideration, we obtain the explicit representation of the d-linear terms and d-quadratic terms, which are ingredients to construct CSSs and CCCs. In particular, we derive the d-quadratic terms determined by DFT matrices and BH matrices constructed from 2-level autocorrelation sequences, which yields two type of new contructions. We show that inequivalent BH matrices produce different CSSs and CCCs, which proves that our constructed CSSs and CCCs are new. As a consequence of the first type of the constructions, not only a large number of p-ary CSSs and CCCs of size p (p prime) have been proposed, which were never reported in the literature, but also a theory linking these CSSs of p-ary sequences and the generalized Reed-Muller codes proposed by Kasami et al. is shown. These codes enjoy good error-correcting capability, tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using p(n) subcarriers. As a consequence of the second type of the constructions, we reveal an extremely fascinating hidden connection between the sequences in aperiodic CSSs and CCCs and the sequences with ideal period 2-level autocorrelation, through their trace representations and permutation polynomials over finite fields.

关键词： complementary sequence set complete com-plementary codes permutation polynomial generalized Reed-Muller codes 2-level autocorrelation

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New z-complementary/complementary sequence sets with non-power-of-two length and low PAPR

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND sequenceS 2022年第4期14卷 817-832页

作者： Shen, Bingsheng Yang, Yang Fan, Pingzhi Zhou, Zhengchun Southwest Jiaotong Univ Sch Math Chengdu Peoples R China Southwest Jiaotong Univ Key Lab Informat Coding & Transmiss Chengdu Peoples R China

sequences with low peak-to-average power ratio (PAPR) and desirable lengths are useful and important for orthogonal frequency division multiplexing (OFDM) systems. In this paper, based on the generalized Boolean functions (GBFs), a class of q-ary Z-complementary sequence sets (ZCSSs) and a class of complementary sequence sets (CSSs) are constructed. The obtained new ZCSSs and CSSs have low PAPR and non-power-of-two lengths.

关键词： Orthogonal frequency division multiplexing (OFDM) Peak-to-average power ratio (PAPR) Z-complementary sequence set complementary sequence set Generalized Boolean function

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BER Performance of Walsh Hadamard Like Codes Based on complementary sequence sets in a CDMA and Cognitive Underlay System

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WIRELESS PERSONAL COMMUNICATIONS 2013年第2期71卷 1311-1329页

作者： Suchitra, G. Valarmathi, M. L. Sri Krishna Coll Technol Dept ECE Coimbatore Tamil Nadu India Govt Coll Technol Dept CSE Coimbatore Tamil Nadu India

In this paper, a method of constructing a sequence set similar to Walsh Hadamard (WH) codes is described. In general, two complementary sequence set of length 2 is used as a basic kernel to construct WH codes. In this work, four complementary sequence set of length 3 is used as a basic kernel. The proposed code set have a nearly non linear phase sequences with a more evenly spread frequency spectrum when compared with WH codes. It is shown that the proposed spreading codes perform comparable to WH in a Direct sequence code division multiple access (DS-CDMA) system in an Additive White Gaussian Noise and Rayleigh channel at a reduced code length. In this work, bit error rate performance of the Underlay Cognitive Radio system implemented using DS-CDMA system is simulated. Primary and Secondary Users are distinguished by assigning spreading codes from different families and it is assumed that the channel information is known by both the Primary and Secondary User receivers. This new code set offers good performance in a Cognitive Radio Underlay system.

关键词： complementary sequence set Multi-path interference Multiple access interference Primary User Secondary User Cognitive Radio

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Two constructions for 16-QAM complementary sequence sets with non-power-of-two length

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND sequenceS 2020年第3期12卷 349-362页

作者： Zhou, Yajing Zhou, Zhengchun Yang, Yang Wang, Yong Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu Sichuan Peoples R China State Key Lab Cryptol POB 5159 Beijing 100878 Peoples R China Southwest Jiaotong Univ Sch Math Chengdu Sichuan Peoples R China Southwest Jiaotong Univ Sch Phys Sci & Technol Chengdu Sichuan Peoples R China

complementary sequences with quadrature amplitude modulation (QAM) symbols have important applications in OFDM communication systems. The objective of this paper is to present two constructions of 16-QAM complementary sequence sets of size 4. The first construction generates four complementary sequences of length L = 2(m- 1) + 2(v), where m and v are two positive integers with 1 <= v <= m - 1. The second one leads to four complementary sequences of length L = 2(m- 1) + 1. It turns out that the peak-to-mean envelope power ratios (PMEPRs) of constructed complementary sequence sets are upper bounded by 4.

关键词： complementary sequence set QAM OFDM Peak-to-mean envelope power ratio (PMEPR)

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Designing complementary sequence sets With Impulse Like complementary Auto-Correlation Function

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IEEE COMMUNICATIONS LETTERS 2021年第5期25卷 1417-1421页

作者： Sankuru, Surya Prakash Babu, Prabhu Indian Inst Technol Delhi New Delhi 110016 India

In this letter, we address the problem of designing unit modulus complementary sequence set with impulse-like complementary auto-correlation function which has immense potential with applications in ultra wide-band (UWB) communication system, code-division multiple-access (CDMA) system and active sensing systems like MIMO RADAR and SONAR. We have formulated the design problem as the minimization of complementary peak side-lobe level and proposed a monotonic algorithm based on the majorization-minimization technique. Through numerical simulations, we show the construction of sequence sets (of different lengths) with impulse like complementary auto-correlation - which is first of its kind in the sequence design literature. We also discuss the computationally efficient implementation of the proposed algorithm via FFT, IFFT operations.

关键词： Cascading style sheets Manganese Measurement Multiaccess communication Correlation Minimization MIMO radar complementary sequence set UWB CDMA majorization-minimization MIMO RADAR peak side-lobe level waveform design

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4^q-QAM complementary sequence sets with Non-Power-of-Two Length 9

4<SUP>q</SUP>-QAM Complementary Sequence Sets with Non-Power...

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9th International Workshop on Signal Design and its Applications in Communications (IWSDA)

作者： Zhou, Yajing Zhou, Zhengchun Yang, Yang Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu Peoples R China Southwest Jiaotong Univ Sch Math Chengdu Peoples R China

ISBN: (纸本)9781728116693

complementary sequences with quadrature amplitude modulation (QAM) are proposed to deal with the high peak-to-mean envelope power ratio (PMEPR) problem in Orthogonal frequency-division multiplexing (OFDM) systems. There have been many constructions of 4(q)-QAM Golay complementary sequences of length 2(m). This paper presents a construction of 4(q)-QAM complementary sequence sets of size 4 with non-power-of-two lengths, whose PMEPRs are upper bounded by 4. The number of 4(q)-QAM complementary sequences generated from this construction is also calculated in this paper.

关键词： complementary sequence set quadrature amplitude modulation (QAM) Orthogonal frequency-division multiplexing (OFDM) peak-to-mean envelope power ratio (PMEPR) Reed-Muller code

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16-QAM Golay, Periodic and Z-complementary sequence sets

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2012年第11期E95A卷 2084-2089页

作者： Zeng, Fanxin Zeng, Xiaoping Zhang, Zhenyu Xuan, Guixin Chongqing Univ Coll Commun Engn Chongqing 400044 Peoples R China Chongqing Commun Inst Chongqing Key Lab Emergency Commun Chongqing 400035 Peoples R China

In contemporary communications, Golay, periodic and Z-complementary sequence sets play a very important role, since such sequence sets possess impulse-like or zero correlation zone (ZCZ) autocorrelation. On the other hand, the advantages of the signals over the quadrature amplitude modulation (QAM) constellation are more and more prominent. Hence, the design of such sequence sets over the QAM constellation has turned into one of the all-important issues in communications. Therefore, the construction methods of such sequence sets over the 16-QAM constellation are investigated, in this letter, and our goals are arrived at by the known quaternary Golay, periodic and Z-complementary sequence sets. Finally, many examples illuminate the validity of the proposed methods,

关键词： complementary sequence set aperiodic and periodic correlation 16-QAM constellation quaternary sequence

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New Construction of complementary sequence (or Array) sets and Complete complementary Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第7期67卷 4902-4928页

作者： Wang, Zilong Ma, Dongxu Gong, Guang Xue, Erzhong Xidian Univ Sch Cyber Engn State Key Lab Integrated Serv Networks Xian 710071 Peoples R China Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

A new method to construct q-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size N is proposed by using desired para-unitary (PU) matrices. The concept of seed PU matrices is introduced and a systematic approach on how to compute the explicit forms of the functions in constructed CSSs and CCCs from the seed PU matrices is given. A general form of these functions only depends on a basis of the functions from Z(N) to Z(q) and representatives in the equivalent class of Butson-type Hadamard (BH) matrices. Especially, the realization of Golay pairs from our general form exactly coincides with the standard Golay pairs. The realization of ternary complementary sequences of size 3 is first reported here. For the realization of the quaternary complementary sequences of size 4, almost all the sequences derived here are never reported before. Generalized seed PU matrices and the recursive constructions of the desired PU matrices are also studied, and a large number of new constructions of CSSs and CCCs are given accordingly. From the perspective of this paper, all the known results of CSSs and CCCs with explicit GBF form in the literature (except non-standard Golay pairs) are constructed from the WHT matrices. This suggests that the proposed method with other BH matrices will yield a large number of new CSSs and CCCs with the significantly increasing number of the sequences of low peak-to-mean envelope power ratio.

关键词： complementary sequence set complete complementary codes Hadamard matrix Boolean function PMEPR

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sequences with ideal auto-correlation derived from group actions

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND sequenceS 2024年第5期16卷 909-920页

作者： Xiao, Hongyang Cao, Xiwang Nanjing Univ Aeronaut & Astronaut Coll Math Nanjing 211106 Jiangsu Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Math Key Lab Math Modelling & High Performance Comp Air MIIT Nanjing 211106 Peoples R China

Bent functions have a number of practical applications in cryptography, coding theory, and other fields. Fourier transform is a key tool to study bent functions on finite abelian groups. Using Fourier transforms, in this paper, we first present two necessary and sufficient conditions on the existence of bent functions via faithful actions of finite abelian groups and then show two constructions of sequences with ideal auto-correlation (SIACs). In addition, we construct a periodic complementary sequence set (PCSS) by rearranging a periodic multiple shift sequence (PMSS) corresponding to a bent function on a finite abelian group. Some concrete constructions of SIACs and PCSSs are provided to illustrate the efficiency of our methods.

关键词： Bent function Fourier transform Group action complementary sequence set

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