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Yong Liang Guan - One of the best experts on this subject based on the ideXlab platform.
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New Sets of Optimal Odd-Length Binary Z-Complementary Pairs
IEEE Transactions on Information Theory, 2020Co-Authors: Avik Ranjan Adhikary, Zilong Liu, Sudhan Majhi, Yong Liang GuanAbstract:A Pair of sequences is called a Z-Complementary Pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay Complementary Pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width $({N}+1)/2$ (where N is the sequence length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths $2^{\alpha } \pm 1$ , where $\alpha $ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^\alpha 10^\beta 26^\gamma +1$ (where $\alpha,~\beta,~\gamma $ are non-negative integers and $\alpha \geq 1$ ) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn’s method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of $4 \times 10^{\beta -1} +1$ , $12 \times 26^{\gamma -1}+1$ and $12 \times 10^\beta 26^{\gamma -1}+1$ through proper insertions of GCPs of lengths $10^\beta,~26^\gamma, \text {and } 10^\beta 26^\gamma $ , respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs).
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Cross-Complementary Pairs for Optimal Training in Spatial Modulation over Frequency Selective Channels
arXiv: Information Theory, 2019Co-Authors: Zilong Liu, Yong Liang Guan, Ping Yang, Pei XiaoAbstract:The contributions of this paper are twofold: Firstly, we introduce a novel class of sequence Pairs, called "cross-Complementary Pairs (CCPs)". Unlike a Golay Complementary Pair (GCP) which must be transmitted in two non-interfering channels, a CCP may be transmitted in two non-orthogonal channels and hence proper design should be conducted to minimize the cross-interference of the two constituent sequences. Properties and systematic constructions (from selected GCPs) of perfect CCPs are presented in this paper. Secondly, we show that CCPs can be utilized as a key component in designing training sequences for spatial modulation (SM) systems. In spite of a massive body of literature on SM, little has been understood on broadband SM training design. We prove and validate through simulation that our proposed SM training sequences derived from CCPs lead to optimal channel estimation performance over frequency-selective channels.
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New Optimal Binary Z -Complementary Pairs of Odd Length $2^m+3$
IEEE Signal Processing Letters, 2019Co-Authors: Bingsheng Shen, Yang Yang, Zhengchun Zhou, Pingzhi Fan, Yong Liang GuanAbstract:A Pair of sequences is called odd-length binary Z-Complementary Pair (OB-ZCP) if it is of odd-length and has zero aperiodic autocorrelation sums (AACSs) for all time-shifts within a certain region around the in-phase position, commonly known as zero correlation zone (ZCZ). There are two types of OB-ZCPs, namely Type-I OB-ZCPs and Type-II OB-ZCPs. Type-I OB-ZCPs have ZCZ around the in-phase position. Type-II OB-ZCPs have the ZCZ around the end-shift position. An OB-ZCP (Type-I or Type-II) of odd-length $N$ is called Z-optimal if it achieves a maximum ZCZ width of $(N+1)/2$ . To date, a systematic construction of Type-II Z-optimal OB-ZCPs exist only for very limited lengths of the form $2^{m}\pm 1$ , where $m$ is a positive integer. It employs insertion method and delete method on binary Golay Complementary Pairs (GCPs) of length $2^m$ derived from second order Reed-Muller codes. In this article, based on iterative insertion method, we construct Type-II Z-optimal OB-ZCPs of lengths $2^m+3$ .
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Optimal Binary Periodic Almost-Complementary Pairs
IEEE Signal Processing Letters, 2016Co-Authors: Avik Ranjan Adhikary, Zilong Liu, Yong Liang Guan, Sudhan Majhi, Srdjan Z. BudishinAbstract:A Pair of sequences is called a periodic Complementary Pair (PCP) if the periodic autocorrelations of the constituent sequences sum up to zero for all nonzero time shifts. Owing to the scarcity of PCPs, we investigate optimal binary periodic almost-Complementary Pairs (BP-ACPs), each displaying correlation property closest to that of PCP. We show that an optimal BP-ACP of even length $N$ has zero out-of-phase periodic autocorrelation sums (PACSs) except at the time shift of $N/2$ , where the corresponding PACS has minimum magnitude of 4. We also show that for any arbitrary odd $N$ , all the out-of-phase PACSs of an optimal BP-ACP should have identical magnitude of $\text{2}$ . A number of optimal BP-ACPs from analytical constructions as well as computer search are presented. In addition, our proposed optimal BP-ACPs for the even-length case lead to two new families of base-two almost difference families.
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On Even-Period Binary Z-Complementary Pairs with Large ZCZs
IEEE Signal Processing Letters, 2014Co-Authors: Zilong Liu, Udaya Parampalli, Yong Liang GuanAbstract:For an even-period binary Z-Complementary Pair (EB-ZCP), if it is not a Golay Complementary Pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2m+1+2m and Z=2m+1. Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2m+1, thus displaying a very close correlation property to that of GCPs.
Zilong Liu - One of the best experts on this subject based on the ideXlab platform.
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New Sets of Optimal Odd-Length Binary Z-Complementary Pairs
IEEE Transactions on Information Theory, 2020Co-Authors: Avik Ranjan Adhikary, Zilong Liu, Sudhan Majhi, Yong Liang GuanAbstract:A Pair of sequences is called a Z-Complementary Pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay Complementary Pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width $({N}+1)/2$ (where N is the sequence length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths $2^{\alpha } \pm 1$ , where $\alpha $ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^\alpha 10^\beta 26^\gamma +1$ (where $\alpha,~\beta,~\gamma $ are non-negative integers and $\alpha \geq 1$ ) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn’s method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of $4 \times 10^{\beta -1} +1$ , $12 \times 26^{\gamma -1}+1$ and $12 \times 10^\beta 26^{\gamma -1}+1$ through proper insertions of GCPs of lengths $10^\beta,~26^\gamma, \text {and } 10^\beta 26^\gamma $ , respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs).
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Cross-Complementary Pairs for Optimal Training in Spatial Modulation over Frequency Selective Channels
arXiv: Information Theory, 2019Co-Authors: Zilong Liu, Yong Liang Guan, Ping Yang, Pei XiaoAbstract:The contributions of this paper are twofold: Firstly, we introduce a novel class of sequence Pairs, called "cross-Complementary Pairs (CCPs)". Unlike a Golay Complementary Pair (GCP) which must be transmitted in two non-interfering channels, a CCP may be transmitted in two non-orthogonal channels and hence proper design should be conducted to minimize the cross-interference of the two constituent sequences. Properties and systematic constructions (from selected GCPs) of perfect CCPs are presented in this paper. Secondly, we show that CCPs can be utilized as a key component in designing training sequences for spatial modulation (SM) systems. In spite of a massive body of literature on SM, little has been understood on broadband SM training design. We prove and validate through simulation that our proposed SM training sequences derived from CCPs lead to optimal channel estimation performance over frequency-selective channels.
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Optimal Binary Periodic Almost-Complementary Pairs
IEEE Signal Processing Letters, 2016Co-Authors: Avik Ranjan Adhikary, Zilong Liu, Yong Liang Guan, Sudhan Majhi, Srdjan Z. BudishinAbstract:A Pair of sequences is called a periodic Complementary Pair (PCP) if the periodic autocorrelations of the constituent sequences sum up to zero for all nonzero time shifts. Owing to the scarcity of PCPs, we investigate optimal binary periodic almost-Complementary Pairs (BP-ACPs), each displaying correlation property closest to that of PCP. We show that an optimal BP-ACP of even length $N$ has zero out-of-phase periodic autocorrelation sums (PACSs) except at the time shift of $N/2$ , where the corresponding PACS has minimum magnitude of 4. We also show that for any arbitrary odd $N$ , all the out-of-phase PACSs of an optimal BP-ACP should have identical magnitude of $\text{2}$ . A number of optimal BP-ACPs from analytical constructions as well as computer search are presented. In addition, our proposed optimal BP-ACPs for the even-length case lead to two new families of base-two almost difference families.
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On Even-Period Binary Z-Complementary Pairs with Large ZCZs
IEEE Signal Processing Letters, 2014Co-Authors: Zilong Liu, Udaya Parampalli, Yong Liang GuanAbstract:For an even-period binary Z-Complementary Pair (EB-ZCP), if it is not a Golay Complementary Pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2m+1+2m and Z=2m+1. Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2m+1, thus displaying a very close correlation property to that of GCPs.
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Optimal Odd-Length Binary Z-Complementary Pairs
IEEE Transactions on Information Theory, 2014Co-Authors: Zilong Liu, Udaya Parampalli, Yong Liang GuanAbstract:A Pair of sequences is called a Golay Complementary Pair (GCP) if their aperiodic auto-correlation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 21026 (where α, β, γ are non-negative integers). To fill the gap left by the odd-lengths, we investigate the optimal oddlength binary Pairs which display the closest correlation property to that of GCPs. Our criteria of “closeness” is that each Pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic auto-correlation sums. Such optimal Pairs are called optimal odd-length binary Z-Complementary Pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families (ADF) which are useful in studying partially balanced incomplete block design (BIBD). Index Terms Aperiodic correlation, almost difference set (ADS), almost difference families (ADF), Golay Complementary Pair (GCP), zero-correlation zone (ZCZ), Z-Complementary Pair (ZCP).
Udaya Parampalli - One of the best experts on this subject based on the ideXlab platform.
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On Even-Period Binary Z-Complementary Pairs with Large ZCZs
IEEE Signal Processing Letters, 2014Co-Authors: Zilong Liu, Udaya Parampalli, Yong Liang GuanAbstract:For an even-period binary Z-Complementary Pair (EB-ZCP), if it is not a Golay Complementary Pair (GCP), we show that Z ≤ N-2, where N and Z denote the sequence length and the zero correlation zone (ZCZ) width, respectively. This result partially answers the Fan-Yuan-Tu conjecture in 2007. In addition, we present a construction of EB-ZCPs with large ZCZ widths, where N=2m+1+2m and Z=2m+1. Interestingly, each of the proposed EB-ZCPs features zero out-of-phase aperiodic auto-correlation sums except for the time-shift of ±2m+1, thus displaying a very close correlation property to that of GCPs.
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Optimal Odd-Length Binary Z-Complementary Pairs
IEEE Transactions on Information Theory, 2014Co-Authors: Zilong Liu, Udaya Parampalli, Yong Liang GuanAbstract:A Pair of sequences is called a Golay Complementary Pair (GCP) if their aperiodic auto-correlation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 21026 (where α, β, γ are non-negative integers). To fill the gap left by the odd-lengths, we investigate the optimal oddlength binary Pairs which display the closest correlation property to that of GCPs. Our criteria of “closeness” is that each Pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic auto-correlation sums. Such optimal Pairs are called optimal odd-length binary Z-Complementary Pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families (ADF) which are useful in studying partially balanced incomplete block design (BIBD). Index Terms Aperiodic correlation, almost difference set (ADS), almost difference families (ADF), Golay Complementary Pair (GCP), zero-correlation zone (ZCZ), Z-Complementary Pair (ZCP).
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on optimal binary z Complementary Pair of odd period
International Symposium on Information Theory, 2013Co-Authors: Zilong Liu, Yong Liang Guan, Udaya ParampalliAbstract:In this paper we introduce the optimal odd-period binary Z-Complementary Pairs (OB-ZCPs), which display properties similar to Golay Complementary Pairs. These Pairs have the maximum possible zero-correlation-zone (ZCZ) of width (N + 1)/2, where N denotes the sequence length, and the minimum possible magnitude of 2 for each out-of-zone aperiodic auto-correlation sum. Furthermore, we show that the optimal OB-ZCPs correspond to sets of almost difference families and present some of their interesting properties.
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ISIT - On optimal binary Z-Complementary Pair of odd period
2013 IEEE International Symposium on Information Theory, 2013Co-Authors: Zilong Liu, Yong Liang Guan, Udaya ParampalliAbstract:In this paper we introduce the optimal odd-period binary Z-Complementary Pairs (OB-ZCPs), which display properties similar to Golay Complementary Pairs. These Pairs have the maximum possible zero-correlation-zone (ZCZ) of width (N + 1)/2, where N denotes the sequence length, and the minimum possible magnitude of 2 for each out-of-zone aperiodic auto-correlation sum. Furthermore, we show that the optimal OB-ZCPs correspond to sets of almost difference families and present some of their interesting properties.
Robert W. Heath - One of the best experts on this subject based on the ideXlab platform.
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A quaternion-based approach to construct quaternary periodic Complementary Pairs
arXiv: Signal Processing, 2020Co-Authors: Nitin Jonathan Myers, Robert W. HeathAbstract:Two arrays form a periodic Complementary Pair if the sum of their periodic autocorrelations is a delta function. Finding such Pairs, however, is challenging for large arrays whose entries are constrained to a small alphabet. One such alphabet is the quaternary set which contains the complex fourth roots of unity. In this paper, we propose a technique to construct periodic Complementary Pairs defined over the quaternary set using perfect quaternion arrays. We show how new Pairs of quaternary sequences, matrices, and four-dimensional arrays that satisfy a periodic Complementary property can be constructed with our method.
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A Quaternion-Based Approach to Construct Quaternary Periodic Complementary Pairs
IEEE Communications Letters, 2020Co-Authors: Nitin Jonathan Myers, Robert W. HeathAbstract:Two arrays form a periodic Complementary Pair if the sum of their periodic autocorrelations is a delta function. Finding such Pairs, however, is challenging for large arrays whose entries are constrained to a small alphabet. One such alphabet is the quaternary set which contains the complex fourth roots of unity. In this letter, we propose a technique to construct periodic Complementary Pairs defined over the quaternary set using perfect quaternion arrays. We show how new Pairs of quaternary sequences, matrices, and four-dimensional arrays that satisfy a periodic Complementary property can be constructed with our method.
Minsoo Park - One of the best experts on this subject based on the ideXlab platform.
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a Complementary Pair lms algorithm for adaptive filtering
International Conference on Acoustics Speech and Signal Processing, 1997Co-Authors: Woojin Song, Minsoo ParkAbstract:This paper presents a new algorithm that can solve the problem of selecting appropriate update step size in the LMS algorithm. The proposed algorithm, called a Complementary Pair LMS (CP-LMS) algorithm, consists of two adaptive filters with different update step sizes operating in parallel, one filter re-initializing the other with the better coefficient estimates whenever possible. This new algorithm provides the faster convergence speed and the smaller steady-state error than those of a single filter with a fixed or variable step size.
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ICASSP - A Complementary Pair LMS algorithm for adaptive filtering
1997 IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: Woojin Song, Minsoo ParkAbstract:This paper presents a new algorithm that can solve the problem of selecting appropriate update step size in the LMS algorithm. The proposed algorithm, called a Complementary Pair LMS (CP-LMS) algorithm, consists of two adaptive filters with different update step sizes operating in parallel, one filter re-initializing the other with the better coefficient estimates whenever possible. This new algorithm provides the faster convergence speed and the smaller steady-state error than those of a single filter with a fixed or variable step size.