最优单次重合跳频序列集设计
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摘要
单次重合跳频序列可以最大限度地提高频率的使用率,降低频率相互之间的碰撞,被广泛用于多址通信中。文章基于中国剩余定理,构造了3类关于周期汉明相关理论界最优的单次重合跳频序列集,并给出了单次重合跳频序列集汉明相关的性质。
One-coincident frequency hopping sequence can maximize the frequencies usage and reduce the collision of frequencies with each other,and is widely used in multiple access communication. Based on the Chinese remainder theorem,this paper constructs three classes of one-coincident frequency hopping sequence sets with the optimal theoretical bounds of periodic Hamming correlation,and the properties of Hamming correlation of one-coincident frequency hopping sequence sets are given.
One-coincident frequency hopping sequence can maximize the frequencies usage and reduce the collision of frequencies with each other,and is widely used in multiple access communication. Based on the Chinese remainder theorem,this paper constructs three classes of one-coincident frequency hopping sequence sets with the optimal theoretical bounds of periodic Hamming correlation,and the properties of Hamming correlation of one-coincident frequency hopping sequence sets are given.
引文
[1]梅文华,王淑波,邱永红.跳频通信[M].北京:国防工业出版社,2005:28-87.
[2]SIMON M K,OMURA J K,SCHOLTZ R A,et al.Spread spectrum communications handbook[M].[S.l.]:Mc Graw-Hill Companies,2002.
[3]牛宪华,陈思利,王瑜.跳频序列研究综述[J].西华大学学报(自然科学版),2016,35(2):25-29.
[4]LEMPEL A,GREENBERGER H.Families of sequences with optimal hamming correlation properties[J].IEEE Transactions on Information Theory,1974,20(1):90-94.
[5]PENG D Y,FAN P Z.Lower bounds on the hamming auto-and cross-correlations of frequency-hopping sequences[J].IEEE Transactions on Information Theory,2004,50(9):2149.
[6]CHUNG J H,YANG K.Optimal frequency-hopping sequences with new parameters[J].IEEE Transactions on Information Theory,2010,56(4):1685-1693.
[7]GE G N,MIAO Y,YAO Z H,Optimal frequency hopping sequences:Auto-and cross-correlation properties[J].IEEE Transactions on Information Theory,2009,55(2):867-879.
[8]XU S D,CAO X W,XU G K.Recursive construction of optimal frequency-hopping sequence sets[J].IET Communications,2016,10(9):1080-1086.
[9]GONG G.New designs for signal sets with low cross correlation,balance property and large linear span:GF(p)case[J].IEEETransactions on Information Theory,2002,48(11):2847-2867.
[10]SHAAR A A,DAVIES P A.A survey of one-coincidence sequences for frequency-hopped spread-spectrums CDMA systems[J].IEEProceedings F-Communications Radar and Sign Processing,1984,131(7):719-724.
[11]CAO Z F,GE G N,MIAO Y.Combinatorial characterizations of one-coincidence frequency-hopping sequences[J].Designs,Codes and Cryptography,2006,41(2):177-184.
[12]PENG D Y,PENG T,TANG X H,et al.A class of optimal frequency hopping sequences based upon the theory of power residues[C]//International Conference on Sequences and Their Applications.Berlin Heidelberg:Springer,2008:188-196.
[13]WANG H,HUANG P.Construction of a one-coincidence frequency-hopping sequence set with optimal performance[C]//Proc Second Int Conf on Mechatronics and Automatic Control.Cham,Switzerland:Lecture Notes in Electrical Engineering,2015(334):915-923.
[14]CHUNG J H,GONG G,YANG K.New families of optimal frequency-hopping sequences of composite lengths[J].IEEE Transactions on Information Theory,2014,60(6):3688-3697.
[15]REN W L,FU F W,ZHOU Z C.New sets of frequencyhopping sequences with optimal Hamming correlation[J].Designs,Codes and Cryptography,2014,72(2):423-434.
[16]徐善顶,曹喜望,许广魁.由交织技术构建新的最优跳频序列族[J].工程数学学报,2017,34(3):221-231.
[17]NIU X H,PENG D Y,LIU F.Lower bounds on the maximum partial correlations of frequency-hopping sequence set with low hit zone[J].IEICE Transactions on Fundamentals of Electronics Communications&Computer Sciences,2010,93(11):2227-2231.
[18]IVAN N,HERBERT S Z,HUGH L M.An introduction to the theory of numbers[M].5th.Hoboken,NJ,USA:John Wiley Sons,1991.
[19]REN W L,FU F W,WANG F,et al.A class of optimal onecoincidence frequency-hopping sequence sets with composite length[J].IEICE Transactions on Fundamentals of Electronics Communications&Computer Sciences,2017,100(11):2528-2533.
[2]SIMON M K,OMURA J K,SCHOLTZ R A,et al.Spread spectrum communications handbook[M].[S.l.]:Mc Graw-Hill Companies,2002.
[3]牛宪华,陈思利,王瑜.跳频序列研究综述[J].西华大学学报(自然科学版),2016,35(2):25-29.
[4]LEMPEL A,GREENBERGER H.Families of sequences with optimal hamming correlation properties[J].IEEE Transactions on Information Theory,1974,20(1):90-94.
[5]PENG D Y,FAN P Z.Lower bounds on the hamming auto-and cross-correlations of frequency-hopping sequences[J].IEEE Transactions on Information Theory,2004,50(9):2149.
[6]CHUNG J H,YANG K.Optimal frequency-hopping sequences with new parameters[J].IEEE Transactions on Information Theory,2010,56(4):1685-1693.
[7]GE G N,MIAO Y,YAO Z H,Optimal frequency hopping sequences:Auto-and cross-correlation properties[J].IEEE Transactions on Information Theory,2009,55(2):867-879.
[8]XU S D,CAO X W,XU G K.Recursive construction of optimal frequency-hopping sequence sets[J].IET Communications,2016,10(9):1080-1086.
[9]GONG G.New designs for signal sets with low cross correlation,balance property and large linear span:GF(p)case[J].IEEETransactions on Information Theory,2002,48(11):2847-2867.
[10]SHAAR A A,DAVIES P A.A survey of one-coincidence sequences for frequency-hopped spread-spectrums CDMA systems[J].IEEProceedings F-Communications Radar and Sign Processing,1984,131(7):719-724.
[11]CAO Z F,GE G N,MIAO Y.Combinatorial characterizations of one-coincidence frequency-hopping sequences[J].Designs,Codes and Cryptography,2006,41(2):177-184.
[12]PENG D Y,PENG T,TANG X H,et al.A class of optimal frequency hopping sequences based upon the theory of power residues[C]//International Conference on Sequences and Their Applications.Berlin Heidelberg:Springer,2008:188-196.
[13]WANG H,HUANG P.Construction of a one-coincidence frequency-hopping sequence set with optimal performance[C]//Proc Second Int Conf on Mechatronics and Automatic Control.Cham,Switzerland:Lecture Notes in Electrical Engineering,2015(334):915-923.
[14]CHUNG J H,GONG G,YANG K.New families of optimal frequency-hopping sequences of composite lengths[J].IEEE Transactions on Information Theory,2014,60(6):3688-3697.
[15]REN W L,FU F W,ZHOU Z C.New sets of frequencyhopping sequences with optimal Hamming correlation[J].Designs,Codes and Cryptography,2014,72(2):423-434.
[16]徐善顶,曹喜望,许广魁.由交织技术构建新的最优跳频序列族[J].工程数学学报,2017,34(3):221-231.
[17]NIU X H,PENG D Y,LIU F.Lower bounds on the maximum partial correlations of frequency-hopping sequence set with low hit zone[J].IEICE Transactions on Fundamentals of Electronics Communications&Computer Sciences,2010,93(11):2227-2231.
[18]IVAN N,HERBERT S Z,HUGH L M.An introduction to the theory of numbers[M].5th.Hoboken,NJ,USA:John Wiley Sons,1991.
[19]REN W L,FU F W,WANG F,et al.A class of optimal onecoincidence frequency-hopping sequence sets with composite length[J].IEICE Transactions on Fundamentals of Electronics Communications&Computer Sciences,2017,100(11):2528-2533.