长度为奇素数的完备高斯整数序列构造法
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摘要
提出一类基于分圆类构造完备高斯整数序列的方法。分别通过有限域GF(p)上的2阶和4阶分圆类,构造得到自由度分别为3和5的高斯整数序列,序列长度为奇素数,该序列具有良好的完备自相关性能。该构造方法解决了以往利用分圆类计算复杂度较高,不易求解的问题,简化了序列的生成方法。该序列在无线通信中具有良好的应用前景。
Constructions of perfect Gaussian integer sequences(PGIS) based on the cyclotomic classes were proposed. The PGIS with degree 3 and 5 were constructed respectively from the cyclotomic classes of order 2 and 4. The presented sequences with odd prime length have ideal autocorrelations. The methods solved the problem that the traditional constructions of PGIS from the cyclotomic classes have high computational complexity. As a result, this kind of sequences will be useful in the applications of wireless communications.
Constructions of perfect Gaussian integer sequences(PGIS) based on the cyclotomic classes were proposed. The PGIS with degree 3 and 5 were constructed respectively from the cyclotomic classes of order 2 and 4. The presented sequences with odd prime length have ideal autocorrelations. The methods solved the problem that the traditional constructions of PGIS from the cyclotomic classes have high computational complexity. As a result, this kind of sequences will be useful in the applications of wireless communications.
引文
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[15]CHANG K J,CHANG H H.Perfect Gaussian integer sequences of period pk with degrees equal to or less than k+1[J].IEEE Transactions on Communications,2017,65(9):3723-3733.
[16]YANG Y,TANG X H,ZHOU Z C.Perfect Gaussian integer sequences of odd prime length[J].IEEE Signal Processing Letters,2012,19(10):615-618.
[17]STORER T.Cyclotomy and difference sets[M].Chicago:Markham Publishing Company.1967.
[18]DING C,YIN J.Sets of optimal frequency hopping sequences[J].IEEE Transactions on Information Theory,2008,54(8):3741-3745.
[19]BENEDETTO J J,KONSTANTINIDIS I,RANGASWAMY M.Phase-coded waveforms and their design[J].IEEE Signal Processing Magazine,2009,26(1):22-31.
[2]YU N Y,GONG G.New binary sequences with optimal autocorrelation magnitude[J].IEEE Transactions on Information Theory,2008,54(10):4771-4779.
[3]WANG S H,LI C P,LEE K C,et al.A novel low-complexity precoded OFDM system with reduced PAPR[J].IEEE Transactions on Signal Processing,2015,63(6):1366-1376.
[4]MILEWSKI A.Periodic sequences with optimal properties for channel estimation and fast start-up equalization[J].Journal of Research&Development,1983,27(5):426-431.
[5]LUKE H D,SCHOTTEN H D,HADINEJAD M H.Binary and quadriphase sequences with optimal autocorrelation properties:a survey[J].IEEE Transactions on Information Theory,2003,49(12):3271-3282.
[6]FAN P Z,DARNELL M.Maximal length sequences over Gaussian integers[J].Electronics Letters,1994,30(16):1286-1287.
[7]PEI S C,CHANG K W.Perfect Gaussian integer sequences of arbitrary length[J].IEEE Signal Processing Letters,2014,22(8):1040-1044.
[8]CHANG H H,LI C P,LEE C D,et al.Perfect Gaussian integer sequences of arbitrary composite length[J].IEEE Transactions on Information Theory,2015,61(7):4107-4115.
[9]PENG X P,XU C Q.New constructions of perfect Gaussian integer sequences of even length[J].IEEE Communications Letters,2014,18(9):1547-1550.
[10]WANG S H,LI C P,CHANG H H,et al.A systematic method for constructing sparse Gaussian integer sequences with ideal periodic autocorrelation functions[J].IEEE Transactions on Communications,2016,64(1):365-376.
[11]LEE C D,HUANG Y P,CHANG Y,et al.Perfect Gaussian integer sequences of odd period 2m-1[J].IEEE Signal Processing Letters,2015,22(7):881-885.
[12]LEE C D,LI C P,CHANG H H,et al.Further results on degree-2perfect Gaussian integer sequences[J].IET Communications,2016,10(12):1542-1552.
[13]LEE C D,HONG S H.Generation of long perfect Gaussian integer sequences[J].IEEE Signal Processing Letters,2017,24(4):515-519.
[14]LEE C D,CHEN Y H.Families of Gaussian integer sequences with high energy efficiency[J].IET Communications,2016,10(17):2416-2421.
[15]CHANG K J,CHANG H H.Perfect Gaussian integer sequences of period pk with degrees equal to or less than k+1[J].IEEE Transactions on Communications,2017,65(9):3723-3733.
[16]YANG Y,TANG X H,ZHOU Z C.Perfect Gaussian integer sequences of odd prime length[J].IEEE Signal Processing Letters,2012,19(10):615-618.
[17]STORER T.Cyclotomy and difference sets[M].Chicago:Markham Publishing Company.1967.
[18]DING C,YIN J.Sets of optimal frequency hopping sequences[J].IEEE Transactions on Information Theory,2008,54(8):3741-3745.
[19]BENEDETTO J J,KONSTANTINIDIS I,RANGASWAMY M.Phase-coded waveforms and their design[J].IEEE Signal Processing Magazine,2009,26(1):22-31.