Golomb Costas序列的结构及其在OFDM系统中的应用

doi:10.3969/j.issn.1000-436x.2013.07.001

Abstract

Abstract:

Theory of structures of Golomb Costas arrays with 1-gap row and 1-gap column was established with the study of the properties and mathematical models of Golomb Costas arrays and their families which are obtained by the cyclic shift method. By conducting a number of researches on algebraic constructions and the auto- and cross-correlation properties of Golomb Costas arrays with 1-gap row and 1-gap column, certain theorems were confirmed. The design of frequency hopping codes and the distribution of them to the users were illustrated while the design of frequency hopping patterns was explored in OFDM system with Golomb Costas arrays with 1-gap row and 1-gap column. By designing fre-quency hopping codes with Golomb Costas ayrays with 1-gap row and 1-gap column, an algebraically constructed fre-quency hop code family can achieve ideal auto-correlation properties. And excellent cross-correlation performance can be obtained when the Doppler shifts are restricted in a w less communication system.

Key words: Golomb Costas arrays, cross-correlation function, cyclic shift, orthogonal frequency division multiplexing;, frequency hopping patterns

Jian-guo YAO,Yu-feng WANG,Wei HENG. Constructions of Golomb Costas arrays and their applications in OFDM systems[J]. Journal on Communications, 2013, 34(7): 1-13.

Figures/Tables 16

References 24

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本原元	本原元的各次幂
a=x=s³=s₁2=s₂6	a²=x2	a³=x+1	a⁴=x²+x	a⁵=x²+x+1	a⁶=x²+1	a⁷=1
?=x+1=?2=?15=?26	?²=x²+1	?³=x2	?⁴=x²+x+1	?⁵=x	?⁶=x²+x	?⁷=1
s=?=x²+x+1	s²=x+1	s³=x	s⁴=x²+1	s⁵=x²+x	s⁶=x2	s⁷=1
s₁=x²+x	s²=1 x	s₁3=x²+x+1	s₁4=x2	s₁5=x²+1	?16=x+1	s₁7=1
?1=x²	?12=x²+x	?13=x²+1	? 4=1 x	?15=x+1	?16=x²+x+1	?17=1
s₂=x²+1	s₂2=x²+x+1	s₂3=x²+x	s₂4=x+1	s₂5=x2	s⁶=2 x	s₂7=1
?2=s₁=x²+x	? 2=2 x	?23=x²+x+1	?24=x2	?25=x²+1	?26=x+1	?27=1

a=s=x+1	?=2x+1=?7=?-1	?=2x+2
a²=2x	?²=x	?2=2x
a³=2x+1	?³=x+1	?3=x+2
a⁴=2	?⁴=2	?4=2
a⁵=2x+2	?⁵=x+2	?5=x+1
a⁶=x	?⁶=2x	?6=x
a⁷=x+2	?⁷=2x+2	?7=2x+1
a⁸=1	?⁸=1	?8=1

Constructions of Golomb Costas arrays and their applications in OFDM systems

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频率	小区中子载波的分配1
	第1帧				第2帧				第3帧				第4帧
	1	2	3		1	2	3		1	2	3		1	2	3
0	1	10	9	8	7	6	5	4	3	2	1	10
1	6	5	4	3	2	1	10	9	8	7	6	5
2	2	1	10	9	8	7	6	5	4	3	2	1
3	5	4	3	2	1	10	9	8	7	6	5	4
4	10	9	8	7	6	5	4	3	2	1	10	9
5	8	7	6	5	4	3	2	1	10	9	8	7
6	7	6	5	4	3	2	1	10	9	8	7	6
7	9	8	7	6	5	4	3	2	1	10	9	8
8	3	2	1	10	9	8	7	6	5	4	3	2
9	4	3	2	1	10	9	8	7	6	5	4	3
10	×	×	×	×	×	×	×	×	×	×	×	×

频率	小区2中子载波的分配
	第1帧				第2帧				第3帧				第4帧
	1	2	3		1	2	3		1	2	3		1	2	3
0	1	10	9	8	7	6	5	4	3	2	1	10
1	10	9	8	7	6	5	4	3	2	1	10	9
2	8	7	6	5	4	3	2	1	10	9	8	7
3	7	6	5	4	3	2	1	10	9	8	7	6
4	9	8	7	6	5	4	3	2	1	10	9	8
5	3	2	1	10	9	8	7	6	5	4	3	2
6	4	3	2	1	10	9	8	7	6	5	4	3
7	×	×	×	×	×	×	×	×	×	×	×	×
8	6	5	4	3	2	1	10	9	8	7	6	5
9	2	1	10	9	8	7	6	5	4	3	2	1
10	5	4	3	2	1	10	9	8	7	6	5	4

频率	小区3中子载波的分配
	第1帧				第2帧				第3帧				第4帧
	1	2	3		1	2	3		1	2	3		1	2	3
0	1	10	9	8	7	6	5	4	3	2	1	10
1	9	8	7	6	5	4	3	2	1	10	9	8
2	3	2	1	10	9	8	7	6	5	4	3	2
3	4	3	2	1	10	9	8	7	6	5	4	3
4	×	×	×	×	×	×	×	×	×	×	×	×
5	6	5	4	3	2	1	10	9	8	7	6	5
6	2	1	10	9	8	7	6	5	4	3	2	1
7	5	4	3	2	1	10	9	8	7	6	5	4
8	10	9	8	7	6	5	4	3	2	1	10	9
9	8	7	6	5	4	3	2	1	10	9	8	7
10	7	6	5	4	3	2	1	10	9	8	7	6

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