CN114499737A - Method for constructing non-periodic inter-group complementary sequence set based on DFT matrix - Google Patents

Method for constructing non-periodic inter-group complementary sequence set based on DFT matrix Download PDF

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CN114499737A
CN114499737A CN202210024018.XA CN202210024018A CN114499737A CN 114499737 A CN114499737 A CN 114499737A CN 202210024018 A CN202210024018 A CN 202210024018A CN 114499737 A CN114499737 A CN 114499737A
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CN114499737B (en
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陈晓玉
彭秀英
王成瑞
张钇涵
孙连峰
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Yanshan University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J11/00—Orthogonal multiplex systems, e.g. using WALSH codes
    • H04J11/0023—Interference mitigation or co-ordination
    • H04J11/005—Interference mitigation or co-ordination of intercell interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J11/00—Orthogonal multiplex systems, e.g. using WALSH codes
    • H04J11/0023—Interference mitigation or co-ordination
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Abstract

The invention provides a construction method of non-periodic intercycle complementary sequence set based on DFT matrix, which constructs a sequence set h of a multiplied by G sequences by arbitrarily selecting a circular Florentine array F of a multiplied by b order, arbitrarily selecting a positive integer G which is more than 1, G which is more than or equal to 0 and less than G, and making N be b.G.

Description

Method for constructing non-periodic inter-group complementary sequence set based on DFT matrix
Technical Field
The invention relates to the field of wireless spread spectrum communication, in particular to a construction method of a non-periodic inter-group complementary sequence set based on a DFT matrix.
Background
With the rapid development of the wireless communication field, the wireless communication field faces the problem of processing interference caused by access of massive users, and therefore, a wireless communication system is required to have higher frequency spectrum utilization rate and data transmission rate to support access of massive users. Sequence design has been a relatively critical technology in wireless communication systems, and especially, various sequences with excellent characteristics have important applications in various wireless communication fields.
Complementary sequences are of great interest because of their desirable auto-and cross-correlation properties and are widely used in modern communication systems. In a multi-carrier CDMA system, a complementary sequence with good performance can not only eliminate multiple access interference and multipath interference in the system, but also solve the problem of peak-to-average power ratio in the system, and simultaneously ensure higher information transmission rate and spectrum utilization rate. According to the theoretical limit of the complementary sequences, the number of complementary sequences must not exceed the number of subsequences, which greatly limits the number of users that can be supported by the complementary sequence set. To solve this problem for the set of complementary sequences, the scholars introduce the zero-correlation region into the set of complementary sequences to propose the set of zero-correlation region complementary sequences. As long as the time delay of the signal of the zero correlation zone complementary sequence set is within the length range of the zero correlation zone, the interference between users can be effectively inhibited and eliminated, and the purpose of expanding the number of sequences is achieved by reducing the correlation between the sequences. In a quasi-synchronous CDMA communication system in a multi-cell cellular environment, a single ZCZ sequence set can only solve the multi-address interference and the multi-path interference between users in a cell, and the user interference between cells still exists. In order to solve the interference caused by the user signals of the adjacent cells, the traditional communication system adopts a complex multi-user detection algorithm and a power control algorithm to reduce the interference among the cells. The traditional method can not completely eliminate the interference, but also increases the complexity of the system. According to the research, the interference among cells can be suppressed by designing a multi-subset spread spectrum sequence set with good cross-correlation performance among sets, and then scholars put forward the concept of an inter-set complementary sequence set. The interclass complementary sequence set is a special ZCZ complementary sequence set, and the sequence set is divided into groups, each group comprises a plurality of complementary sequences, the cross-correlation function of the sequences in the same group is zero in the range of a zero-correlation zone, and the correlation function between the sequences in different groups is zero in the range of the whole sequence length. Theoretically, when the time delay of the signal is in the length range of the zero correlation zone, the interference between users in the same cell can be suppressed and eliminated, and the interference from different cells can be completely eliminated. During actual communication, the inter-group complementary sequence sets are allocated to different cell users. The intergroup complementary sequence set can be applied to a quasi-synchronous CDMA communication system and can also well work in an asynchronous CDMA system. Compared with other systems, the IGC-CDMA system based on inter-group sequence set communication has higher frequency spectrum utilization rate and good anti-interference capability, and can effectively eliminate the interference among different cells. However, the current methods for constructing the inter-group complementary sequence set are not many, and the existing construction methods almost construct periodic inter-group complementary sequence sets, and it can be known from the definition of the correlation function that the sequences satisfying the aperiodic character certainly satisfy the corresponding periodic character, and vice versa, so the aperiodic inter-group complementary sequences have wider application in communication systems.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a construction method of a non-periodic intercycle complementary sequence set based on a DFT matrix, which is suitable for a quasi-synchronous CDMA system, realizes complete elimination of inter-cell interference, completely eliminates the interference in a cell within the length Z of a zero correlation zone, can flexibly set the length Z of the zero correlation zone, has good flexibility and easy generation, and can provide a considerable amount of intercycle complementary sequence sets for a communication system.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a construction method of non-periodic interclass complementary sequence sets based on DFT matrix includes the following steps:
s1, selecting any circular Florentine array F with a step of a multiplied by b;
s2, randomly selecting a positive integer G > 1, enabling G to be more than or equal to 0 and less than G, and enabling N to be b.G to construct a sequence set h of a multiplied by G sequences;
s3, constructing an aperiodic intercycle inter-group complementary sequence set based on the circular Florentine array and the multiphase DFT matrix.
The technical scheme of the invention is further improved as follows: the a-th of the circular Florentine array F in the step S1iThe rows are represented as
Figure BDA0003463698550000021
0≤ai＜a；
Figure BDA0003463698550000022
Is ZbA permutation function of (a), wherein Zb(0, 1,2, …, b-1), provided that for any 0 < τ < b, 0 ≦ l < b, there is
Figure BDA0003463698550000031
And
Figure BDA0003463698550000032
are all aiThe value of the row; a isi，ajAre all [0, a-1 ]]Any number within the range, for any 0 < ai≠ajA, 0 ≦ τ < b, with and with only one solution such that
Figure BDA0003463698550000033
This is true.
The technical scheme of the invention is further improved as follows: in step S1, the maximum number of rows of the circular Florentine array F is denoted as F (b), a circular Florentine array of F (b) × b order may be constructed, and when b is an even number, F (b) ═ 1; when p is the minimum prime factor of b, p-1 is less than or equal to F (b) is less than or equal to b-1; when b is a prime number, f (b) b-1; when b.ident.15 (mod18), F (b). ltoreq.b-3.
The technical scheme of the invention is further improved as follows: the specific steps of step S2 are as follows:
s21, selecting a positive integer G > 1, wherein G is more than or equal to 0 and less than G, and enabling N to be b.G;
s22, constructing a sequence set h, wherein the sequence set h comprises a multiplied by G sequences, and the sequence set h is expressed as
Figure BDA0003463698550000034
Each sequence
Figure BDA0003463698550000035
B, and each sequence is specifically constructed as follows:
Figure BDA0003463698550000036
wherein
Figure BDA0003463698550000037
The technical scheme of the invention is further improved as follows: the step S3 selects two NxN-order multi-phase DFT matrixes
Figure BDA0003463698550000038
And
Figure BDA0003463698550000039
having the form:
Figure BDA00034636985500000310
wherein
Figure BDA00034636985500000311
Wherein
Figure BDA00034636985500000312
Representing the elements in row i and column j of the matrix U,
Figure BDA00034636985500000313
representing the elements in row i and column j of the matrix V.
The technical scheme of the invention is further improved as follows: in the step S3, a pieces of a matrix are constructed based on the circular Florentine array and the multiphase DFT matrix
Figure BDA00034636985500000314
Non-periodic inter-group complementary sequence set S ═ S (S)0,S1,…,Sa-1)；
Complementary sequence set between each group
Figure BDA0003463698550000041
A sequence set comprising G groups;
each group consisting of
Figure BDA0003463698550000042
Comprises N complementary sequences;
each complementary sequence
Figure BDA0003463698550000043
Comprises N subsequences;
each subsequence
Figure BDA0003463698550000044
The length is N;
the length Z of the zero correlation zone in the group is b;
the specific construction of each subsequence is as follows:
Figure BDA0003463698550000045
wherein: m is more than or equal to 0 and less than or equal to N-1, N is more than or equal to 0 and less than or equal to N-1, and t is more than or equal to 0 and less than or equal to N-1.
The technical scheme of the invention is further improved as follows: when 0 is more than or equal to ai≠ajWhen a is less than or equal to a-1, for
Figure BDA0003463698550000046
Two sequences of any of
Figure BDA0003463698550000047
And
Figure BDA0003463698550000048
is a cross-correlation function of
Figure BDA0003463698550000049
Wherein tau is more than or equal to 0 and less than or equal to Z-1; when 0 is less than or equal to gi≠gj≤G-1，gi，gjIs [0, G-1 ]]Any number within the range to
Figure BDA00034636985500000410
Two sequences of any of
Figure BDA00034636985500000411
And
Figure BDA00034636985500000412
is a cross-correlation function of
Figure BDA00034636985500000413
Wherein tau is more than or equal to 0 and less than or equal to N-1.
Due to the adoption of the technical scheme, the invention has the technical progress that:
the invention provides a method for constructing an aperiodic intercycle inter-group complementary sequence set based on a multiphase DFT matrix and a circular Florentine array. Constructing a sequence set h of a x G sequences by taking an a x b-order circular Florentine array F, taking a positive integer G > 1, making G more than or equal to 0 and less than G, making N equal to b.G, taking two N x N-order multiphase DFT matrixes, and constructing a plurality of a on the basis of the generated multiphase DFT matrixes and the circular Florentine array
Figure BDA00034636985500000414
A method of aperiodic interclass complementary sequence sets, each interclass complementary sequence set comprising G group sequence sets, each sequence set comprising N complementary sequences, each complementary sequence comprising N subsequences of length N, and the length Z of the zero correlation region within a group being b. In addition, there is a low correlation between the complementary sequence sets between different groups, i.e., when 0. ltoreq. ai≠ajWhen a is less than or equal to a-1, for
Figure BDA00034636985500000415
Two sequences of any of
Figure BDA00034636985500000416
And
Figure BDA00034636985500000417
is a cross-correlation function of
Figure BDA0003463698550000051
Wherein tau is more than or equal to 0 and less than or equal to Z-1; when 0 is less than or equal to gi≠gjG-1 or less, for
Figure BDA0003463698550000052
Figure BDA0003463698550000053
Two sequences of any of
Figure BDA0003463698550000054
And
Figure BDA0003463698550000055
is a cross-correlation function of
Figure BDA0003463698550000056
Wherein tau is more than or equal to 0 and less than or equal to N-1. The construction method of the invention is suitable for quasi-synchronous CDMA system, can realize complete elimination of inter-cell interference, complete elimination of inter-cell interference in the length Z of the zero correlation zone, flexible setting of the length Z of the zero correlation zone, good flexibility, easy generation, low correlation among different inter-group complementary sequence sets, and can provide a considerable number of inter-group complementary sequence sets for the communication system.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is the sequence within the group in example 1
Figure BDA00034636985500000513
And
Figure BDA00034636985500000514
a simulated graph of the correlation function;
FIG. 3 is the sequence between groups in example 1
Figure BDA00034636985500000515
And
Figure BDA00034636985500000516
a simulated graph of the correlation function;
FIG. 4 is a sequence set
Figure BDA00034636985500000519
Any two of the sequences
Figure BDA00034636985500000517
And
Figure BDA00034636985500000518
simulation graphs of the correlation functions.
Detailed Description
The present invention is further illustrated in detail below with reference to examples:
as shown in fig. 1, a method for constructing an aperiodic interclass complementary sequence set based on a DFT matrix includes the following steps:
s1, selecting any circular Florentine array F with a step of a multiplied by b;
a of circular Florentine array FiThe rows are represented as
Figure BDA0003463698550000057
0≤ai＜a；
Figure BDA0003463698550000058
Is ZbA permutation function of (a), wherein Zb(0, 1,2, …, b-1), provided that for any 0 < τ < b, 0 ≦ l < b, there is
Figure BDA0003463698550000059
Figure BDA00034636985500000510
And
Figure BDA00034636985500000511
are all aiThe value of the row; a isi，ajAre all [0, a-1 ]]Any number within the range, for any 0 < ai≠ajA, 0 ≦ τ < b, with and with only one solution such that
Figure BDA00034636985500000512
This is true.
In step S1, the maximum number of rows of the circular Florentine array F is denoted as F (b), a circular Florentine array of F (b) × b order may be constructed, and when b is an even number, F (b) ═ 1; when p is the minimum prime factor of b, p-1 is less than or equal to F (b) is less than or equal to b-1; when b is a prime number, f (b) b-1; when b.ident.15 (mod18), F (b). ltoreq.b-3.
S2, randomly selecting a positive integer G > 1, enabling G to be more than or equal to 0 and less than G, and enabling N to be b.G to construct a sequence set h of a multiplied by G sequences; the method comprises the following specific steps:
s21, selecting a positive integer G > 1, wherein G is more than or equal to 0 and less than G, and enabling N to be b.G;
s22, constructing a sequence set h, wherein the sequence set h comprises a multiplied by G sequences, and the sequence set h is expressed as
Figure BDA0003463698550000061
Each sequence
Figure BDA0003463698550000062
B, and each sequence is specifically constructed as follows:
Figure BDA0003463698550000063
wherein
Figure BDA0003463698550000064
0≤l＜b。
S3, constructing an aperiodic intercycle inter-group complementary sequence set based on the circular Florentine array and the multiphase DFT matrix. Selecting two NXN-order polyphase DFT matrices
Figure BDA0003463698550000065
And
Figure BDA0003463698550000066
having the form:
Figure BDA0003463698550000067
wherein
Figure BDA0003463698550000068
Wherein
Figure BDA0003463698550000069
Representing the elements in row i and column j of the matrix U,
Figure BDA00034636985500000610
representing the elements in row i and column j of matrix V.
A pieces of structure are constructed based on circular Florentine array and multiphase DFT matrix
Figure BDA00034636985500000611
Non-periodic inter-group complementary sequence set S ═ S (S)0,S1,…,Sa-1)；
Complementary sequence set between each group
Figure BDA00034636985500000612
A sequence set comprising G groups;
each group consisting of
Figure BDA00034636985500000613
Comprises N complementary sequences;
each complementary sequence
Figure BDA00034636985500000614
Comprises N subsequences;
each subsequence
Figure BDA0003463698550000071
The length is N;
the length Z of the zero correlation zone in the group is b;
the specific construction of each subsequence is as follows:
Figure BDA0003463698550000072
wherein: m is more than or equal to 0 and less than or equal to N-1, N is more than or equal to 0 and less than or equal to N-1, and t is more than or equal to 0 and less than or equal to N-1.
When 0 is more than or equal to ai≠ajWhen a is less than or equal to a-1, for
Figure BDA0003463698550000073
Two sequences of any of
Figure BDA0003463698550000074
And
Figure BDA0003463698550000075
is a cross-correlation function of
Figure BDA0003463698550000076
Wherein tau is more than or equal to 0 and less than or equal to Z-1; when 0 is less than or equal to gi≠gj≤G-1，gi，gjIs [0, G-1 ]]Any number within the range to
Figure BDA0003463698550000077
Two sequences of any of
Figure BDA0003463698550000078
And
Figure BDA0003463698550000079
is a cross-correlation function of
Figure BDA00034636985500000710
Wherein tau is more than or equal to 0 and less than or equal to N-1. .
Example 1
S1, taking a circular Florentine array F with a step of a multiplied by b;
f (b) is the maximum row number of the array F, and let b be 5, F (b) b-1 be 4, then the circular Florentine array is:
Figure BDA00034636985500000711
s2, randomly selecting a positive integer G > 1, enabling G to be more than or equal to 0 and less than G, and enabling N to be b.G to construct a sequence set h of a multiplied by G sequences;
let G be 2, N be 5 × 2 be 10, and construct 4 sequence sets containing 2 sequences
Figure BDA00034636985500000712
Each sequence
Figure BDA00034636985500000713
Length of 5, and the specific construction of each sequence is as follows:
Figure BDA00034636985500000714
the specific sequence is as follows: h is0,0＝(0,1,2,3,4),h0,1＝(5,6,7,8,9),h1,0＝(0,2,4,1,3),h1,1＝(5,7,9,6,8),h2,0＝(0,3,1,4,2),h2,1＝(5,8,6,9,7),h3,0＝(0,4,3,2,1),h3,1＝(5,9,8,7,6)；
Taking two 10 multiplied by 10 order multiphase DFT matrixes;
Figure BDA0003463698550000081
s3, constructing a pieces based on the circular Florentine array and the multi-phase DFT matrix
Figure BDA0003463698550000082
And (3) non-periodic intercycle complementary sequence sets. The specific construction of each subsequence is as follows:
Figure BDA0003463698550000083
4 of the generated
Figure BDA0003463698550000084
And (2) non-periodic inter-group complementary sequence sets, each inter-group complementary sequence set comprising 2 group sequence sets, each sequence set comprising 10 complementary sequences, each complementary sequence comprising 10 subsequences of length 10, and the length of the zero correlation region in each group being Z-5. Only partial sequences are listed below:
Figure BDA0003463698550000085
Figure BDA0003463698550000091
as can be seen in example 1, when ai＝ajIn time, that is, in the same inter-group complementary sequence set, the cross-correlation function value between the sequences in a group is zero in the length Z of the zero correlation zone, as shown in fig. 2, thereby achieving complete cancellation of the interference in the cell in the length Z of the zero correlation zone. The cross-correlation function value between the inter-group sequences is zero for the entire sequence length as shown in fig. 3, thereby achieving complete cancellation of inter-cell interference. In addition, when 0 is not more than ai≠ajA-1 or less, i.e. the value of the cross-correlation function between sequences in the complementary sequence set between different groups
Figure BDA0003463698550000092
As shown in fig. 4, thereby achieving low correlation between complementary sequence sets between different groups.
The invention provides a method for constructing an aperiodic intercycle inter-group complementary sequence set based on a multiphase DFT matrix and a circular Florentine array. Constructing a sequence set h of a x G sequences by taking an a x b-order circular Florentine array F, taking a positive integer G > 1, making G more than or equal to 0 and less than G, making N-b.G, taking two N x N-order multiphase DFT matrixes, and constructing F (B) circular Florentine arrays based on the generated multiphase DFT matrixes and the circular Florentine arrays
Figure BDA0003463698550000093
A method of aperiodic interclass complementary sequence sets, each interclass complementary sequence set comprising G group sequence sets, each sequence set comprising N complementary sequences, each complementary sequence comprising N subsequences of length N, and the length Z of the zero correlation region within a group being b. In addition, there is a low correlation between the complementary sequence sets between different groups, i.e., when 0. ltoreq. ai≠ajWhen a is less than or equal to a-1, for
Figure BDA0003463698550000094
Two sequences of any of
Figure BDA0003463698550000095
And
Figure BDA0003463698550000096
is a cross-correlation function of
Figure BDA0003463698550000097
Wherein tau is more than or equal to 0 and less than or equal to Z-1; when 0 is less than or equal to gi≠gj≤G-1，gi，gjIs [0, G-1 ]]Any number within the range to
Figure BDA00034636985500000910
Two sequences of any of
Figure BDA0003463698550000098
And
Figure BDA0003463698550000099
is a cross-correlation function of
Figure BDA0003463698550000101
Wherein tau is more than or equal to 0 and less than or equal to N-1. The construction method of the invention is suitable for quasi-synchronous CDMA system, can realize complete elimination of inter-cell interference, complete elimination of intra-cell interference in the length Z of the zero correlation zone, flexible setting of the length Z of the zero correlation zone, good flexibility, easy generation, and can provide considerable inter-group complementary sequence sets for the communication system.

Claims (7)

1. A construction method of non-periodic inter-group complementary sequence set based on DFT matrix is characterized in that: the method comprises the following steps:
s1, selecting any circular Florentine array F with a step of a multiplied by b;
s2, randomly selecting a positive integer G > 1, enabling G to be more than or equal to 0 and less than G, and enabling N to be b.G to construct a sequence set h of a multiplied by G sequences;
s3, constructing an aperiodic intercycle inter-group complementary sequence set based on the circular Florentine array and the multiphase DFT matrix.
2. The method of claim 1, wherein the method comprises the following steps: the a-th of the circular Florentine array F in the step S1iThe rows are represented as
Figure FDA0003463698540000011
0≤ai＜a；
Figure FDA0003463698540000012
Is ZbA permutation function of (a), wherein Zb(0, 1,2, …, b-1), provided that for any 0 < τ < b, 0 ≦ l < b, there is
Figure FDA0003463698540000013
Figure FDA0003463698540000014
And
Figure FDA0003463698540000015
are all aiThe value of the row; a isi，ajAre all [0, a-1 ]]Any number within the range, for any 0 < ai≠ajA, 0 ≦ τ < b, with and with only one solution such that
Figure FDA0003463698540000016
This is true.
3. The method of claim 2, wherein the method comprises the following steps: in step S1, the maximum number of rows of the circular Florentine array F is denoted as F (b), a circular Florentine array of F (b) × b order may be constructed, and when b is an even number, F (b) ═ 1; when p is the minimum prime factor of b, p-1 is less than or equal to F (b) is less than or equal to b-1; when b is a prime number, f (b) b-1; when b.ident.15 (mod18), F (b). ltoreq.b-3.
4. The method of claim 3, wherein the method comprises the following steps: the specific steps of step S2 are as follows:
s21, selecting a positive integer G > 1, wherein G is more than or equal to 0 and less than G, and enabling N to be b.G;
s22, constructing a sequence set h, wherein the sequence set h comprises a multiplied by G sequences, and the sequence set h is expressed as
Figure FDA0003463698540000017
Each sequence
Figure FDA0003463698540000018
B, and each sequence is specifically constructed as follows:
Figure FDA0003463698540000021
wherein
Figure FDA0003463698540000022
5. The method of claim 4, wherein the method comprises the following steps: the step S3 selects two NxN-order multi-phase DFT matrixes
Figure FDA0003463698540000023
And
Figure FDA0003463698540000024
having the form:
Figure FDA0003463698540000025
wherein
Figure FDA0003463698540000026
Wherein
Figure FDA0003463698540000027
Representing the elements in row i and column j of the matrix U,
Figure FDA0003463698540000028
representing the elements in row i and column j of the matrix V.
6. The method of claim 5, wherein the method comprises the following steps: in the step S3, a pieces of a matrix are constructed based on the circular Florentine array and the multiphase DFT matrix
Figure FDA0003463698540000029
Non-periodic inter-group complementary sequence set S ═ S (S)0,S1,…,Sa-1)；
Complementary sequence set between each group
Figure FDA00034636985400000210
A sequence set comprising G groups;
each group consisting of
Figure FDA00034636985400000211
Comprises N complementary sequences;
each complementary sequence
Figure FDA00034636985400000212
Comprises N subsequences;
each subsequence
Figure FDA00034636985400000213
The length is N;
the length Z of the zero correlation zone in the group is b;
the specific construction of each subsequence is as follows:
Figure FDA00034636985400000214
wherein: m is more than or equal to 0 and less than or equal to N-1, N is more than or equal to 0 and less than or equal to N-1, and t is more than or equal to 0 and less than or equal to N-1.
7. The method of claim 6, wherein the method comprises the following steps: when 0 is more than or equal to ai≠ajWhen a is less than or equal to a-1, for
Figure FDA00034636985400000215
Two sequences of any of
Figure FDA00034636985400000216
And
Figure FDA0003463698540000031
is a cross-correlation function of
Figure FDA0003463698540000032
Wherein tau is more than or equal to 0 and less than or equal to Z-1; when 0 is less than or equal to gi≠gj≤G-1，gi，gjIs [0, G-1 ]]Any number within the range to
Figure FDA0003463698540000033
Two sequences of any of
Figure FDA0003463698540000034
And
Figure FDA0003463698540000035
is a cross-correlation function of
Figure FDA0003463698540000036
Wherein tau is more than or equal to 0 and less than or equal to N-1.
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