CN106330252A - Low-correlation code set construction method based on cross-correlation matrix concentration - Google Patents

Low-correlation code set construction method based on cross-correlation matrix concentration Download PDF

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CN106330252A
CN106330252A CN201610886993.6A CN201610886993A CN106330252A CN 106330252 A CN106330252 A CN 106330252A CN 201610886993 A CN201610886993 A CN 201610886993A CN 106330252 A CN106330252 A CN 106330252A
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correlation
cross
matrix
code set
code
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CN106330252B (en
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万佳君
李国梁
李峰
刘飞
段鹏
岳鹏
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CETC 20 Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/707—Spread spectrum techniques using direct sequence modulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/713—Spread spectrum techniques using frequency hopping
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J13/00—Code division multiplex systems
    • H04J13/0007—Code type
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04J—MULTIPLEX COMMUNICATION
    • H04J13/00—Code division multiplex systems
    • H04J13/10—Code generation

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention provides a low-correlation code set construction method based on cross-correlation matrix concentration. The method comprises the steps that a code space is traversed to form a balanced code set; codes with the excellent self-correlation property are found out, and an excellent self-correlation code set is formed; cyclically equivalent codes are removed from the excellent self-correlation code set, and an alternative code set is formed; pairwise cross-correlation value vectors of all the codes are calculated, and peak values of the pairwise cross-correlation value vectors are selected to form a cross-correlation matrix; the cross-correlation matrix is converted into a cross-correlation 01 matrix and concentrated into a full 1 matrix; the codes corresponding to the full 1 matrix form an optimum code set, the alternative codes which have good cross-correlation with all the codes in the optimum code set are added, and the low-correlation code set is formed. According to the method, the low-correlation code set in which the codes are flexible in length range and excellent in correlation property is generated, and the code number in the set is considerable.

Description

A kind of low associated code set construction method concentrated based on cross-correlation matrix
Technical field
The present invention relates to frequency hopping (FH) communication and DS CDMA (DS-CDMA) technical field, for structure Build low associated code set.
Background technology
In frequency hopping communications, a frame message comprises the pulse of multiple different frequent points.When this message frame is carried out synchronization acquistion, Local use synchronous code modulated signal carries out slip related operation with receiving signal, when receiving synchronous code and local synchronization in signal After code alignment, sharp-pointed relevant peaks occurs, determines sync bit according to this relevant peaks, thus complete synchronization acquistion.Should in reality In with, in multiple pulses, typically use different synchronous codes, multiple synchronous code correlations are overlapped, increase relevant peaks Value, to improve the sensitivity of synchronization acquistion, this kind of method is multiple-pulse synchronization acquistion.For reducing the void of multiple-pulse synchronization acquistion Alert, not only require that synchronous code has good autocorrelation performance, also require to have between multiple synchronous code good cross correlation Can, prevent the cross correlation value generation peak value between different synchronous codes in slip correlated process.
In DS-CDMA, each user shares same channel, and spread spectrum code is to discriminate between the unique designation of user, different spread spectrums Cross correlation value between Ma determines the mutual interference degree of different user, therefore it is required that have good mutual between spread spectrum code Close performance；It addition, for meeting the requirements such as synchronization, anti-multipath, spread spectrum code also needs have good autocorrelation performance.
In above two application scenarios, it is required for one and there is excellent oneself, the low associated code collection of cross-correlation performance simultaneously Close, and this set has the chip of considerable amount, as synchronous code for frequency-hopping system multiple-pulse synchronization acquistion, or make Access for spread spectrum code multiple access of different user in spread spectrum system.
At present, low associated code set has m-sequence code set, Gold code set, Kasami code set etc..M-sequence is to utilize The sequence that feedback shift register produces, oneself, cross-correlation performance are best, but in m-sequence code set, number of chips is few, it is impossible to meet The needs of actual application；Gold code and Kasami code are the composite sequence codes of m-sequence, and oneself, cross-correlation performance are good, chip in set A considerable number of, but chip lengths is only 2n-1 (n is positive integer), limits Gold code, the range of Kasami code.Example As, in frequency hopping communications, for increasing the useful information length of transmission, need on the basis of ensureing synchronization acquistion performance, as far as possible Shortening synchronous code leaf length, therefore, suitable synchronous code length is not typically the most 2n-1。
Summary of the invention
In order to overcome the deficiencies in the prior art, the present invention provides a kind of low associated code set concentrated based on cross-correlation matrix Construction method, good from, the code set of cross-correlation performance for producing having of a length of N-bit, wherein N is positive integer.
The technical solution adopted for the present invention to solve the technical problems comprises the following steps:
(1) binary code that all length is N-bit is constituted a code space, travel through code space, select whole Equilibrium code formed equilibrium code set；Described equilibrium code refers to that the number difference of 1 and 0 is not more than the two of the 10% of total bit number Ary codes；
(2) in equilibrium code set, calculate the autocorrelation value vector of whole chip, find out wherein autocorrelation performance excellent Chip, forms excellent auto-correlation code set；The excellent ratio referring to autocorrelation value vector centre forward and wing of described autocorrelation performance Value is more than setting ratio value；
(3) in excellent auto-correlation code set, some chips that circulation is of equal value arbitrarily retain one, for there being many groups The chip that different circulations are of equal value, arbitrarily retains one respectively from often group, and the chip of equal value with there is not circulation collectively forms standby Code selection set；Described circulation equivalence refers to that a chip is identical with other chip after cyclic shift；
(4) in alternative code set, calculate the vector of cross correlation value two-by-two of whole chip, take its peak value composition cross-correlation square Battle array；
(5) good cross-correlation performance threshold is set；Cross-correlation matrix is converted to cross-correlation 01 matrix, i.e. cross-correlation matrix In element less than or equal to good cross-correlation performance threshold, then in cross-correlation 01 matrix, the element value of correspondence position is 1, cross-correlation Element in matrix is more than good cross-correlation performance threshold, then in cross-correlation 01 matrix, the element value of correspondence position is 0；
(6) judge whether cross-correlation 01 matrix is all 1's matrix, if then performing (8), if it is not, then to cross-correlation 01 square Battle array, by row summation, is formed and weighs vector；Find out and weigh the position number that in vector, element value is minimum, by corresponding with this sequence number The row and column of cross-correlation 01 matrix is deleted；If the unit that in measurement vector, value is minimum have several, the most arbitrarily choose wherein One；
(7) repeated execution of steps (6), until cross-correlation 01 matrix is all 1's matrix；
(8) by the chip composition optimum code set corresponding with all 1's matrix；
(9) travel through whole alternative code set, find out whole chip cross-correlation with in optimum code set of good performance alternative Code, adds optimum code set, forms final low associated code set；Described cross-correlation is functional refers to the mutual of two chips Correlation peak is less than good cross-correlation performance threshold.
In described step (2), set ratio value more than 3.
In described step (5), good cross-correlation performance threshold is less than N/2.
The invention has the beneficial effects as follows: create the low associated code set that chip lengths value is flexible, correlated performance is excellent, And in gathering, chip is a considerable number of, it is adaptable to synchronous code a length of non-2nThe frequency-hopping communication system of-1, or spread code length For non-2nThe DS-CDMA system of-1, overcomes the shortcoming that m-sequence code set number of chips is few, also overcomes Gold code collection simultaneously Close and be only 2 with chip lengths in Kasami setnThe shortcoming of-1.
Accompanying drawing explanation
Fig. 1 is that the present invention applies at frequency-hopping communication system schematic diagram；
Fig. 2 is that the present invention applies at DS-CDMA systematic schematic diagram；
Fig. 3 is the process chart that the present invention realizes；
Fig. 4 is the autocorrelation value schematic diagram using the inventive method to produce low associated code set；
Fig. 5 is the cross correlation value schematic diagram using the inventive method to produce low associated code set.
Detailed description of the invention
The present invention is further described with embodiment below in conjunction with the accompanying drawings, and the present invention includes but are not limited to following enforcement Example.
Present invention firstly provides and according to cross-correlation matrix, the chip set with excellent autocorrelation performance is concentrated Method, constructs chip lengths value and flexibly and has the low associated code set of excellent auto-correlation and cross-correlation performance, as jumping Different synchronous codes used by pulse in frequency communication, effectively support multiple-pulse synchronization acquistion；Or as the expansion in DS-CDMA system Frequency code, effectively reduces interfering with each other between multi-user.
The present invention comprises the following steps:
(1) travel through the whole binary code space of a length of N-bit, exhaustive go out all equilibrium code form equilibrium code set. Equilibrium is after code refers to be N-bit binary number by chip transition, and wherein 1 is roughly the same with the number of 0, it is considered that 1 and 0 individual Number difference is not more than the 10% of sum.
(2) in equilibrium code set, calculate the autocorrelation value vector of whole chip, find out wherein autocorrelation performance excellent Chip, forms excellent auto-correlation code set.Autocorrelation performance is excellent refers to autocorrelation value vector centre forward (centre forward's size is N) and limit The ratio of cutting edge of a knife or a sword is relatively big, exceedes certain ratio value (ratio value is generally higher than 3).
(3) in excellent auto-correlation code set, some chips of circulation equivalence only retain one, organize difference for existing more The chip that circulation is of equal value, arbitrarily selects a reservation respectively from often group, and the chip of equal value with there is not circulation collectively forms shape Become alternative code set.Circulation equivalence refers to that a chip is identical with other chip after cyclic shift.
(4) in alternative code set, calculate the vector of cross correlation value two-by-two of whole chip, take its peak value composition cross-correlation square Battle array.
(5) setting good cross-correlation performance threshold (generally less than N/2), the cross-correlation peak value of two chips is less than thresholding, Then think that the two chip cross-correlation is functional.According to this thresholding, cross-correlation matrix is converted in 01 matrix, i.e. matrix Element is converted to 1 less than or equal to thresholding, is converted to 0 more than thresholding.
(6) judge whether cross-correlation 01 matrix is all 1's matrix, be then execution (8), otherwise, to cross-correlation 01 matrix by row Summation, is formed and weighs vector.Find out and weigh the position number that in vector, element value is minimum, by the cross-correlation corresponding with this sequence number The row and column of 01 matrix is deleted, and is equivalent to concentrate relevant 01 matrix.Wherein, if weighing the unit that in vector, value is minimum Have several, then take first, or optionally take one.
(7) (6) are repeated, until cross-correlation 01 matrix is all 1's matrix.
(8) by the chip composition optimum code set corresponding with all 1's matrix.
(9) travel through whole alternative code set, find out whole chip cross-correlation with in optimum code set of good performance alternative Code, adds optimum code set by this alternative code, forms final low associated code set.
Fig. 1 is the frequency-hopping communication system application principle figure at place of the present invention.Difference in transmitting terminal, low associated code set Chip is treated in tune information as what synchronous code was inserted into different pulse, and after modulates information with frequency hopping modulation, formation radiofrequency signal is sent out Go out.At receiving terminal, forming baseband signal after radiofrequency signal is downconverted, when jumping according to frequency hopping, baseband signal is slided by pattern Intercept, then carry out related operation with the synchronous code modulated signal of local respective pulses, after correlation superposition, participate in synchronization decisions, super Crossing decision threshold and then thought synchronization acquistion, by sync bit notification demodulation module, baseband signal is carried out by this module Demodulation obtains transmission information.During synchronization acquistion, due to excellent oneself, the cross correlation of each chip in low associated code set Can, when reaching synchronous regime, the correlation after superposition there will be sharp-pointed prominent peak value, exceedes synchronization decisions thresholding, and Asynchronous regime, then the correlation after superposition is less, less than synchronization decisions thresholding.
Fig. 2 is the DS-CDMA system application principle figure at place of the present invention.In DS-CDMA system, in low associated code set Different chips and different user one_to_one corresponding.When transmitting terminal sends message, according to the destination address of message from low associated code collection Close and select corresponding chip as spread spectrum code, after information is spread, form radiofrequency signal through modulates information and up-conversion and send out Go out；At receiving terminal, different user uses respective spread spectrum code to de-spread the signal after down coversion, then is demodulated acquisition To the information of this user.Due to excellent oneself, the cross-correlation performance of each chip, mutually doing between user in low associated code set Disturb the least.
Fig. 3 is the process chart that the present invention realizes.Assume to produce the low relevant of a length of N (N is positive integer) bit Code set.Specifically comprise the following steps that
[step 1]
In the code space of a length of N-bit, traversal is from 0 to 2NEach numeral of-1, is converted to N ratio by each numeral Special binary code, is set to CiIf, Ci1 roughly the same with the number of 0, such as | b1-b0|=0,1,2 (wherein b1, b0It is respectively CiIn 1 and 0 number), then CiFor equilibrium code.By all equilibrium code composition equilibrium code set { Ci'}。
[step 2]
At equilibrium code set { Ci' in, calculate each code Ci' autocorrelation value vector Vi, ViCentre forward be Vi m(wherein Vi m =N), wing is Vi sIf, Vi m/Vi sExceed certain ratio value R (wherein R ＞ 1), such as, take R=3, then Ci' auto-correlation Function admirable, Ci' for excellent auto-correlation code.Whole excellent auto-correlation codes are formed excellent auto-correlation code set { Ci”}。
[step 3]
At excellent auto-correlation code set { Ci" in, if two code Ck”、Cl" circulation equivalence, then from { Ci" middle deletion Cl", Ultimately form alternative code set { Ci”'}.Circulation equivalent definition is:WhereinRepresent Cl" ring shift right moves m (0 ＜ m ＜ N) bit.
[step 4]
Calculate the cross-correlation peak value matrix of alternative code set, according to matrix, alternative code set is concentrated, concrete sub-step Rapid as follows:
[step 4.1]
Equipment code selection set { Ci" ' in number of chips be L, calculate { Ci" ' in all chips cross correlation value two-by-two to Amount, takes its peak value rijComposition cross-correlation matrix M, M are the square formation of L × L, symmetrical along leading diagonal, i.e. rij=rji, and it is main Cornerwise element takes 0 value.Set a threshold value B, such as B=N/3, if rij≤ B then thinks Ci" ' and Cj" ' cross-correlation Functional.In M, if rij≤ B, then this position element is converted to 1, is otherwise converted to 0, and M is converted to 01 matrix M01。 M01Being still the matrix along leading diagonal symmetry, the elements in a main diagonal is all 1.
[step 4.2]
Judge M01Whether it is all 1's matrix, is then to perform step 4.4, otherwise, to M01By row summation, it is thus achieved that weigh vector W, The a length of M of W01Total columns, be set to L'.Find out the minima element in W, if its position number in W is u (wherein u= 1,2 ..., L'), then by M01U row and u row delete, form new cross-correlation 01 matrix, substitute original M01.Wherein, as Really W has multiple minima element simultaneously, can take first, takes one it is of course also possible to appoint.
[step 4.3]
Repeated execution of steps 4.2, until M01Till all 1's matrix.
[step 4.4]
Will be with M01Corresponding Ci" ' form optimum code set
[step 5]
Travel through alternative code set, therefrom find out and all there is the chip of excellent cross-correlation performance, to most preferably with whole optimum codes Code set supplements, and concrete sub-step is as follows:
[step 5.1]
Choose alternative code set { Ci" ' in first chip, as Cx”'。
[step 5.2]
IfAnd Cx" ' withIn cross-correlation peak value r of all chipsxi≤ B, then by Cx" ' add EnterFormed new
[step 5.3]
Choose alternative code set { Ci" ' in next chip, as Cx”'。
[step 5.4]
Repeated execution of steps 5.2 and 5.3, until by alternative code set { Ci" ' in chip all travel through complete.Now The optimum code set formedIt it is exactly final low associated code set
Such as, taking N=24, now autocorrelation value main peak is 24, sets excellent auto-correlation main peak big with the ratio value of wing In 3, excellent cross-correlation thresholding 12, the low associated code collection that the method using the present invention to provide produces is combined into:
Having 123 chips in table, decimally number represents, each chip autocorrelation value curve is shown in Fig. 4, cross correlation value two-by-two Curve is shown in Fig. 5.

Claims (3)

1. the low associated code set construction method concentrated based on cross-correlation matrix, it is characterised in that comprise the steps:
(1) binary code that all length is N-bit is constituted a code space, travel through code space, select whole equal Weighing apparatus code forms equilibrium code set；Described equilibrium code refers to that the number difference of 1 and 0 is not more than the binary system of the 10% of total bit number Code；
(2) in equilibrium code set, calculate the autocorrelation value vector of whole chip, find out the code that wherein autocorrelation performance is excellent Sheet, forms excellent auto-correlation code set；The excellent ratio referring to autocorrelation value vector centre forward and wing of described autocorrelation performance More than setting ratio value；
(3) in excellent auto-correlation code set, some chips that circulation is of equal value arbitrarily retain one, organize difference for existing more The chip that circulation is of equal value, arbitrarily retains one respectively from often group, and the chip of equal value with there is not circulation collectively forms alternative code Set；Described circulation equivalence refers to that a chip is identical with other chip after cyclic shift；
(4) in alternative code set, calculate the vector of cross correlation value two-by-two of whole chip, take its peak value composition cross-correlation matrix；
(5) good cross-correlation performance threshold is set；Cross-correlation matrix is converted to cross-correlation 01 matrix, i.e. in cross-correlation matrix Element is less than or equal to good cross-correlation performance threshold, then in cross-correlation 01 matrix, the element value of correspondence position is 1, otherwise cross-correlation In 01 matrix, the element value of correspondence position is 0；
(6) judge whether cross-correlation 01 matrix is all 1's matrix, if then performing (8), if it is not, then cross-correlation 01 matrix is pressed Row summation, is formed and weighs vector；Find out and weigh the position number that element value is minimum in vector, by corresponding with this sequence number mutual The row and column closing 01 matrix is deleted；If the unit that in measurement vector, value is minimum have several, the most arbitrarily choose one of them；
(7) repeated execution of steps (6), until cross-correlation 01 matrix is all 1's matrix；
(8) by the chip composition optimum code set corresponding with all 1's matrix；
(9) travel through whole alternative code set, find out whole chip cross-correlation alternative codes of good performance with in optimum code set, add Enter optimum code set, form final low associated code set；The functional cross-correlation referring to two chips of described cross-correlation Peak value is less than good cross-correlation performance threshold.
The low associated code set construction method concentrated based on cross-correlation matrix the most according to claim 1, it is characterised in that: In described step (2), set ratio value more than 3.
The low associated code set construction method concentrated based on cross-correlation matrix the most according to claim 1, it is characterised in that: In described step (5), good cross-correlation performance threshold is less than N/2.
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