CN106330252A - A method for constructing low-correlation code set based on cross-correlation matrix enrichment - Google Patents

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 method for constructing low-correlation code set based on cross-correlation matrix enrichment

technical field

The invention relates to the technical fields of frequency hopping (FH) communication and direct sequence spread spectrum code division multiple access (DS-CDMA), and is used for constructing a low-correlation code set.

Background technique

In frequency hopping communication, a frame message contains multiple pulses of different frequencies. When synchronously capturing the message frame, the local synchronization code modulation signal is used to perform sliding correlation calculations with the received signal. When the synchronization code in the received signal is aligned with the local synchronization code, a sharp correlation peak appears, and the synchronization position is determined according to this correlation peak. , thus completing the synchronous capture. In practical applications, different synchronization codes are generally used in multiple pulses, and the correlation values of multiple synchronization codes are superimposed to increase the correlation peak value to improve the sensitivity of synchronization acquisition. This method is called multi-pulse synchronization acquisition. In order to reduce the false alarm of multi-pulse synchronization capture, not only the synchronization code is required to have good autocorrelation performance, but also the multiple synchronization codes are required to have good cross-correlation performance to prevent the cross-correlation between different synchronization codes in the sliding correlation process value produces a peak value.

In DS-CDMA, each user shares the same channel, and the spreading code is the only sign to distinguish users, and the cross-correlation value between different spreading codes determines the degree of mutual interference between different users, so it is required that the spreading codes have Good cross-correlation performance; in addition, in order to meet the requirements of synchronization and anti-multipath, the spreading code also needs to have good auto-correlation performance.

In the above two application scenarios, a low-correlation code set with excellent self-correlation and cross-correlation performance is required, and there are a considerable number of chips in the set, which are used as synchronization codes for multi-pulse synchronization acquisition in frequency hopping systems, or As a spreading code, it is used for multiple access of different users in a spreading system.

Currently, low-correlation code sets include m-sequence code sets, Gold code sets, Kasami code sets, and so on. The m-sequence is a sequence generated by a feedback shift register, and has the best self-correlation performance, but the number of chips in the m-sequence code set is small, which cannot meet the needs of practical applications; Gold code and Kasami code are combined sequence codes of m-sequence , the self-correlation performance is good, and the number of chips in the set is considerable, but the chip length can only be 2 ⁿ -1 (n is a positive integer), which limits the application range of Gold codes and Kasami codes. For example, in frequency hopping communication, in order to increase the length of useful information transmitted, it is necessary to shorten the length of synchronization chips as much as possible on the basis of ensuring the performance of synchronization acquisition. Therefore, the appropriate length of synchronization codes is generally not 2 ⁿ -1.

Contents of the invention

In order to overcome the deficiencies in the prior art, the present invention provides a method for constructing a low-correlation code set based on cross-correlation matrix enrichment, which is used to generate a code set with good self-correlation and cross-correlation performance with a length of N bits, where N is a positive integer .

The technical solution adopted by the present invention to solve its technical problems comprises the following steps:

(1) All the binary codes with a length of N bits form a code space, traverse the code space, and select all of the equalizing codes to form an equalizing code set; the equalizing code means that the number difference between 1 and 0 is not greater than 10% of the total number of bits in binary code;

(2) In the equalization code set, calculate the autocorrelation value vector of all chips, find out wherein the good chip of autocorrelation performance, form the excellent autocorrelation code set; Described good autocorrelation performance refers to the autocorrelation value vector The ratio of center to winger is greater than the set ratio;

(3) In the set of excellent autocorrelation codes, one of the several chips that are cyclically equivalent is arbitrarily reserved, and for multiple groups of different cyclically equivalent chips, one is arbitrarily reserved from each group, which is equivalent to the absence of cyclic equivalence The chips together constitute a candidate code set; the cyclic equivalence means that a chip is the same as other chips after cyclic shift;

(4) In the set of candidate codes, calculate the pairwise cross-correlation value vectors of all chips, and get their peak values to form a cross-correlation matrix;

(5) Set a good cross-correlation performance threshold; convert the cross-correlation matrix into a cross-correlation 01 matrix, that is, if the elements in the cross-correlation matrix are less than or equal to the good cross-correlation performance threshold, then the value of the element at the corresponding position in the cross-correlation 01 matrix is 1 , the elements in the cross-correlation matrix are greater than the good cross-correlation performance threshold, then the value of the element at the corresponding position in the cross-correlation 01 matrix is 0;

(6) Determine whether the cross-correlation 01 matrix is a matrix of all 1s, if so, execute (8), if not, then sum the cross-correlation 01 matrix by column to form a measurement vector; find out the position where the element value in the measurement vector is the smallest Serial number, delete the row and column of the cross-correlation 01 matrix corresponding to the serial number; if there are several elements with the smallest value in the measurement vector, select one of them arbitrarily;

(7) Repeat step (6) until the cross-correlation 01 matrix is a matrix of all 1s;

(8) form the best code set with the chip corresponding to all 1 matrix;

(9) traverse the whole set of candidate codes, find out the good candidate codes with good cross-correlation performance of all chips in the best code set, add the best code set to form the final low-correlation code set; described cross-correlation performance Good means that the cross-correlation peak value of two chips is less than the good cross-correlation performance threshold.

In the step (2), the set ratio value is greater than 3.

In the step (5), the good cross-correlation performance threshold is less than N/2.

The beneficial effects of the present invention are: a low-correlation code set with flexible chip length and excellent correlation performance is produced, and the number of chips in the set is considerable, which is suitable for frequency hopping communication systems with a synchronization code length other than ²ⁿ -1, Or the DS-CDMA system whose spreading code length is not 2 ⁿ -1 overcomes the shortcoming of the small number of chips in the m-sequence code set, and also overcomes the fact that the chip length in the Gold code set and the Kasami set can only be 2 ⁿ - 1 disadvantage.

Description of drawings

Fig. 1 is a schematic diagram of the present invention applied in a frequency hopping communication system;

Fig. 2 is that the present invention is applied in the schematic diagram of DS-CDMA system;

Fig. 3 is the processing flowchart that the present invention realizes;

Fig. 4 is the autocorrelation value schematic diagram that uses the method of the present invention to produce low correlation code set;

Fig. 5 is a schematic diagram of cross-correlation values generated by using the method of the present invention to generate a set of low-correlation codes.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, and the present invention includes but not limited to the following embodiments.

The present invention proposes for the first time a method of condensing a chip set with excellent autocorrelation performance according to a cross-correlation matrix, and constructs a low-correlation code set with flexible chip length and excellent autocorrelation and cross-correlation performance as a frequency hopping The synchronization code used by different pulses in communication can effectively support multi-pulse synchronization acquisition; or it can be used as the spreading code in DS-CDMA system to effectively reduce the mutual interference between multiple users.

The present invention comprises the following steps:

(1) Traverse the entire binary code space with a length of N bits, exhaustively enumerate all equalization codes to form an equalization code set. The equalized code means that after the chip is converted into an N-bit binary number, the number of 1s and 0s is approximately equal, and it is generally believed that the difference between the number of 1s and 0s is not more than 10% of the total number.

(2) In the equalization code set, calculate the autocorrelation value vectors of all chips, find out the chips with excellent autocorrelation performance, and form an excellent autocorrelation code set. Excellent autocorrelation performance means that the ratio of the autocorrelation value vector center forward (the center size is N) to the winger is relatively large, exceeding a certain ratio value (the ratio value is generally greater than 3).

(3) In the set of excellent autocorrelation codes, only one of the chips that are cyclically equivalent is reserved. For the chips that have multiple groups of different cyclic equivalents, one of them is arbitrarily selected from each group. The chips together form a set of candidate codes. Cyclic equivalence means that one chip is the same as other chips after cyclic shift.

(4) In the set of candidate codes, calculate pairwise cross-correlation value vectors of all chips, and take their peak values to form a cross-correlation matrix.

(5) A good cross-correlation performance threshold (generally less than N/2) is set. If the cross-correlation peak value of two chips is smaller than the threshold, the two chips are considered to have good cross-correlation performance. According to the threshold, the cross-correlation matrix is converted into a 01 matrix, that is, the elements in the matrix are converted to 1 if they are less than or equal to the threshold, and are converted to 0 if they are greater than the threshold.

(6) Judging whether the cross-correlation 01 matrix is a matrix of all 1s, if yes, execute (8); otherwise, sum the cross-correlation 01 matrix by column to form a measurement vector. Find out the serial number of the position with the smallest element value in the measurement vector, and delete the row and column of the cross-correlation 01 matrix corresponding to the serial number, which is equivalent to condensing the correlation 01 matrix. Among them, if there are several elements with the smallest value in the measurement vector, the first one is selected, or one is selected arbitrarily.

(7) Repeat (6) until the cross-correlation 01 matrix is a matrix of all 1s.

(8) Compose the chips corresponding to the matrix of all 1s into an optimal code set.

(9) Traversing the entire set of candidate codes, finding a candidate code with good cross-correlation performance with all chips in the best code set, and adding the candidate code to the best set of codes to form the final set of low-correlation codes.

Fig. 1 is an application schematic diagram of the frequency hopping communication system in which the present invention is located. At the sending end, different chips in the low-correlation code set are inserted as synchronization codes into the information to be modulated in different pulses, and are sent out as radio frequency signals after information modulation and frequency hopping modulation. At the receiving end, the radio frequency signal is down-converted to form a baseband signal, and the baseband signal is slid and intercepted according to the frequency-hopping and time-hopping pattern, and then correlated with the synchronization code modulation signal of the local corresponding pulse, and the correlation value is superimposed to participate in the synchronization judgment. The judgment threshold considers that the synchronization capture is completed, and the synchronization position is notified to the information demodulation module, which demodulates the baseband signal to obtain the transmission information. In the process of synchronous acquisition, due to the excellent self-correlation and cross-correlation performance of each chip in the low-correlation code set, when the synchronous state is reached, the superimposed correlation value will have a sharp and prominent peak, which exceeds the synchronous decision threshold. state, the correlation value after superposition is small, lower than the synchronization decision threshold.

Fig. 2 is an application principle diagram of the DS-CDMA system in which the present invention is located. In the DS-CDMA system, different chips in the low-correlation code set correspond to different users one by one. When the sending end sends a message, according to the destination address of the message, the corresponding chip is selected from the low-correlation code set as the spreading code. Use their respective spread spectrum codes to despread the down-converted signals, and then demodulate to obtain the information sent to the user. Due to the excellent self-correlation and cross-correlation performance of each chip in the low-correlation code set, the mutual interference between users is very small.

Fig. 3 is a processing flowchart realized by the present invention. It is assumed that a low-correlation code set with a length of N (N is a positive integer) bits is to be generated. Specific steps are as follows:

[step 1]

In the code space with a length of N bits, traverse each number from 0 to 2 ^N -1, convert each number into an N-bit binary code, set it as C _i , if the number of 1s and 0s in C _i is approximately Correspondingly, for example |b ₁ -b ₀ |=0, 1, 2 (where b ₁ and b ₀ are the numbers of 1s and 0s in C _i respectively), then C _i is an equalized code. All equalization codes are composed into an equalization code set {C _i '}.

[step 2]

In the equalization code set {C _i '}, the autocorrelation value vector V _i of each code C _i ' is calculated, the center of V _i is V _i ^m (where V _i ^m =N), and the wing is V _i ^s , if V _i ^m /V _i ^s exceeds a certain ratio R (wherein R>1), for example, if R=3, then C _i ' has excellent autocorrelation performance, and C _i ' is an excellent autocorrelation code. All excellent autocorrelation codes are composed of excellent autocorrelation code set {C _i ”}.

[Step 3]

In the excellent autocorrelation code set {C _i ”}, if two codes C _k ” and C _l ” are cyclically equivalent, then C _l ” is deleted from {C _i ”}, and finally the candidate code set {C _i "'}. The circular equivalence is defined as: in Indicates that C _l ” is cyclically shifted to the right by m (0<m<N) bits.

[Step 4]

Calculate the cross-correlation peak matrix of the candidate code set, and condense the candidate code set according to the matrix. The specific sub-steps are as follows:

[Step 4.1]

The number of chips in the device code selection set {C _i ”'} is L, and the pairwise cross-correlation value vectors of all chips in {C _i ”’} are calculated, and the peak value ri _j is taken to form a cross-correlation matrix M, M is The square matrix of L×L is symmetrical along the main diagonal, that is, r _ij =r _ji , and the elements of the main diagonal take the value of 0. A threshold value B is set, for example, B=N/3, and if ri _j ≤ B, it is considered that the cross-correlation performance between C _i "' and C _j "' is good. In M, if r _ij ≤ B, the position element is converted to 1, otherwise it is converted to 0, and M is converted to a 01 matrix M ⁰¹ . M ⁰¹ is still a symmetric matrix along the main diagonal, and the elements on the main diagonal are all 1.

[Step 4.2]

Determine whether M ⁰¹ is a matrix of all 1s, if yes, execute step 4.4, otherwise, sum M ⁰¹ column by column to obtain the weight vector W, the length of W is the total number of columns of M ⁰¹ , set as L'. Find the minimum value element in W, set its position number in W as u (where u=1, 2, ..., L'), then delete the uth row and uth column of M ⁰¹ to form a new The cross-correlation 01 matrix replaces the original M ⁰¹ . Among them, if W has multiple minimum value elements at the same time, the first one can be selected, of course, one can also be selected randomly.

[Step 4.3]

Repeat step 4.2 until M ⁰¹ is a matrix of all 1s.

[Step 4.4]

Form the best code set with C _i "' corresponding to M ⁰¹

[step 5]

Traverse the set of candidate codes, find out the chips that have excellent cross-correlation performance with all the best codes, and supplement the best code set, the specific sub-steps are as follows:

[Step 5.1]

Select the first chip in the candidate code set {C _i "'} as C _x "'.

[Step 5.2]

if and C _x "' with The cross-correlation peak r _xi ≤ B of all chips in , then add C _x "' into form new

[Step 5.3]

Select the next chip in the candidate code set {C _i "'} as C _x "'.

[Step 5.4]

Repeat steps 5.2 and 5.3 until all the chips in the candidate code set {C _i ”'} have been traversed. The optimal code set formed at this time is the final set of low-correlation codes

For example, get N=24, now autocorrelation value main peak is 24, set the ratio value of excellent autocorrelation main peak and winger greater than 3, excellent cross-correlation threshold 12, use a low correlation code set that the method provided by the present invention produces as :

There are 123 chips in the table, represented by decimal numbers, the autocorrelation value curve of each chip is shown in Figure 4, and the pairwise cross-correlation value curve is shown in Figure 5.

Claims (3)

1. A low-correlation code set construction method based on cross-correlation matrix enrichment, is characterized in that comprising the steps: (1) All the binary codes with a length of N bits form a code space, traverse the code space, and select all of the equalizing codes to form an equalizing code set; the equalizing code means that the number difference between 1 and 0 is not greater than 10% of the total number of bits in binary code; (2) In the equalization code set, calculate the autocorrelation value vector of all chips, find out wherein the good chip of autocorrelation performance, form the excellent autocorrelation code set; Described good autocorrelation performance refers to the autocorrelation value vector The ratio of center to winger is greater than the set ratio; (3) In the set of excellent autocorrelation codes, one of the several chips that are cyclically equivalent is arbitrarily reserved, and for multiple groups of different cyclically equivalent chips, one is arbitrarily reserved from each group, which is equivalent to the absence of cyclic equivalence The chips together constitute a candidate code set; the cyclic equivalence means that a chip is the same as other chips after cyclic shift; (4) In the set of candidate codes, calculate the pairwise cross-correlation value vectors of all chips, and get their peak values to form a cross-correlation matrix; (5) Set a good cross-correlation performance threshold; convert the cross-correlation matrix into a cross-correlation 01 matrix, that is, if the elements in the cross-correlation matrix are less than or equal to the good cross-correlation performance threshold, then the value of the element at the corresponding position in the cross-correlation 01 matrix is 1 , otherwise the value of the element at the corresponding position in the cross-correlation 01 matrix is 0; (6) Determine whether the cross-correlation 01 matrix is a matrix of all 1s, if so, execute (8), if not, then sum the cross-correlation 01 matrix by column to form a measurement vector; find out the position where the element value in the measurement vector is the smallest Serial number, delete the row and column of the cross-correlation 01 matrix corresponding to the serial number; if there are several elements with the smallest value in the measurement vector, select one of them arbitrarily; (7) Repeat step (6) until the cross-correlation 01 matrix is a matrix of all 1s; (8) form the best code set with the chip corresponding to all 1 matrix; (9) traverse the whole set of candidate codes, find out the good candidate codes with good cross-correlation performance of all chips in the best code set, add the best code set to form the final low-correlation code set; described cross-correlation performance Good means that the cross-correlation peak value of two chips is less than the good cross-correlation performance threshold. 2. The method for constructing a low-correlation code set based on cross-correlation matrix enrichment according to claim 1, characterized in that: in the described step (2), the setting ratio is greater than 3. 3. The method for constructing a low-correlation code set based on cross-correlation matrix enrichment according to claim 1, characterized in that: in the step (5), the good cross-correlation performance threshold is less than N/2.