JP3697548B2 - Two-phase code generation method with high autocorrelation - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for generating a two-phase code with high autocorrelation, and particularly an improved two-phase code having a low autocorrelation side lobe and a further improved autocorrelation for cyclic codes such as an M-sequence code or an L-sequence code. The present invention relates to a method for searching and generating code.
[0002]
[Prior art]
The two-phase code is a code composed of a code string in which a plurality of codes having values “1” and “−1” are arranged, and its autocorrelation gives a sharp pulse having a large amplitude. Taking advantage of this feature, it is used to improve the signal-to-noise ratio (S / N), broaden the signal band, and the like. As an example of this code, the autocorrelation result of Barker Code 13 is shown in FIG.
[0003]
FIG. 4A shows an example of the code sequence of Barker Code having a code length of 13, FIG. 4B shows the calculation formula of the autocorrelation, and FIG. 4C is a graph showing the autocorrelation result of Barker Code13. It represents by.
[0004]
However, when finding a code having a high autocorrelation, if the code length is N, the autocorrelation is obtained for 2 ^N types of codes, and the signal-to-noise ratio (S / N) is the best among them. An operation that finds a code with a low lobe level must be performed, and generating an optimum code with high autocorrelation for a code with a long code length requires a large amount of calculation and takes a long time. It was.
[0005]
The optimum code is currently known up to a code having a code length of about 100, but the optimum code has not been completely investigated for a longer code, and an M-sequence code that is a cyclic code as an alternative code or An L series code or the like is used. The M sequence code and the L sequence code will be described below.
[0006]
The M-sequence code will be described with reference to FIG. The M-sequence code gives the initial values (C ₁ , C ₂ ,..., C _N ) and coefficients (X ₁ , X ₂ ,..., X _N ) of the N columns of codes, and the equation (1) shown in FIG. Are sequentially generated by the code C _{N + k} (k = 1, 2,..., M−N; M = 2 ^N −1) given by ## EQU1 ## until the code length becomes M = 2 ^N −1. Calculate and generate code. As a feature of this M-sequence code, when autocorrelation is obtained by periodically generating the code, as shown in FIG. 6, the autocorrelation is only a binary value of code lengths “M” and “−1”. It becomes.
[0007]
Next, the L sequence code will be described with reference to FIG. As shown in FIGS. 7A and 7B, the L-sequence code has a head code of “+1” or “−1”, and the remaining code strings other than the head are the first half and the second half. Thus, the arrangement of “+1” or “−1” is left-right symmetric or left-right opposite.
[0008]
(A) of FIG. 7 shows an L-sequence code when the code length P is P = 1 mod 4 (that is, a value with which the remainder when the code length P is divided by 4 is, for example, P = 5). FIG. 7B shows an L-sequence code when P = 3 mod 4 (that is, a value that gives a remainder of 3 when the code length P is divided by 4, for example, P = 7).
[0009]
The code length P of the L-sequence code takes a prime number, and as shown in FIG. 7C, numbers 1, 2,..., P-1 are sequentially assigned to the position numbers of the code string following the head code. If so, the code of the column position number Ln calculated by the equation (2) in FIG. 7 is set to “+1”, the code of the remaining column positions is set to “−1”, and this code string is cyclically shifted to obtain L A sequence code is generated.
[0010]
Then, in both cases where the head code is “+1” and “−1”, the autocorrelation is obtained while cyclically shifting the code string one by one, and the optimum code having the lowest sidelobe level is searched. As an example of searching for the optimum code, the case where the code length is 5 and the case where the code length is 7 are shown in FIGS. In FIGS. 8 and 9, the symbols “+1” and “−1” are simply indicated as “+” and “−”.
[0011]
The table of FIG. 8 shows the side lobe level of autocorrelation of each code when the head code is “+1” and “−1” for an L-sequence code with a code length of 5. In the table of FIG. 8, the code with the number 1 is the code with the head code “+1”, and the codes with the numbers 2 to 5 are codes obtained by cyclically shifting the code with the number 1 to the shift numbers 1 to 4, respectively. is there. Here, the code arrangement of the code of No. 4 is symmetrical with the code arrangement of the code of No. 2, and the code of No. 5 is symmetrical with the code arrangement of the No. 1 code.
[0012]
Since the autocorrelation has the same value for the code with the opposite sign and the code with the left and right arrangement reversed, it is only necessary to calculate the autocorrelation for only one code. Therefore, the autocorrelation is obtained for the codes from number 1 to number 3 with respect to the code whose head code is “+1”, and the code of number 2 or number 3 whose sidelobe level is the minimum value 2 is determined as the optimum code. Choose as.
[0013]
On the other hand, the code of No. 6 is a code having a leading code of “−1”, and the codes of No. 7 to No. 10 are codes obtained by cyclically shifting the code of No. 6 to shift numbers 1 to 4 respectively. Here, the code of number 9 is symmetric with the code of number 7, and the code of number 10 is symmetric with the code of number 6, so autocorrelation is performed with respect to the codes of number 6 to number 8. The code of number 6 or number 7 whose side lobe level is the minimum value 2 is selected as the optimum code.
[0014]
The table of FIG. 9 shows the case where the code length is 7, and the autocorrelation with respect to the codes of numbers 2 to 7 that are cyclically shifted to the shift numbers 1 to 6 for the code of number 1 with the head code “+1”, respectively. And the number 5 code whose side lobe level is the minimum value 1 is selected as the optimum code.
[0015]
For the code of number 8 with the head code “−1”, the code of number 8 is the code of the code of number 7 for the codes of number 9 to number 14 that are cyclically shifted to the shift numbers 1 to 6, respectively. Similarly, the number 9 code is the number 6 code, the number 10 code is the number 5 code, the number 11 code is the number 4 code, and the number 12 code is the number. 3 code, No. 13 code is No. 2 code, No. 14 code is No. 1 code, and sign inversion code is bilaterally symmetric, and their autocorrelation is the same as the corresponding symmetrical code As a result, the code of number 5 calculated and determined for the codes from number 1 to number 7 can be selected as the optimum code.
[0016]
[Problems to be solved by the invention]
The present invention provides a two-phase code generation method capable of easily and quickly searching for an improved code having higher autocorrelation with respect to a two-phase code such as an M-sequence code or an L-sequence code that is a cyclic code. The purpose is to do.
[0017]
[Means for Solving the Problems]
In the two-phase code generation method of the present invention, (1) each autocorrelation of each two-phase code obtained by inverting only one sign of the two-phase code constituting the cyclic code is calculated, and each two of the code inverting positions are changed. It is characterized by searching for and generating a two-phase code having the highest autocorrelation among the phase codes.
[0018]
Also, (2) calculating each autocorrelation of each two-phase code obtained by inverting only one sign of the two-phase code constituting the cyclic code, and whether the autocorrelation is higher than the two-phase code before the sign inversion Determine the autocorrelation of the two-phase code in which only the sign of the other one is inverted with respect to the two-phase code determined to have higher autocorrelation than before the sign inversion. The process of determining whether or not the property is higher than the two-phase code before sign inversion is repeated until a higher autocorrelation is not obtained, and the two-phase code having the highest autocorrelation is searched and generated. Features.
[0019]
(3) An M-sequence code or an L-sequence code is used as the cyclic code. Further, (4) when calculating the autocorrelation of the two-phase code obtained by inverting only one sign of the two-phase code, based on the statistical characteristics regarding the code length, the sidelobe improvement value, and the code inverting position parameter. The sign inversion position is determined. Further, (5) it is generated as a two-phase code used for a pulse compression signal, an interference countermeasure signal, a spread code signal, or a secret communication signal.
[0020]
DETAILED DESCRIPTION OF THE INVENTION
A procedure for searching and generating an improved two-phase code according to the present invention will be described with reference to FIG. The method for generating a two-phase code according to the present invention generates a code obtained by sequentially inverting the code of only one place with respect to the original code A, calculates an autocorrelation for each of those codes, Determine if there is an improved code with a low sidelobe level. At this time, the reduction amount of the side lobe level is evaluated as the improvement amount.
[0021]
In FIG. 1, the improvement amount of the code B obtained by inverting the sign of the N ₁ th column position of the original code A is 1, and the improvement amount of the code C obtained by inverting the sign of the N ₂ th column position of the original code A is the same. 1, the improvement amount of the code D obtained by inverting the sign of the N _3rd column position of the original code A is 2, and the improvement amount of the code E obtained by inverting the sign of the N _4th column position of the original code A is 1. Suppose that it is determined that there is.
[0022]
Next, the improvement amount of the code F obtained by inverting the code of the N _5th column position with respect to the code B is 2, and the improvement amount of the code G obtained by inverting the code of the N _6th column position with respect to the code B is the same. 2. Even if the code at any column position is inverted with respect to the code C, there is no improvement of the improvement amount 1 or more, and the improvement amount of the code H obtained by inverting the code at the N _7th column position with respect to the code E is 2. Is determined to be.
[0023]
Next, the improvement amount of the code I obtained by inverting the code of the N _8th column position with respect to the code F is 3, and the improvement of 2 or more is improved even if the code of any column position is inverted with respect to the code G. The improvement amount of the code K obtained by inverting the code of the N _10th column position with respect to the code D is 4, and the improvement amount of the code K obtained by inverting the code of the N _11th column position with respect to the code D is 4 Suppose that it is determined that there is no improvement of the improvement amount 2 or more even if the code at any column position is inverted with respect to the code H.
[0024]
Next, it is determined that the improvement amount of the code J obtained by inverting the code at the N _9th column position with respect to the code I is 3, and that there is no improvement amount of the code obtained by inverting the code at the other column positions. In this way, a code is generated by inverting the sign for the remaining column positions until no further improvement is obtained for code J, code K, and code L, and the largest improvement is obtained. Generated code as the optimal code.
[0025]
In this way, a code obtained by inverting the code of only one column position for each code is generated, and the presence / absence determination of the improved code by calculating the autocorrelation is performed for N codes when the code length is N. Compared with the conventional improved code search that calculates autocorrelation over all 2 ^N codes, the improved code can be found and generated with a significantly smaller amount of computation. be able to. The present invention can be applied regardless of the length of the two-phase cord.
[0026]
FIG. 2 shows a numerical example of the improved code searched for by the procedure of the present invention and its improved amount. The table of (a) of the figure shows an example of the M series improvement code, and (b) of the figure shows an example of the L series improvement code. In FIG. 2A, N is N shown in FIG. 5, and the code length is 2 ^N −1. Here, in the first row of the table of FIG. 2A, the sidelobe level of the code obtained by inverting the 20th code at the column position for a code of N = 5 and code length 31 is 4. This shows that an improvement of 1 can be obtained from the side lobe level (5, not shown) of the original code without sign inversion.
[0027]
Further, the fifth row of the table of FIG. 2A shows a code obtained by inverting the codes of the column positions 10th, 170th, 381th, and 448th with respect to the code of N = 9 and the code length 511. The side lobe level is 18, which indicates that an improvement amount of 4 can be obtained from the side lobe level (22 not shown) of the original code whose sign is not inverted. The other rows are as shown in the same table, so the explanation is omitted.
[0028]
In the L-sequence improved code table of FIG. 2B, the code length is given by P shown in FIG. 7, and its value is a prime number. Here, the first row of the table of FIG. 2B shows the 62nd, 207th, and 651th codes for the code obtained by cyclically shifting the code having the code length of 1021 and the head code “+1” by 248 times. The side lobe level of the code with the sign inverted is 23, which indicates that an improvement of 3 can be obtained from the side lobe level of the original code without sign inversion (not shown). Since the other lines are as shown in the table, the description is omitted.
[0029]
Furthermore, as an efficient search method for improved codes of M-sequence code and L-sequence code, the improved code can be obtained with a small amount of calculation by statistically investigating the parameter relationship such as code length, sidelobe improvement value, sign inversion position, etc. Can be explored.
[0030]
FIG. 3 is a graph showing the statistical correlation between the sign inversion position and the improved code appearance number. As shown in the figure, it can be seen that there is a tendency that more improved codes appear by sign inversion near the both ends of the code. By paying attention to such statistical characteristics, it is possible to search for an improved two-phase code with a smaller amount of calculation.
[0031]
Next, a preferred application example of the improved two-phase cord obtained by the present invention will be described below.
(1) Signal for Pulse Compression of Surveillance Radar Pulse compression is performed on the surveillance radar in order to improve the performance of detection distance and distance resolution. Pulse compression requires a frequency or phase modulated signal that reduces the side lobe in calculating autocorrelation. The improved two-phase code according to the present invention can be used as this phase modulation signal.
[0032]
(2) Signals for spreading codes of mobile phones Some wireless devices for mobile phones employ a code division multiple access (CDMA) communication system, and two-phase code spreading is used for this code division multiple access (CDMA) communication. A code is used. An improved two-phase code according to the present invention can be used for this spreading code.
[0033]
(3) In an ultrasonic flaw detection apparatus that nondestructively inspects a signal material for pulse compression of ultrasonic flaw detection, a pulse compression technique is often used to increase flaw detection sensitivity and resolution. The signal for pulse compression requires a signal of frequency or phase modulation that reduces the autocorrelation side lobe. The improved two-phase code according to the present invention can be used as this phase modulation signal.
[0034]
(4) Signals for pulse compression of ground penetrating radars Pulse compression technology is often used to increase the detection distance and resolution of ground penetrating radars that inspect the ground nondestructively. The signal for pulse compression requires a signal of frequency or phase modulation that reduces the autocorrelation side lobe. The improved two-phase code according to the present invention can be used as this phase modulation signal.
[0035]
(5) Active sonar pulse compression signal Pulse compression technology can be applied to increase the detection distance and resolution of active sonar. The pulse compression signal requires a frequency or phase modulation signal that reduces the autocorrelation side lobe. The improved two-phase code according to the present invention can be used as this phase modulation signal.
[0036]
(6) Pulse compression technology for increasing sensitivity and resolution is applied in ultrasonic diagnosis for diagnosing the inside of a body without damaging a signal body for pulse compression in ultrasonic diagnosis. The pulse compression signal requires a frequency or phase modulation signal that reduces the autocorrelation side lobe. The improved two-phase code according to the present invention can be used as this phase modulation signal.
[0037]
(7) When transmitting / receiving the confidential communication signal confidential information, the transmitting side modulates the transmission signal with the encryption code and transmits it, and the receiving side can obtain the confidential information by demodulating the reception signal with the same encryption code. The receiving side cannot decipher unless the encryption code is informed. The improved two-phase code according to the present invention can be used for this encryption code.
[0038]
【The invention's effect】
As described above, according to the present invention, the autocorrelation of a code obtained by inverting only one sign of a two-phase code is calculated, and the highest autocorrelation among the two-phase codes having different sign inverting positions. By searching for and generating a two-phase code, an improved code with higher autocorrelation can be searched easily and quickly. This improved code with high autocorrelation can be used for pulse compression signals and anti-jamming measures. By using it for signals, spreading code signals, secret communication signals, etc., the pulse compression ratio (ratio of signal to sidelobe) is improved over the code before improvement, and code division multiple access (CDMA) communication, It is possible to perform communication with a high signal-to-noise ratio (S / N) in secret communication, communication in a jamming environment, and the like.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram of a procedure for searching for an improved two-phase code according to the present invention.
FIG. 2 is a diagram showing a numerical example of an improved code searched for according to the present invention and its improved amount.
FIG. 3 is a diagram showing a statistical correlation between a sign inversion position and the improved code appearance number.
FIG. 4 is a diagram showing the autocorrelation of Barker Code 13;
FIG. 5 is an explanatory diagram of generation of an M-sequence code.
FIG. 6 is a diagram illustrating autocorrelation of an M-sequence code.
FIG. 7 is an explanatory diagram of generation of an L-sequence code.
FIG. 8 is an explanatory diagram of optimum code search for an L-sequence code having a code length of 5;
FIG. 9 is an explanatory diagram of optimum code search for an L-sequence code with a code length of 7.
[Explanation of symbols]
A Original code B to L The column position of the code string constituting the codes N _{1 to} N ₁₁ generated by inverting the sign one by one from the original code

Claims (5)

Calculates the autocorrelation of each two-phase code obtained by inverting only one sign of the two-phase code constituting the cyclic code, and selects the two-phase code having the highest autocorrelation among the two-phase codes whose sign inversion positions are changed. A two-phase code generation method characterized by searching for and generating a code. Calculate each autocorrelation of each two-phase code obtained by inverting only one sign of the two-phase code constituting the cyclic code, and determine whether the autocorrelation is higher than the two-phase code before the code inversion Then, for the two-phase code determined to have higher autocorrelation than before the sign inversion, the autocorrelation of the two-phase code obtained by inverting only the sign at one other place is calculated, and the autocorrelation is calculated before the sign inversion. The process of determining whether or not the two-phase code is higher than the two-phase code is repeated until a higher autocorrelation is not obtained, and the two-phase code having the highest autocorrelation is searched and generated. Code generation method. 3. The two-phase code generation method according to claim 1, wherein an M-sequence code or an L-sequence code is used as the cyclic code. When calculating the autocorrelation of the two-phase code obtained by inverting only one sign of the two-phase code, the code inversion position is determined based on the statistical characteristics regarding the code length, the sidelobe improvement value, and the code inversion position parameter. The two-phase code generation method according to claim 1, wherein the two-phase code generation method is determined. 5. The two-phase code generation method according to claim 1, wherein the two-phase code is generated as a two-phase code used for a pulse compression signal, an interference countermeasure signal, a spread code signal, or a secret communication signal.

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