CN114301496A - Long-period spread spectrum sequence generation method based on m-sequence preferred pairs - Google Patents

Abstract

The invention provides a long-period spread spectrum sequence generation method based on m-sequence optimal pairs, and belongs to the field of satellite navigation system pseudo code design. The invention takes 4 m sequences which are preferably paired with each other as basic sequences, respectively generates two composite spread spectrum sequences by the two sequences through the basic sequences which are prime numbers in length, the lengths of the generated two composite sequences are prime numbers, and then generates the final long-period spread spectrum sequence by compounding again, wherein the sequences have good correlation performance, and the method has feasibility.

Description

Long-period spread spectrum sequence generation method based on m-sequence preferred pairs

Technical Field

The invention relates to a long-period spread spectrum sequence generation method based on m-sequence optimal pairs, and belongs to the technical field of satellite navigation system pseudo code design.

Background

The satellite navigation system can provide continuous real-time three-dimensional position, speed and time information for users all over the world, and brings great convenience to production and life of the human society. Four global satellite navigation systems, such as GPS, GLONASS, Galileo and BDS, have been developed worldwide. In the aspect of navigation signal system, besides the traditional GLONASS adopts Frequency Division Multiple Access (FDMA) technology, the GPS, Galileo and BDS all adopt frequency division multiple access (CDMA) technology, and the signal system in the GLONASS modernization will also be converted to CDMA. Therefore, the design of the spreading sequence is one of the basic problems in the design of the satellite navigation signal system.

Currently, signals of a satellite navigation system are divided into open service signals and authorized service signals. The ranging code of the public service signal adopts short code period sequences such as Gold code family and Weil code family, and is easy for the user terminal to quickly acquire and track. The authorization service signal generally adopts encryption technology for long period spread spectrum code or non-period spread spectrum code, ensures the non-periodicity of the sequence and has stronger anti-detection and anti-deception capabilities. In the authorized service signals, the P code signal design of the GPS adopts a composite sequence formed by 4 12-bit linear shift registers, and the selected generating polynomials have good cross correlation, so that the correlation performance of the composite sequence is minimized as much as possible.

However, the existing spread spectrum sequence generation method cannot flexibly select the number of stages of the linear shift register, the period of the pseudorandom sequence and the number of code families according to different requirements, and is low in applicability.

Disclosure of Invention

The invention provides a long-period spread spectrum sequence generation method based on m-sequence optimal selection pairs in order to solve the problem of long-period spread spectrum sequence generation.

The invention is realized by the following technical scheme:

a method for generating long-period spread spectrum sequence based on m-sequence preferred pairs includes using 4 m-sequences of preferred pairs as basic sequences, generating two composite spread spectrum sequences by using two sequences through basic sequences of prime length, generating two composite sequences of prime length, and generating final long-period spread spectrum sequence again.

A method for generating a long-period spreading sequence based on m-sequence preferred pairs comprises the following steps:

step 1, selecting the order of m sequence as n ≠ 0(mod 4), and then the period is p ≠ 2ⁿ-1；

Step 2, obtaining the integer of p prime, using multiplication as operator, forming group, and recording as Z/(p)^*；

Step 3, the group Z/(p)^*Number H ═ 2⁰,2¹...2^n-1Form an n-order subgroup, and divide it into cosets G according to subgroup H₁＝H,G₂…G_zIn total, z is phi (2)ⁿ-1)/n, where φ (·) represents a Euler function;

step 4, randomly selecting one element from the generated cosets to form a set

R＝{r_i|r_i∈G_i,i＝1,2,…z}；

Step 5, using the known primitive polynomial f (x) as a feedback function to generate an m sequence

And for the generated sequence

Sampling by R epsilon R to obtain a sequence

Sample sequence formation set

Step 6, randomly selecting four sequences a, b, c and d from the generated sequence set A, wherein the cross correlation among the sequences satisfies the requirement

Then, order

Step 7, compounding the generated sequences X1A and X1B to generate an X1 sequence, and compounding the sequences X2A and X2B to generate an X2 sequence, wherein the generation mode is as follows:

L1＝(p-1)*p-1，i∈{0,1…L1}，

L2＝(p-1)*p-1+k，j∈{0,1…L2}，

m＝mod(j,p-1)，n＝mod(j,p)，

gcd(L1,L2)＝1；

the generated X1 and X2 are compounded to generate a sequence X in the following mode:

thus, a long period spreading sequence based on the m-sequence preferred pair is obtained.

The invention has the beneficial effects that:

1. the long-period spread spectrum sequence obtained by the invention has the advantages of flexible and adjustable parameter, low local correlation and strong applicability.

2. The invention takes 4 m sequences which are preferably paired with each other as basic sequences, respectively generates two composite spread spectrum sequences by the two sequences through the basic sequences which are prime numbers in length, the lengths of the generated two composite sequences are prime numbers, and then generates the final long-period spread spectrum sequence by compounding again, wherein the sequences have good correlation performance, and the method has feasibility.

Detailed Description

In order to better illustrate the objects and advantages of the present invention, the following further describes the technical solution of the present invention.

A method for generating long-period spread spectrum sequence based on m-sequence preferred pairs includes using 4 m-sequences as basic sequences, generating two composite spread spectrum sequences by using two sequences through basic sequences with prime number length, generating final long-period spread spectrum sequence by recombination, and obtaining good correlation performance.

The method specifically comprises the following steps:

step 1, selecting the order of m sequence as n ≠ 0(mod 4), and then the period is p ≠ 2ⁿ-1；

Step 2, obtaining the integer of p prime, using multiplication as operator, forming group, and recording as Z/(p)^*；

Step 3, the group Z/(p)^*Number H ═ 2⁰,2¹…2^n-1Form an n-order subgroup, and divide it into cosets G according to subgroup H₁＝H,G₂…G_zIn total, z is phi (2)ⁿ-1)/n, where φ (·) represents a Euler function;

step 4, randomly selecting one element from the generated cosets to form a set

R＝{r_i|r_i∈G_i,i＝1,2,…z}；

Step 5, using the known primitive polynomial f (x) as a feedback function to generate an m sequence

And for the generated sequence

Sampling by R epsilon R to obtain a sequence

Sample sequence formation set

Step 6, randomly selecting four sequences a, b, c and d from the generated sequence set A, wherein the cross correlation among the sequences satisfies the requirement

Then, order

And 7, compounding the generated sequences X1A and X1B to generate an X1 sequence, and compounding the sequences X2A and X2B to generate an X2 sequence in the following mode

L1＝(p-1)*p-1，i∈{0,1…L1}，

L2＝(p-1)*p-1+k，j∈{0,1…L2}，

m＝mod(j,p-1)，n＝mod(j,p)，

gcd(L1,L2)＝1

The generated X1 and X2 are compounded to generate a sequence X in the following mode

t＝mod(h,L1)，s＝mod(h,L2)，h∈{0,1…L}。

To this end, a long-period spreading sequence generation method based on m-sequence preferred pairs ends.

Wherein the selected m-sequence cross-correlations of step 6 satisfy a preferred pair criterion; the method of generating a long-period composite sequence of step 7 has low local cross-correlation.

In the following, the details are described by taking as an example an m sequence with an order n of 11:

step 1, selecting the order of m sequence as n-11, and then the period is p-2ⁿ-1＝2047；

Step 2, obtaining an integer which is mutually prime with p 2047, using multiplication as an operator to form a group,

Z/(p)^*＝{1,2,3,4,5,6,7,8…2045,2046}；

step 3, the group Z/(p)^*The number H of (1), (2), (4) 4 … 512,1024, and (1024) constitutes an 11-step subgroup, and is divided into cosets G according to the subgroup H₁＝H,G₂…G_zAs shown in the following table, z ═ Φ (2) is commonⁿ-1)/n 176;

step 4, arbitrarily selecting one element forming set from the generated cosets, wherein in the example, the first column forming set R of the selected cosets is {1,3,5,7,9,11,13, … 767,879, 887,895,959,991,1023 };

step 5, using known primitive polynomial f (X) 1+ X¹+X⁷+X⁸+X⁹+X¹⁰+X¹¹For the feedback function, the m-sequence is generated at the initial state of (0,1,0,1,0,10,1,0,1,0)

And for the generated sequence

Sampling with r-3 to obtain sequence

Sampling rate	Sequence state
		r＝1	0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,0,1,1……
r＝3	0,1,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,1,0,0,1,0,0,1,0,1……

In this way a set a of complete sample sequences can be acquired.

Step 6, randomly selecting four sequences a, b, c and d from the generated sequence set A, wherein the cross correlation among the sequences satisfies the requirement

The selected sequence sampling rate r is 1,5,9,315 satisfies the preferred pair criterion and is X1A, X1B, X2A, X2B, respectively;

step 7, compounding the generated sequences X1A and X1B to generate an X1 sequence, and compounding the sequences X2A and X2B to generate an X2 sequence, wherein the generation mode is as follows:

L1＝(p-1)*p＝4188162，i∈{0,1…L1}，

L2＝(p-1)*p+k＝4188162+37＝4188199，j∈{0,1…L2}，

m＝mod(j,p-1)，n＝mod(j,p)，

gcd(L1,L2)＝1

the generated X1 and X2 are compounded to generate a sequence X in the following mode:

t＝mod(h,L1)，s＝mod(h,L2)，h∈{0,1…L}。

to this end, a long-period spreading sequence generation method based on m-sequence preferred pairs ends.

In short, on the basis of analyzing the P code design idea, the invention provides a long-period composite spread spectrum code generation method based on m-sequence preferred pairs, provides a new path for the long-period spread spectrum code generation method, and can flexibly select the series number of the linear shift register, the period of the pseudo-random sequence and the number of the code family according to different requirements.

Claims (2)

1. A method for generating long-period spread spectrum sequence based on m-sequence preferred pairs is characterized in that 4 m-sequences which are mutually preferred pairs are used as basic sequences, two composite spread spectrum sequences are generated by the two sequences through the basic sequences which are mutually prime length, the lengths of the generated two composite sequences are mutually prime, and then the two composite sequences are compounded to generate the final long-period spread spectrum sequence.

2. A method for generating a long-period spreading sequence based on m-sequence preferred pairs is characterized by comprising the following steps:

step 1, selecting the order of m sequence as n ≠ 0(mod 4), and then the period is p ≠ 2ⁿ-1；

Step 2, obtaining the integer of p prime, using multiplication as operator, forming group, and recording as Z/(p)^*；

Step 3, the group Z/(p)^*Number H ═ 2⁰,2¹…2^n-1Form an n-order subgroup, and divide it into cosets G according to subgroup H₁＝H,G₂…G_zIn total, z is phi (2)ⁿ-1)/n, where φ (·) represents a Euler function;

step 4, randomly selecting one element from the generated cosets to form a set

R＝{r_i|r_i∈G_i,i＝1,2,…z}；

Step 5, using the known primitive polynomial f (x) as a feedback function to generate an m sequence

Are in mutual oppositionIn a sequence of

Sampling by R epsilon R to obtain a sequence

Sample sequence formation set

Step 6, randomly selecting four sequences a, b, c and d from the generated sequence set A, wherein the cross correlation among the sequences satisfies the requirement

Then, order

Step 7, compounding the generated sequences X1A and X1B to generate an X1 sequence, and compounding the sequences X2A and X2B to generate an X2 sequence, wherein the generation mode is as follows:

L1＝(p-1)*p-1，i∈{0,1…L1}，

L2＝(p-1)*p-1+k，j∈{0,1…L2}，

m＝mod(j,p-1)，n＝mod(j,p)，

gcd(L1,L2)＝1；

the generated X1 and X2 are compounded to generate a sequence X in the following mode:

t＝mod(h,L1)，s＝mod(h,L2)，h∈{0,1…L}；

thus, a long period spreading sequence based on the m-sequence preferred pair is obtained.