CN110830080B - Generation method of aperiodic Hamming related short frequency hopping sequence set - Google Patents

Abstract

The invention discloses a method for generating an aperiodic Hamming correlation short frequency hopping sequence set, which solves the problem that the construction process of the frequency hopping sequence set in the prior art is too cumbersome, requires a large amount of software and hardware storage space, and greatly increases the computational complexity. complexity issue. The present invention includes a method for generating aperiodic Hamming correlation short frequency hopping sequence sets. The present invention only needs to perform calculation on the basis of polynomials to generate a frequency hopping sequence set, the implementation is very simple, the algorithm complexity is small, excessive software and hardware storage space is not required, and the software and hardware overhead and cost can be greatly reduced.

Description

A Generation Method of Aperiodic Hamming Correlation Short Frequency Hopping Sequence Set

technical field

The invention relates to the field of frequency hopping communication, in particular to a method for generating aperiodic Hamming correlation short frequency hopping sequence sets.

Background technique

Regarding the introduction of frequency hopping sequence, the law of carrier frequency hopping can be represented by frequency hopping sequence. The purpose of frequency hopping is: avoiding interference, preventing interception, multiple access networking and combating fading; the purpose of the above four kinds of frequency hopping communication are all It needs to rely on the hopping of the carrier frequency to achieve, so a key problem in the frequency hopping communication is: designing a frequency hopping sequence with excellent performance. Frequency hopping is used to realize spectrum expansion; in frequency hopping networking, different frequency hopping sequences are used as address codes, and the sender selects the communication object according to the address code of the receiver. When many users work at the same frequency hopping in the same frequency band, the frequency hopping sequence is the only sign to distinguish each user.

The definition of maximum aperiodic Hamming correlation in the prior art and the existing method for extracting and constructing short sequence sets with excellent aperiodic Hamming correlation using cyclic code subcodes are introduced here, as follows:

Definition of aperiodic Hamming correlation function: Let F = { f ₁ , f ₂ ,..., f _q } be a frequency slot set of size q , and S is composed of M frequency hopping sequences of length N on F For any set of f ₁ , f ₂ ∈ F , let

For any two hopping sequences x =( x ₀ , x ₁ ,..., x _{N −1} ), y =( y ₀ , y ₁ ,..., y _{N −1} )∈ S and any integer τ , the aperiodic Hamming correlation function H ( x , y ; τ ) of x and y at time delay τ is defined as

where only positive delays are considered.

For the frequency hopping sequence S , the maximum aperiodic Hamming autocorrelation H _a ( S ), the maximum aperiodic Hamming cross-correlation H _c ( S ) and the maximum aperiodic Hamming correlation H _m ( S ) are defined as

For simplicity, we let _Ha = _Ha ( S ), Hc = Hc ₍ S ) , _and Hm ₌ Hm ( _S ) .

Basic definitions related to methods in the prior art: GF( q ) is a finite field, q is the power of a prime number, if q is a prime number 7, that is, GF( q ) = {0,1,2,3,4,5 ,6}. Let q be the power of a prime number and k be an integer such that 1≤ k ≤ q −1. definition

Define n = q −1 and C _RS

Among them, α is the generator of GF( q ), then C _RS is Reed-Solomon code, RS code for short.

Define the cyclic shift operator ρ , when it acts on the sequence x = ( x ₀ , x ₁ , ¼, x _{n −1} ), we have

ρx =( x ₁ ,¼, x _{n −1} , x ₀ )

。

中的两个不同的码字的循环移位后的对应位重叠的数目不会超过n−d，其中d为C _RS 的汉明距离。For any x , y ∈ C _RS , if x = ρ ^m y for any integer m , then x and y are said to be ρ equivalent. ρ equivalence divides C _RS into different subsets, and the subset formed by all elements of each ρ equivalence is called a circular equivalence class. The number of codewords in an equivalence class is called the cycle length of the equivalence class. In this way, we select an element from each equivalence class, and then reassemble all the selected elements into a set, thus obtaining a subcode of C _RS , denoted as

.

The number of cyclically shifted corresponding bits of two different codewords in , does not exceed n − d , where d is the Hamming distance of the C _RS .

Below we define the subset A _RS as follows:

Definition: A _RS contains all codewords that satisfy the following conditions

In this way, the cycle length of each codeword in the A _RS is n , and the A _RS is called a full cycle equivalence class.

We use ( N , M , q , H _m ) to denote a set of M frequency hopping sequences of sequence length N over a set of frequency slots of size q , where H _m is its maximum aperiodic Hamming correlation .

Let Δ( n )=min{ s : s | n , s >1} and Ω( n )=min{ t : t | n , t >Δ( n )} denote the smallest factor of n other than 1 and The second smallest factor.

The following is an introduction to the prior art based on the above basic definitions as follows:

The prior art is Sets of frequency hopping sequences under aperiodic Hammingcorrelation: upper bound and optimal constructions [J]. Advances inMathematics of Communications, Vol.8, No.3, pp.359-373, Aug. 2014.

At present, there have been constructions of short sequence sets with excellent aperiodic Hamming correlation, but these methods are all methods of extracting cyclic code subcodes. The construction method is too redundant and cumbersome, and the required software and hardware storage space is too large. more difficult. A typical method of constructing short sequence sets with excellent aperiodic Hamming correlation using cyclic codes (using RS codes, which is a relatively simple type of cyclic codes) is as follows:

For any integer k , 1≤ k <Ω( q −1), we can construct the frequency hopping sequence S ₁ in the following two cases:

Case 1: 1≤k <Δ( q −1)

In this case, first let n = q −1, A _RS is defined as before. For a given integer l , l | n and 1 < l ≤ n − k +1, we have

where all subscripting operations are performed modulo n .

Case 2: Δ( q −1) ≤ k <Ω( q −1)

的定义如前。对于给定的整数l，l|[n/Δ(n)]且1<l≤ n−k+1，我们有in this case,

is defined as before. For a given integer l , l |[ n /Δ( n )] and 1< l ≤ n − k +1, we have

and

where all subscripting operations are performed modulo n . Taking the union of the set Q and the set R , we can get the frequency hopping sequence S ₁ as follows

S ₁ = Q ∪ R

, q, k −1)跳频序列。Theorem: The set S ₁ is a ( l + k −1,

, q , k −1) frequency hopping sequence.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is that the construction process of the short frequency hopping sequence in the prior art is too complicated, requires a large amount of software and hardware storage space, and greatly increases the complexity of the operation. The present invention provides a method for generating an excellent aperiodic Hamming correlation short frequency hopping sequence set to solve the above problems.

In practical applications, the aperiodic Hamming correlation of short frequency hopping sequences can measure the performance of the frequency hopping communication system more accurately than the periodic Hamming correlation. The constructed short frequency hopping sequences use aperiodic Hamming correlation to measure its anti-interference performance. ; The generated short frequency hopping sequence contains a large number of sequences under aperiodic Hamming correlation, which is suitable for a communication system in which a large number of users share a limited bandwidth.

In order to obtain a short frequency hopping sequence, the prior art needs to use a polynomial to generate an RS code, and then perform the equivalent judgment and screening of the codeword on the RS code, and then judge the cycle length of the screened codeword before classifying the codeword. Truncating the classified codewords to construct short frequency hopping sequences, the implementation process is redundant and complex, requiring a large storage space of software and hardware, and the complexity of the algorithm is also very large.

The present invention is achieved through the following technical solutions:

A generation method of aperiodic Hamming correlation short frequency hopping sequence set:

Multiple groups of users share a carrier frequency band, there are a known limited number of frequency slots within the carrier frequency band, and multiple groups of users transmit information within the carrier frequency band;

When the number of frequency slots within the carrier frequency band is a prime number, construct a short frequency hopping sequence and assign a short frequency hopping sequence to each group of users: the short frequency hopping sequence performs frequency band encryption and anti-interference for the information transmitted by each group of users Addition, specifically, the short frequency hopping sequence moves the information sent by each group of users on the shared carrier frequency band in frequency, and the short frequency hopping sequence is used for each group of users on the shared carrier frequency band. Information is shifted in reverse in frequency;

The frequency slots constitute a set GF( p ), the set GF( p ) is a finite field of the number of ranges of frequency points used by the carrier for frequency hopping, p represents the number of frequency slots and p is a prime number, and the set GF( p ) is based on frequency. The elements of the slot are in descending order as GF( p ) = {0,1,..., p -1}, and the value range of the frequency points of the short frequency hopping sequence is 0,1,..., p -1;

The short frequency hopping sequence of each group of users is:

where m is an integer and satisfies 1≤ m ≤ p −1, f ( x ) is the function of generating a short frequency hopping sequence for carrier frequency hopping with respect to x , f ( x ) = ax ^m + bx ^{m −1} + c _{m - 2} x ^{m - 2} + ... + c ₁ x + c ₀ , a , b are two arbitrary values and a , b ∈ GF( p ), a ≠ 0, the coefficients c _0, c ₁ ,.. ., c _{m -2} ∈ GF( p ), c _0, c ₁ ,..., c _{m -2} take any value in GF( p ) after c _0, c ₁ ,..., c _{m -2} Generate the m −1 power combination of p , where n is a positive integer less than or equal to p − m +1.

共n+m−1项，所述短跳频序列S的序列长度为n+m−1。The short frequency hopping sequence S has

There are a total of n + m −1 items, and the sequence length of the short frequency hopping sequence S is n + m −1.

为p除以n并向下取整数。The total number of sequences in the short frequency hopping sequence S is

Divide p by n and round down.

The size of the frequency slot set of the short frequency hopping sequence S is p , and according to GF( p ) = {0,1,..., p −1}, the value range of the frequency point of the short frequency hopping sequence is 0,1 ,..., p −1 has a total of p frequency points.

The maximum aperiodic Hamming correlation of the short frequency hopping sequence S is m −1;

For the short frequency hopping sequence S , the maximum aperiodic Hamming autocorrelation H _a ( S ) is a parameter that characterizes the frequency coincidence between the information of each group of users in the information transmission, and the maximum aperiodic Hamming cross correlation H _c ( S ) is The frequency coincidence parameters that characterize the information between users and users in the information transmission of multiple groups of users, the maximum aperiodic Hamming autocorrelation H _a ( S ), the maximum aperiodic Hamming cross-correlation H c ( S ) and the maximum aperiodic Hamming correlation H _c ( S ) and maximum aperiodic Hamming correlation The clear correlation H _m ( S ) is defined as

，

，

，

，对于任意的f ₁ , f ₂ ∈S，

，a为x上的频点，b为y上的频点，

的取值为

，N =n+m−1，所述短跳频序列S的

。where x =( x ₀ , x ₁ , ..., x _{N −1} ), y =( y ₀ , y ₁ , ..., y _{N −1} ) are two different sequences in S , τ is the time delay,

,

,

,

, for any f ₁ , f ₂ ∈ S ,

, a is the frequency point on x , b is the frequency point on y ,

value of

, N = n + m −1, the short frequency hopping sequence S

.

All operations are performed modulo p , and any operation is divided by p and the remainder is taken.

The present invention has the following advantages and beneficial effects:

The method of the present invention is simple to implement, and the generation sequence only needs to be calculated by the function f ( x ).

The present invention can generate short frequency hopping sequence only by calculating on the basis of polynomial, the realization is very simple, the algorithm complexity is small, the excessive software and hardware storage space is not required, and the software and hardware overhead and cost can be greatly reduced.

Description of drawings

The accompanying drawings described herein are used to provide further understanding of the embodiments of the present invention, and constitute a part of the present application, and do not constitute limitations to the embodiments of the present invention. In the attached image:

FIG. 1 is a block diagram of generating a short frequency hopping sequence S according to the present invention.

FIG. 2 is a block diagram comparing the short frequency hopping sequence generated by the present invention and the prior art.

Detailed ways

Before any embodiment of the invention is described in detail, it is to be understood that the invention is not limited to the details of construction shown in the following description or in the drawings. The invention is capable of other embodiments and of being carried out or being carried out in various ways. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative improvements shall fall within the protection scope of the present invention.

As shown in Figure 1,

A method for generating aperiodic Hamming correlation short frequency hopping sequence sets.

In practical applications, the aperiodic Hamming correlation of short frequency hopping sequences can measure the performance of the frequency hopping communication system more accurately than the periodic Hamming correlation. The constructed short frequency hopping sequences use aperiodic Hamming correlation to measure its anti-interference performance. ; The generated short frequency hopping sequence contains a large number of sequences under aperiodic Hamming correlation, which is suitable for a communication system in which a large number of users share a limited bandwidth.

In order to obtain a short frequency hopping sequence, the prior art needs to use a polynomial to generate an RS code, and then perform the equivalent judgment and screening of the codeword on the RS code, and then judge the cycle length of the screened codeword before classifying the codeword. Truncating the classified codewords to construct short frequency hopping sequences, the implementation process is redundant and complex, requiring a large storage space of software and hardware, and the complexity of the algorithm is also very large.

The present invention is achieved through the following technical solutions:

A generation method of aperiodic Hamming correlation short frequency hopping sequence set:

Multiple groups of users share a carrier frequency band, there are a known limited number of frequency slots within the carrier frequency band, and multiple groups of users transmit information within the carrier frequency band;

When the number of frequency slots within the carrier frequency band is a prime number, construct a short frequency hopping sequence and assign a short frequency hopping sequence to each group of users: the short frequency hopping sequence performs frequency band encryption and anti-interference for the information transmitted by each group of users Addition, specifically, the short frequency hopping sequence moves the information sent by each group of users on the shared carrier frequency band in frequency, and the short frequency hopping sequence is used for each group of users on the shared carrier frequency band. Information is shifted in reverse in frequency;

The frequency slots constitute a set GF( p ), the set GF( p ) is a finite field of the number of ranges of frequency points used by the carrier for frequency hopping, p represents the number of frequency slots and p is a prime number, and the set GF( p ) is based on frequency. The elements of the slot are in descending order as GF( p )={0,1,..., p -1}, and the value range of the frequency points of the short frequency hopping sequence is 0,1,..., p -1;

The short frequency hopping sequence of each group of users is:

where m is an integer and satisfies 1≤ m ≤ p −1, a , b are two arbitrary values and a , b ∈ GF( p ), a ≠ 0, f ( x ) is the generation of short-circuit for carrier frequency hopping. Frequency hopping sequence as a function of x , f ( x ) = ax ^m + bx ^{m -1} + c _{m -2} x ^{m -2} +...+ c ₁ x + c ₀ , coefficients c _0, c ₁ ,.. ., c _{m -2} ∈ GF( p ), c _0, c ₁ ,..., c _{m -2} take any value in GF( p ) after c _0, c ₁ ,..., c _{m -2} Generate the m −1 power combination of p , where n is a positive integer less than or equal to p − m +1.

共n+m−1项，所述短跳频序列S的序列长度为n+m−1。The short frequency hopping sequence S has

There are a total of n + m −1 items, and the sequence length of the short frequency hopping sequence S is n + m −1.

为p除以n并向下取整数。The total number of sequences in the short frequency hopping sequence S is

Divide p by n and round down.

The size of the frequency slot set of the short frequency hopping sequence S is p , and according to GF( p ) = {0,1,..., p −1}, the value range of the frequency point of the short frequency hopping sequence is 0,1 ,..., p −1 has a total of p frequency points.

The maximum aperiodic Hamming correlation of the short frequency hopping sequence S is m −1;

For the short frequency hopping sequence S , the maximum aperiodic Hamming autocorrelation H _a ( S ) is a parameter that characterizes the frequency coincidence between the information of each group of users in the information transmission, and the maximum aperiodic Hamming cross correlation H _c ( S ) is The frequency coincidence parameters that characterize the information between users and users in the information transmission of multiple groups of users, the maximum aperiodic Hamming autocorrelation H _a ( S ), the maximum aperiodic Hamming cross-correlation H _c ( S ) and the maximum aperiodic Hamming correlation H c ( S ) and the maximum aperiodic Hamming The clear correlation H _m ( S ) is defined as

，

，

，

，对于任意的f ₁ , f ₂ ∈S，

，a为x上的频点，b为y上的频点，

的取值为

，N =n+m−1，所述短跳频序列S的

。where x =( x ₀ , x ₁ , ..., x _{N −1} ), y =( y ₀ , y ₁ , ..., y _{N −1} ) are two different sequences in S , τ is the time delay,

,

,

,

, for any f ₁ , f ₂ ∈ S ,

, a is the frequency point on x , b is the frequency point on y ,

value of

, N = n + m −1, the short frequency hopping sequence S

.

All operations are performed modulo p, and any operation is divided by p and the remainder is taken.

On the basis of the previous embodiment, the excellent functional effect of the present invention is proved from the mathematical level, and the proof process is as follows:

, p，我们只需证明其最大非周期汉明相关为m−1。对于时延n≤τ≤n+m−2的情况，对任意

其非周期汉明相关为Obviously, the sequence length, the number of sequences and the size of the frequency slot set are n + m −1, respectively,

, p , we only need to prove that its maximum aperiodic Hamming correlation is m −1. For the case of delay n ≤ τ ≤ n + m −2, for any

Its aperiodic Hamming correlation is

的非周期汉明自相关为Below we discuss the case where 0 ≤ τ ≤ n −1. For the aperiodic Hamming autocorrelation of the sequence, we consider the case where the sequence is delayed 0 < τ ≤ n −1,

The aperiodic Hamming autocorrelation of

According to the definition of f ( x ), it can be known that

Since a polynomial of degree m −1 over GF( p ) has at most m −1 roots, so

(i ≠ j)的非周期汉明互相关为Similarly, we can show that in the case of delay 0 ≤ τ ≤ n −1,

The aperiodic Hamming cross-correlation of ( i ≠ j ) is

So the maximum aperiodic Hamming correlation of S is m −1.

Certificate completed.

生成短跳频序列

如下：In one embodiment, selecting p=7, n=3, m=3, a=1, b=0, then the polynomial

Generate short frequency hopping sequences

as follows:

......

......

......

生成，实现方法简单，所需的软硬件存储空间和运算复杂度都较小。It can be verified by applying the present invention that the sequence set is a (5, 98, 7, 2) short frequency hopping sequence. The method directly takes the polynomial

The method of generation and implementation is simple, and the required software and hardware storage space and computational complexity are small.

On the basis of the previous embodiment, the short frequency hopping sequence generation is compared between the prior art and the method of the present invention, and the comparison results are as follows:

Existing technology: Using the existing technology, as shown in FIG. 2 , selecting q = 7, l = 3, and k = 3, the (5, 114, 7, 2) short frequency hopping sequence can be obtained.

The present invention: using the present invention, as shown in Figure 2, select p = 7, n = 3, m = 3, a = 1, b = 0, then (5, 98, 7, 2) short frequency hopping sequence can be obtained .

It can be seen that although the number of sequences obtained by the prior art is 114-98=16 more than that obtained by the present invention, the implementation is very complicated. In order to obtain a short frequency hopping sequence, the prior art needs to use a polynomial to generate an RS code, and then perform the equivalent judgment and screening of the codeword on the RS code, and then judge the cycle length of the screened codeword before classifying the codeword. Truncating the classified codewords to construct short frequency hopping sequences, the implementation process is redundant and complex, requiring a large storage space of software and hardware, and the complexity of the algorithm is also very large.

However, the present invention can generate short frequency hopping sequences only by calculating on the basis of polynomials, the implementation is simple, the algorithm complexity is small, excessive software and hardware storage space is not required, and the software and hardware overhead and cost can be greatly reduced.

The specific embodiments described above further describe the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (5)

1. A method for generating an aperiodic Hamming related short frequency hopping sequence set is characterized in that:

a plurality of groups of users share one carrier frequency band, a known limited number of frequency slots exist in the carrier frequency band range, and the plurality of groups of users transmit information in the carrier frequency band;

when the number of frequency slots in the carrier frequency band range is a prime number, constructing a short frequency hopping sequence and distributing the short frequency hopping sequence for each group of users: the short frequency hopping sequence carries out frequency band encryption and anti-interference addition on information transmitted by each group of users, specifically, the short frequency hopping sequence carries out frequency shift on information sent by each group of users on a shared carrier frequency band, and the short frequency hopping sequence carries out reverse frequency shift on the information sent by a receiving end of each group of users on the shared carrier frequency band;

frequency slot forming set GF (p) The set GF: (p) A finite field of the number of ranges of carrier waves used for hopping frequency bins,pindicates the number of frequency slots andpis a prime number, set GF: (p) Push buttonThe value range of the element of the irradiation gap is GF (p) = {0,1,...,p-1 }, which is the value range of the frequency points of the short hopping sequence, the value number of the frequency points isp；

The short hopping sequence for each group of users is:

in the formulamIs an integer and satisfies 1 ≦m≤p−1，f(x) For generating short hopping sequences for carrier hoppingxAs a function of (a) or (b),f(x) =ax ^m +bx ^m－1+c _m－2 x ^m－2+...+c ₁ x+c ₀，a,bis two arbitrary values anda,b∈GF(p)，anot equal to 0, coefficientc _0, c ₁,...,c _m－2∈GF(p)，c _0, c ₁,...,c _m－2Optionally GF (p) The value of (1) is (b),c _0, c ₁,...,c _m－2generate a relationpIs/are as followsm-1 power combination of formula (I) whereinnIs less than or equal top−mA positive integer of + 1.

2. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSIs provided with

In totaln+m-1 item, the short hopping sequenceSHas a sequence length ofn+m−1。

3. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSThe number of sequences in (a) totals

Is composed ofpIs divided bynAnd take the integer downward.

4. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSHas a frequency slot set size ofpAccording to GF (p) = {0,1,...,p-1, the frequency point of the short hopping sequence has a value range of 0, 1.,p-1 is a wholepAnd (4) frequency points.

5. The method of claim 1, wherein the short hopping sequence set is generated according to aperiodic Hamming correlation short hopping sequence setSThe maximum aperiodic Hamming correlation of ism−1；

For short frequency hopping sequencesSMaximum aperiodic Hamming autocorrelationH _a (S) Maximum aperiodic Hamming cross-correlation for characterizing frequency coincidence parameters between information of each group of users in information transmissionH _c (S) Maximum aperiodic Hamming autocorrelation for characterizing frequency coincidence parameters of information between users in information transmission of multiple groups of usersH _a (S) Maximum aperiodic hamming cross-correlationH _c (S) Correlation with maximum aperiodic HammingH _m (S) Is defined as

In the formula,x=(x ₀,x ₁, ...,x _N−1),y=(y ₀,y ₁, ...,y _N−1) Is composed ofSIn the case of two different sequences of the sequence,τin order to be a time delay,

，

，

，

for arbitraryf ₁ , f ₂ ∈S，

，aIs composed ofxThe frequency points at the upper part of the frequency band,bis composed ofyThe frequency points at the upper part of the frequency band,

is taken as

，N=n+m-1, the short hopping sequenceSIs/are as follows

。

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