CN105162494A - Frequency hopping sequence model reconstructing method based on RS code generation - Google Patents

Abstract

The invention belongs to the technology of signal treatment in non-cooperative frequency hopping frequency communication and especially relates to non-cooperative frequency hopping sequence predication. According to the invention, by utilizing a special number of frequency points generated in frequency hopping sequence model construction employing the RS code and an L-G model in combination, different parameters of the model is worked out so as to achieve the aim of reconstructing the model. The parameters include a primitive polynomial of the RS code, a user address code, a feedback polynomial of the L-G model and a tap position. The method can be employed for helping in analyzing whether a sequence in actual use of a frequency hopping broadcasting station is constructed based on the combination model of the RS code or not in non-cooperative frequency hopping communication. Once that the sequence is constructed based on the model is determined, good predication of frequency hopping sequence can be realized by using the method.

Description

A kind of frequency hop sequences model reconstruction method generated based on RS code

Technical field

The invention belongs to the signal processing technology belonged in non-cooperation frequency hopping communications, particularly relate to non-cooperation frequency hop sequences Predicting Technique.

Background technology

Frequency-hopping communication system utilizes the rule of frequency hopping code control frequency saltus step.Along with the development of Frequency-hopping Communication Technology, the application of Families of Frequency-Hopping Sequences in frequency hopping communications based on RS code structure is increasingly extensive.

RS code is proposed by Reed and Solomon the earliest, and it is a kind of cyclic code of q system, and the generator matrix in galois field GF (q) is defined as code word generates expression formula and can be written as code word C can be designated as c (N, t+1 again; I), wherein, V=[v ₀, v ₁..., v _t] be information vector and v _j∈ GF (q), j=0,1 ..., t, t are positive integer, q=2 ⁿ, α is a primitive element in described GF (q), and determined by primitive polynomial, i represents the cyclicity of RS code, i.e. code word c (N, t+1; I) represent at code word c (N, t+1; 0) basic cocycle i time.

During based on RS code structure frequency hop sequences, the sequence of getting two information bit structures is best, have non-repeatability, and autocorrelation and cross correlation all reaches optimum.Code word expression formula is defined as

$\begin{array}{c}C=\[v_0,1\]\×\left[\begin{array}{cccc}1& 1& ...& 1\\ 1& \mathrm{\α}& ...& {\mathrm{\α}}^{q-2}\end{array}\right]\\ =\[v_0,v_0,\mathrm{...},v_0\]+\[1,\mathrm{\α},\mathrm{...},{\mathrm{\α}}^{q-2}\]\end{array}$

Wherein, v ₀multi-user's property of ∈ GF (q) control sequence, sequence length is q-1.This sequence can produce with Jia Luohua type shift register, and feedback tap position and the primitive polynomial of Jia Luohua type shift register are inconsistent, have duality relation, as follows: set primitive polynomial as g (x)=1+b ₁x+b ₂x ²+ ... + b _nx ⁿ, then each feedback factor is c _n=1, c _n-1=b ₁, c _n-2=b ₂..., c ₂=b _n-2, c ₁=b _n-1.As shown in Figure 1, the status switch of shift register is the RS code sequence of generation.

The RS sequence period of two information bits structure only has q-1, and the cycle is too short, therefore a kind ofly the mode that the L-G model of m sequencer or discontinuous tap model (being referred to as L-G model below) and RS code combination get up to construct frequency hop sequences is suggested.The sequence of such structure sacrifices correlation to a certain extent, reaches macrocyclic object, although the correlation of sequence does not reach optimum, but uses as frequency hop sequences and is still a good selection.Its concrete make is first produce q=2 with L-G model ⁿindividual length is 2 ^mthe random sequence of-1 (m is described m sequencer number of shift register stages), then by each frequency in each sequence with one long be q-1 RS code word replace, such frequency hop sequences cycle is just extended to (q-1) (2 ^m-1), number of users is still q.Wherein each user has q RS code word and takes from c (q-1,3; Q-2), its generation expression formula is $\begin{array}{c}S=\left[\begin{array}{ccc}\mathrm{\β}& \mathrm{\γ}& 1\end{array}\right]\×\left[\begin{array}{ccccc}1& 1& 1& \mathrm{...}& 1\\ 1& \mathrm{\α}& {\mathrm{\α}}^2& \mathrm{...}& {\mathrm{\α}}^{q-2}\\ 1& {\mathrm{\α}}^{(q-2)}& {\mathrm{\α}}^{2(q-2)}& \mathrm{...}& {\mathrm{\α}}^{(q-2)(q-2)}\end{array}\right]\\ =\[{\mathrm{\β}}_j,{\mathrm{\β}}_j,\mathrm{...},{\mathrm{\β}}_j\]+{\mathrm{\γ}}_j\[1,\mathrm{\α},\mathrm{...},{\mathrm{\α}}^{q-2}\]+\[1,{\mathrm{\α}}^{q-2},\mathrm{...},{\mathrm{\α}}^{(q-2)(q-2)}\]\end{array},$ Wherein, β _j, γ _j∈ GF (q), β _jcontrol to generate q user, γ _jcontrol q the RS code word generating each user.Operation rule according to field element in galois field can construct [1, α with the shift register on n rank ^q-2..., α ^{(q-2) (q-2)}], [β _j, β _j..., β _j]+γ _j[1, α ..., α ^q-2] be essentially the RS code word that two information bits produce, its make as Fig. 1, parameter γ _jonly change the initial condition of shift register.L-G model passes through γ _jcouple together with the production model of RS code word, namely L-G model produces a frequency at every turn, just the binary system transition of this frequency is assigned to the shift register of generation RS code word as initial state, after shift register circulation q-1 time of RS code word, L-G model again produces new frequency and is assigned to RS code word shift register, until L-G mold cycle 2 ^m-1 time, the clock cycle ratio of two shift registers is 1/ (2 ⁿ-1).Its concrete model can represent with Fig. 2, wherein, if the feedback polynomial of L-G model is f (x)=1+q ₁x+q ₂x ²+ ... q _mx ^m, user code be V=[v0, v1 ..., v _n-1], the primitive polynomial of RS code is g (x)=1+b ₁x+b ₂x ²+ ... + b _nx ⁿ.

In non-cooperation frequency hopping communications, the analysis and research structure of frequency hop sequences, model reconstruction and sequence prediction method are significant.The reconstructs prediction frequency hop sequences method of existing comparative maturity all for m sequence, as to L-G model, the reconstruct etc. of discontinuous tap model and universal model.RS code has excellent character as a kind of cyclic code of multi-system, the application of frequency hop sequences in frequency hopping communications based on RS code structure is also increasingly extensive, the existing research to RS sequence is all only limitted to the research to make, and it is very few to the reconstructs prediction research of the frequency hop sequences constructed based on RS code, the present invention does analysis and research forefathers on the basis of the frequency hop sequences reconstructs prediction method of institute, proposes a kind of reconstruct constructs frequency hop sequences model method based on RS code.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, propose a kind of frequency hop sequences model reconstruction method generated based on RS code, the frequency of the some that the method utilizes RS code and L-G model composite construction frequency hop sequences model to produce, solve the parameters of this model to reach the object of this model of reconstruct, described parameter comprises the primitive polynomial of RS code, user code, the feedback polynomial of L-G model and tap position.

Based on the frequency-hopping sequences model reconstruction method that RS code generates, its step is as follows:

S1, intercept and capture length be the frequency hop sequences of x, guarantee length be have in the frequency hop sequences of x value of frequency point be 0 frequency, find out frequency maximum f _max, determine the number of shift register stages of RS code word wherein, x>=2n _lG(2 ⁿ-1), n _lGrepresent the number of shift register stages of L-G model, now n _lGfor unknown number, exist as intermediate variable;

S2, determine the initial frequency position of RS code and the user code of superposition in final output sequence, show that the initial frequency position concrete steps of RS code in final output sequence are as follows:

S21, from the frequency hop sequences described in S1, get a segment length be 2 (2 ⁿ-1) sequence, is denoted as { L (j) }, j=1,2 ..., 2 (2 ⁿ-1), j represents that frequency is numbered;

S22, { L (j) } described in S21 is divided into (2 ⁿ-1) individual short data records:

$\begin{array}{c}{l}_1^v=\{L\left(j\right),j=1,2,\mathrm{...},2^n,\mathrm{...},2^n-1\}\\ l_2^v=\{L\left(j\right),j=2,3,\mathrm{...},2^n\}\\ \mathrm{...}\\ l_{2^n-1}^v=\{L\left(j\right),j=2^n,2^n+1,\mathrm{...},2(2^n-1)\}\end{array},$ Remember that these short data records are for set $\{l_p^v,p=1,2,\mathrm{...},2^n-1\},$ With these short data records for training sequence, the initial frequency position of a RS code in { L (j) } described in search S21;

S3, generate the primitive polynomial of RS code word according to the initial frequency position calculation of S2 gained RS code, be specially:

S31, from the frequency hop sequences intercepted and captured, to take out arbitrarily two adjacent RS code words according to the initial frequency position of the RS code of s22 gained, be denoted as R respectively ₁and R ₂;

S32, by R described in S31 ₁and R ₂the frequency step-by-step of correspondence position is carried out mould two and is added, and each value of the result after being added by mould two is converted into the binary vector of a n position, and is write the binary vector of all values as n × (2 ⁿ-1) matrix, wherein, matrix the first row represents the highest order of the binary vector of each frequency, most end line display lowest order;

S33, get the first row of matrix described in S32 and be applied to BM algorithm and solve the feedback polynomial generating RS code word, be designated as f ₁(x)=1+q ₁x+q ₂x ²+ ... + x ⁿ, wherein, q _ifor feedback factor;

S34, the generator polynomial obtaining RS code according to the feedback polynomial of Jia Luohua type shift register and the duality relation of primitive polynomial are g (x)=x ⁿ+ q ₁x ^n-1+ q ₂x ^n-2+ ... + 1;

S4, calculating L-G model feedback multinomial, be specially: according to the initial frequency position of RS code in the final output sequence that S2 obtains, taken out by the first frequency of several RS code words continuous in intercepted and captured sequence, composition sequence, is designated as LG ₁={ LG ₁(j) }, use described LG ₁replace, described in S21 { L (j) }, repeating S21-S22, calculating stable feedback polynomial f (x) of LG sequence, determine the number of shift register stages n of L-G model _lGsize;

S5, determine the tap position of L-G model;

S6, reconstruct the generation model of the primitive polynomial composite construction frequency hop sequences of RS code word required by L-G model and S3.

Further, the initial frequency position concrete steps of searching for a RS code in { L (j) } described in S21 described in S22 are:

S221, make p=1;

S222, general adjacent two frequency bins step-by-step carry out mould two and add, obtain the sequence removing address code, be denoted as { l _p(j) }, wherein, j=1,2 ..., 2 ⁿ-2;

S223, by { l described in S222 _p(j) } each frequency step-by-step be launched into n position binary vector, and write the binary vector of all frequencies as n × (2 ⁿ-2) matrix, wherein, the first row of matrix represents the highest order of the binary vector of each frequency, most end line display lowest order;

S224, get the first row of matrix described in S223, utilize BM Algorithm for Solving feedback polynomial and record the feedback polynomial often walking in solution procedure and obtain, taking out the feedback polynomial that the occurrence number of record is maximum, be denoted as $f_2\left(x\right)=1+c_{1}x+c_2{x}^2+...c_{n_{temp}}{x}^{n_{temp}},$ Note f ₂x the feedback factor vector of () is $cx=\[1,c_1,c_2,\mathrm{...}{c}_{n_{temp}}\],$ Wherein f ₂x the highest power of () is n _temp;

S225, to get beginning n _temp+ 1 frequency, is launched into the binary vector of n position, by n by each frequency step-by-step _tempthe binary vector of+1 frequency is write as a n × (n _temp+ 1) matrix, matrix the first row represents the highest order of the binary vector of each frequency, and footline represents lowest order, remembers that each row vector is A (k), k=1,2 ... n, wherein, k represents line number;

S226, get each row vector of matrix described in S225, calculate w _k=cx × A (k) ', note W=[w ₁, w ₂..., w _n], then use short data records l _p ^vthe address code of the user obtained is V _p=[v ₀, v ₁..., v _n-1]=W;

S227, to get the n of beginning _tempindividual frequency, by V described in each frequency and S226 _pstep-by-step is carried out mould two and is added, and result is converted into n position binary vector, by n _tempthe binary vector of individual frequency is write as a n × n _tempmatrix, the first row of matrix represents the highest order of the binary vector of frequency, and footline represents lowest order, remembers that each row vector is B (k);

S228, using first of matrix described in S227 row vector B (1) as n _tempthe initial condition of rank shift register, with f described in S224 ₂x (), as feedback polynomial, circulates 2 ⁿ-1 time, obtain a binary sequence, be designated as C ₁, then using second row vector B (2) as initial condition, with f described in S224 ₂x (), as feedback polynomial, circulates 2 ⁿ-1 time, obtain binary sequence, be designated as C ₂, the like, obtain n binary sequence;

S229, the n of a S228 gained binary sequence is arranged in n × (2 ⁿ-1) matrix H, the sequence that the first behavior of described matrix H produces for initial state with B (1), the sequence that the second behavior produces for initial state with B (2), the like.Each row of described matrix H are mapped as a decimal number, wherein the first behavior highest order, and most end behavior lowest order, by V described in each decimal number and S226 _pstep-by-step is carried out mould two and is added, and result is denoted as d={d ₁, d ₂, d _2n-1, remove d and front n _tempindividual frequency, compares the corresponding identical number of residue frequency and is designated as same, calculating reconstruct probability if accu=100%, then p is the initial frequency of a RS code word in the sequence { L (j) } described in S21, and V _pfor the address code that system is used, otherwise proceed to S229;

S2210, make p=p+1, searching loop S222-S229.

Further, determine the tap position of L-G model described in S5, concrete steps are as follows:

S51, by continuous 2n _lGthe first frequency of individual RS code word takes out, and forms new sequence;

S52, sequence new described in S51 and frequency 1 step-by-step are carried out mould two add, be denoted as { LG ₂(j) }, wherein, j=0,1 ..., 2n _lG-1;

S53, by { LG described in S52 ₂(j) } step-by-step expands into the binary vector of n position, is denoted as LG ₂(j)={ LG ₂(j, k) };

S54, use LG ₂(j) composition n × 2n _lGmatrix, a kth row vector is denoted as LG ₂' (k)={ LG ₂(1, k), LG ₂(2, k) ..., LG ₂(2n _lG, k) };

S55, get n × 2n described in S54 _lGkth-1 row vector of matrix and described kth-1 row vector before continuous print n _lGindividual value, judges described continuous print n _lGwhether individual value occurs in other row vectors,

If do not occur, then set the register taps position of the (n-1)th row vector as 0, i.e. j _k=0, note kth-1 row vector rower is k ₀,

If occurred, then make k=k+1, repeat S54-S55;

S56, described in S55 k ₀in be that starting point gets continuous n with i _lGindividual value, is denoted as G _i={ LG ₂(j, k ₀), j=i, i+1 ..., i+n _lG-1}, wherein, i=2,3 ..., n _lG;

S57, get n × 2n described in S54 _lGmatrix except k described in S55 ₀the front n of row _lGindividual value, is denoted as $G_0^k=\{{\mathrm{LG}}_2(j,k),j=0,1,\mathrm{...},n_{LG}-1\}|k\≠k_0;$

If S58 then the tap position of row k is i, i.e. j _k=i;

S59, obtain the tap position of all row, be denoted as { j _n-1..., j ₁, j ₀.

The invention has the beneficial effects as follows:

The present invention, on the basis of the make of analysis and research RS code, proposes the method for reconstruct based on the frequency hop sequences model of RS code structure.Whether the method can help to analyze actual frequency hopping radio set sequence used and construct based on the built-up pattern of RS code in non-cooperation frequency hopping communications, once be defined as this model, just realizes good prediction by the method to frequency hop sequences.

Accompanying drawing explanation

Fig. 1 is the RS sequence production model of two information bits.

Fig. 2 is that RS code and LG model combine tectonic sequence production model.

Fig. 3 is each sequence reconstruct probability statistics figure finding RS code original position.

Fig. 4 is [1, α in embodiment ^q-2..., α ^{(q-2) (q-2)}] register form.

Fig. 5 is flow chart of the present invention.

Embodiment

Below in conjunction with embodiment and accompanying drawing, describe technical scheme of the present invention in detail.

As shown in Figure 5:

Suppose that the primitive polynomial that RS code word is selected is g (x)=1+x ²+ x ³+ x ⁴+ x ⁸, the feedback polynomial of LG model is f (x)=1+x ²+ x ³+ x ⁸+ x ¹⁰, tap position is Position_r=[10,9,7,6,5,3,2,1], and user code is adduser=1=[0,0,0,0,0,0,0,1], and life grows into (2 ¹⁰-1) (2 ⁸-1) sequence of=260865 is:

Sequence＝{254,110,153,15,130,219,70,248,91,97,171,125,109,147,29,165,26,16,190,162,58,71,149,56,117,234,69,64,105,164,226,128,51,253,168,104,192,25,14,107,239,221,36,11,53,121,249,232,204,135,158,101,100,19,73,167,75,22,224,55,151,77,41,9,61,111,214,57,186,129,231,35,178,143,244,140,59,229,156,2,21,32,201,201,32,21,2,156,229,59,140,244,143,178,35,231,129,186,57,214,111,61,9,41,77,151,55,224……}

If continuous 6000 points are the frequency intercepted and captured from underscore partial data backward, be designated as L (i), i=1,2 ..., 6000}.Reconstruct according to these frequencies and produce the LG model of this sequence race and the parameters of RS code combination make.

The maximum of frequency can be found from L to be x _max=255, therefore the primitive polynomial progression of RS code is

From first frequency of L, get continuous 2 × (2 ⁿ-1)=510 frequencies, are designated as $\begin{array}{c}S=\{L\left(i\right),i=1,2,\mathrm{...},510\}=\{249,232,204,135,158,101,100,19,73,167,75,22,224,\\ 55,151,77,41,9,61,111,214,57,186,129,231,35,178,143,244,140,\mathrm{...}\}\end{array},$ Be divided into following short data records:

$\begin{array}{c}{s}_1^v=\{S\left(i\right),i=1,2,\mathrm{...},255\}=\{249,232,204,135,158,101,100,19,73,167,75,22,\mathrm{...}\}\\ s_2^v=\{S\left(i\right),i=2,3,\mathrm{...},256\}=\{232,204,135,158,101,100,19,73,167,75,22,\mathrm{224...}\}\\ \begin{array}{cc}.& .\\ .& .\\ .& .\end{array}\\ s_{255}^v=\{S\left(i\right),i=256,257,\mathrm{...},510\}=\{218,174,64,130,148,113,76,67,233,250,241,\mathrm{...}\}\end{array}$

Make j=1, will adjacent two frequency bins step-by-step mould two add after, be converted into the binary number of 8, and write as the matrix of 8 × 254, be designated as s ₁, specific as follows:

get

Go out s ₁the first row, i.e. dashed part, uses BM Algorithm for Solving, obtains the polynomial f that an occurrence number is maximum ₁(x)=1+x ²+ x ³+ x ⁵+ x ⁸+ x ¹¹+ x ¹³+ x ¹⁴+ x ¹⁶, note feedback vector is cx=[1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1];

Will beginning 17 frequencies, be launched into the binary vector of 8, and write as the matrix of 8 × 17, specific as follows as follows:

row k is designated as $s_j^v\left(k\right)_{\′},k=7,6,\mathrm{...},0.$

Calculate respectively obtain w ₇=0, w ₆=0, w ₅=0, w ₄=0, w ₃=0, w ₂=0, w ₁=0, w ₀=1, therefore the address code of system is: V ₁=[w ₇, w ₆, w ₅, w ₄, w ₃, w ₂, w ₁, w ₀]=[0,0,0,0,0,0,0,1].

Take out beginning 16 frequencies, and carry out mould two with V step-by-step and add, result is converted into the binary vector of 8, is write as the matrix of 8 × 16, specific as follows:

initial condition respectively using every a line of this matrix as 16 rank shift registers, tries to achieve f ₁(x)=1+x ²+ x ³+ x ⁵+ x ⁸+ x ¹¹+ x ¹³+ x ¹⁴+ x ¹⁶for feedback polynomial, circulate 255 times respectively, obtain 8 long be 255 m sequence, and write as the matrix of 8 × 255, specific as follows:

by each row and address code V ₁step-by-step mould two adds, and is converted into decimal system frequency, obtains sequence as follows: d={249,232,204,135,158,101,100,19,73,167,75,22,224,55,151,77,41,9,61,111,214,57,186,129,231,35,178,143,244,140,59,229,156,2,21,32,201,201,32,21,2,156,229,59,140,244,143,178,35,231,129,186,57,214,111,61,9,41,77,151,55,224,22,75,167,73,19,100,101,158 ....

Remove d and front 16 frequencies, the number calculating remaining frequency correspondent equal is 192, so reconstruct probability be ${\mathrm{accu}}_j=\frac{192}{255-16}=80.33\%,$

Make j=j+1, calculate reconstruct probability.

When calculating j=209, reconstruct probability reaches 100%, therefore the 209th frequency in L is the first frequency of a RS code word, and user code is V=V ₂₀₉=[0,0,0,0,0,0,0,0,1].

The RS code word that taking-up two is adjacent from L accordingly, specific as follows:

R ₁＝{L(i),i＝209,210,…,463}＝{255,108,157,7,146,251,6,120,70,91,223，149,160,20,14,131,86,136,147,248,142,50,127,241,250,233,67,…}，

R ₂=L (i), i=464,465 ..., 718}={253,104,149,23,178,187,134,101,124,47,55,88,39,7,40,207,206,165,201,76,251,216,182,126,249,239,79,84 ..., by R ₁and R ₂in the corresponding step-by-step of frequency carry out mould two and add, the sequence obtained is:

$\begin{array}{c}R=\{2,4,16,32,64,128,29,58,116,232,205,135,19,38,76,152,45,\\ 90,180,117,234,201,143,3,6,12,24,48,96,182,157,39,78,156,\mathrm{...}\}\end{array},$ R is converted into the binary number of 8, and is write as the matrix of 8 × 255, specific as follows:

take out the first row BM Algorithm for Solving, obtain polynomial f ₂(x)=1+x ⁴+ x ⁵+ x ⁶+ x ⁸, so the primitive polynomial generating RS code is g (x)=1+x ²+ x ³+ x ⁴+ x ⁸.

The all first frequency of the RS code in L is taken out, specific as follows:

$\begin{array}{c}{\mathrm{LG}}_1=\{255,253,248,251,244,226,206,215,172,27,125,176,107,213,224,\\ 138,86,167,12,91,188,51,109\}\end{array},$ To LG ₁process, the feedback polynomial solving LG model is f (x)=1+x ²+ x ³+ x ⁸+ x ¹⁰.

From L, take out the first frequency of 20 RS code words, add with 1 mould two, be designated as LG ₂, specific as follows:

$\begin{array}{c}{\mathrm{LG}}_2=\{254,252,249,250,245,227,207,214,173,26,124,177,106,212,225\\ 139,87,166,13,90\}\end{array},$ By LG ₂each frequency be converted into binary vector and write as the matrix of 8 × 20, as follows:

suppose that LG model is ring shift left, and set Far Left as No. 0 register, rightmost is No. 9 registers, and as can be seen from above-mentioned matrix, the dashed part of the first row did not all occur in other row, so the first row sequence is from No. 0 register, i.e. j ₇front 10 values of the=0, second row are 2nd ~ 11 values of the first row, so the register-bit of the second row is set to j ₆=1; Front 10 values of the third line are 4th ~ 13 values of the first row, so the register-bit of the third line is set to j ₅=3; Front 10 values of fourth line are 5th ~ 14 values of the first row, and the register-bit mainly with fourth line is set to j ₄=4; Front 10 values of fifth line are 6th ~ 15 values of the first row, so the register-bit of fifth line is set to j ₃=5; Front 10 values of the 6th row are 8th ~ 17 values of the first row, so the register-bit of the 6th row is set to j ₂=7; Front 10 values of the 7th row are 9th ~ 18 values of the first row, so the register-bit of the 7th row is set to j ₁=8; Front 10 values of the 8th row are 10th ~ 19 values of the first row, so the register-bit of the 8th row is set to j ₀=9.

By above-mentioned steps, the primitive polynomial having obtained RS code is g (x)=1+x ²+ x ³+ x ⁴+ x ⁸, user code is V=[0,0,0,0,0,0,0,1], and the feedback polynomial of LG model is f (x)=1+x ²+ x ³+ x ⁸+ x ¹⁰, tap position is [0,1,3,4,5,7,8,9] (tap position arranged before being equivalent to experiment), can find out that required result and the simulated conditions provided fit like a glove, thus can according to these parameters complete reconstruct original series.Wherein according to primitive polynomial g (x)=1+x ²+ x ³+ x ⁴+ x ⁸structure [1, α ^q-2..., α ^{(q-2) (q-2)}] shift register structure process as follows: [1, α ^q-2..., α ^{(q-2) (q-2)}] what represent is the multiplication of field element, is namely multiplied by α at every turn ^q-2, when primitive polynomial is g (x)=1+x ²+ x ³+ x ⁴+ x ⁸time, α ^q-2=α ²⁵⁴=α+α ²+ α ³+ α ⁷if arbitrarily-shaped domain element is γ=b ₀+ b ₁α+b ₂α ²+ b ₃α ³+ b ₄α ⁴+ b ₅α ⁵+ b ₆α ⁶+ b ₇α ⁷, then α ^q-2γ=α ^q-2(b ₀+ b ₁α+b ₂α ²+ b ₃α ³+ b ₄α ⁴+ b ₅α ⁵+ b ₆α ⁶+ b ₇α ⁷)=b ₁+ (b ₀+ b ₂) α+(b ₀+ b ₃) α ²+ (b ₀+ b4) α ³+ b ₅α ⁴+ b ₆α ⁵+ b ₇α ⁶+ b ₀α ⁷.

Claims (3)

1., based on the frequency-hopping sequences model reconstruction method that RS code generates, it is characterized in that, comprise the steps:

S1, intercept and capture length be the frequency hop sequences of x, guarantee length be have in the frequency hop sequences of x value of frequency point be 0 frequency, find out frequency maximum f _max, determine the number of shift register stages of RS code word wherein, x>=2n _lG(2 ⁿ-1), n _lGrepresent the number of shift register stages of L-G model;

S2, determine the initial frequency position of RS code and the user code of superposition in final output sequence, show that the initial frequency position concrete steps of RS code in final output sequence are as follows:

S21, from the frequency hop sequences described in S1, get a segment length be 2 (2 ⁿ-1) sequence, is denoted as { L (j) }, j=1,2 ..., 2 (2 ⁿ-1), j represents that frequency is numbered;

S22, { L (j) } described in S21 is divided into (2 ⁿ-1) individual short data records:

$\begin{array}{c}{l}_1^v=\{L\left(j\right),j=1,2,\mathrm{...},2^2-1\}\\ l_2^v=\{L\left(j\right),j=2,3,\mathrm{...},2^n\}\\ \mathrm{...}\\ l_{2^n-1}^v=\{L\left(j\right),j=2^n,2^n+1,\mathrm{...},2(2^n-1)\}\end{array},$ Remember that these short data records are for set $\{l_p^v,p=1,2,\mathrm{...},2^n-1\},$ With these short data records for training sequence, the initial frequency position of a RS code in { L (j) } described in search S21;

S3, generate the primitive polynomial of RS code word according to the initial frequency position calculation of S2 gained RS code, be specially:

S31, from the frequency hop sequences intercepted and captured, to take out arbitrarily two adjacent RS code words according to the initial frequency position of the RS code of s22 gained, be denoted as R respectively ₁and R ₂;

S32, by R described in S31 ₁and R ₂the frequency step-by-step of correspondence position is carried out mould two and is added, and each value of the result after being added by mould two is converted into the binary vector of a n position, and is write the binary vector of all values as n × (2 ⁿ-1) matrix, wherein, matrix the first row represents the highest order of the binary vector of each frequency, most end line display lowest order;

S33, get the first row of matrix described in S32 and be applied to BM algorithm and solve the feedback polynomial generating RS code word, be designated as f ₁(x)=1+q ₁x+q ₂x ²+ ... + x ⁿ, wherein, q _ifor feedback factor;

S34, the generator polynomial obtaining RS code according to the feedback polynomial of Jia Luohua type shift register and the duality relation of primitive polynomial are g (x)=x ⁿ+ q ₁x ^n-1+ q ₂x ^n-2+ ... + 1;

S4, calculating L-G model feedback multinomial, be specially: according to the initial frequency position of RS code in the final output sequence that S2 obtains, taken out by the first frequency of several RS code words continuous in intercepted and captured sequence, composition sequence, is designated as LG ₁={ LG ₁(j) }, use described LG ₁replace, described in S21 { L (j) }, repeating S21-S22, calculating stable feedback polynomial f (x) of LG sequence, determine the number of shift register stages n of L-G model _lGsize;

S5, determine the tap position of L-G model;

S6, reconstruct the generation model of the primitive polynomial composite construction frequency hop sequences of RS code word required by L-G model and S3.

2. according to claim 1 a kind of based on RS code generate frequency-hopping sequences model reconstruction method, it is characterized in that: the initial frequency position concrete steps of searching for a RS code in { L (j) } described in S21 described in S22 are:

S221, make p=1;

S222, general adjacent two frequency bins step-by-step carry out mould two and add, obtain the sequence removing address code, be denoted as { l _p(j) }, wherein, j=1,2 ..., 2 ⁿ-2;

S223, by { l described in S222 _p(j) } each frequency step-by-step be launched into n position binary vector, and write the binary vector of all frequencies as n × (2 ⁿ-2) matrix, wherein, the first row of matrix represents the highest order of the binary vector of each frequency, most end line display lowest order;

S224, get the first row of matrix described in S223, utilize BM Algorithm for Solving feedback polynomial and record the feedback polynomial often walking in solution procedure and obtain, taking out the feedback polynomial that the occurrence number of record is maximum, be denoted as $f_2\left(x\right)=1+c_{1}x+c_2{x}^2+\mathrm{...}{c}_{n_{temp}}{x}^{n_{temp}},$ Note f ₂x the feedback factor vector of () is $cx=\[1,c_1,c_2,\mathrm{...}{c}_{n_{temp}}\],$ Wherein f ₂x the highest power of () is n _temp;

S225, to get beginning n _temp+ 1 frequency, is launched into the binary vector of n position, by n by each frequency step-by-step _tempthe binary vector of+1 frequency is write as a n × (n _temp+ 1) matrix, matrix the first row represents the highest order of the binary vector of each frequency, and footline represents lowest order, remembers that each row vector is A (k), k=1,2 ... n, wherein, k represents line number;

S226, get each row vector of matrix described in S225, calculate w _k=cx × A (k) ', note W=[w ₁, w ₂..., w _n], then use short data records l _p ^vthe address code of the user obtained is V _p=[v ₀, v ₁..., v _n-1]=W;

S227, to get the n of beginning _tempindividual frequency, by V described in each frequency and S226 _pstep-by-step is carried out mould two and is added, and result is converted into n position binary vector, by n _tempthe binary vector of individual frequency is write as a n × n _tempmatrix, the first row of matrix represents the highest order of the binary vector of frequency, and footline represents lowest order, remembers that each row vector is B (k);

S228, using first of matrix described in S227 row vector B (1) as n _tempthe initial condition of rank shift register, with f described in S224 ₂x (), as feedback polynomial, circulates 2 ⁿ-1 time, obtain a binary sequence, be designated as C ₁, then using second row vector B (2) as initial condition, with f described in S224 ₂x (), as feedback polynomial, circulates 2 ⁿ-1 time, obtain binary sequence, be designated as C ₂, the like, obtain n binary sequence;

S229, the n of a S228 gained binary sequence is arranged in n × (2 ⁿ-1) matrix H, the sequence that the first behavior of described matrix H produces for initial state with B (1), the sequence that the second behavior produces for initial state with B (2), the like.Each row of described matrix H are mapped as a decimal number, wherein the first behavior highest order, and most end behavior lowest order, by V described in each decimal number and S226 _pstep-by-step is carried out mould two and is added, and result is denoted as remove d and front n _tempindividual frequency, compares the corresponding identical number of residue frequency and is designated as same, calculating reconstruct probability if accu=100%, then p is the initial frequency of a RS code word in the sequence { L (j) } described in S21, and V _pfor the address code that system is used, otherwise proceed to S229;

S2210, make p=p+1, searching loop S222-S229.

3. according to claim 1 a kind of based on RS code generate frequency-hopping sequences model reconstruction method, it is characterized in that: the tap position determining L-G model described in S5, concrete steps are as follows:

S51, by continuous 2n _lGthe first frequency of individual RS code word takes out, and forms new sequence;

S52, sequence new described in S51 and frequency 1 step-by-step are carried out mould two add, be denoted as { LG ₂(j) }, wherein, j=0,1 ..., 2n _lG-1;

S53, by { LG described in S52 ₂(j) } step-by-step expands into the binary vector of n position, is denoted as LG ₂(j)={ LG ₂(j, k) };

S54, use LG ₂(j) composition n × 2n _lGmatrix, a kth row vector is denoted as LG ₂' (k)={ LG ₂(1, k), LG ₂(2, k) ..., LG ₂(2n _lG, k) };

S55, get n × 2n described in S54 _lGkth-1 row vector of matrix and described kth-1 row vector before continuous print n _lGindividual value, judges described continuous print n _lGwhether individual value occurs in other row vectors,

If do not occur, then set the register taps position of the (n-1)th row vector as 0, i.e. j _k=0, note kth-1 row vector rower is k ₀,

If occurred, then make k=k+1, repeat S54-S55;

S56, described in S55 k ₀in be that starting point gets continuous n with i _lGindividual value, is denoted as G _i={ LG ₂(j, k ₀), j=i, i+1 ..., i+n _lG-1}, wherein, i=2,3 ..., n _lG;

S57, get n × 2n described in S54 _lGmatrix except k described in S55 ₀the front n of row _lGindividual value, is denoted as $G_0^k=\{{\mathrm{LG}}_2(j,k),j=0,1,\mathrm{...},n_{LG}-1\}|k\≠k_0;$

If S58 then the tap position of row k is i, i.e. j _k=i;

S59, obtain the tap position of all row, be denoted as { j _n-1..., j ₁, j ₀.