CN106230556A - A kind of m-sequence pseudo random interleaving recognition methods under non-condition for cooperation - Google Patents

Abstract

The invention discloses the m-sequence pseudo random interleaving recognition methods under a kind of non-condition for cooperation, including: to the periodicity analyzing m-sequence pseudo random interleaving, the m-sequence cycle in pseudo random interleaving is estimated, matrix derivation method is used to draw the mathematic(al) representation of m-sequence e (t), calculate the correlation function of pseudo random interleaving signal f (t), calculate the correlation function of pseudo random interleaving signal f (t), calculate the power spectrum of intercepted data, secondary power is asked to compose, push over the cycle of m-sequence pseudo random interleaving, the steps such as the multiple correlation averaging method identification m-sequence pseudo random interleaving of reference PN sequence.The present invention can efficiently accomplish the identification problem of pseudo random interleaving sequence under non-condition for cooperation, has that method is simple, recognition accuracy is high, be easy to the features such as application, is greatly improved the identification ability of communication signal.

Description

A kind of m-sequence pseudo random interleaving recognition methods under non-condition for cooperation

Technical field

The invention belongs to communication signal identification field, particularly to the recognition methods of a kind of m-sequence pseudo random interleaving.

Background technology

The purpose of digital carrier system is safely and effectively to send, transmit and reception information.Communicating pair is usually Partner, for partner, after recipient receives the signal of transmission, need to be according to the Modulation Types of partner's use to letter Number being demodulated, then implement channel-decoding, source decoding etc., these steps could extract, after completing, the information transmitted.And The Modulation Types of employing, Channel coding parameters (including: interleave parameter, Error Correction of Coding parameter, scrambling code parameter), letter during transmission signal Source code parameter, password etc. are that communicating pair is arranged in advance or inform recipient by communication protocol.But, at some Special field, such as information acquisition field, non-partner (third party in addition to communicating pair) needs without any priori Acquisition and the interpretation of information is realized in the environment of knowledge or few priori.Thus, the channel under non-condition for cooperation is studied Code identification has important application meaning, and wherein to the recognition methods research always difficulties interweaved, current intertexture is known Other method interweaves and convolutional interleave sequence mainly for determinant, and the recognition methods about pseudo random interleaving sequence proposes relatively Few.

Pseudo random interleaving is due to code element mapping relations relative complex in its interleaving process to its interleaving permutation relation Identification the most difficult, current identification technological means is mainly by corresponding pass between three road coded sequences in Turbo code System is identified, the method has bigger limitation.Therefore, be badly in need of a kind of performance of research more preferably, the wider array of puppet of range of application Random interleaving recognition methods.

Summary of the invention

It is an object of the invention to: the m-sequence pseudo random interleaving recognition methods under a kind of non-condition for cooperation is provided, can be the completeest Become the identification problem of pseudo random interleaving sequence under non-condition for cooperation, have that method is simple, recognition accuracy is high, be easy to the spies such as application Point, is greatly improved the identification ability of communication signal.

The technical scheme is that the m-sequence pseudo random interleaving recognition methods under a kind of non-condition for cooperation, under it includes Row step:

Step one: analyze the periodicity of m-sequence pseudo random interleaving；

The structure of m-sequence generator is high-speed linear feedback shift register generator, analyzes the structure of generator, permissible Obtain feedback link to be determined by multinomial (1):

G (D)=1+g₁D+g₂D²+…+g_rD^r (1)

It is output as:

Wherein D is unit time delay variable, and its power represents time delay, g_iSelected from set, { 0,1}, a (D) represent shift LD The original state of device；

If g (D) is primitive polynomial, then the sequence that high-speed linear feedback shift register produces has and greatly enhances most Degree, derives as follows:

Load each of high-speed linear feedback shift register and may be referred to as high-speed linear feedback shift register State, due to total r level depositor, and every one-level may be incorporated within 0 or 1, so having 2^rIndividual state；

Owing to these states there being one be full 0 state, if high-speed linear feedback shift register is displaced to full 0 just State, then it will be in full 0 state all the time；

Therefore, the maximum rating number of feedback arrangement is 2^r-1, this is also the maximum of output sequence before its output repeats Length；So drawing, m-sequence is periodic sequence, and the cycle is 2^r-1；

Pseudo random interleaving is exactly the process that original information sequence is modulated by m-sequence and sent, and can realize information by m-sequence Randomly ordered；Owing to m-sequence is periodic, so the coded sequence in each cycle uses identical modulation system, Then being carried out address ram reading by identical pseudo-random sequence, these descriptive information data are periodically adjusted by m-sequence repeatedly System；

Step 2: the m-sequence cycle in pseudo random interleaving is estimated；

Assume that the ascending order pseudo random interleaving of intercepting and capturing is carried out descending reduction treatment by non-partner, then obtain at noise n (t) Pseudo random interleaving signal f (t) under environment is:

F (t)=p (t-T_x)·e(t-T_x)+n(t) (3)

P (t) is original information sequence:

Wherein T_xFor being uniformly distributed in [0, T₀Random delay on], T₀For m-sequence cycle, T_cFor m-sequence subpulse width Degree, and have T₀=NT_c, N is m-sequence figure place, and q (t) is a square-wave pulse, and n (t) is zero mean Gaussian white noise, and variance is σ²；

Step 3: use matrix derivation method to draw the mathematic(al) representation of m-sequence e (t)；

E (t) is m-sequence, by the analysis to pseudo random interleaving process, can retouch being replaced property of p (t) e (t) State: the pseudo random interleaving formed in unit period is exactly the sequence obtained after original information sequence is multiplied with matrix E', and this Individual matrix E' can obtain by unit matrix E is implemented simple elementary transformation；

To original information sequence P={u assumed₀,u₁,u₂,u₃,u₄,u₅,u₆,u₇,u₈,u₉... carry out pseudo random interleaving；

Assume that the m-sequence obtained is:

E'={2,1,4,0,3,2,1,4,0,3...}

By the rule from small to large of absolute value in unit period, m-sequence is recombinated, obtain the number after pseudo random interleaving According to for:

F={u₂,u₁,u₀,u₄,u₃,u₇,u₆,u₅,u₉,u₈...}

Said process is also the process of a matrixing simultaneously, and original information sequence P can regard an one-dimensional row as Vector, obtained data F after pseudo random interleaving are also one-dimensional row vectors, m-sequence are converted into matrix form, then Have:

Analysis matrix E' can obtain: the line number of matrix E' is determined by total bit number of original information sequence, i.e. row vector P has many Tieing up matrix less, E' just has how many row；Owing to the m-sequence cycle is 5, then matrix E' starts all to be filled by 0 element from the 6th row；Row Vector once circulates every 5 row, and its cycle period is exactly the cycle of m-sequence just；

Before matrix E' in 5 row, every the matrix in block form of 5 rowIt is by a unit matrix E warp Cross elementary row/rank transformation to obtain；

If: original information sequence be P, P be limited { 0,1} information sequence；The cycle of m-sequence E' be N, E' be limited { 0,1} information sequence；Utilize original information sequence P and m-sequence E' to realize pseudo random interleaving, obtain the general formula of matrix E' For:

The line number of matrix E' is to be determined by total bit number of original information sequence, i.e. how many showing of row vector P ties up, square Battle array E' just requires that row has how many dimension；Owing to the m-sequence cycle is N, then matrix E' is from the beginning of N+1 row, and all elements is all filled out by 0 Fill；The column vector of matrix E' once circulates repetition every N row, and lucky and m-sequence the cycle N of its cycle period is identical 's；Before matrix E' in N row, every the matrix in block form E of N row^*, it is to be obtained through elementary row/rank transformation by a unit matrix E 's；

Thus, the mathematic(al) representation obtaining m-sequence is:

Wherein E' is the elementary transformation of unit battle array, and q (t) is a chip pulse；Assume that pseudo random interleaving signal is made an uproar with channel Sound is perfect condition, eliminates random delay T with this_x, according to formula (4) and formula (5):

F (t)=m_e(t)+n(t) (6)

Wherein

Step 4: calculate the correlation function of pseudo random interleaving signal f (t)；

Because n (t) and m_eT () is separate, therefore E [m_e(t₁)·n(t₂)]=E [n (t₁)·m_e(t₂)]=0, and n T () is zero mean Gaussian white noise, variance is σ², so there being E [n (t₁)·n(t₂)]=σ²δ(t₁-t₂)；

Substitution formula (7):

Owing to original information sequence p (t) is uncorrelated with m-sequence e (t), so having:

Original information sequence p (t) and m-sequence e (t) are all to use binary number representation, i.e. random value in 0,1}, So p (t) and e (t) is random binary pulse trains；

For random binary pulse trains h (t):

Wherein g (t) is a cycle rectangular wave, and the cycle is T；h_kIt is general { the 0,1} stationary random sequences such as an independence；

The auto-correlation function R of random binary sequence pulse signal can be obtained_h(τ) be:

Utilize formula (11) original information sequence p (t) to be substituted into m-sequence e (t) respectively, calculate the correlation function of correspondence； It is to be kNT in the cycle due to e (t)_cPseudo-random sequence, the correlation function R of e (t) can be obtained_e(τ):

Step 5: calculate the power spectrum of intercepted data, and ask its secondary power to compose, obtain the week of m-sequence pseudo random interleaving Phase；

The power spectrum of corresponding e (t) is S_e(f):

In like manner can obtain the correlation function R of p (t)_p(τ):

The power spectrum of corresponding p (t) is S_p(f):

By the power spectrum of e (t) Yu p (t), carry out m_eThe calculating of (t)=p (t) e (t) power spectrum；

Formula (8) is utilized to calculate power spectrum

Because T₀=NT_c, andAbove formula can be reduced to:

Work as T₀＞ ＞ T_cTime, formula (17) is changed to:

The power spectrum utilizing white Gaussian noise n (t) does not have time dimensional characteristic after making after-treatment, it is known that m_e(t) Power spectrumAfter, pseudo random interleaving signal f (t) can be carried out secondary power spectrum process, remove noise；

Process can obtain:

Formula (19) shows, the secondary power spectrum of interleaved signal is sharp-pointed periodic group triangular pulse sequence, period pitch Cycle for m-sequence；By correspondingly to S_fE () is added up, obtain recurrent pulse, and the interval between pulse is exactly m-sequence Cycle；

Step 6: use for reference the multiple correlation averaging method of PN sequence, identifies m-sequence pseudo random interleaving；

Intercepting and capturing use the m-sequence pseudo random interleaving rising sequential mode carry out descending process, obtains sequence F；Assume original letter Breath sequence is exactly m-sequence cycle T₀Multiple, F is carried out dividing processing, by the m-sequence cycle T estimated₀By pseudo-for m-sequence with Machine interweaves and is divided into N section, each tract F after segmentation_iAll comprise a complete information sequence modulated by same m-sequence Row, the dependency between them is now maximum；

Data after segmentation are expressed in matrix as:

F in formula (20)_ijThe code element of the m-sequence pseudo random interleaving for intercepting and capturing；

Start to carry out related calculation every data line successively with other row data from the first row data of matrix F, obtain r^* _ij；

By all of correlation r^* _ijArrange in order as new data setMatrix table is shown as:

MatrixIt is a symmetrical matrix being made up of mark, willIn all elements take absolute value after be added summation, Again divided by matrixIn element sum, obtain meansigma methods r₀；

R is set₀For quantization threshold, by r^* _ijWith r₀Compare, by matrixIn all of element r^* _ijIt is quantized into {0,1}；According to r^* _ijPosition, { 0,1} sequence r that obtains after quantifying_ijArrange in order；Press m-sequence cycle T again₀Obtain new To data split, set up new matrix R_kFormula (22), this completes being once correlated with to m-sequence pseudo random interleaving F Process；

To R_kAgain carry out correlation computations process, from matrix R_kThe first row data start, by every data line successively with its Its row data carries out related operation, and the correlation of gained is formed new data segmentTake its meansigma methods amount of carrying out the most again Changing, successor takes the one of which data estimated value as m-sequence pseudo random interleaving.

The present invention is by by to analyzing the periodicity of m-sequence pseudo random interleaving, to the m-sequence week in pseudo random interleaving Phase carries out estimating, using matrix derivation method to draw the mathematic(al) representation of m-sequence e (t), calculate pseudo random interleaving signal f (t) Correlation function,；Calculate the correlation function of pseudo random interleaving signal f (t), calculate the power spectrum of intercepted data, and seek its secondary merit Rate is composed, and obtains the cycle of m-sequence pseudo random interleaving；Use for reference the multiple correlation averaging method of PN sequence, identify that m-sequence pseudorandom is handed over Knit；

, the identification problem of pseudo random interleaving sequence under non-condition for cooperation can be efficiently accomplished, have that method is simple, identify accurately Degree is high, be easy to the features such as application, is greatly improved the identification ability of communication signal.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention.

Detailed description of the invention

Embodiment 1: see Fig. 1, the m-sequence pseudo random interleaving recognition methods under a kind of non-condition for cooperation, it includes following Step:

Step one: analyze the periodicity of m-sequence pseudo random interleaving；

The structure of m-sequence generator is high-speed linear feedback shift register generator, analyzes the structure of generator, permissible Obtain feedback link to be determined by multinomial (1):

G (D)=1+g₁D+g₂D²+…+g_rD^r (1)

It is output as:

Wherein D is unit time delay variable, and its power represents time delay, g_iSelected from set, { 0,1}, a (D) represent shift LD The original state of device；

If g (D) is primitive polynomial, then the sequence that high-speed linear feedback shift register produces has and greatly enhances most Degree, derives as follows:

Load each of high-speed linear feedback shift register and may be referred to as high-speed linear feedback shift register State, due to total r level depositor, and every one-level may be incorporated within 0 or 1, so having 2^rIndividual state；

Owing to these states there being one be full 0 state, if high-speed linear feedback shift register is displaced to full 0 just State, then it will be in full 0 state all the time；

Therefore, the maximum rating number of feedback arrangement is 2^r-1, this is also the maximum of output sequence before its output repeats Length；So drawing, m-sequence is periodic sequence, and the cycle is 2^r-1；

Pseudo random interleaving is exactly the process that original information sequence is modulated by m-sequence and sent, and can realize information by m-sequence Randomly ordered；Owing to m-sequence is periodic, so the coded sequence in each cycle uses identical modulation system, Then being carried out address ram reading by identical pseudo-random sequence, these descriptive information data are periodically adjusted by m-sequence repeatedly System；

Step 2: the m-sequence cycle in pseudo random interleaving is estimated；

Assume that the ascending order pseudo random interleaving of intercepting and capturing is carried out descending reduction treatment by non-partner, then obtain at noise n (t) Pseudo random interleaving signal f (t) under environment is:

F (t)=p (t-T_x)·e(t-T_x)+n(t) (3)

P (t) is original information sequence:

Wherein T_xFor being uniformly distributed in [0, T₀Random delay on], T₀For m-sequence cycle, T_cFor m-sequence subpulse width Degree, and have T₀=NT_c, N is m-sequence figure place, and q (t) is a square-wave pulse, and n (t) is zero mean Gaussian white noise, and variance is σ²；

Step 3: use matrix derivation method to draw the mathematic(al) representation of m-sequence e (t)；

E (t) is m-sequence, by the analysis to pseudo random interleaving process, can retouch being replaced property of p (t) e (t) State: the pseudo random interleaving formed in unit period is exactly the sequence obtained after original information sequence is multiplied with matrix E', and this Individual matrix E' can obtain by unit matrix E is implemented simple elementary transformation；

To original information sequence P={u assumed₀,u₁,u₂,u₃,u₄,u₅,u₆,u₇,u₈,u₉... carry out pseudo random interleaving；

Assume that the m-sequence obtained is:

E'={2,1,4,0,3,2,1,4,0,3...}

By the rule from small to large of absolute value in unit period, m-sequence is recombinated, obtain the number after pseudo random interleaving According to for:

F={u₂,u₁,u₀,u₄,u₃,u₇,u₆,u₅,u₉,u₈...}

Said process is also the process of a matrixing simultaneously, and original information sequence P can regard an one-dimensional row as Vector, obtained data F after pseudo random interleaving are also one-dimensional row vectors, m-sequence are converted into matrix form, then Have:

Analysis matrix E' can obtain: the line number of matrix E' is determined by total bit number of original information sequence, i.e. row vector P has many Tieing up matrix less, E' just has how many row；Owing to the m-sequence cycle is 5, then matrix E' starts all to be filled by 0 element from the 6th row；Row Vector once circulates every 5 row, and its cycle period is exactly the cycle of m-sequence just；

Before matrix E' in 5 row, every the matrix in block form of 5 rowIt is by a unit matrix E warp Cross elementary row/rank transformation to obtain；

If: original information sequence be P, P be limited { 0,1} information sequence；The cycle of m-sequence E' be N, E' be limited { 0,1} information sequence；Utilize original information sequence P and m-sequence E' to realize pseudo random interleaving, obtain the general formula of matrix E' For:

The line number of matrix E' is to be determined by total bit number of original information sequence, i.e. how many showing of row vector P ties up, square Battle array E' just requires that row has how many dimension；Owing to the m-sequence cycle is N, then matrix E' is from the beginning of N+1 row, and all elements is all filled out by 0 Fill；The column vector of matrix E' once circulates repetition every N row, and lucky and m-sequence the cycle N of its cycle period is identical 's；Before matrix E' in N row, every the matrix in block form E of N row^*, it is to be obtained through elementary row/rank transformation by a unit matrix E 's；

Thus, the mathematic(al) representation obtaining m-sequence is:

Wherein E' is the elementary transformation of unit battle array, and q (t) is a chip pulse；Assume that pseudo random interleaving signal is made an uproar with channel Sound is perfect condition, eliminates random delay T with this_x, according to formula (4) and formula (5):

F (t)=m_e(t)+n(t) (6)

Wherein

Step 4: calculate the correlation function of pseudo random interleaving signal f (t)；

Because n (t) and m_eT () is separate, therefore E [m_e(t₁)·n(t₂)]=E [n (t₁)·m_e(t₂)]=0, and n T () is zero mean Gaussian white noise, variance is σ², so there being E [n (t₁)·n(t₂)]=σ²δ(t₁-t₂)；

Substitution formula (7):

Owing to original information sequence p (t) is uncorrelated with m-sequence e (t), so having:

Original information sequence p (t) and m-sequence e (t) are all to use binary number representation, i.e. random value in 0,1}, So p (t) and e (t) is random binary pulse trains；

For random binary pulse trains h (t):

Wherein g (t) is a cycle rectangular wave, and the cycle is T；h_kIt is general { the 0,1} stationary random sequences such as an independence；

The auto-correlation function R of random binary sequence pulse signal can be obtained_h(τ) be:

Utilize formula (11) original information sequence p (t) to be substituted into m-sequence e (t) respectively, calculate the correlation function of correspondence； It is to be kNT in the cycle due to e (t)_cPseudo-random sequence, the correlation function R of e (t) can be obtained_e(τ):

Step 5: calculate the power spectrum of intercepted data, and ask its secondary power to compose, obtain the week of m-sequence pseudo random interleaving Phase；

The power spectrum of corresponding e (t) is S_e(f):

In like manner can obtain the correlation function R of p (t)_p(τ):

The power spectrum of corresponding p (t) is S_p(f):

By the power spectrum of e (t) Yu p (t), carry out m_eThe calculating of (t)=p (t) e (t) power spectrum；

Formula (8) is utilized to calculate power spectrum

Because T₀=NT_c, andAbove formula can be reduced to:

Work as T₀＞ ＞ T_cTime, formula (17) is changed to:

The power spectrum utilizing white Gaussian noise n (t) does not have time dimensional characteristic after making after-treatment, it is known that m_e(t) Power spectrumAfter, pseudo random interleaving signal f (t) can be carried out secondary power spectrum process, remove noise；

Process can obtain:

Formula (19) shows, the secondary power spectrum of interleaved signal is sharp-pointed periodic group triangular pulse sequence, period pitch Cycle for m-sequence；By correspondingly to S_fE () is added up, obtain recurrent pulse, and the interval between pulse is exactly m-sequence Cycle；

Step 6: use for reference the multiple correlation averaging method of PN sequence, identifies m-sequence pseudo random interleaving；

Intercepting and capturing use the m-sequence pseudo random interleaving rising sequential mode carry out descending process, obtains sequence F；Assume original letter Breath sequence is exactly m-sequence cycle T₀Multiple, F is carried out dividing processing, by the m-sequence cycle T estimated₀By pseudo-for m-sequence with Machine interweaves and is divided into N section, each tract F after segmentation_iAll comprise a complete information sequence modulated by same m-sequence Row, the dependency between them is now maximum；

Data after segmentation are expressed in matrix as:

F in formula (20)_ijThe code element of the m-sequence pseudo random interleaving for intercepting and capturing；

Start to carry out related calculation every data line successively with other row data from the first row data of matrix F, obtain r^* _ij；

By all of correlation r^* _ijArrange in order as new data setMatrix table is shown as:

MatrixIt is a symmetrical matrix being made up of mark, willIn all elements take absolute value after be added summation, Again divided by matrixIn element sum, obtain meansigma methods r₀；

R is set₀For quantization threshold, by r^* _ijWith r₀Compare, by matrixIn all of element r^* _ijIt is quantized into {0,1}；According to r^* _ijPosition, { 0,1} sequence r that obtains after quantifying_ijArrange in order；Press m-sequence cycle T again₀Obtain new To data split, set up new matrix R_kFormula (22), this completes being once correlated with to m-sequence pseudo random interleaving F Process；

To R_kAgain carry out correlation computations process, from matrix R_kThe first row data start, by every data line successively with its Its row data carries out related operation, and the correlation of gained is formed new data segmentTake its meansigma methods amount of carrying out the most again Changing, successor takes the one of which data estimated value as m-sequence pseudo random interleaving.

Claims (1)

1. the m-sequence pseudo random interleaving recognition methods under a non-condition for cooperation, it is characterised in that it comprises the following steps:

Step one: analyze the periodicity of m-sequence pseudo random interleaving；

The structure of m-sequence generator is high-speed linear feedback shift register generator, analyzes the structure of generator, can obtain Feedback link is determined by multinomial (1):

G (D)=1+g₁D+g₂D²+…+g_rD^r (1)

It is output as:

$b\left(D\right)=\frac{a\left(D\right)}{g\left(D\right)}---\left(2\right)$

Wherein D is unit time delay variable, and its power represents time delay, g_iSelected from set, { 0,1}, a (D) represent shift register Original state；

If g (D) is primitive polynomial, then the sequence that high-speed linear feedback shift register produces has greatest length, pushes away Lead as follows:

Load each of high-speed linear feedback shift register and may be referred to as the state of high-speed linear feedback shift register, Due to total r level depositor, and every one-level may be incorporated within 0 or 1, so having 2^rIndividual state；

Owing to these states there being one be full 0 state, if high-speed linear feedback shift register is displaced to full 0 shape just State, then it will be in full 0 state all the time；

Therefore, the maximum rating number of feedback arrangement is 2^r-1, this is also the greatest length of output sequence before its output repeats； So drawing, m-sequence is periodic sequence, and the cycle is 2^r-1；

Pseudo random interleaving is exactly the process that original information sequence is modulated by m-sequence and sent, by m-sequence can realize information with Machine sorts；Owing to m-sequence is periodic, so the coded sequence in each cycle uses identical modulation system, then Being carried out address ram reading by identical pseudo-random sequence, these descriptive information data are periodically modulated by m-sequence repeatedly；

Step 2: the m-sequence cycle in pseudo random interleaving is estimated；

Assume that the ascending order pseudo random interleaving of intercepting and capturing is carried out descending reduction treatment by non-partner, then obtain at noise n (t) environment Under pseudo random interleaving signal f (t) be:

F (t)=p (t-T_x)·e(t-T_x)+n(t) (3)

P (t) is original information sequence:

$p\left(t\right)=\underset{k=-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\mathrm{\Σ}}}{m}_{k}q(t-{\mathrm{kT}}_c),m_k\∈\{1,0\}---\left(4\right)$

Wherein T_xFor being uniformly distributed in [0, T₀Random delay on], T₀For m-sequence cycle, T_cFor m-sequence subpulse width, and have T₀=NT_c, N is m-sequence figure place, and q (t) is a square-wave pulse, and n (t) is zero mean Gaussian white noise, and variance is σ²；

Step 3: use matrix derivation method to draw the mathematic(al) representation of m-sequence e (t)；

E (t) is m-sequence, by the analysis to pseudo random interleaving process, can describe being replaced property of p (t) e (t): The pseudo random interleaving formed in unit period is exactly the sequence obtained after original information sequence is multiplied with matrix E', and this matrix E' can obtain by unit matrix E is implemented simple elementary transformation；

To original information sequence P={u assumed₀,u₁,u₂,u₃,u₄,u₅,u₆,u₇,u₈,u₉... carry out pseudo random interleaving；

Assume that the m-sequence obtained is:

E'={2,1,4,0,3,2,1,4,0,3...}

Recombinating m-sequence by the rule from small to large of absolute value in unit period, obtaining the data after pseudo random interleaving is:

F={u₂,u₁,u₀,u₄,u₃,u₇,u₆,u₅,u₉,u₈…}

Said process is also the process of a matrixing simultaneously, and original information sequence P can regard an one-dimensional row vector as, Obtained data F after pseudo random interleaving are also one-dimensional row vectors, m-sequence is converted into matrix form, then has:

Analysis matrix E' can obtain: the line number of matrix E' is determined by total bit number of original information sequence, i.e. row vector P has how many dimension Matrix, E' just has how many row；Owing to the m-sequence cycle is 5, then matrix E' starts all to be filled by 0 element from the 6th row；Column vector Once circulating every 5 row, its cycle period is exactly the cycle of m-sequence just；

Before matrix E' in 5 row, every the matrix in block form of 5 rowIt is through just by a unit matrix E Obtain etc. row/column conversion；

If: original information sequence be P, P be limited { 0,1} information sequence；The cycle of m-sequence E' be N, E' be limited 0, 1} information sequence；Utilizing original information sequence P and m-sequence E' to realize pseudo random interleaving, the general formula obtaining matrix E' is:

The line number of matrix E' is to be determined by total bit number of original information sequence, i.e. how many showing of row vector P ties up, matrix E' Just require that row has how many dimension；Owing to the m-sequence cycle is N, then matrix E' is from the beginning of N+1 row, and all elements is all filled by 0；Square The column vector of battle array E' once circulates repetition every N row, and lucky and m-sequence the cycle N of its cycle period is identical；Square Before battle array E' in N row, every the matrix in block form E of N row^*, a unit matrix E obtain through elementary row/rank transformation；

Thus, the mathematic(al) representation obtaining m-sequence is:

$e\left(t\right)=\underset{j=-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\Σ}}{E}^{\′}q(t-{\mathrm{jT}}_0)---\left(5\right)$

Wherein E' is the elementary transformation of unit battle array, and q (t) is a chip pulse；Assume that pseudo random interleaving signal is equal with interchannel noise For perfect condition, eliminate random delay T with this_x, according to formula (4) and formula (5):

F (t)=m_e(t)+n(t) (6)

Wherein

Step 4: calculate the correlation function of pseudo random interleaving signal f (t)；

$\begin{array}{c}{R}_f\left(t_1,t_2\right)\\ =E\[f\left(t_1\right)\·f\left(t_2\right)\]\\ =E\left\{\[m_e\left(t_1\right)+n\left(t_1\right)\]\·\[m_e\left(t_2\right)+n\left(t_2\right)\]\right\}\\ =E\[m_e\left(t_1\right)\·m_e\left(t_2\right)+n\left(t_1\right)\·n\left(t_2\right)+m_e\left(t_1\right)\·n\left(t_2\right)+n\left(t_1\right)\·m_e\left(t_2\right)\]\\ =E\[m_e\left(t_1\right)\·m_e\left(t_2\right)\]+E\[n\left(t_1\right)\·n\left(t_2\right)\]+E\[m_e\left(t_1\right)\·n\left(t_2\right)\]+E\[n\left(t_1\right)\·m_e\left(t_2\right)\]\end{array}---\left(7\right)$

Because n (t) and m_eT () is separate, therefore E [m_e(t₁)·n(t₂)]=E [n (t₁)·m_e(t₂)]=0, and n (t) is zero Average white Gaussian noise, variance is σ², so there being E [n (t₁)·n(t₂)]=σ²δ(t₁-t₂)；

Substitution formula (7):

$\begin{array}{c}{R}_f(t_1,t_2)\\ =E\[f\left(t_1\right)\·f\left(t_2\right)\]\\ =E\[m_e\left(t_1\right)\·m_e\left(t_2\right)\]+E\[n\left(t_1\right)\·n\left(t_2\right)\]\\ =R_{m_e}\left(t_1,t_2\right)+{\mathrm{\σ}}^2\mathrm{\δ}\left(t_1-t_2\right)\end{array}---\left(8\right)$

Owing to original information sequence p (t) is uncorrelated with m-sequence e (t), so having:

$\begin{array}{c}{R}_{m_e}(t_1,t_2)\\ =E\[m_e\left(t_1\right)\·m_e\left(t_2\right)\]\\ =E\[p\left(t_1\right)\·p\left(t_2\right)\·e\left(t_1\right)\·e\left(t_2\right)\]\\ =R_p\left(t_1,t_2\right)\·R_e\left(t_1,t_2\right)\end{array}---\left(9\right)$

Original information sequence p (t) and m-sequence e (t) are all to use binary number representation, i.e. { random value in 0,1}, so p T () and e (t) are random binary pulse trains；

For random binary pulse trains h (t):

$h\left(t\right)=\underset{k=-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\Σ}}{h}_{k}g(t-kT)---\left(10\right)$

Wherein g (t) is a cycle rectangular wave, and the cycle is T；h_kIt is general { the 0,1} stationary random sequences such as an independence；

The auto-correlation function R of random binary sequence pulse signal can be obtained_h(τ) be:

$R_h\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{cc}1-\frac{\left|\mathrm{\&tau;}\right|}{T},& \left|\mathrm{\&tau;}\right|<T\\ 0,& \left|\mathrm{\&tau;}\right|>T\end{array}\right.---\left(11\right)$

Utilize formula (11) original information sequence p (t) to be substituted into m-sequence e (t) respectively, calculate the correlation function of correspondence；Due to E (t) is to be kNT in the cycle_cPseudo-random sequence, the correlation function R of e (t) can be obtained_e(τ):

Step 5: calculate the power spectrum of intercepted data, and ask its secondary power to compose, obtain the cycle of m-sequence pseudo random interleaving；Right The power spectrum answering e (t) is S_e(f):

$S_e\left(f\right)=\frac{kN+1}{{\left(kN\right)}^2}{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_c}{{\mathrm{\&pi;fT}}_c}\&rsqb;}^2\&CenterDot;\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}\&lsqb;f-\frac{m}{{\mathrm{\&pi;fT}}_c}\&rsqb;-\frac{\mathrm{\&delta;}\left(f\right)}{kN}---\left(13\right)$

In like manner can obtain the correlation function R of p (t)_p(τ):

The power spectrum of corresponding p (t) is S_p(f):

$S_p\left(f\right)=T_0{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_0}{{\mathrm{\&pi;fT}}_0}\&rsqb;}^2={\mathrm{NT}}_c{\&lsqb;\frac{{\mathrm{sin\&pi;fNT}}_c}{{\mathrm{\&pi;fNT}}_c}\&rsqb;}^2---\left(15\right)$

By the power spectrum of e (t) Yu p (t), carry out m_eThe calculating of (t)=p (t) e (t) power spectrum；

Formula (8) is utilized to calculate power spectrum

$\begin{array}{c}{S}_{m_e}\left(f\right)\\ =S_p\left(f\right)*S_e\left(f\right)\\ =T_0{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_0}{{\mathrm{\&pi;fT}}_0}\&rsqb;}^2*\left\{\frac{kN+1}{{\left(kN\right)}^2}{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_c}{{\mathrm{\&pi;fT}}_c}\&rsqb;}^2\&CenterDot;\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}\&lsqb;f-\frac{m}{{\mathrm{\&pi;fT}}_c}\&rsqb;-\frac{\mathrm{\&delta;}\left(f\right)}{kN}\right\}\\ =T_0{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_0}{{\mathrm{\&pi;fT}}_0}\&rsqb;}^2*\left\{\frac{kN+1}{{\left(kN\right)}^2}\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_c}{{\mathrm{\&pi;fT}}_c}\&rsqb;}^2\&CenterDot;\mathrm{\&delta;}\&lsqb;f-\frac{m}{{\mathrm{\&pi;fT}}_c}\&rsqb;-\frac{\mathrm{\&delta;}\left(f\right)}{kN}\right\}\\ =T_0\left\{\frac{kN+1}{{\left(kN\right)}^2}\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\mathrm{\&Sigma;}}}{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_c}{{\mathrm{\&pi;fT}}_c}\&rsqb;}^2\&CenterDot;{\&lsqb;\frac{\sin \mathrm{\&pi;}\left(f-\frac{m}{{\mathrm{\&pi;fT}}_c}\right)T_0}{\mathrm{\&pi;}\left(f-\frac{m}{{\mathrm{\&pi;fT}}_c}\right)T_0}\&rsqb;}^2\right\}-\frac{1}{kN}{\&lsqb;\frac{{\mathrm{sin\&pi;fT}}_0}{{\mathrm{\&pi;fT}}_0}\&rsqb;}^2\end{array}---\left(16\right)$

Because T₀=NT_c, andAbove formula can be reduced to:

$S_{m_e}\left(f\right)=T_0\{\frac{kN+1}{{\left(kN\right)}^2}{S}_a^2\&lsqb;\frac{\mathrm{\&pi;}m}{kN}\&rsqb;\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{S}_a^2\&lsqb;\mathrm{\&pi;}(f-\frac{m}{{\mathrm{\&pi;fT}}_c})T_0\&rsqb;-\frac{1}{kN}{S}_a^2\&lsqb;{\mathrm{\&pi;fT}}_0\&rsqb;\}---\left(17\right)$

Work as T₀＞ ＞ T_cTime, formula (17) is changed to:

$S_{m_e}\left(f\right)=\left\{\begin{array}{cc}\frac{1}{kN}\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}{S}_a^2\&lsqb;\frac{\mathrm{\&pi;}m}{kN}\&rsqb;\mathrm{\&delta;}(f-\frac{m}{{\mathrm{kT}}_0}),& m\&NotEqual;0\\ 0,& m=0\end{array}\right.---\left(18\right)$

The power spectrum utilizing white Gaussian noise n (t) does not have time dimensional characteristic after making after-treatment, it is known that m_eThe power of (t) SpectrumAfter, pseudo random interleaving signal f (t) can be carried out secondary power spectrum process, remove noise；

Process can obtain:

$S_f\left(e\right)=\left|FFT\right\{S_{m_e}\left(f\right)\}{|}^2\&cong;|T_c\underset{k=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}(1-\frac{|e-{\mathrm{kT}}_0|}{T_c}){|}^2---\left(19\right)$

Formula (19) shows, the secondary power spectrum of interleaved signal is sharp-pointed periodic group triangular pulse sequence, and period pitch is m sequence The cycle of row；By correspondingly to S_fE () is added up, obtain recurrent pulse, and the interval between pulse is exactly the m-sequence cycle；

Step 6: use for reference the multiple correlation averaging method of PN sequence, identifies m-sequence pseudo random interleaving；

Intercepting and capturing use the m-sequence pseudo random interleaving rising sequential mode carry out descending process, obtains sequence F；Assume raw information sequence Row exactly m-sequence cycle T₀Multiple, F is carried out dividing processing, by the m-sequence cycle T estimated₀M-sequence pseudorandom is handed over Knit and be divided into N section, each tract F after segmentation_iAll comprise a complete information sequence modulated by same m-sequence, it Dependency between is now maximum；

Data after segmentation are expressed in matrix as:

F in formula (20)_ijThe code element of the m-sequence pseudo random interleaving for intercepting and capturing；

Start to carry out related calculation every data line successively with other row data from the first row data of matrix F, obtain r^* _ij；

By all of correlation r^* _ijArrange in order as new data setMatrix table is shown as:

MatrixIt is a symmetrical matrix being made up of mark, willIn all elements take absolute value after be added summation, then remove With matrixIn element sum, obtain meansigma methods r₀；

R is set₀For quantization threshold, by r^* _ijWith r₀Compare, by matrixIn all of element r^* _ijIt is quantized into { 0,1}； According to r^* _ijPosition, { 0,1} sequence r that obtains after quantifying_ijArrange in order；Press m-sequence cycle T again₀To newly obtained number According to splitting, set up new matrix R_kFormula (22), this completes a relevant treatment to m-sequence pseudo random interleaving F；

To R_kAgain carry out correlation computations process, from matrix R_kThe first row data start, by every data line successively with other row Data carry out related operation, and the correlation of gained is formed new data segmentTake its meansigma methods the most again to quantify, Successor takes the one of which data estimated value as m-sequence pseudo random interleaving.