CN102064849B - Matrix encoding GA (Genetic Algorithm) based PN (Pseudo Noise) code estimation method of DS/SS (Direct Sequence/Spread Spectrum) signals - Google Patents

Abstract

The invention belongs to the technical field of communication and particularly discloses a matrix encoding GA (Genetic Algorithm) based PN (Pseudo Noise) code estimation method of a DS/SS (Direct Sequence/Spread Spectrum) signals in a DS/SS communication system. In the invention, a novel matrix encoding GA based PN code estimation method of the DS/SS signals by using matrix encoding for improving a basic GA. Besides the advantage of improving the estimating efficiency of PN codes of the DS/SS signals, more importantly, the method is favorable for improving the estimating accuracy of the PN codes of the DS/SS signals. Moreover, the method has no any prior knowledge requirements on the properties (such as the structures, the linear complexity and the like) of the PN codes, and only needs the periods of the PN codes. Therefore, the method has application prospects in many fields of wireless management, military communication investigation, interception, (relevant) interference and the like.

Description

The PN code method of estimation of the DS/SS signal of a kind of matrix coder GA

Technical field

The present invention relates to field of wireless communications, be specifically related to PN (pseudo noise) the code method of estimation of the DS/SS based on matrix coder GA (genetic algorithm) (Direct swquence spread spectrum) signal in a kind of communication system.

Background technology

Under the condition of low signal-to-noise ratio, under the prerequisite be estimated in parameters such as DS/SS signal PN code cycle, spreading rate, carrier waves, PN code sequencal estimation algorithm is had to method for feature analysis, neural network, maximum likelihood estimate etc. at present.

Document (Xiao first grants. the application study [J] of computational intelligence method in non-co-operation signal parameter estimation. and Chengdu: University of Electronic Science and Technology's thesis for the doctorate, 2005.) maximum likelihood is estimated to be incorporated in the PN code estimation of DS/SS signal the maximum likelihood model that the PN code of research DS/SS signal is estimated.

Suppose that the DS/SS signal meets following hypothesis:

A) mould of spreading code c (t) is constant, | c (t) |=1.

B) spreading code c (t) directly multiplies each other with information code a (t), and spread-spectrum signal x (t) is

x(t)＝c(t)a(t) (1)

Base band DS/SS signal y (t) can be expressed as:

y(t)＝x(t)+n(t) (2)

Wherein n (t) is receiving filter output zero-mean white Gaussian noise, and variance is σ _n ², and uncorrelated with x (t).The process of the maximum likelihood model that the PN code of DS/SS signal is estimated is as follows: it is T that the base band DS/SS signal y (t) that formula (2) is meaned is divided into a plurality of non-overlapped width _sand the window (T that there is no step-out point _sput available covariance matrix m with step-out ₂the norm method is estimated), a window only includes an information data code and a cycle P PN code so.In a window, over-sampling is counted as M (M is integer and M>=P), and the sampling period is T _e, T is arranged _s=MT _e.Y _imean the signal sampling column vector in i window, have:

y _i＝Ca _i+n _i (3)

A wherein _ii information data code, y _i, C and n _iit is M * 1 vector

y _i＝[y(iT _s+T _e)，...，y(iT _s+MT _e)] ^T (4a)

n _i＝[n(iT _s+T _e)，...，n(iT _s+MT _e)] ^T (4b)

C＝[c(iT _s+T _e)，...，c(iT _s+MT _e)] ^T (4c)

Known according to the characteristics of DS/SS signal, vectorial C is the spreading code that needs the user of estimation.Tentation data sampling window number is Q, and all sampled datas can be expressed as:

Y＝CD+N (5)

Wherein Y and N are M * Q matrixes, and D is 1 * Q vector

Y＝[y ₁，...，y _Q] (6a)

N＝[n ₁，...，n _Q] (6b)

D＝[a ₁，...，a _Q] (6c)

Suppose that noise { n (t) } is steady ergodic white Gaussian noise, average is zero, and variance is σ _n ², and uncorrelated with x (t).And be separate between each sampled point of noise.The associating maximum likelihood function that can obtain so sampled data is

$f\left(Y\right)=\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HSA00000394512400021.png"\; state="\{\{state\}\}">Q</figure-callout>}}{\mathrm{\&Pi;}}}\frac{1}{\mathrm{\&pi;}\det \left[{{\mathrm{\&sigma;}}_n}^{2}I\right]}\exp (-\frac{1}{{{\mathrm{\&sigma;}}_n}^2}{|y_i-{\mathrm{Ca}}_i|}^2)---\left(7\right)$

Wherein, det[] mean to ask determinant.Ignore after constant term and can obtain the logarithm maximum likelihood function and be

$L=-\mathrm{QM}\log {{\mathrm{\&sigma;}}_n}^2-\frac{1}{{{\mathrm{\&sigma;}}_n}^2}\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-{\mathrm{Ca}}_i|}^2---\left(8\right)$

The maximum likelihood of parameter estimates just to be equivalent to the logarithm maximum likelihood estimation of parameter.Fixation of C and a _i, to σ _n ²ask extreme value, can obtain:

${{\widehat{\mathrm{\&sigma;}}}_n}^2=\frac{1}{\mathrm{QM}}\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-{\mathrm{Ca}}_i|}^2---\left(9\right)$

The result of gained is taken back to the logarithm maximum likelihood function, ignores constant term, can obtain following maximum likelihood and estimate:

$\underset{C,a_i}{\max }\{-\mathrm{QM}\log \left(\frac{1}{\mathrm{QM}}\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-{\mathrm{Ca}}_i|}^2\right)\}---\left(10\right)$

Because logarithmic function is monotonic function, above formula maximum problem can be equivalent to the following formula minimum:

$\underset{C,a_i}{\min }\left\{\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-{\mathrm{Ca}}_i|}^2\right\}---\left(11\right)$

Above formula is exactly a least-squares estimation.In order to estimate this least square, fixation of C is to a _iask minimum.Can obtain:

${\hat{a}}_i={\left(C^{H}C\right)}^{-1}{C}^H{y}_i---\left(12\right)$

Wherein H means conjugate transpose.Formula (12) substitution formula (11) can be obtained to following minimum problem:

$\underset{C}{\min }\left\{\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-C{\left(C^{H}C\right)}^{-1}{C}^H{y}_i|}^2\right\}---\left(13\right)$

According to the mould of hypothesis spreading code c (t), be constant, | c (t) |=1, so

${\left(C^{H}C\right)}^{-1}=\frac{1}{M}---\left(14\right)$

Formula (13) becomes

$\underset{C\&Element;{\{+1,-1\}}^M}{\min }\left\{\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-\frac{1}{M}{\mathrm{CC}}^H{y}_i|}^2\right\}---\left(15\right)$

Above formula can be rewritten as $\underset{C}{\min }\left\{\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{|y_i-P_C{y}_i|}^2\right\}---\left(16a\right)$

P wherein _cit is the projection operator in space of the column vector institute generate of C

$P_C=\frac{1}{M}{\mathrm{CC}}^H---\left(16b\right)$

So the maximal possibility estimation that C is estimated makes likelihood function L (C) maximum exactly

$L\left(C\right)=\underset{C\&Element;{\{+1,-1\}}^M}{\max }\left\{\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{\left|P_C{y}_i\right|}^2\right\}---\left(17\right)$

Ignore constant term, formula (17) is rewritten as

$L\left(C\right)=\underset{C\&Element;{\{+1,-1\}}^M}{\max }\left\{\mathrm{tr}\right[{\mathrm{CC}}^{H}R\left]\right\}---\left(18a\right)$

Tr[wherein] mean to ask matrix trace in square brackets, and matrix R is the covariance matrix of sampled data

$R=\frac{1}{Q}\underset{i=1}{\overset{Q}{\mathrm{\&Sigma;}}}{y}_i{y_i}^H---\left(18b\right)$

According to the character of Matrix Calculating mark, formula (18a) can be written as

$L\left(C\right)=\underset{C\&Element;{\{+1,-1\}}^M}{\max }\left\{C^H\mathrm{RC}\right\}---\left(19\right)$

Above analysis is known, and the value of each component of the user's who need to estimate spreading code vector C can only be+1 or-1, the dimension of the solution space of maximum likelihood function L (C) is 2 so ^m, travel through all 2 ^mthe combination of individual feasible solution, therefrom find out make likelihood function value maximum one as testing result, the optimal estimation that the PN code of Here it is DS/SS signal is estimated.Obviously, optimal estimation has the computation complexity of spread spectrum yardage M exponent function relation with sampling.So the MLE (maximal possibility estimation) of the PN code of DS/SS signal is the np hard problem (nonpolynomial algorithmic issue) of a combinatorial optimization, need to carry out the peaked global search of multivariable nonlinearity, the operand of its search is surprising.When M=31, possible frequency expansion sequence just has 2.1475 * 10 ⁹individual.

Xiao first grants document and solves the maximum likelihood estimation problem of the PN code of DS/SS signal with the GA of theoretical research comparative maturity in intelligent algorithm.But standard GA has precocity and is absorbed in the problem of locally optimal solution, make the efficiency of GA, precision decrease.In the document, standard GA is improved, utilize parallel gradient G A to estimate the PN code of DS/SS signal.What adopt due to the method is parallel gradient, and improved place is mainly the search efficiency that has improved algorithm, but can not solve premature convergence problem.And making algorithm just converge to local optimum for the precocity of standard GA, the precision that the PN code is estimated is lower.

Summary of the invention

Technical problem to be solved by this invention is, for prior art, adopt Genetic Algorithms to estimate pseudo noise PN code mid-early maturity problem and the low problem of PN code estimated accuracy of Direct swquence spread spectrum DS/SS signal, utilize a kind of new PN code being estimated based on matrix coder GA, avoid being absorbed in local optimum, thereby obtain globally optimal solution, improve estimated accuracy and efficiency.

The technical scheme that the present invention solves the problems of the technologies described above is the PN code method of estimation that proposes a kind of DS/SS signal based on matrix coder GA.The concrete implementation step of the method is as follows:

Initialization, produce the initial population of PN code, coding unit carries out matrix coder to each individuality in initial population (PN code), and each individuality after matrix coder is carried out to up-sampling, calculate the appropriateness value of up-sampling individuality, according to the appropriateness value, select initial optimum individual; Individuality after matrix coder is carried out to the crossover and mutation operation, produce new colony, each individuality in new colony is carried out to up-sampling, and the appropriateness value of each individuality in the new colony of calculating sampling, select new optimum individual according to new appropriateness value, comparing unit compares new optimum individual and initial optimum individual, selects wherein optimum individuality, repeat above-mentioned steps until reach the iterations of reservation, the optimum individual obtained is estimates the PN code.

Further, calculate and estimate convergent iterations number of times G according to Meng Te-Carlow Monte-Carlo emulation mode _max.Described calculating moderate value fitness is specially, by each coded sample individuality

with the reception signal carry out the inner product summation, obtain the appropriateness value fitness of each coded sample individuality _i(i=1,2 ..., N).Select initial optimum individual concrete grammar to be, select the coded sample individuality corresponding to value of absolute value maximum in the appropriateness value fitness of individuality in all coded sample initial population, obtain the optimum individual of this selection

using it as initial optimum individual.Describedly individuality is carried out to crossover and mutation operation concrete grammar be, except initial optimum individual

outward, to carry out crossover probability be p to remaining coded sample individuality _cinterlace operation; Producing the variation probability by initial optimum individual is p _m(N-1)/2 variation individual, obtain new colony; If optimum individual in the new colony obtained

the absolute value of appropriateness value than the initial optimum individual obtained last time

the absolute value of corresponding appropriateness value is large, uses new optimum individual the optimum individual that replaces last time

otherwise or by initial optimum individual

as optimum individual.

The mode of determining new PN code in matrix coder GA of the present invention is more flexible, more diversified, has overcome precocity and the low problem of PN code estimated accuracy in former GA, also has better search efficiency simultaneously.

The accompanying drawing explanation

Fig. 1 is two-phase PSK bpsk signal DS/SS communication system

Fig. 2 is DS/SS signal PN code estimation principle block diagram

The theory diagram that Fig. 3 estimates for the PN code of realizing the DS/SS signal based on GA

The flow chart that Fig. 4 is matrix coder GA algorithm

Fig. 5 is-15dB under the iterations curve of up-sampling point number

Fig. 6 is-15dB under the PN code ber curve of up-sampling point number

Fig. 7 is 200 signal to noise ratio curves under up-sampling point

Fig. 8 is-convergence curve under 15dB, 200 up-sampling points

The error rate comparison curves of the PN code that Fig. 9 (a) is this paper method and basic GA

The error rate comparison curves of the information code that Fig. 9 (b) is this paper method and basic GA

Embodiment

It is a combinatorial optimization that the maximum likelihood of the PN code of DS/SS signal is estimated, a kind of higher-dimension, non-linear, complicated function optimization problem, and the matrix coder method is a kind of higher-dimension, multimodal, non-linear, non-protruding fine method that even there is no the function optimization problem of Mathematical Modeling of solving, especially when processing the large-scale complex problem, during the more multi-objective optimization question of higher-dimension Numerical Optimization or sub-goal number, its efficiency more can be embodied.And, because the 2-D data structure of matrix can be enjoyed larger representation space than the one-dimensional data structure, so use the chromosome of matrix coder, the new individual mode of its breeding is more flexible, more diversified, also makes algorithm have search efficiency preferably simultaneously.

Now reaching by reference to the accompanying drawings embodiment is specifically described as follows to the matrix coder GA method and technology scheme that realizes the present invention and propose:

Fig. 1 means the basic principle of bpsk signal DS/SS communication system.The figure shows information code and launch by transmitter by PN code spread spectrum with after modulating, then at receiving terminal, with identical PN code, carry out despreading and demodulation.

Because the existence of carrier wave is just moved the frequency spectrum of DS/SS signal, the information of transmission itself is not produced to materially affect, so this paper to adopt base band DS/SS signal be that example is analyzed.The information code figure place N=10000 of baseband signal, the PN code is the m sequence, the code cycle T _cget 31, carry out the Monte-Carlo emulation experiment.

Suppose that information signal a (t) is

$a\left(t\right)=\underset{k=-\&infin;}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}{a}_{k}p(t-{\mathrm{kT}}_s)---\left(20\right)$

Wherein, a _k=± 1 and equiprobability, p (t) is that a duration is T _srectangular pulse.

Suppose that c is the PN sequence that length is P, has

c＝c ₀，c ₁，…，c _P-1 (21)

The conveyer signal be exactly these waveform generation.If we consider a muting DS/SS system, have

${\hat{c}}_k=a_{k}c---\left(22\right)$

Suppose that receiver knows this sequence, and carry out this signal of despreading with correlator, have

$<{\hat{c}}_k,c>=<a_{k}c,c>=a_k<c,c>=a_{k}P---\left(23\right)$

According to the characteristic of PN sequence, so data message just can be resumed.

But, in non-collaboration communication, receiver is not known the sequence that conveyer sends fully, at this time wants to recover data message and will become very difficult.

Yet, although we do not know the specific code sequence that conveyer sends, we know that the code sequence that conveyer sends is ± 1 sequence, and can estimate the cycle that this conveyer sends yard sequence.So we design a code sequence library C, the length of each yard sequence c (k) of this yard sequence library C the inside be the length with the PN code that will estimate the same long ± 1 sequence, it is the symbol difference of each code word of each sequence, may comprise the PN code that needs are estimated in the code sequence library C of initial designs, also may not comprise.The time not to be covered, we constantly update this yard sequence library C, make it finally comprise the PN code that needs are estimated, we just can be to code sequence library C optimizing like this, be about to list entries respectively with code sequence library C in each yard sequence c (k) inner product, get the maximum of its absolute value, code sequence c (k) corresponding to maximum is the PN code estimated again

so just obtain needing the PN code of estimating, then, according to the characteristic of PN sequence, just can recover data message.Its theory diagram as shown in Figure 2.

Here the DS/SS signal meets following hypothesis:

1) mould of spreading code c (t) is constant, | c (t) |=1.

2) spreading code c (t) directly multiplies each other with information code a (t), and spread-spectrum signal x (t) is

x(t)＝c(t)a(t) (24)

DS/SS signal s (t) can be expressed as:

s(t)＝x(t)+n(t) (25)

Wherein n (t) is receiving filter output zero-mean white Gaussian noise, and variance is σ _n ², and uncorrelated with s (t).

$x\left(t\right)=\underset{i=-\&infin;}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}{a}_{i}c(t-{\mathrm{iT}}_s)---\left(26\right)$

$c\left(t\right)=\underset{k=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{c}_{k}p(t-{\mathrm{kT}}_c)---\left(27\right)$

A _ifor independent same distribution (i.i.d) equiprobability bipolarity information data code; The convolution that p (t) is emission filter, channel impulse response, receiving filter; { c _k, k=0 ..., P-1} is the PN code sequence that code length is P; T _sfor information data code a _isymbol width; T _cfor PN code chip width, what suppose the employing of DS/SS signal here is the short code modulation, and a data information code is by the PN code sequence synchronous modulation of one-period, therefore T is arranged _c=T _s/ P; The convolution that c (t) is PN code sequence and p (t).

The mathematical model of optimization of Fig. 2 is as follows:

According to the Cycle Length P of PN code to be estimated, can design following perfect code sequence library

$C=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000394512400032.png,HSA00000394512400042.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^1,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000394512400021.png"\; state="\{\{state\}\}">c</figure-callout>}}_1^1,c_2^1,...,c_{P-1}^1\\ {\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000394512400032.png,HSA00000394512400042.png"\; state="\{\{state\}\}">c</figure-callout>}}_0^2,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000394512400021.png"\; state="\{\{state\}\}">c</figure-callout>}}_1^2,c_2^2,...,c_{P-1}^2\\ .\\ .\\ .\\ c_0^{2^P},{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HSA00000394512400021.png"\; state="\{\{state\}\}">c</figure-callout>}}_1^{2^P},c_2^{2^P},...,c_{P-1}^{2^P}\end{array}\right]---\left(28\right)$

In above formula (28)

l=0 ..., P-1; K=1,2 ... 2 ^p, code sequence of every line display in above formula (28)

k=1,2 ... 2 ^p, this perfect code sequence library C has 2 ^pindividual code sequence, line number means with subscript, and the length of each yard sequence is the P position, and columns means by subscript.

Be to received signal DS/SS signal s (t) respectively with code sequence library C in each yard sequence c (k) inner product, select the code sequence c (k) mated the most with signal s to be decomposed from perfect code sequence library C, i.e. inner product absolute value maximum, for

$|<s,c\left(k\right)>|=\underset{k}{\max }|<s,C>|---\left(29\right)$

Wherein,

and the component of x on c (k) is:

${\mathrm{\&alpha;}}_k=|<s,c\left(k\right)>|=\underset{k}{\max }|<s,C>|---\left(30\right)$

In this reception signal, comprise following PN code sequence:

$c\left(k\right)=[c_0^k,c_1^k,c_2^k,...,c_{P-1}^k]---\left(31\right)$

Make the component α of x on c (k) _kvalue is maximum, is the PN code be estimated

This paper adopts computing intelligence to carry out optimizing, by the genetic algorithm in computational intelligence, carrys out the optimum code sequence c (k) in optimizing code sequence library C.

The theory diagram that Fig. 3 estimates for the PN code of realizing the DS/SS signal based on GA.The flow chart that Fig. 4 is matrix coder GA.

N code sequence (N<2 are chosen at random in initialization from above-mentioned perfect code sequence library ^p), produce the initial population of estimating the PN code, each individuality in initial population is carried out to matrix coder, sampling unit each individuality after to matrix coder carries out up-sampling, algorithm unit calculates the appropriateness value of up-sampling individuality, select initial optimum individual according to the appropriateness value, individuality after matrix coder is carried out to the crossover and mutation operation, produce new colony, each individuality in new colony is carried out to up-sampling, and calculate new appropriateness value, select new optimum individual according to new appropriateness value, select optimum individuality in new optimum individual and initial optimum individual, repeat above-mentioned steps until reach the iterations of reservation, the optimum individual obtained is estimates the PN code.Specifically can adopt following steps to implement.(initial population is if be comprised of the code sequence, and " individuality " is a code sequence, and after each individuality in initial population is carried out to matrix coder, " individuality " after matrix coder is an encoder matrix.)

At first, calculate the maximum iteration time G of method of estimation convergence according to Monte-Carlo _max.The core that Monte-Carlo calculates method of estimation is to do many experiments to average.Maximum iteration time G _maxdefinite method be: estimate the PN code by genetic algorithm, when the PN code error rate reaches 0, i.e. the entirely true PN code that estimates, be designated as once experiment.The iterations of the i time experiment is designated as G _i,

do altogether L emulation experiment (the L value is generally 100, also can strengthen according to actual conditions), maximum iteration time G _maxmean value for this L time iterations.

Step 1: receiver s (n) to received signal carries out matrix coder and obtains code signal S (n), and the code signal S (n) after matrix coder is carried out to up-sampling obtains sampled signal

wherein up-sampling is counted as M;

Step 2: initialization: choose at random N code sequence (N<2 from the perfect code sequence library ^p), produce the random initial population X that number is N that produces, then to each individual X in initial population _i(i=1,2 ..., N) carry out matrix coder and obtain encoder matrix X _i(i=1,2 ..., N), to each individual X of encoder matrix _i(i=1,2 ..., N) carry out up-sampling and obtain the coded sample individuality

wherein up-sampling is counted as M;

The specific coding mode is as follows:

By a vectorial X _ibe encoded to the matrix form of the 1/-1 of m * n.If this vector X _ilength can be expressed as m * n, and | when m * n| is very little, can be by this variable X _ibe expressed as the matrix form of the 1/-1 of m * n.As follows: suppose vectorial X=(1,1 ,-1,1,1,1 ,-1 ,-1 ,-1 ,-1,1,1), vectorial X can be expressed as to matrix form, for

$X={\left[\begin{array}{cccc}1& 1& -1& 1\\ 1& 1& -1& -1\\ -1& -1& 1& 1\end{array}\right]}_{3\&times;4}.$

While sometimes can not mean m * n, by 0 replacement for space.As follows: suppose vectorial X=(1,1 ,-1,1,1,1 ,-1 ,-1 ,-1 ,-1), vectorial X can be expressed as to matrix form, for

$X={\left[\begin{array}{cccc}1& 1& -1& 1\\ 1& 1& -1& -1\\ -1& -1& 0& 0\end{array}\right]}_{3\&times;4}.$

This matrix coder mode is that one-dimensional vector is become to two-dimentional matrix form, is applicable to extensive, large space, the long especially situation of one-dimensional vector element.As long as this structure, fixing, can not affect any genetic manipulation thereafter.

Step 3: calculate individual appropriateness value fitness.By each coded sample individuality with the reception signal

carry out the inner product summation, obtain the appropriateness value fitness of each coded sample individuality _i(i=1,2 ..., N);

Step 4: select the coded sample individuality corresponding to value of absolute value maximum in the appropriateness value fitness of all coded sample individualities, obtain the optimum individual of this iteration

using it as initial optimum individual.By initial optimum individual

directly enter the next generation, and the coded sample individuality is carried out to crossover and mutation obtain the new colony of code signal.

Crossover and mutation: two chromosomal part-structures of parent are replaced to restructuring and just can generate the operation of new individuality, so infinite multiple operation is arranged in theory.By intersecting, can generate and there is more multimodal individuality, certainly also destroy some parents' natural modes.

Intersect: except optimum individual

outward, to carry out crossover probability be p to remaining (N-1)/2 coded sample individuality _cinterlace operation (in this experiment, crossover probability is definite value 0.9 based on experience value, the crossover probability available expression that variation is set if want means, or write a crossover probability function, the value for example obtained with neural metwork training, as crossover probability, generally gets 0.4～0.99).

Interlace operation: at first a crossover probability p is set _c, produce at random a number between 0-1, if this number is less than crossover probability p _c, choose at random two submatrixs in parent chromosome, its exchange is obtained to new individuality.As follows:

submatrix by X

and submatrix

the father gets new individuality in return

Variation: by optimum individual

produce the variation of other (N-1)/2 individual, the variation probability is p _m(the variation probability is set is definite value 0.1 in this experiment based on experience value, in like manner also can be set to the variation probability changed, and generally gets 0.001～0.1), obtain the new X ' of colony after variation; Each individual X ' to the new X ' of colony _i(i=1,2 ..., N) carry out up-sampling and count as the up-sampling acquisition new colony of the code signal sampled value of M

Mutation operation: at first a variation Probability p is set _m, produce at random a number between 0-1, if this number is less than crossover probability p _c, choose at random several row in parent chromosome, then these row inverted sequences inserted in origin-location and obtained new individuality.As follows:

the first row of X and the third line inverted sequence insertion origin-location are obtained to new individuality.

Step 5: the appropriateness value fitness ' of the new colony of calculation code signal: by each individual X ' of the new X ' of colony _i(i=1,2 ..., N) with the reception signal

carry out the inner product summation, obtain the appropriateness value fitness ' of each individuality _i=1,2 ..., N);

Step 6: select the maximum individual corresponding individuality of the middle absolute value of the new appropriateness value fitness ' of colony to obtain the optimum individual of this iteration

as new colony optimum individual.

Twice optimum individual compared: if the new colony optimum individual of this acquisition

than the initial optimum individual obtained last time

the absolute value of corresponding appropriateness value is large, uses new optimum individual

the optimum individual that replaces last time

otherwise or by the optimum individual of last time

as optimum individual, the optimum individual now obtained is directly entered to the next generation, remaining carries out crossover and mutation, repeats above-mentioned steps, until reach maximum iteration time.

According to G _maxjudge whether iteration stops, if iterations is greater than G _max, termination of iterations.The optimum individual obtained is and adopts the present invention to estimate the PN code obtained.

Fig. 5 and Fig. 6 are illustrated respectively in the curve of signal to noise ratio for up-sampling point number under-15dB and iterations and the PN code error rate.As shown in Figure 5,1), along with the increase of up-sampling point number, the iterations of PN code under entirely true estimation increasing; 2) growth rate of the iterations before up-sampling number 200 is less than 200 later.And as shown in Figure 6,1) along with the increase of up-sampling point number, the error rate of PN code is reducing; 2) reduction rate of the error rate before up-sampling point number 200 is greater than 200 later.By these two figure, consider the efficiency of this algorithm and the accuracy of estimation, we can say so: up-sampling point 200 should be a good compromise point.Therefore, in follow-up l-G simulation test, our up-sampling point number elects 200 as.Fig. 7 is illustrated in the ber curve of signal to noise ratio and PN code under 200 up-sampling points.

As shown in Figure 7, along with the raising of signal to noise ratio, the error rate of PN code is reducing.In signal to noise ratio, be-during 20dB, the error rate of PN code is in 0.25 left and right; In signal to noise ratio, be-during 19dB, the error rate of PN code is just lower than 0.2; In signal to noise ratio, be-during 16dB, the error rate of PN code is just lower than 0.1; In signal to noise ratio, be-during 14dB, the error rate of PN code is just in 0.05 left and right; And in signal to noise ratio be-during 11dB, the error rate of PN code has reached 0.We from Fig. 7 also, signal to noise ratio is during from-20dB to-16dB, the error rate of PN code descends than very fast; During then from-16dB to-11dB, the PN code error rate descends must be slow a little, until drop to 0; Finally, from-11dB, the error rate of PN code is 0 always, and the PN code can be estimated by entirely true under this signal to noise ratio.

The convergence curve of be illustrated in-15dB of Fig. 8,200 lower PN code error rates of up-sampling point.As shown in Figure 8, along with the increase of iterations, the error rate of PN code is reducing.At the iterations initial stage, the error rate of PN code descends very soon; Then until during 1000 left and right, the error rate of PN code descends gentlyer; From 1000 during to 3000 left and right, the error rate of PN code descends again than comparatively fast; Finally from the error rate of 3000 codes of PN during to 3600 left and right, descend milder again, until reach 0.When the error rate of PN code reaches 0, illustrate that now the ber curve of PN code is restrained.

Fig. 9 (a), (b) mean respectively this paper method and the PN code of basic GA and the comparison curves of information code.From Fig. 9 (a), when signal to noise ratio is low, under identical signal to noise ratio, the PN code error rate of this paper method is lower than basic GA's; During basic reach in signal to noise ratio-3dB of GA, the PN code error rate is reduced to 0, and during reach in signal to noise ratio-11dB of this paper method, the PN code error rate drops to 0.From Fig. 9 (b), when signal to noise ratio is low, under identical signal to noise ratio, the information code error rate of this paper method is lower than basic GA's; Basic GA is when signal to noise ratio reaches 0dB, and the information code error rate is reduced to 10 ^-3left and right, and while adopting reach in signal to noise ratio-2dB of this method, the information code error rate has dropped to 10 ^-5below.Illustrate that by Fig. 9 (a), (b) effect of this paper method is better than the estimation effect of basic GA, thereby embodied the validity of this paper method.

Because the error rate size of PN code and information code has been reacted the accuracy that this paper method is estimated the PN code, and the size of iterations has been reacted the efficiency of this method.By above simulation result, can be drawn, the error rate of up-sampling point number and PN code is proportional, and with the iterations relation that is inversely proportional to, illustrated that the error rate of PN code and iterations are conflicting relations between the two.And, from Fig. 5 and Fig. 6, up-sampling point number is 200 to be our compromise point to be selected.So just select 200 up-sampling points in the experiment of the performance simulation of back, the performance curve effect of the PN code drawn later and the error rate of information code is also better, and with the comparing of basic GA, verified the validity of this paper method.

Claims (5)

1. the PN code method of estimation of the DS/SS signal of a matrix coder GA, is characterized in that, comprises the following steps: set up perfect code sequence library C, in this yard sequence library C each yard sequence c (k) be length with the PN code that will estimate the same long ± 1 sequence; Receiver s (n) to received signal carries out matrix coder and obtains code signal S (n), and the code signal S (n) after matrix coder is carried out to up-sampling obtains sampled signal

wherein up-sampling is counted as M; Choose at random N code sequence generation initial population X from the perfect code sequence library; Each individuality in PN code initial population is carried out to matrix coder and obtain PN code encoder matrix, each individuality in PN code encoder matrix is carried out to up-sampling, calculate the appropriateness value of up-sampling individuality, select initial optimum individual according to the appropriateness value, individuality after matrix coder is carried out to the crossover and mutation operation, produce new colony, each individuality in new colony is carried out to up-sampling, and calculate new appropriateness value, determine new optimum individual according to new appropriateness value, newer optimum individual and initial optimum individual, the large optimum individual of absolute value of its appropriateness value is the PN code of estimation.

2. PN code method of estimation according to claim 1, is characterized in that, described calculating moderate value fitness is specially, by each coded sample individuality

with the reception signal carry out the inner product summation, obtain the appropriateness value fitness of each coded sample individuality _i(i=1,2 ..., N).

3. PN code method of estimation according to claim 1, it is characterized in that, select initial optimum individual to be specially, select the coded sample individuality corresponding to value of absolute value maximum in the appropriateness value fitness of all coded sample individualities, obtain the optimum individual of this iteration

using it as initial optimum individual.

4. PN code method of estimation according to claim 1, is characterized in that, describedly individuality is carried out to crossover and mutation operation is specially, except initial optimum individual

outward, to carry out crossover probability be p to remaining coded sample individuality _cinterlace operation; Producing the variation probability by initial optimum individual is p _m(N-1)/2 variation individual, obtain new colony.

5. PN code method of estimation according to claim 4, is characterized in that, if the new colony optimum individual of this acquisition

than the initial optimum individual obtained last time

the absolute value of corresponding appropriateness value is large, uses new optimum individual the optimum individual that replaces last time

otherwise or by the optimum individual of last time

as optimum individual.

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