CN102361475B - Wavelet weighted multi-mode blind equalization method based on chaos optimization of support vector machine - Google Patents

Abstract

The invention discloses a wavelet weighted multi-mode blind equalization method based on the chaos optimization of a support vector machine. The method comprises the following steps of: operating a complex signal source transmission signal by using a pulse response channel, and thus obtaining a channel output vector; summating a channel noise and the channel output vector, and thus obtaining an input signal of an orthogonal wavelet transformer; performing orthogonal wavelet transformation on the input signal of an equalizer, and thus obtaining the input signal of the equalizer; operating the input signal of the equalizer by using the equalizer, and thus obtaining an output signal of the equalizer; and operating the output signal of the equalizer by using a judger, and updating the weight vector of the equalizer by using a weighted multi-mode blind equalization method. The method has the advantages that: by using the support vector machine, the weight vector of the wavelet weighted multi-mode blind equalization method is initialized; a convergence speed can be improved, and the immergence of a local minimal value point is avoided; parameters of the support vector machine are selected for parameter combined optimization; combined optimization target functions are established; the optimum target function value is searched by chaos optimization; and the fitting capacity of the support vector machine is improved.

Description

The Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs

Technical field

The present invention relates to the Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs in a kind of underwater acoustic channel.

Background technology

In underwater acoustic channel, Bandwidth-Constrained and the multipath transmisstion of channel cause intersymbol interference, cause and receive data generation error code, have had influence on the quality of communication system.In order to improve the band efficiency of channel, usually adopt high-order QAM modulation mode, in order to overcome intersymbol interference, need to introduce balancing technique at receiving terminal, Blind Equalization Technique is because being widely used without sending training sequence.

In existing blind balance method, constant modeling method (Constant Modulus Algorithm, CMA) simple in structure, amount of calculation is little, good stability, (see that document [1] records beautiful and be widely used, Guo Yecai. the Odd symmetry error function blind equalization algorithm [J] based on orthogonal wavelet transformation. Journal of System Simulation, 2010,22 (10), 2247-2249).Because CMA has only utilized the amplitude information of equalizer output signal, there is phase ambiguity, and in the time processing Higher Order QAM Signals, convergence rate is slowly, steady-state error is also suitable large.Document (is shown in document [2] Yang J, Werner J J, and Dumont G A.The multiple modulus blind equalization and its generalized algorithm.IEEE Journal on Sel.Area in Commun., 2002, 20 (5): 997-1015) multimode blind balance method (the Multiple Modulus Algorithm in, MMA) amplitude and the phase information of equalizer output signal have been utilized, improve stable state constringency performance, but the homophase of weight vector and quadrature component are all to utilize single judgement circle to adjust in MMA, along with the raising of QAM exponent number, to the degradation of channel equalization, convergence rate and mean square error do not reach desirable effect.Document [3]～[4] (see: document [3] Xu little Dong, Dai Xuchu, Xu Peixia. be applicable to the weighting multimode blind equalization algorithm [J] of Higher Order QAM Signals. electronics and information journal, 2007,29 (6): 1352-1355, document [4] Dou Gaoqi, Gao Jun. be applicable to the multimode Multiple Modulus Blind Equalization [J] of high-order QAM system. electronics and information journal, 2008,30 (2), 388-391) show weighting multimode blind balance method (Weighted Multiple Modulus Algorithm, WMMA) the index underworld of introducing judgement symbol is adjusted the mould value in cost function, has utilized further the information of high-order QAM planisphere, and channel is had to good equalization performance, utilize the decorrelation of orthogonal wavelet transformation, equalizer input signal is carried out to preliminary treatment, reduce the autocorrelation of input signal, accelerate convergence rate and (seen document [5] Guo Yecai, Yang Chao. the decision feedback blind equalization algorithm [J] based on orthogonal wavelet packet transform. Journal of System Simulation, 2010,23 (3): 570-574), because adopting steepest descent method, the weight vector in Wavelet weighted multi-mode blind equalization method (WT-WMMA) carries out iteration, similar with CMA, easily be absorbed in local minizing point, document [6]～[7] (are seen: document [6] Li Jinming, Zhao Junwei. the initialized constant mould of SVMs blind equalization algorithm emulation [J]. Computer Simulation, 2008,25 (1): 84-87, document [7] Feng Liu, Hu-cheng An, Jia-ming Li.Blind Equalization Using v-Support Vector Regressor for Constant Modulus Signal[J] .IEEE International Joint Conference on Neural Networks, 2008, pp:161-164) show to utilize SVMs to carry out initialization to the weight vector of WT-WMMA, can avoid being absorbed in local minizing point, in the process of SVMs initialization weight vector, (see document [8] Qing Yu according to document [8], Ying Liu, Feng Rao.Paramater Selection of Support Vector Regression Machine Based on Differential Evolution Algorithm[J] .IEEE Six International Conference on Fuzzy Systems and Knowledge Discovery, 2009, VOL.2, pp:596-598), choosing of SVMs parameter regarded as to the Combinatorial Optimization of parameter, set up Combinatorial Optimization target function, document [9]～[11] (see document [9] Yuan little Fang, Wang Yaonan. the SVMs parameter selection method [J] based on chaotic optimization algorithm. control and decision-making 2006,21 (1): 111-113, document [10] Chang Shuang, Guo Jian-qin.Application of chaos optimization algorithm in the solution of combination optimization problems[J] .Modern Electronic Technique, 2008,31 (18): 68 – 70, document [11] Guo Li-hua, Tang Wen-cheng, Zhan Chun-hua.A new hybrid global optimization algorithm based on chaos search and complex method[C] .IEEE International Conference on Computer Modeling and Simulation.2010, VOL.3, pp:233 – 237) show, search for optimum target function value by chaos optimization, can improve the capability of fitting of SVMs.

Summary of the invention

The present invention seeks to, for avoiding weight vector to be absorbed in local minizing point, to utilize SVMs to carry out initialization to the weight vector of equalizer, and in this process, by chaos optimization, the parameter of SVMs is optimized, improve its capability of fitting; Utilize orthogonal wavelet transformation to carry out preliminary treatment to the input signal of equalizer, reduce the autocorrelation of input signal, reduce mean square error; In weight vector iterative process, adopt weighting Multiple model approach further to utilize planisphere information, adjust the mould value of weight vector in iterative process.The simulation result of underwater acoustic channel shows, compares with other method with weighting multimode blind balance method, and the inventive method has convergence rate and less steady-state error faster.

The present invention for achieving the above object, adopts following technical scheme:

The present invention is based on the Wavelet weighted multi-mode blind equalization method that chaos SVMs is optimized, comprise the steps:

A.) letter in reply source is transmitted a (n) obtains channel output vector x (n) through impulse response channel, and wherein n is time series, lower with;

B.) the channel output vector x (n) described in employing interchannel noise w (n) and step a obtains the input signal of orthogonal wavelet transformation device (WT): y (n)=x (n)+w (n);

C.) the input signal y (n) of the orthogonal wavelet transformation device described in step b is obtained to the input signal R (n) of equalizer through orthogonal wavelet transformation;

D.) the input signal R (n) of the equalizer described in step c is obtained to output signal z (the n)=f of equalizer through equalizer ^t(n) R (n), the weight vector that f (n) is equalizer, subscript T represents transposition;

The output signal z of the equalizer described in steps d (n) is upgraded to equalizer weight vector by weighting multimode blind balance method after decision device:

$f(n+1)=f\left(n\right)-\mathrm{\μ}{\hat{R}}^{-1}\left(n\right)[e_{\mathrm{Re},\mathrm{WMMA}}\left(n\right)+j\·e_{\mathrm{Im},\mathrm{WMMA}}\left(n\right)]R^{*}\left(n\right)---\left(1\right)$

In formula, μ is step factor, and Re represents real part, and Im represents imaginary part, e _{re, WMMA}(n), e _{im, WMMA}(n) be expressed as equalizer output error e _wMMA(n) real part and imaginary part, ${\hat{R}}^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\σ}}_{l,0}^2\left(n\right),{\mathrm{\σ}}_{l,1}^2\left(n\right),...{\mathrm{\σ}}_{l,k_L}^2\left(n\right),{\mathrm{\σ}}_{L+\mathrm{1,0}}^2\left(n\right),...$ ${\mathrm{\σ}}_{L+1,k_L}^2\left(n\right)]$ For orthogonal wavelet power normalization matrix, wherein, diag[] expression diagonal matrix, with represent respectively wavelet coefficient r _l,kwith scale coefficient s _l,kaverage power estimate, r _l,k(n) represent k the signal that wavelet space l layer decomposes, S _l,k(n) k signal when maximum decomposition level is counted L in expression metric space, can be obtained by following formula recursion:

$\left\{\begin{array}{c}{\mathrm{\σ}}_{l,k}^2(n+1)=\mathrm{\β}{\mathrm{\σ}}_{l.k}^2\left(n\right)+(1-\mathrm{\β}){\left|r_{l.k}\left(n\right)\right|}^2\\ {\mathrm{\σ}}_{L+1,k}^2(n+1)=\mathrm{\β}{\mathrm{\σ}}_{L,k}^2\left(n\right)+(1-\mathrm{\β}){\left|s_{L.k}\left(n\right)\right|}^2\end{array}---\left(2\right)\right.$

In formula, β is smoothing factor, and 0< β <1;

In weighting multimode blind balance method, its cost function is:

$J_{\mathrm{WMMA}}=E\left\{\right[z_{\mathrm{Re}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Re}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Re}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Re}}}^2{]}^2+[z_{\mathrm{Im}}^2\left(n\right)-\left|{\hat{z}}_{\mathrm{Im}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Im}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Im}}}^2{]}^2\right\}---\left(3\right)$

In formula, weighted factor λ _re, λ _im∈ [0,2], wherein a _re(n), a _im(n) be respectively transmit real part and the imaginary part of a (n) of information source; it is judgement symbol real part and imaginary part, z _re(n), z _im(n) represent respectively real part and the imaginary part of equalizer output signal z (n), the error function of weighting multimode blind equalizer is:

$\left\{\begin{array}{c}{e}_{\mathrm{Re},\mathrm{WMMA}}\left(n\right)=z_{\mathrm{Re}}\left(n\right)[z_{\mathrm{Re}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Re}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Re}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Re}}}^2]\\ e_{\mathrm{Im},\mathrm{WMMA}}\left(n\right)=z_{\mathrm{Im}}\left(n\right)[z_{\mathrm{Im}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Im}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Im}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Im}}}^2]\end{array}\right.---\left(4\right).$

Further, the Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs of the present invention, adopts support vector machine method the problem of blind equalization to be converted into the SVMs regression problem of global optimum:

For the QAM signal of high-order, make α=[0,1 ..., m], m=M-1, η=M-QAM (α), η represents the output signal after α quadrature amplitude modulation, the order of modulation that M is Higher Order QAM Signals, order η _mfor the modulated output signal corresponding to m input signal; Transmitting as a (n) of information source, the input signal of orthogonal wavelet transformation device is expressed as:

$y\left(n\right)=\underset{i}{\mathrm{\&Sigma;}}c\left(i\right)a(n-i)+w\left(n\right)---\left(5\right)$

In formula, the white Gaussian noise that w (n) is zero-mean, c (i) is that length is N _cthe response of i base band pulse;

In initialized process, n output signal of equalizer is z (n), has:

e _i(n)=|z(n)-η _i| ² （6）

In formula, η _ifor i element in η, i=1 ..., M, e _i(n) represent output signal z (n) and η _idistance;

Make R'=[R'(1), R'(2) ..., R'(n) ..., R'(N)], n=1 ..., N, the e of minimum in modus ponens (6) _i(n) corresponding η _i ²for R'(n) value, namely when in the signal z (n) of the equalizer output planisphere at QAM, from η _ithat puts is nearest;

For the signal of a high-order QAM, according to the structural risk minimization of SVMs matching, with the weight vector f of precision ε estimation balancing device, need to minimize following cost function,

$J_{\mathrm{cma}}\left(f\right)=\frac{1}{2}{\left|\right|f\left|\right|}^2+c\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}|R^{\&prime;}\left(n\right)-{\left[f^{T}y\left(n\right)\right]}^2{|}_{\mathrm{\&epsiv;}}---\left(7\right)$

In formula, C>0 is punishment variable, according to the ε insensitive loss function of Vapnik, has

|R'(n)-[f ^Ty(n)] ²| _ε=max{0,|R'(n)-[f ^Ty(n)] ²|-ε} （8）

Introduce slack variable ξ (n) and quadratic constraints in formula (8) changes linear restriction into

$\begin{array}{c}z\left(n\right)\left[f^{T}y\left(n\right)\right]-R^{\&prime;}\left(n\right)\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(n\right)\\ R^{\&prime;}\left(n\right)-z\left(n\right)\left[f^{T}y\left(n\right)\right]\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(n\right)\end{array}---\left(9\right)$

Punishment variable C is

$C=\stackrel{\&OverBar;}{g}\left(n\right)+3{\mathrm{\&sigma;}}_g---\left(10\right)$

In formula, g (n) be orthogonal wavelet transformation device n moment input signal y (n) mould value square, i.e. g (n)=| y (n) | ², expression is averaged, σ _gfor the mean square deviation of g (n);

The value of parameter ε can be determined by following formula

$\mathrm{\&epsiv;}=3\sqrt{{\mathrm{\&sigma;}}_n^2\frac{\ln N}{N}}---\left(11\right)$

In formula, for noise variance, N is the length of equalizer input signal in initialization procedure, and lnN represents the natural logrithm of N;

Optimal problem is converted into: given C and ε, ask following Lagrange saddle point problem,

$\begin{array}{c}L(f,\mathrm{\&xi;},\widetilde{\mathrm{\&xi;}},\mathrm{\&alpha;},\widetilde{\mathrm{\&alpha;}},\mathrm{\&gamma;},\widetilde{\mathrm{\&gamma;}})=\frac{1}{2}{\left|\right|f\left|\right|}^2+C\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&xi;}\left(n\right)+\widetilde{\mathrm{\&xi;}}\left(n\right)]\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&gamma;}\left(n\right)\mathrm{\&xi;}\left(n\right)+\widetilde{\mathrm{\&gamma;}}\left(n\right)\widetilde{\mathrm{\&xi;}}\left(n\right)]\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right)\{R^{\&prime;}\left(n\right)-z\left(n\right)[f^{T}y\left(n\right)]+\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(n\right)\}\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\widetilde{\mathrm{\&alpha;}}\left(n\right)\left\{z\left(n\right)\right[f^{T}y\left(n\right)]-R^{\&prime;}\left(n\right)+\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(n\right)\}\end{array}---\left(12\right)$

In formula, α (n), γ (n) and for Lagrange multiplier, and α (n)>=0, γ (n)>=0, n=1,2 ..., N, carries out saddle point to above formula and solves, and minimizes and solves f, and the solution of linear equalizer is expressed as

$f=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\widetilde{\mathrm{\&alpha;}}\left(n\right)-\mathrm{\&alpha;}\left(n\right)]z\left(n\right)y\left(n\right)---\left(13\right)$

The weight vector of equalizer is definite by formula (13), and in the process of SVMs study, the more new formula of weight vector is

f _k=f _k-1+(1-λ)f （14）

In formula, λ is the constant close to 1, and k expresses support for the study number of times of vector machine;

In initialization procedure, definition average modulation error is

$\mathrm{AME}\left(k\right)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[R_k^{\&prime;}\left(n\right)-{\left|z_k\left(n\right)\right|}^2]---\left(15\right)$

In formula, z _k(n) express support for vector machine in the learning process of the k time, the output signal of equalizer; The condition that initialization procedure is switched to Wavelet weighted multi-mode blind equalization method can be expressed as

AME(k-1)-AME(k)<ζ （16）

In formula, ζ is a positive number that value is very little.

Further, the Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs of the present invention, the parameters C of SVM and ε are chosen to the Combinatorial Optimization of regarding parameter as, target function using AME (k) as Combinatorial Optimization, search for optimum target function value by chaos optimization, thereby find suitable parameter value;

The Logistic mapping of employing formula (17) is as the iterative formula of Chaos Variable

d(n+1)=μd(n)[1-d(n)] （17）

In formula, d (n) is Chaos Variable, and μ is a constant, and in the time of μ=4, system, completely in chaos state, returns the deviation between reference model, using AME (k) minimum value as SVM

f(z ₁,z ₂)=min(AME)（18）

a _i≤z _i≤b _i,i=1,2

In formula, z ₁, z ₂for optimized variable, correspond respectively to SVMs parameters C and ε, [a _i, b _i] be variable z _ithe domain of definition, the step that chaos optimization is chosen SVM parameter is as follows:

Step1, initializing variable, making Chaos Search number of times is M ₁, chaos is searching times M again ₂; Counter I=0, k=0; Give the Chaos Variable d optimizing _iinitialize d _i=d _i(0), d _i ^*=d _i(0), i=1,2; Current optimal objective function value is initialized as f ^*;

Step2, by d _ithe interval that is mapped to optimized variable becomes z _i

z _i=a _i+(b _i-a _i)d _i i=1,2 （19）

Step3, optimized variable is optimized to search, if f is (z _i)≤f ^*, f ^*=f (z _i), d _i ^*=d _i, otherwise continue;

Step4、I=I+1，d _i(n+1)=μd _i(n)[1-d _i(n)]；

If Step5 is through M ₁inferior search f ^*remain unchanged, make d _i=d _i ^*+ Δ d _i, Δ d _ibe a very little number, k=k+1;

Step6, repetition Step2～4, if k>M ₂, by d _i ^*as optimum Chaos Variable, corresponding z _ifor SVM Optimal Parameters.

The present invention is by weighting multimode blind balance method (Weighted Multi-Modulus Algorithm, WMMA) in, introduce the index underworld of judgement symbol and adjust the mould value in cost function, the information of having utilized further high-order QAM planisphere, has good equalization performance to channel, utilize the decorrelation of orthogonal wavelet transformation, equalizer input signal is carried out to preliminary treatment, reduced the autocorrelation of input signal, accelerated convergence rate, because adopting steepest descent method, the weight vector in Wavelet weighted multi-mode blind equalization method (WT-WMMA) carries out iteration, similar with CMA, easily be absorbed in local minizing point, utilizing SVMs to carry out initialization to the weight vector of WT-WMMA can improve convergence rate and avoid being absorbed in local minizing point, in the process of SVMs initialization weight vector, choosing of SVMs parameter regarded as to the Combinatorial Optimization of parameter, set up Combinatorial Optimization target function, search for optimum target function value by chaos optimization, can improve the capability of fitting of SVMs.Therefore, orthogonal wavelet transformation, chaos optimization method and SVMs are incorporated in WMMA, invent a kind of Wavelet weighted multi-mode blind equalization method (Wavelet Transform Weighted Multiple Modulus blind equalization Algorithm based on Chaos and Support Vector Machines optimization, CSVM-WTWMMA) of optimizing based on chaos SVMs.

Brief description of the drawings

Fig. 1: orthogonal wavelet weighting multimode blind balance method schematic diagram;

Fig. 2: the structured flowchart of chaos optimization SVMs parameter;

Fig. 3: the present invention: the Wavelet weighted multi-mode blind equalization method schematic diagram of optimizing based on chaos SVMs

Fig. 4: embodiment simulation result figure: (a) mean square error; (b) SVM learning process; (c) equalizer input;

(d) WMMA output; (e) WT-WMMA output; (f) CSVM-WTWMMA output of the present invention.

Embodiment

Orthogonal wavelet weighting multimode blind balance method

For reducing the correlation of input signal, accelerate weight vector convergence rate, orthogonal wavelet transformation is incorporated in weighting multimode blind balance method, will obtain the weighting multimode blind balance method (WT-WMMA) based on wavelet transformation, as shown in Figure 1.

In Fig. 1, a (n) is that letter in reply source transmits, and can be expressed as a (n)=a _re(n)+ja _im(n), " j " is the empty unit of imaginary number; a _reand a (n) _im(n) be respectively real part and the imaginary part of source signal.C (n) is that length is N _cbaseband channel response vector, w (n) is noise vector, and Q is orthogonal wavelet transformation matrix, and y (n) is channel output vector, the input signal that R (n) is equalizer, weight vector and length that f (n) is equalizer are N _l, (subscript T represents transposition), the output that z (n) is equalizer, for the output of decision device.

The input signal of orthogonal wavelet transformation device after orthogonal wavelet transformation, the reception signal indication of equalizer is

R(n)=Qy(n) （1）

Equalizer is output as

z(n)=f ^T(n)R(n) （2）

If z _rand z (n) _i(n) represent respectively real part and the imaginary part of equalizer output signal z (n), z (n) can be expressed as

z(n)=z _Re(n)+jz _Im(n) （3）

In the blind balance method (WMMA) of weighting multimode, its cost function is

$J_{\mathrm{WMMA}}=E\left\{\right[z_{\mathrm{Re}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Re}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Re}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Re}}}^2{]}^2+[z_{\mathrm{Im}}^2\left(n\right)-\left|{\hat{z}}_{\mathrm{Im}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Im}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Im}}}^2{]}^2\right\}---\left(4\right)$

In formula, weighted factor λ _re, λ _im∈ [0,2], wherein a _re(n), a _im(n) be respectively transmit real part and the imaginary part of a (n) of information source; it is judgement symbol real part and imaginary part, z _re(n), z _im(n) represent respectively real part and the imaginary part of equalizer output signal z (n), the error function of weighting multimode blind equalizer is:

$\left\{\begin{array}{c}{e}_{\mathrm{Re},\mathrm{WMMA}}\left(n\right)=z_{\mathrm{Re}}\left(n\right)[z_{\mathrm{Re}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Re}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Re}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Re}}}^2]\\ e_{\mathrm{Im},\mathrm{WMMA}}\left(n\right)=z_{\mathrm{Im}}\left(n\right)[z_{\mathrm{Im}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Im}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Im}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Im}}}^2]\end{array}\right.---\left(5\right)$

In formula, e _{r, WMMA}(n), e _{i, WMMA}(n) be expressed as equalizer output error e _wMMA(n) real part and imaginary part.

The iterative formula of WMMA equalizer tap coefficient is

$f(n+1)=f\left(n\right)-\mathrm{\&mu;}{\hat{R}}^{-1}\left(n\right)[e_{\mathrm{Re},\mathrm{WMMA}}\left(n\right)+j\&CenterDot;e_{\mathrm{Im},\mathrm{WMMA}}\left(n\right)]R^{*}\left(n\right)---\left(6\right)$

In formula, μ is step factor, and Re represents real part, and Im represents imaginary part, e _{re, WMMA}(n), e _{im, WMMA}(n) be expressed as equalizer output error e _wMMA(n) real part and imaginary part, ${\hat{R}}^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\&sigma;}}_{l,0}^2\left(n\right),{\mathrm{\&sigma;}}_{l,1}^2\left(n\right),...{\mathrm{\&sigma;}}_{l,k_L}^2\left(n\right),{\mathrm{\&sigma;}}_{L+\mathrm{1,0}}^2\left(n\right),...$ ${\mathrm{\&sigma;}}_{L+1,k_L}^2\left(n\right)]$ For orthogonal wavelet power normalization matrix.Wherein, diag[] expression diagonal matrix, with represent respectively wavelet coefficient r _l,kwith scale coefficient s _l,kaverage power estimate, r _l,k(n) represent k the signal that wavelet space l layer decomposes, s _l,k(n) k signal when maximum decomposition level is counted L in expression metric space, can be obtained by following formula recursion:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}_{l,k}^2(n+1)=\mathrm{\&beta;}{\mathrm{\&sigma;}}_{l.k}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|r_{l.k}\left(n\right)\right|}^2\\ {\mathrm{\&sigma;}}_{L+1,k}^2(n+1)=\mathrm{\&beta;}{\mathrm{\&sigma;}}_{L,k}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|s_{L.k}\left(n\right)\right|}^2\end{array}---\left(7\right)\right.$

In formula, β is smoothing factor, and 0< β <1, generally gets the number that is slightly less than 1.Formula (1)～(7) are called the weighting multimode blind balance method (Wavelet Transform based WMMA, WT-WMMA) based on orthogonal wavelet.

SVMs initialization weight vector

Because the weight vector iteration in WT-WMMA is utilized steepest descent method, be easily absorbed in local minizing point, utilize SVMs the problem of blind equalization can be converted into the SVMs regression problem of global optimum.On the initialized basis of weight vector, make further improvements norm signal being carried out with SVMs, make SVMs be applicable to Higher Order QAM Signals, and the weight vector of equalizer is carried out to initialization.

For the QAM signal of high-order, make α=[0,1 ..., m], m=M-1, η=M-QAM (α), η represents the output signal after α quadrature amplitude modulation, the exponent number that M is Higher Order QAM Signals makes η=[η ₀, η ₁..., η _m], η _mfor the modulated output signal corresponding to m input signal.Make transmitting as a (n) of information source, the input signal of orthogonal wavelet transformation device can be expressed as:

$y\left(n\right)=\underset{i}{\mathrm{\&Sigma;}}c\left(i\right)a(n-i)+w\left(n\right)---\left(8\right)$

In formula, the white Gaussian noise that w (n) is zero-mean, c (i) is that length is N _cthe response of i base band pulse.

In initialized process, n output signal of equalizer is z (n), has:

e _i(n)=|z(n)-η _i| ² （9）

In formula, η _ifor i element in η, i=1 ..., M, e _i(n) represent output signal z (n) and η _idistance.

Make R'=[R'(1), R'(2) ..., R'(n) ..., R'(N)], n=1 ..., N, the e of minimum in modus ponens (9) _i(n) corresponding η _i ²for R'(n) value, namely when in the signal z (n) of the equalizer output planisphere at QAM, from η _ithat puts is nearest.

For the signal of a high-order QAM, according to the structural risk minimization of SVMs matching, with the weight vector f of precision ε estimation balancing device, need to minimize following cost function,

$J_{\mathrm{cma}}\left(f\right)=\frac{1}{2}{\left|\right|f\left|\right|}^2+c\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}|R^{\&prime;}\left(n\right)-{\left[f^{T}y\left(n\right)\right]}^2{|}_{\mathrm{\&epsiv;}}---\left(10\right)$

In formula, C>0 is punishment variable, according to the ε insensitive loss function of Vapnik, has

|R'(n)-[f ^Ty(n)] ²| _ε=max{0,|R'(n)-[f ^Ty(n)] ²|-ε} （11）

Introduce slack variable ξ (n) and quadratic constraints in formula (11) changes linear restriction into

$\begin{array}{c}z\left(n\right)\left[f^{T}y\left(n\right)\right]-R^{\&prime;}\left(n\right)\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(n\right)\\ R^{\&prime;}\left(n\right)-z\left(n\right)\left[f^{T}y\left(n\right)\right]\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(n\right)\end{array}---\left(12\right)$

Punishment variable C is

$C=\stackrel{\&OverBar;}{g}\left(n\right)+3{\mathrm{\&sigma;}}_g---\left(13\right)$

In formula, g (n) be orthogonal wavelet transformation device n moment input signal y (n) mould value square, i.e. g (n)=| y (n) | ². expression is averaged, σ _gfor the mean square deviation of g (n).

The value of parameter ε can be determined by following formula

$\mathrm{\&epsiv;}=3\sqrt{{\mathrm{\&sigma;}}_n^2\frac{\ln N}{N}}---\left(14\right)$

In formula, for noise variance, N is the length of equalizer input signal in initialization procedure.

Optimal problem can be converted into: given C and ε, ask following Lagrange saddle point problem,

$\begin{array}{c}L(f,\mathrm{\&xi;},\widetilde{\mathrm{\&xi;}},\mathrm{\&alpha;},\widetilde{\mathrm{\&alpha;}},\mathrm{\&gamma;},\widetilde{\mathrm{\&gamma;}})=\frac{1}{2}{\left|\right|f\left|\right|}^2+C\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&xi;}\left(n\right)+\widetilde{\mathrm{\&xi;}}\left(n\right)]\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&gamma;}\left(n\right)\mathrm{\&xi;}\left(n\right)+\widetilde{\mathrm{\&gamma;}}\left(n\right)\widetilde{\mathrm{\&xi;}}\left(n\right)]\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right)\{R^{\&prime;}\left(n\right)-z\left(n\right)[f^{T}y\left(n\right)]+\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(n\right)\}\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\widetilde{\mathrm{\&alpha;}}\left(n\right)\left\{z\left(n\right)\right[f^{T}y\left(n\right)]-R^{\&prime;}\left(n\right)+\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(n\right)\}\end{array}---\left(15\right)$

In formula, α (n), γ (n) and for Lagrange multiplier, and α (n)>=0, γ (n)>=0, n=1,2 ..., N.Above formula is carried out to saddle point and solve, minimize and solve f, the solution of linear equalizer can be expressed as

$f=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\widetilde{\mathrm{\&alpha;}}\left(n\right)-\mathrm{\&alpha;}\left(n\right)]z\left(n\right)y\left(n\right)---\left(16\right)$

The weight vector of equalizer is definite by formula (16), and in the process of SVMs study, the more new formula of weight vector is

f _k=f _k-1+(1-λ)f （17）

In formula, λ is the constant close to 1, and n expresses support for the study number of times of vector machine.

In initialization procedure, definition average modulation error is

$\mathrm{AME}\left(k\right)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[R_k^{\&prime;}\left(n\right)-{\left|z_k\left(n\right)\right|}^2]---\left(18\right)$

In formula, z _n(k) express support for vector machine in the learning process of the n time, the output signal of equalizer.The condition that initialization procedure is switched to Wavelet weighted multi-mode blind equalization method can be expressed as

AME(k-1)-AME(k)<ζ （19）

In formula, ζ is a positive number that value is very little.

Chaos optimization is chosen the parameter of SVM

Utilizing in the process of SVM initialization equalizer weight vector, the value of SVM parameter has determined its learning ability and generalization ability, choosing of SVM parameter regarded as to the Combinatorial Optimization of parameter, set up Combinatorial Optimization target function, search for optimum target function value by chaos optimization.The parameters C of SVM and ε are chosen the Combinatorial Optimization of regarding parameter as by the present invention, and the target function using AME (k) as Combinatorial Optimization utilizes chaos optimization to search for optimum target function value, thereby finds suitable parameter value.Claim that utilizing the SVM after chaos optimization parameter is chaos SVMs (Chaos & Support Vector Machines, CSVM).

The Logistic mapping of employing formula (20) is as the iterative formula of Chaos Variable

d(n+1)=μd(n)[1-d(n)] （20）

In formula, d (n) is Chaos Variable, and μ is a constant, and in the time of μ=4, system, completely in chaos state, returns the deviation between reference model, using AME (k) minimum value as SVM

f(z ₁,z ₂)=min(AME) （21）

a _i≤z _i≤b _i,i=1,2

In formula, z ₁, z ₂for optimized variable, correspond respectively to SVMs parameters C and ε, [a _i, b _i] be variable z _ithe domain of definition.The step that chaos optimization is chosen SVM parameter is as follows:

Step1, initializing variable, making Chaos Search number of times is M ₁, chaos is searching times M again ₂; Counter I=0, k=0; Give the Chaos Variable d optimizing _iinitialize d _i=d _i(0), d _i ^*=d _i(0), i=1,2; Current optimal objective function value is initialized as f ^*;

Step2, by d _ithe interval that is mapped to optimized variable becomes z _i

z _i=a _i+(b _i-a _i)d _i i=1,2 （22）

Step3, optimized variable is optimized to search, if f is (z _i)≤f ^*, f ^*=f (z _i), otherwise continue;

Step4、I=I+1，d _i(n+1)=μd _i(n)[1-d _i(n)]；

If Step5 is through M ₁inferior search f ^*remain unchanged, make d _i=d _i ^*+ Δ d _i, Δ d _ibe a very little number, k=k+1;

Step6, repetition Step2～4, if k>M ₂, by d _i ^*as optimum Chaos Variable, corresponding z _ifor SVM Optimal Parameters.

The flow chart of chaos optimization SVM parameter, as shown in Figure 2.

For improving the capability of fitting of SVMs, utilize chaos optimization SVMs parameter; For the weight vector of avoiding small echo multimode blind balance method is absorbed in local minizing point, utilize SVMs to carry out initialization to the weight vector of small echo multimode blind equalizer, finally invented a kind of Wavelet weighted multi-mode blind equalization method (CSVM-WTWMMA) of optimizing based on chaos SVMs, its schematic diagram as shown in Figure 3.

Embodiment

In order to verify the validity of CSVM-WTWMMA of the present invention, carry out simulation study with underwater acoustic channel, and and WT-WMMA, WMMA compares.

In emulation experiment, adopt and mix underwater acoustic channel [0.3132-0.10400.89080.3134], signal to noise ratio is 30dB, and the power length of equalizer is 16.

Transmit as 128QAM, WMMA, step factor μ is respectively μ _wMMA=3.8 × 10- ⁷, μ _wT-WMMA=3.5 × 10 ^-5, μ _cSVM-WTWMMA=3.2 × 10 ^-5; M ₁, M ₂value be respectively 300,100, Δ d _ivalue be all 10 ^-3; z ₁traversal interval be (0, C], z ₂traversal interval be (0, ε], the value of C, ε is determined by formula (13), (14); Adopt DB2 orthogonal wavelet to decompose to the input signal of channel, decomposition level is 2 layers, and the initial value of power is 4, forgetting factor β=0.99; Weighted factor λ _im=λ _re=0.78; Adopt carry out initialization to weight vector at first 300 of equalizer input data, initialized switching condition ζ is 10 ^-5.The simulation result that Monte Carlo is 800 times, as shown in Figure 3.

From Fig. 4 (a), after CSVM-WTWMMA convergence of the present invention, the approximately little 0.2dB of MSER WT-WMMA, than the approximately little 1dB of WMMA; Convergence rate is than fast approximately 1000 steps of WT-WMMA, than WMMA fast approximately 1200 steps; From Fig. 4 (b), CSVM in each learning process, the little about 0.05dB of SVM before average modulation error ratio parameter optimization; Fig. 4 (c)～(f) is equalizer input and output planispheres, can find out, the planisphere of CSVM-WTWMMA of the present invention is than WT-WMMA, and WMMA is clear, compact, concentrate.

In order to improve the equalization performance of equalizer to Higher Order QAM Signals, the Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs is proposed.The method method utilizes SVMs to carry out initialization to the weight vector of equalizer, has avoided it to be absorbed in local minizing point, by chaos optimization, the parameter of SVMs is optimized, and has improved its capability of fitting; Equalizer input signal is carried out to orthogonal wavelet transformation, reduced correlation, reduced mean square error; Weighting multimode blind balance method can make full use of the information of Higher Order QAM Signals planisphere, adjusts the mould value of weight vector in iterative process, has improved the convergence rate of method.The simulation result of underwater acoustic channel shows: compared with WT-WMMA, WMMA, CSVM-WTWMMA of the present invention has convergence rate and less mean square error faster.

Claims (3)

1. a Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs, comprises the steps:

A.) letter in reply source is transmitted a (n) obtains channel output vector x (n) through impulse response channel, and wherein n is time series, lower with;

B.) the channel output vector x (n) described in employing interchannel noise w (n) and step a obtains the input signal of orthogonal wavelet transformation device (WT): y (n)=x (n)+w (n);

C.) the input signal y (n) of the orthogonal wavelet transformation device described in step b is obtained to the input signal R (n) of equalizer through orthogonal wavelet transformation;

D.) the input signal R (n) of the equalizer described in step c is obtained to output signal z (the n)=f of equalizer through equalizer ^t(n) R (n), the weight vector that f (n) is equalizer, subscript T represents transposition;

It is characterized in that:

The output signal z of the equalizer described in steps d (n) is upgraded to equalizer weight vector by weighting multimode blind balance method after decision device:

$f(n+1)=f\left(n\right)-\mathrm{\&mu;}{\hat{R}}^{-1}\left(n\right)[e_{\mathrm{Re},\mathrm{WMMA}}\left(n\right)+j\&CenterDot;e_{\mathrm{Im},\mathrm{WMMA}}\left(n\right)]R^{*}\left(n\right)---\left(1\right)$

In formula, μ is step factor, and Re represents real part, and Im represents imaginary part, e _{re, WMMA}(n), e _{im, WMMA}(n) be expressed as equalizer output error e _wMMA(n) real part and imaginary part, ${\hat{R}}^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\&sigma;}}_{l,0}^2\left(n\right),{\mathrm{\&sigma;}}_{l,1}^2\left(n\right),...{\mathrm{\&sigma;}}_{l,k_L}^2\left(n\right),{\mathrm{\&sigma;}}_{L+\mathrm{1,0}}^2\left(n\right),...$ ${\mathrm{\&sigma;}}_{L+1,k_L}^2\left(n\right)]$ For orthogonal wavelet power normalization matrix, wherein, diag[] expression diagonal matrix, with represent respectively wavelet coefficient r _l,kwith scale coefficient s _l,kaverage power estimate, r _l,k(n) represent k the signal that wavelet space l layer decomposes, S _l,k(n) k signal when maximum decomposition level is counted L in expression metric space, can be obtained by following formula recursion:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}_{l,k}^2(n+1)=\mathrm{\&beta;}{\mathrm{\&sigma;}}_{l.k}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|r_{l.k}\left(n\right)\right|}^2\\ {\mathrm{\&sigma;}}_{L+1,k}^2(n+1)=\mathrm{\&beta;}{\mathrm{\&sigma;}}_{L,k}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|s_{L.k}\left(n\right)\right|}^2\end{array}---\left(2\right)\right.$

In formula, β is smoothing factor, and 0< β <1;

In weighting multimode blind balance method, its cost function is:

$J_{\mathrm{WMMA}}=E\left\{\right[z_{\mathrm{Re}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Re}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Re}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Re}}}^2{]}^2+[z_{\mathrm{Im}}^2\left(n\right)-\left|{\hat{z}}_{\mathrm{Im}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Im}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Im}}}^2{]}^2\right\}---\left(3\right)$

In formula, weighted factor λ _re, λ _im∈ [0,2], wherein a _re(n), a _im(n) be respectively transmit real part and the imaginary part of a (n) of information source; it is judgement symbol real part and imaginary part, z _re(n), z _im(n) represent respectively real part and the imaginary part of equalizer output signal z (n), the error function of weighting multimode blind equalizer is:

$\left\{\begin{array}{c}{e}_{\mathrm{Re},\mathrm{WMMA}}\left(n\right)=z_{\mathrm{Re}}\left(n\right)[z_{\mathrm{Re}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Re}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Re}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Re}}}^2]\\ e_{\mathrm{Im},\mathrm{WMMA}}\left(n\right)=z_{\mathrm{Im}}\left(n\right)[z_{\mathrm{Im}}^2\left(n\right)-|{\hat{z}}_{\mathrm{Im}}\left(n\right){|}^{{\mathrm{\&lambda;}}_{\mathrm{Im}}}{R}_{{\mathrm{\&lambda;}}_{\mathrm{Im}}}^2]\end{array}\right.---\left(4\right).$

2. the Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs according to claim 1, is characterized in that: adopt support vector machine method the problem of blind equalization to be converted into the SVMs regression problem of global optimum:

For the QAM signal of high-order, make α=[0,1 ..., m], m=M-1, η=M-QAM (α), η represents the output signal after α quadrature amplitude modulation, the order of modulation that M is Higher Order QAM Signals makes η=[η ₀, η ₁..., η _m], η _mfor the modulated output signal corresponding to m input signal; Transmitting as a (n) of information source, the input signal of orthogonal wavelet transformation device is expressed as:

$y\left(n\right)=\underset{i}{\mathrm{\&Sigma;}}c\left(i\right)a(n-i)+w\left(n\right)---\left(5\right)$

In formula, the white Gaussian noise that w (n) is zero-mean, c (i) is that length is N _cthe response of i base band pulse;

In initialized process, n output signal of equalizer is z (n), has:

e _i(n)=|z(n)-η _i| ² （6）

In formula, η _ifor i element in η, i=1 ..., M, e _i(n) represent output signal z (n) and η _idistance;

Make R'=[R'(1), R'(2) ..., R'(n) ..., R'(N)], n=1 ..., N, the e of minimum in modus ponens (6) _i(n) corresponding η _i ²for R'(n) value, namely when in the signal z (n) of the equalizer output planisphere at QAM, from η _ithat puts is nearest;

For the signal of a high-order QAM, according to the structural risk minimization of SVMs matching, with the weight vector f of precision ε estimation balancing device, need to minimize following cost function,

$J_{\mathrm{cma}}\left(f\right)=\frac{1}{2}{\left|\right|f\left|\right|}^2+c\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}|R^{\&prime;}\left(n\right)-{\left[f^{T}y\left(n\right)\right]}^2{|}_{\mathrm{\&epsiv;}}---\left(7\right)$

In formula, C>0 is punishment variable, according to the ε insensitive loss function of Vapnik, has

|R'(n)-[f ^Ty(n)] ²| _ε=max{0,|R'(n)-[f ^Ty(n)] ²|-ε} （8）

Introduce slack variable ξ (n) and quadratic constraints in formula (8) changes linear restriction into

$\begin{array}{c}z\left(n\right)\left[f^{T}y\left(n\right)\right]-R^{\&prime;}\left(n\right)\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(n\right)\\ R^{\&prime;}\left(n\right)-z\left(n\right)\left[f^{T}y\left(n\right)\right]\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(n\right)\end{array}---\left(9\right)$

Punishment variable C is

$C=\stackrel{\&OverBar;}{g}\left(n\right)+3{\mathrm{\&sigma;}}_g---\left(10\right)$

In formula, g (n) be orthogonal wavelet transformation device n moment input signal y (n) mould value square, i.e. g (n)=| y (n) | ², expression is averaged, σ _gfor the mean square deviation of g (n);

The value of parameter ε can be determined by following formula

$\mathrm{\&epsiv;}=3\sqrt{{\mathrm{\&sigma;}}_n^2\frac{\ln N}{N}}---\left(11\right)$

In formula, for noise variance, N is the length of equalizer input signal in initialization procedure, and lnN represents the natural logrithm of N;

Optimal problem is converted into: given C and ε, ask following Lagrange saddle point problem,

$\begin{array}{c}L(f,\mathrm{\&xi;},\widetilde{\mathrm{\&xi;}},\mathrm{\&alpha;},\widetilde{\mathrm{\&alpha;}},\mathrm{\&gamma;},\widetilde{\mathrm{\&gamma;}})=\frac{1}{2}{\left|\right|f\left|\right|}^2+C\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&xi;}\left(n\right)+\widetilde{\mathrm{\&xi;}}\left(n\right)]\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&gamma;}\left(n\right)\mathrm{\&xi;}\left(n\right)+\widetilde{\mathrm{\&gamma;}}\left(n\right)\widetilde{\mathrm{\&xi;}}\left(n\right)]\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(n\right)\{R^{\&prime;}\left(n\right)-z\left(n\right)[f^{T}y\left(n\right)]+\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(n\right)\}\\ -\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\widetilde{\mathrm{\&alpha;}}\left(n\right)\left\{z\left(n\right)\right[f^{T}y\left(n\right)]-R^{\&prime;}\left(n\right)+\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(n\right)\}\end{array}---\left(12\right)$

In formula, α (n), γ (n) and for Lagrange multiplier, and α (n)>=0, γ (n)>=0, n=1,2 ..., N, carries out saddle point to above formula and solves, and minimizes and solves f, and the solution of linear equalizer is expressed as

$f=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[\widetilde{\mathrm{\&alpha;}}\left(n\right)-\mathrm{\&alpha;}\left(n\right)]z\left(n\right)y\left(n\right)---\left(13\right)$

The weight vector of equalizer is definite by formula (13), and in the process of SVMs study, the more new formula of weight vector is

f _k=f _k-1+(1-λ)f （14）

In formula, λ is the constant close to 1, and k expresses support for the study number of times of vector machine;

In initialization procedure, definition average modulation error is

$\mathrm{AME}\left(k\right)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}[R_k^{\&prime;}\left(n\right)-{\left|z_k\left(n\right)\right|}^2]---\left(15\right)$

In formula, z _k(n) express support for vector machine in the learning process of the k time, the output signal of equalizer; The condition that initialization procedure is switched to Wavelet weighted multi-mode blind equalization method can be expressed as

AME(k-1)-AME(k)<ζ （16）

In formula, ζ is a positive number that value is very little.

3. the Wavelet weighted multi-mode blind equalization method of optimizing based on chaos SVMs according to claim 2, it is characterized in that: the parameters C of SVM and ε are chosen to the Combinatorial Optimization of regarding parameter as, target function using AME (k) as Combinatorial Optimization, search for optimum target function value by chaos optimization, thereby find suitable parameter value;

The Logistic mapping of employing formula (17) is as the iterative formula of Chaos Variable

d(n+1)=μd(n)[1-d(n)] （17）

In formula, d (n) is Chaos Variable, and μ is a constant, and in the time of μ=4, system, completely in chaos state, returns the deviation between reference model, using AME (k) minimum value as SVM

f(z ₁,z ₂)=min(AME) （18）

a _i≤z _i≤b _i,i=1,2

In formula, z ₁, z ₂for optimized variable, correspond respectively to SVMs parameters C and ε, [a _i, b _i] be variable z _ithe domain of definition, the step that chaos optimization is chosen SVM parameter is as follows:

Step1, initializing variable, making Chaos Search number of times is M ₁, chaos is searching times M again ₂; Counter I=0, k=0; Give the Chaos Variable d optimizing _iinitialize d _i=d _i(0), d _i ^*=d _i(0), i=1,2; Current optimal objective function value is initialized as f ^*;

Step2, by d _ithe interval that is mapped to optimized variable becomes z _i

z _i=a _i+(b _i-a _i)d _i i=1,2 （19）

Step3, optimized variable is optimized to search, if f is (z _i)≤f ^*, f ^*=f (z _i), d _i ^*=d _i, otherwise continue;

Step4、I=I+1，d _i(n+1)=μd _i(n)[1-d _i(n)]；

If Step5 is through M ₁inferior search f ^*remain unchanged, make d _i=d _i ^*+ Δ d _i, Δ d _ibe a very little number, k=k+1;

Step6, repetition Step2～4, if k>M ₂, by d _i ^*as optimum Chaos Variable, corresponding z _ifor SVM Optimal Parameters.