CN102299875B - Wavelet multimode blind equalization method introducing immune-optimized SVM (Support Vector Machine) - Google Patents

Abstract

The invention discloses a wavelet multimode blind equalization method introducing an immune-optimized SVM (Support Vector Machine). Based on the global searching capability of an immune clonal selection algorithm, parameter selection in an SVM blind equalization method is changed from manual selection into automatic determination, and then, the SVM is introduced into an orthogonal wavelet multimode blind equalization method, so that the wavelet multimode blind equalization method introducing the immune-optimized SVM is invented. The method comprises the following steps of: training a small segment of extracted initial data through the SVM to estimate the initial weight value of a blind equalizer, simultaneously, executing optimum selection for the parameters in the SVM by use of an immune algorithm, and taking the initial weight value estimated through the SVM as a weight vector of the orthogonal wavelet multimode blind equalization method. Compared with a multimode blind equalization method, the orthogonal wavelet multimode blind equalization method and an SVM orthogonal wavelet multimode blind equalization method, the method provided by the invention has the advantages of high convergence rate and small steady-state error, and can be used for improving the quality of underwater sound communication better.

Description

Introduce the wavelet multi-mode blind balance method of immune optimization support vector machines

Technical field

The present invention relates to the wavelet multi-mode blind balance methods that immune optimization support vector machines is introduced in a kind of underwater sound communication of Bandwidth-Constrained.

Background technique

In the underwater sound communication of Bandwidth-Constrained, (the Inter-symbol Interference of the intersymbol interference as caused by channel fading and Multipath Transmission etc., ISI communication quality) is seriously affected, reduce the reliability and transmission rate of underwater data transmission, therefore it needs to eliminate using effective channel equalization technique (see document [1] Shafayat Abrar, Asoke K.Nandi.Blind equalization of square-QAM signals:a multi-modulus approach.IEEE Trans.Commun.2010.6 (58): pp.1601-1604).Traditional adaptive equilibrium method is replaced using constant mould blind balance method, is not required to send training sequence, massive band width can be saved, effectively improve the transmission rate of information.But for the high-order orthogonal amplitude-modulated signal (QAM) with different modulus value, its convergence rate is slow, steady-state error is big (see document [2] Jenq-Tay Yuan, and Tzu-Chao Lin.Equalization and Carrier Phase Recovery of CMA and MMA in Blind Adaptive Receivers.IEEE Trans.Signal Process.2010.6 (58): pp.3206-3217;Document [3] Wu Di, Ge Lindong, Wang Bin is suitable for mixed type blind equalization algorithm [J] information engineering college journal .2010,1 (11): pp.45-48 of Higher Order QAM Signals;Document [4] Xu little Dong, Dai Xuchu, Xu Peixia is suitble to weighting multimode blind equalization algorithm [J] the electronics and information journal of Higher Order QAM Signals, 2007.29 (6): pp.1352-1355.).In order to overcome this disadvantage, Yang proposes multi-mode blind equalization method (Multi-Modulus Algorithm, MMA), it is primarily adapted for use in high-order QAM system, and the phase rotation of planisphere is corrected while eliminating intersymbol interference, but its convergence rate is still relatively slow, steady-state error is also larger (see document [5] Yang J, Werner J J, Dumont G A.The multimodulus blind equalization and its generalized algorithm [J] .IEEE Journal On Sel.Areas in Commun, 2002,20 (5): 997-1015;Document [6] Jenq-Tay Yuan, Kun-Da Tsai.Analysis of the Multimodulus Blind Equalization Algorithm in QAM Communication Systems.IEEE Trans.Commun.2005.9 (53): pp.1427-1431;Document [7] Dou Gaoqi, Gao Jun is suitable for multimode Multiple Modulus Blind Equalization [J] the electronics and information journal .2008,2 (30): pp.388-391 of high-order QAM system;Document [8] Gholami M R, Esfahani S N.Improving the convergence rate of blind equalization using transform domain [C] //ISSPA, Shush, United Arab Emirates:University of Sharjah.2007;pp.l-4;).Document [9] [10] [11] is (see document: [9] Han Yingge, Guo Yecai, Wu Zaolin, Zhou Qiaoxi study [J] Chinese journal of scientific instrument with algorithm simulating based on the multimode blind equalizer design of orthogonal wavelet transformation, 2008,29 (7): pp.1441-1445;Document [10] Zhu jie, Guo Ye-cai, Yang Chao.Decision feedback blind equalization algorithm based on momentum and orthogonal wavelet packet transform.WiCOM'09Proceedings of the5th International Conference on Wireless communications, networking and mobile computin G, IEEE, 2009:pp.2161-2164;Document [11] Han Yingge, orthogonal wavelet transformation blind equalization algorithm [J] the Journal of System Simulation .2008 of Guo Yecai introducing momentum term, 20 (6): pp.1559~1562) research shows that, wavelet transformation is carried out to the input signal of balanced device, and energy normalized processing is carried out to signal, the autocorrelation between each component can be made to be effectively reduced, accelerate convergence rate, but these blind equalization algorithms are all that balanced device optimal weight vector is found using gradient descent algorithm, it is more sensitive to the initialization of weight vector, improperly initialization easily makes algorithmic statement to local minimum, even dissipate.Document [12] [13] [14] [15] is (see document: [12] Feng Liu, Hu-cheng An, Jia-ming Li, and Lin-dong Ge.Build Equalization Using v-Support Vector Regressor for Constant Modulus Signals [J] .2008International Joint Conference on Neural Networks (IJCNN2008), IEEE, 2008:pp.161~164;Document [13] Marcelino Lazaro, Jonathan Gonzalez-Olasola.Blind equalization using the IRWLS formulation of the Support Vector Machine [J] .Signal Processing.2009,7 (89): pp.1265-1270;Document [14] Cooklev.T.An Efficient Architecture for Orthogonal Wavelet Transforms [J] .IEEE Signal Processing Letters, 2006,13 (2): pp.77~79;Document [15] Song Heng, decision feedback equalizer [J] electronics of the Wang Chen based on non-single-point fuzzy support vector machine and information journal .2008,30 (1): pp.117~120) propose a kind of algorithm that support vector machines (SVM) is introduced to blind equalization problem, the algorithm is due to the characteristics of being optimized using support vector machines and structure risk, so that convergence rate greatly improves and has globally optimal solution.But in the construction process of support vector machines, the parameter setting of SVM has large effect to final classification accuracy.Reasonable parameter selection can make support vector machines have higher precision, better generalization ability (see document [16] Yao Quanzhu, supporting vector machine model selection algorithm [J] computer engineering .2008 of the Tian Yuan based on artificial immunity, 15 (34): pp.223~225.Yao Quan-zhu, Tian Yuan.Model Selection Algorithm of SVM Based on Artificial Immune [J] .Computer Engineering.2008,15 (34): pp.223~225).

Summary of the invention

Object of the present invention is to be directed to orthogonal wavelet transformation multi-mode blind equalization method (WT-MMA) convergence rate slowly and there are problems that local convergence, a kind of wavelet multi-mode blind balance method (CSA-SVM-WT-MMA) for introducing immune optimization support vector machines has been invented.The inventive method carries out orthogonal wavelet transformation by the input signal to multimode blind equalizer, to reduce the autocorrelation of signal, and multimode blind equalization problem is converted to using support vector machines the support vector regression problem of global optimum, by extracting a bit of primary data, the weight vector of blind equalizer is initialized, while selection also is optimized to the parameter in support vector machines using immune algorithm.Theory analysis shows that the inventive method is substantially better than multi-mode blind equalization method, orthogonal wavelet multi-mode blind equalization method and support vector machines orthogonal wavelet multi-mode blind equalization method with underwater acoustic channel simulation result.Therefore, there is certain practical value.

The present invention to achieve the above object, adopts the following technical scheme that

The present invention proposes a kind of wavelet multi-mode blind balance method for introducing immune optimization support vector machines, includes the following steps:

A. impulse response channel c (k)) is passed through into transmitting signal a (k) and obtains channel output vector x (k), wherein k is time series, similarly hereinafter；

B. the input signal of orthogonal wavelet transformation device (WT): y (k)=v (k)+x (k)) is obtained using channel output vector x (k) described in interchannel noise v (k) and step a；

C.) the input signal y (k) of balanced device described in step b is equalized device input R (k) after orthogonal wavelet transformation, balanced device input R (k) is updated into balanced device weight vector by multi-mode blind equalization method；

When transmitter emits signal, equalizer input signal y (k)=y is taken_Re(k)+jy_Im(k) preceding N group vector carries out balanced, k=1,2 ... N, y to this N group data using support vector machines_Re(k) real part for being y (k), y_Im(k) imaginary part for being y (k),

For imaginary unit；According to the statistical property of structural risk minimization and transmitting signal, with the initial weight vector f of precision ε estimation balancing device_svm(n)；Establish following Support vector regression problem

$\min E_{\mathrm{svm}}\left(f_{\mathrm{svm}}\left(n\right)\right)=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2---\left(1\right)$

In formula, E_svm() indicates the precision ε estimation of Support vector regression；Its constraint function is

$\left\{\begin{array}{c}R\left(k\right)-{\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2\≤\mathrm{\ϵ}\\ {\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2-R\left(k\right)\≤\mathrm{\ϵ}\end{array}\right.---\left(2\right)$

In formula (2), R (k)=R_Re(k)+jR_Im(k), parameter ε determines the width in the insensitive region ε and the number of supporting vector；

In order to " soften " above-mentioned hardness ε-band support vector machines, introduce slack variable ξ (k),

With penalty C, the optimization problem of formula (1) and (2), which can be converted into, solves following constrained optimization problem:

$\min E_{\mathrm{svm}}\left(f_{\mathrm{svm}}\left(n\right)\right)=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2+C\underset{k=1}{\overset{N}{\mathrm{\Σ}}}(\mathrm{\ξ}\left(k\right)+\widetilde{\mathrm{\ξ}}\left(k\right))---\left(3\right)$

Constraint condition is

$\left\{\begin{array}{c}R\left(k\right)-{\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2\≤\mathrm{\ϵ}+\mathrm{\ξ}\left(k\right)\\ {\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2-R\left(k\right)\≤\mathrm{\ϵ}+\widetilde{\mathrm{\ξ}}\left(k\right)\\ \mathrm{\ξ}\left(k\right),\widetilde{\mathrm{\ξ}}\left(k\right)\≥0\end{array}\right.---\left(4\right)$

In formula (3) and (4), ξ (k) and

It is to measure that sample peels off apart from size, and punishes variable C and then embody the attention degree to the outlier；

But since constraint condition is for balanced device weight vector f_svm(n) contain quadratic term, optimization problem above can not be solved by linear programming method used by SVM；Then, Novel Algorithm is weighed to solve the problems, such as this according to a kind of iteration, the quadratic constraints in formula (4) can be rewritten as linear restriction；I.e.

$\left\{\begin{array}{c}{\left(f_{\mathrm{svm}}\left(n\right)\right)}^{T}y\left(k\right)z_{\mathrm{svm}}\left(k\right)-R\left(k\right)\≤\mathrm{\ϵ}+\widetilde{\mathrm{\ξ}}\left(k\right)\\ R\left(k\right)-{\left(f_{\mathrm{svm}}\left(n\right)\right)}^{T}y\left(k\right)z_{\mathrm{svm}}\left(k\right)\≤\mathrm{\ϵ}+\mathrm{\ξ}\left(k\right)\end{array}\right.---\left(5\right)$

In formula, z_svm(k)=z_Re,svm(k)+jz_Im,svm(k) it is the dual problem of export primal problem, introduces Lagrange function

$\begin{array}{c}L(f_{\mathrm{svm}},\mathrm{\ξ},\widetilde{\mathrm{\ξ}},\mathrm{\α},\widetilde{\mathrm{\α}},b,\tilde{b})=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2+C\underset{k=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{\ξ}\left(k\right)+\widetilde{\mathrm{\ξ}}\left(k\right)]\\ -\underset{k=1}{\overset{N}{\mathrm{\Σ}}}(b_k\mathrm{\ξ}\left(k\right)+{\tilde{b}}_k\widetilde{\mathrm{\ξ}}\left(k\right))\\ -\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\α}\left(k\right)[R\left(k\right)-\left({{[f}_{\mathrm{svm}}\left(n\right)]}^{2}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)+\mathrm{\ϵ}+\mathrm{\ξ}\left(k\right)]\\ -\underset{k=1}{\overset{N}{\mathrm{\Σ}}}\widetilde{\mathrm{\α}}\left(k\right)[\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{2}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)-R\left(k\right)+\mathrm{\ϵ}+\widetilde{\mathrm{\ξ}}\left(k\right)]\end{array}---\left(6\right)$

Wherein

It is Lagrange multiplier vector；The original optimization problem in formula (1)~(5) is converted into convex quadratic programming problem, i.e.,

$\begin{array}{c}\max E_{\mathrm{svm}}^{\text{'}}\left(f_{\mathrm{svm}}\left(n\right)\right)=-\frac{1}{2}\underset{k,m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))(\widetilde{\mathrm{\&alpha;}}\left(k\right)-\mathrm{\&alpha;}\left(k\right))\left(z_{\mathrm{svm}}\left(m\right)z_{\mathrm{svm}}\left(k\right)\right)K<y_m,y_k>\\ -\mathrm{\&epsiv;}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)+\mathrm{\&alpha;}\left(m\right))+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))\end{array}---\left(7\right)$

In formula, E'_svm() indicates the precision ε estimation of Support vector regression after convex quadratic programming；Its constraint condition is

$\left\{\begin{array}{c}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))=0\\ 0\&le;\widetilde{\mathrm{\&alpha;}}\left(m\right)\&le;C,m=1,...,N\end{array}\right.---\left(8\right)$

In formula, K < y_m,y_kThe inner product of > expression support vector machines；

By being compared to primal problem with dual problem, then the weight vector of balanced device can be expressed as

$f_{\mathrm{svm}}\left(n\right)=\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(k\right)-\mathrm{\&alpha;}\left(k\right))z_{\mathrm{svm}}\left(k\right)y\left(k\right)---\left(9\right)$

In formula, Lagrange multiplier

It can be solved by formula (7) and (8) with α (k)；

By the above process, balanced device initial weight vector f can be calculated_svm(n), then loop iteration is carried out until meeting switching condition；f_svm(n) update is realized using following formula

f_svm(n)=λf_svm(n-1)+(1-λ)f_svm(n)    (10)

In formula, n is the number of iterations, and λ is iteration step length；

When meeting the switching condition of following formula

$\left\{\begin{array}{c}\mathrm{MSE}\left(n\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}({\left|z_{\mathrm{svm}}\left(k\right)\right|}^2-R\left(k\right))\\ |\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1)|\&le;\mathrm{\&eta;}\end{array}\right.---\left(11\right)$

The initialization weight vector f of global optimum can be obtained_svm(n), and using this weight vector as initialization weight vector, in formula (11), MSE (n) indicates the mean square error of n times iteration, and η is switching threshold.

Further, support vector machines parameter selection method is as follows in the wavelet multi-mode blind balance method for being introduced into immune optimization support vector machines of the invention:

(1) initialization of population

It is randomly generated the antibody population of certain amount, each antibody therein respectively corresponds kernel function, one group of value in punishment parameter C and ε；

(2) affine angle value is calculated

Affine angle value between calculating antibody and antigen；

(3) Immune Clone Selection

Immune Clone Selection operation is the inverse operation of clone's increment operation；The operation is to select outstanding individual in the filial generation respectively cloned after rising in value from antibody, is an asexual selection course to form new antibody population；One antibody forms a sub- antibody population after clone's increment, realizes that the affinity of part increases using operating after the operation of affinity maturation by Immune Clone Selection；Antibody first in the antibody population described in second step is arranged by the sequence of affinity from small to large, is evaluated according to the size of affinity, and affinity refers to that an antibody generates the degree of identification to the antigen of an identical chain length；Optimum antibody is selected to carry out clonal expansion operation, it is directly proportional to affinity to clone number by the antibody population A after being expanded；

(4) king-crossover strategy

The principle of king-crossover is as follows: in the realization of immune algorithm, the probability P of a king-crossover given first_kc, wherein kc indicates king-crossover, i.e. king-crossover, the random number R between one [0,1] is generated for each individual a (t) for t in clonal antibody group described in third step, if R is less than king-crossover probability P_kcThen a (t) is selected intersects with the former generation elite individual b (t) that works as saved, its method is: a (t) and b (t) are put into a small mating pond, according to selected Crossover Strategy, crossover operation is carried out to a (t) and b (t), obtain a pair of of offspring individual a'(t) and b'(t), the Crossover Strategy includes single-point, two o'clock, multiple spot and consistent intersection；Then, it is then lost and is not had to a (t), b'(t in a'(t) substitution population)；

(5) high frequency closedown

High frequency closedown is carried out to clonal antibody each in antibody population A, generates variation group A^*；Primary operational operator of the high frequency closedown as Immune Clone Selection can prevent diversity that is precocious and increasing antibody of evolving；

(6) affine angle value is calculated

Each antibody after high frequency closedown described in (5) is recalculated into its corresponding affine angle value；

(7) it selects

From variation group A^*The low antibody of n affinity, n are inversely proportional to the average affine angle value of antibody population in the high antibody replacement initial antibodies group of n affinity of middle selection；

(8) whether judgement terminates

Judged according to the evolutionary generation of antibody, when evolutionary generation is less than maximum evolutionary generation, then go to (2), repeat the operating procedure of (2)~(5), until evolutionary generation is greater than maximum evolutionary generation, such as reach termination condition, then EP (end of program), exports global parameter optimal solution.

The present invention utilizes the ability of searching optimum of Immune Clonal Selection Algorithm, parameter selection in support vector machines blind equalization algorithm is become automatically determining from manually choosing, then support vector machines is introduced into orthogonal wavelet multi-mode blind equalization method, a kind of wavelet multi-mode blind balance method (CSA-SVM-WT-MMA) for introducing immune optimization support vector machines is invented, the inventive method is by training the initial weight to estimate blind equalizer using a bit of initial data of the support vector machines to extraction, selection is optimized to the parameter in SVM using immune algorithm simultaneously, and the initial weight for estimating SVM is as the weight vector of orthogonal wavelet multimode blind equalization algorithm (WT-MMA).The simulation result of underwater acoustic channel shows, compared with multi-mode blind equalization method, orthogonal wavelet multi-mode blind equalization method and support vector machines orthogonal wavelet multi-mode blind equalization method, the inventive method has faster convergence rate and steady-state error, to preferably improve the performance of underwater sound communication.

Detailed description of the invention

Fig. 1: the present invention: the wavelet multi-mode blind balance method schematic diagram of immune optimization support vector machines is introduced；

Fig. 2: implement Simulation results figure, (a) the mean square error curve of 5 kinds of methods, (b) the remaining intersymbol interference curve of 5 kinds of methods, (c) ISI and the SNR comparison curves of 5 kinds of methods, (d) CMA exports planisphere, and (e) MMA exports planisphere, and (f) WT-MMA exports planisphere, (g) SVM-WT-MMA exports planisphere, and (h) CSA-SVM-WT-MMA of the present invention exports planisphere.

Specific embodiment

The wavelet multi-mode blind balance method principle of immune optimization support vector machines is introduced, as shown in Figure 1.In Fig. 1, a (k) is that letter in reply source emits signal, is expressed as a (k)=a_Re(k)+ja_Im(k), a_Re(k) and a_Im(k) be respectively source signal real and imaginary parts；C (k) is channel impulse response vector, length M；Vector v (k) is additive white Gaussian noise；Vector y (k) is the input complex signal of balanced device, and length N is classified as real and imaginary parts, i.e. y (k)=y_Re(k)+jy_Im(k), y_Re(k) real part for being y (k), y_ImIt (k) is the imaginary part of y (k) (similar expression formula, expressed meaning are identical below)；Vector f (k) is balanced device weight vector and length is L, i.e. f (k)=[f₀(k),…,f_L(k)]^T([·]^TIndicate transposition operation)；ψ () is memoryless nonlinear function, indicates memoryless nonlinear estimator；Z (k) is the output complex signal sequence of balanced device.In Fig. 1, the part without dotted line frame is orthogonal wavelet multi-mode blind equalization algorithm (WT-MMA)；Part comprising dotted line frame is the orthogonal wavelet multimode blind equalization algorithm (CSA-SVM-WT-MMA) for introducing immune optimization support vector machines.Now it is described below:

Orthogonal wavelet multimode blind equalization algorithm (WT-MMA) is converted using reception complex signal of the orthogonal wavelet transformation to balanced device, and carries out energy normalized processing, and the autocorrelation of input complex signal is reduced.

Enable a (k)=[a (k) ..., a (k-N_c+1)]^T,y(k)=[y(k+N),…,y(k),…,y(k-N)]^T, as shown in Figure 1

$y\left(k\right)=\underset{i=0}{\overset{N_c-1}{\mathrm{\&Sigma;}}}{c}_{i}a(k-i)+v\left(k\right)=c^{T}a\left(k\right)+v\left(k\right)---\left(1\right)$

According to wavelet transformation theory, balanced device f (k) is FIR filter, be may be expressed as:

In formula, k=0,1 ..., N,Indicate scale parameter be p, the wavelet basis function that translation parameters is q；ψ_P,q(k) indicate scale parameter be P, the scaling function that translation parameters is q, k_p=N/2^p- 1 (p=1,2 ..., J), P are wavelet decomposition out to out, k_PFor the maximal translation under scale p, due to f (n) characteristic by

And F_P,q=<f(k),ψ_P,q(k) > reflect, therefore it is called balanced device weight coefficient.

Input signal point real and imaginary parts by orthogonal wavelet transformation post-equalizer are expressed as

R(k)=R_Re(k)+jR_Im(k)=Qy_Re(k)+j(Qy_Im(k))    (3)

Wherein, R_Re(k) and R_ImIt (k) is respectively R (k) real and imaginary parts, representation is as follows,

$R_r\left(k\right)={[d_{\mathrm{Re}\mathrm{1,0}}\left(k\right),{\mathrm{<figure-callout\; id="1"\; label="d\; Re"\; filenames="HDA0000068377820000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{Re}}\left(k\right),...,d_{\mathrm{ReP},k_P}\left(k\right),s_{\mathrm{ReP},0}\left(k\right),...s_{\mathrm{ReP},k_P}\left(k\right)]}^T---\left(4\right)$

$R_{\mathrm{Im}}\left(k\right)=[d_{\mathrm{<figure-callout\; id="1"\; label="Im"\; filenames="HDA0000068377820000021.png"\; state="\{\{state\}\}">Im</figure-callout>}\mathrm{1,0}}\left(k\right),{\mathrm{<figure-callout\; id="1"\; label="d\; Im"\; filenames="HDA0000068377820000021.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{Im}}\left(k\right),...,d_{\mathrm{ImP},k_p}\left(k\right),s_{\mathrm{ImP},0}\left(k\right),...s_{\mathrm{ImP},k_p}\left(k\right){]}^T---\left(6\right)$

In formula, k=0,1 ..., L-1, L=2^PFor the length of balanced device；Re and Im, which is respectively indicated, takes real and imaginary parts；

And ψ_P,q(n) wavelet function and scaling function, d are respectively indicated_p,q(k)、s_P,qIt (k) is respectively corresponding small echo and change of scale coefficient, Q is orthogonal wavelet transform matrix.

Balanced device exports

$\left\{\begin{array}{c}{z}_{\mathrm{Re}}\left(k\right)=f_{\mathrm{Re}}^H\left(k\right)R_{\mathrm{Re}}\left(k\right)\\ z_{\mathrm{Im}}\left(k\right)=f_{\mathrm{Im}}^H\left(k\right)R_{\mathrm{Im}}\left(k\right)\end{array}\right.---\left(8\right)$

In formula,

With

(H indicates conjugate transposition) is respectively the real part vector sum imaginary part vector of balanced device weight vector, z_Re(k) and z_Im(k) be respectively equalizer output signal real and imaginary parts.

It is by the cost function form of MMA

$J_{\mathrm{MMA}}\left(f\right)=E\{{(z_{\mathrm{Re}}^2\left(k\right)-R_{\mathrm{Re},\mathrm{MMA}}^2)}^2+{(z_{\mathrm{Im}}^2\left(k\right)-R_{\mathrm{Im},\mathrm{MMA}}^2)}^2\}---\left(9\right)$

Wherein $R_{\mathrm{Re},\mathrm{<figure-callout\; id="2"\; label="MMA"\; filenames="HDA0000068377820000012.png"\; state="\{\{state\}\}">MMA</figure-callout>}}^2=E\left\{\left(a_{\mathrm{Re}}^4\left(k\right)\right)\right\}/E\left\{\left(a_{\mathrm{Re}}^2\left(k\right)\right)\right\},R_{\mathrm{Im},\mathrm{<figure-callout\; id="2"\; label="MMA"\; filenames="HDA0000068377820000012.png"\; state="\{\{state\}\}">MMA</figure-callout>}}^2=E\left\{\left(a_{\mathrm{Im}}^4\left(k\right)\right)\right\}/E\left\{\left(a_{\mathrm{Im}}^2\left(k\right)\right)\right\},$ Modulus value of the former with phase direction, the modulus value of the latter's expression orthogonal direction.

The error of balanced device is

$\left\{\begin{array}{c}{e}_{\mathrm{Re},\mathrm{MMA}}\left(k\right)=z_{\mathrm{Re}}\left(k\right)(z_{\mathrm{Re}}^2\left(k\right)-R_{\mathrm{Re},\mathrm{MMA}}^2)\\ e_{\mathrm{Im},\mathrm{MMA}}\left(k\right)=z_{\mathrm{Im}}\left(k\right)(z_{\mathrm{Im}}^2\left(k\right)-R_{\mathrm{Im},\mathrm{MMA}}^2)\end{array}\right.---\left(10\right)$

The iterative formula of its corresponding balanced device weight vector is

$\left\{\begin{array}{c}{f}_{\mathrm{Re}}(k+1)=f_{\mathrm{Re}}\left(k\right)-\mathrm{\&mu;}{\hat{R}}^{-1}\left(k\right)e_{\mathrm{Re},\mathrm{MMA}}\left(k\right)R_{\mathrm{Re}}^{*}\left(k\right)\\ f_{\mathrm{Im}}(k+1)=f_{\mathrm{Im}}\left(k\right)-\mathrm{\&mu;}{\hat{R}}^{-1}\left(k\right)e_{\mathrm{Im},\mathrm{MMA}}\left(k\right)R_{\mathrm{Im}}^{*}\left(k\right)\end{array}\right.---\left(11\right)$

In formula, R^*(k) conjugation for being R (k)；

${\hat{R}}^{-1}\left(k\right)=\mathrm{diag}[{\mathrm{\&sigma;}}_{p,0}^2\left(k\right),{\mathrm{\&sigma;}}_{p,1}^2\left(k\right),...,{\mathrm{\&sigma;}}_{P,k_P-1}^2\left(k\right),{\mathrm{\&sigma;}}_{P+\mathrm{1,0}}^2\left(k\right),...,{\mathrm{\&sigma;}}_{P+1,k_P-1}^2\left(k\right)]---\left(12\right)$

In formula,It respectively indicates to d_p,k(k), s_P,k(k) mean power is estimated,

It is right

Estimated value is derived by by following formula:

$\left\{\begin{array}{c}{\widehat{\mathrm{\&sigma;}}}_{p,q}^2(k+1)=\mathrm{\&beta;}{\widehat{\mathrm{\&sigma;}}}_{p,q}^2\left(k\right)+(1-\mathrm{\&beta;}){\left|d_{p,q}\left(k\right)\right|}^2\\ {\widehat{\mathrm{\&sigma;}}}_{P+1,q}^2(k+1)=\mathrm{\&beta;}{\widehat{\mathrm{\&sigma;}}}_{P+1,q}^2\left(k\right)+(1-\mathrm{\&beta;}){\left|s_{P,q}\left(k\right)\right|}^2\end{array}\right.---\left(13\right)$

Wherein, diag [] indicates that diagonal matrix, β are smoothing factor, and 0 < β < 1.d_p,q(k) q-th of signal of wavelet space p layers of decomposition, s are indicated_P,q(k) q-th of signal when maximum decomposition level number P in scale space is indicated.Formula (2)~formula (13), which is constituted, is based on orthogonal wavelet multimode blind equalization side algorithm (WT-MMA).

Orthogonal wavelet multimode blind equalization algorithm is to seek gradient to balanced device weight vector using the cost function constructed, so that it is determined that the iterative equation of equaliser weights, this method lacks ability of searching optimum, and unsuitable initialization is easy to make algorithmic statement to local minimizers number.In order to overcome this disadvantage, the optimization initial weight vector of WT-MMA algorithm is searched using support vector machines herein, for making up the defect of WT-MMA algorithm, better solves the problem of sinking into local convergence in search process.

When transmitter emits signal, equalizer input signal y (k)=y is taken_Re(k)+jy_Im(k) (k=1,2 ... N, y_Re(k) real part for being y (k), y_Im(k) imaginary part for being y (k).) preceding N group vector, this N group data is carried out using support vector machines balanced.According to the statistical property of structural risk minimization and transmitting signal, with the initial weight vector f of precision ε estimation balancing device_svm(n).Establish following Support vector regression problem

$\min E_{\mathrm{svm}}\left(f_{\mathrm{svm}}\left(n\right)\right)=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2---\left(14\right)$

In formula, E_svm() indicates the precision ε estimation of Support vector regression.Constraint function is

$\left\{\begin{array}{c}R\left(k\right)-{\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2\&le;\mathrm{\&epsiv;}\\ {\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2-R\left(k\right)\&le;\mathrm{\&epsiv;}\end{array}\right.---\left(15\right)$

In formula (15), R (k)=R_Re(k)+jR_Im(k), parameter ε determines the width in the insensitive region ε and the number of supporting vector.

In order to " soften " above-mentioned hardness ε-band support vector machines, introduce slack variable ξ (k),

With penalty C, the optimization problem of formula (14) and (15), which can be converted into, solves following constrained optimization problem:

$\min E_{\mathrm{svm}}\left(f_{\mathrm{svm}}\left(n\right)\right)=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2+C\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(\mathrm{\&xi;}\left(k\right)+\widetilde{\mathrm{\&xi;}}\left(k\right))---\left(16\right)$

Constraint condition is

$\left\{\begin{array}{c}R\left(k\right)-{\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(k\right)\\ {\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2-R\left(k\right)\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(k\right)\\ \mathrm{\&xi;}\left(k\right),\widetilde{\mathrm{\&xi;}}\left(k\right)\&GreaterEqual;0\end{array}\right.---\left(17\right)$

In formula (16) and (17), ξ (k) and

It is to measure that sample peels off apart from size, and punishes variable C and then embody the attention degree to the outlier.

But since constraint condition is for balanced device weight vector f_svm(n) contain quadratic term, optimization problem above can not be solved by linear programming method used by SVM.Then, Novel Algorithm (Iterative Reweighted Quadratic Programming is weighed according to a kind of iteration that document [13] propose, IRWQP it) solves the problems, such as this, the quadratic constraints in formula (17) can be rewritten as linear restriction.I.e.

$\left\{\begin{array}{c}\left({\left(f_{\mathrm{svm}}\left(n\right)\right)}^{T}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)-R\left(k\right)\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(k\right)\\ R\left(k\right)-{(\left(f_{\mathrm{svm}}\left(n\right)\right)}^{T}y\left(k\right))z_{\mathrm{svm}}\left(k\right)\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(k\right)\end{array}\right.---\left(18\right)$

In formula, z_svm(k)=z_Re,svm(k)+jz_Im,svm(k) it is the dual problem of export primal problem, introduces Lagrange function

$\begin{array}{c}L(f_{\mathrm{svm}},\mathrm{\&xi;},\widetilde{\mathrm{\&xi;}},\mathrm{\&alpha;},\widetilde{\mathrm{\&alpha;}},b,\tilde{b})=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2+C\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&xi;}\left(k\right)+\widetilde{\mathrm{\&xi;}}\left(k\right)]\\ -\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(b_k\mathrm{\&xi;}\left(k\right)+{\tilde{b}}_k\widetilde{\mathrm{\&xi;}}\left(k\right))\\ -\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(k\right)[R\left(k\right)-\left({{[f}_{\mathrm{svm}}\left(n\right)]}^{2}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)+\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(k\right)]\\ -\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\widetilde{\mathrm{\&alpha;}}\left(k\right)[\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{2}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)-R\left(k\right)+\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(k\right)]\end{array}---\left(19\right)$

Wherein

It is Lagrange multiplier vector.The original optimization problem in formula (14)~(18) is converted into convex quadratic programming problem (dual problem), i.e.,

$\begin{array}{c}\max E_{\mathrm{svm}}^{\text{'}}\left(f_{\mathrm{svm}}\left(n\right)\right)=-\frac{1}{2}\underset{k,m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))(\widetilde{\mathrm{\&alpha;}}\left(k\right)-\mathrm{\&alpha;}\left(k\right))\left(z_{\mathrm{svm}}\left(m\right)z_{\mathrm{svm}}\left(k\right)\right)K<y_m,y_k>\\ -\mathrm{\&epsiv;}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)+\mathrm{\&alpha;}\left(m\right))+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))\end{array}---\left(20\right)$

In formula, E_s'_vm() indicates the precision ε estimation of Support vector regression after convex quadratic programming.Its constraint condition is

$\left\{\begin{array}{c}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))=0\\ 0\&le;\widetilde{\mathrm{\&alpha;}}\left(m\right)\&le;C,m=1,...,N\end{array}\right.---\left(21\right)$

In formula, K < y_m,y_k> expression indicates the inner product of support vector machines.

By being compared to primal problem with dual problem, then the weight vector of balanced device can be expressed as

$f_{\mathrm{svm}}\left(n\right)=\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(k\right)-\mathrm{\&alpha;}\left(k\right))z_{\mathrm{svm}}\left(k\right)y\left(k\right)---\left(22\right)$

In formula, Lagrange multiplier

It can be solved by formula (20) and (21) with α (k).

By the above process, balanced device initial weight vector f can be calculated_svm(n), then loop iteration is carried out until meeting switching condition.f_svm(n) update is realized using following formula

f_svm(n)=λf_svm(n-1)+(1-λ)f_svm(n)    (23)

In formula, n is the number of iterations, and λ is iteration step length.

When meeting the switching condition of following formula

$\left\{\begin{array}{c}\mathrm{MSE}\left(n\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}({\left|z_{\mathrm{svm}}\left(k\right)\right|}^2-R\left(k\right))\\ |\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1)|\&le;\mathrm{\&eta;}\end{array}\right.---\left(24\right)$

The initialization weight vector f of global optimum can be obtained_svm(n), and using this weight vector as the initialization weight vector of WT-MMA algorithm.In formula (24), MSE (n) indicates the mean square error of n times iteration, and η is switching threshold.

In support vector machines multimode blind equalization algorithm, it needs to be determined that the value of some parameters, such as kernel function, punishment parameter C, ε-insensitive loss function, the setting of different parameters can seriously affect the performance of SVM machine learning, so being all mostly by experiment repeatedly, and the subjective experience of people selects the parameter needed, and needs to pay more time cost.Wherein penalty C and ε-insensitive loss function ε width is the free parameter for controlling approximating function VC dimension (quantitative targets of approximating function set sizes), since it must be adjusted simultaneously in selection, has certain complexity.

Therefore, the present invention utilizes the characteristic of Immune Clonal Selection Algorithm global optimizing, and selection is optimized to the parameter in support vector machines.Mainly antigen is set by the training sample of SVM, C and ε are as antibody for parameter, the value range of parameter C and ε are determined first, by simulation Immune System to antibody Immune Clone Selection, the principle of variation, expand search range using antibody cloning, variation keeps multifarious feature, the parametric optimal solution of objective function is searched out, and as the punishment parameter C, ε-insensitive loss function in support vector machines.When Immune Clonal Selection Algorithm is applied to support vector machines optimization of parameter choice, the basic step of algorithm is as follows:

(1) initialization of population

It is randomly generated the antibody population of certain amount, each antibody therein respectively corresponds kernel function, one group of value in punishment parameter C and ε；

(2) affine angle value is calculated

Affine angle value between calculating antibody and antigen；

(3) Immune Clone Selection

Immune Clone Selection operation is the inverse operation of clone's increment operation.The operation is to select outstanding individual in the filial generation respectively cloned after rising in value from antibody, is an asexual selection course to form new antibody population.One antibody forms a sub- antibody population after clone's increment, realizes that the affinity of part increases using operating after the operation of affinity maturation by Immune Clone Selection.Antibody first in the antibody population described in second step is arranged by the sequence of affinity from small to large, it is evaluated according to the size of affinity (degree that an antibody generates identification to the antigen of an identical chain length is known as affinity), optimum antibody is selected to carry out clonal expansion operation, antibody population A after being expanded, clone's number are directly proportional to affinity.

(4) king-crossover strategy

The principle of king-crossover is as follows: in the realization of immune algorithm, the probability P of a king-crossover given first_kc(kc indicates king-crossover, i.e. king-crossover) generates the random number R between one [0,1] for each individual a (t) for t in clonal antibody group described in third step, if R is less than king-crossover probability P_kcThen a (t) is selected intersects with the former generation elite individual b (t) that works as saved, its method is: a (t) and b (t) are put into a small mating pond, according to selected Crossover Strategy (single-point, two o'clock, multiple spot intersect etc. with consistent), crossover operation is carried out to a (t) and b (t), obtains a pair of of offspring individual a'(t) and b'(t).Then, it is then lost and is not had to a (t), b'(t in a'(t) substitution population).

(5) high frequency closedown

High frequency closedown is carried out to clonal antibody each in antibody population A, generates variation group A^*；Primary operational operator of the high frequency closedown as Immune Clone Selection can prevent diversity that is precocious and increasing antibody of evolving；

(6) affine angle value is calculated

Each antibody after high frequency closedown described in (5) is recalculated into its corresponding affine angle value.

(7) it selects

From variation group A^*The low antibody of n affinity, n are inversely proportional to the average affine angle value of antibody population in the high antibody replacement initial antibodies group of n affinity of middle selection；

(8) whether judgement terminates

Judged according to the evolutionary generation of antibody, when evolutionary generation is less than maximum evolutionary generation, then go to (2), repeat the operating procedure of (2)~(5), until evolutionary generation is greater than maximum evolutionary generation, such as reach termination condition, then EP (end of program), exports global parameter optimal solution.

Pass through above procedure, so that it may parameter in SVM be in optimized selection, so as to improve the performance of support vector machines initialization weight vector.

Embodiment

In order to verify the validity of the method for the present invention CSA-SVM-WT-MMA, using CMA, MMA, WT-MMA and SVM-WT-MMA method as comparison other, emulation experiment is carried out.In l-G simulation test, antibody scale is 100, and clone's controlling elements are 0.6, and king-crossover probability is 0.2, mutation probability 0.1, and algorithm maximum number of iterations is 200.Parameter C and ε optimization value range are set as: 1≤C≤20,0.00001≤ε≤0.1, support vector machines initialize extracted training sample number N=2000;

Mixed-phase underwater acoustic channel c=[0.3132-0.10400.89080.3134];Transmitting signal is 128QAM, and it is 16 that balanced device, which weighs length, signal-to-noise ratio 30dB.In SVM-WT-MMA, C=15, ε=0.1；In CSA-SVM-WT-MMA of the present invention, immune optimization selects optimized parameter for C=17.8477, ε=0.0765.Other parameters setting, as shown in table 1.1000 Kano Meng Te simulation results, as shown in Figure 2.For more each algorithm performance, it is as follows to define remaining intersymbol interference:

$\mathrm{ISI}=101g((\underset{i}{\mathrm{\&Sigma;}}{\left|h_i\right|}^2-{\left|h_{\max }\right|}^2)/{\left|h_{\max }\right|}^2)---\left(25\right)$

In formula, h_iIt is composite channel

In i-th of element, and h_maxIndicate element wherein with maximum value.

The setting of 1 simulation parameter of table

Fig. 2 (a) (b) shows that in convergence rate, CSA-SVM-WT-MMA of the present invention and SVM-WT-MMA is essentially identical, but faster than MMA nearly 6000 steps, faster than WT-MMA nearly 3000 steps.In remaining intersymbol interference, CSA-SVM-WT-MMA ratio WT-MMA and SVM-WT-MMA of the present invention reduce nearly 0.8dB.By Fig. 2 (c) it is found that with signal-to-noise ratio increase, the remaining intersymbol interference of five kinds of methods all constantly reducing, and the amplitude that CSA-SVM-WT-MMA of the present invention reduces is maximum, and same signal-to-noise ratio compares the superiority that can more embody the algorithm.Fig. 2 (e), (f), (g), (h) show, planisphere ratio CMA, MMA, WT-MMA and SVM-WT-MMA of CSA-SVM-WT-MMA of the present invention is more clear, is compact, there is very strong anti-ISI (ISI) ability, there is certain practicability.

Claims (2)

1. a kind of wavelet multi-mode blind balance method for introducing immune optimization support vector machines, it is characterised in that include the following steps:

A. impulse response channel c (k)) is passed through into transmitting signal a (k) and obtains channel output vector x (k), wherein k is time series, similarly hereinafter；

B. the input signal of orthogonal wavelet transformation device (WT): y (k)=v (k)+x (k)) is obtained using channel output vector x (k) described in interchannel noise v (k) and step a；

C.) the input signal y (k) of balanced device described in step b is equalized device input R (k) after orthogonal wavelet transformation, balanced device input R (k) is updated into balanced device weight vector by multi-mode blind equalization method；

When transmitter emits signal, equalizer input signal y (k)=y is taken_Re(k)+jy_Im(k) preceding N group vector carries out balanced, k=1,2 ... N, y to this N group data using support vector machines_Re(k) real part for being y (k), y_Im(k) imaginary part for being y (k),

For imaginary unit；According to the statistical property of structural risk minimization and transmitting signal, with the initial weight vector f of precision ε estimation balancing device_svm(n)；Establish following Support vector regression problem

$\min E_{\mathrm{svm}}\left(f_{\mathrm{svm}}\left(n\right)\right)=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2---\left(1\right)$

In formula, E_svm() indicates the precision ε estimation of Support vector regression；Its constraint function is

$\left\{\begin{array}{c}R\left(k\right)-{\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2\&le;\mathrm{\&epsiv;}\\ {\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2-R\left(k\right)\&le;\mathrm{\&epsiv;}\end{array}\right.---\left(2\right)$

In formula (2), R (k)=R_Re(k)+jR_Im(k), parameter ε determines the width in the insensitive region ε and the number of supporting vector；

In order to " soften " above-mentioned hardness ε-band support vector machines, introduce slack variable ξ (k),

With penalty C, the optimization problem of formula (1) and (2), which can be converted into, solves following constrained optimization problem:

$\min E_{\mathrm{svm}}\left(f_{\mathrm{svm}}\left(n\right)\right)=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2+C\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(\mathrm{\&xi;}\left(k\right)+\widetilde{\mathrm{\&xi;}}\left(k\right))---\left(3\right)$

Constraint condition is

$\left\{\begin{array}{c}R\left(k\right)-{\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(k\right)\\ {\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{T}y\left(k\right)\right)}^2-R\left(k\right)\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(k\right)\\ \mathrm{\&xi;}\left(k\right),\widetilde{\mathrm{\&xi;}}\left(k\right)\&GreaterEqual;0\end{array}\right.---\left(4\right)$

In formula (3) and (4), ξ (k) and

It is to measure that sample peels off apart from size, and punishes variable C and then embody the attention degree to the outlier；

But since constraint condition is for balanced device weight vector f_svm(n) contain quadratic term, optimization problem above can not be solved by linear programming method used by SVM；Then, Novel Algorithm is weighed to solve the problems, such as this according to a kind of iteration, the quadratic constraints in formula (4) can be rewritten as linear restriction；I.e.

$\left\{\begin{array}{c}{\left(f_{\mathrm{svm}}\left(n\right)\right)}^{T}y\left(k\right)z_{\mathrm{svm}}\left(k\right)-R\left(k\right)\&le;\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(k\right)\\ R\left(k\right)-{\left(f_{\mathrm{svm}}\left(n\right)\right)}^{T}y\left(k\right)z_{\mathrm{svm}}\left(k\right)\&le;\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(k\right)\end{array}\right.---\left(5\right)$

In formula, z_svm(k)=z_Re,svm(k)+jz_Im,svm(k) it is the dual problem of export primal problem, introduces Lagrange function

$\begin{array}{c}L(f_{\mathrm{svm}},\mathrm{\&xi;},\widetilde{\mathrm{\&xi;}},\mathrm{\&alpha;},\widetilde{\mathrm{\&alpha;}},b,\tilde{b})=\frac{1}{2}{\left|\right|f_{\mathrm{svm}}\left(n\right)\left|\right|}^2+C\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{\&xi;}\left(k\right)+\widetilde{\mathrm{\&xi;}}\left(k\right)]\\ -\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(b_k\mathrm{\&xi;}\left(k\right)+{\tilde{b}}_k\widetilde{\mathrm{\&xi;}}\left(k\right))\\ -\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{\&alpha;}\left(k\right)[R\left(k\right)-\left({{[f}_{\mathrm{svm}}\left(n\right)]}^{2}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)+\mathrm{\&epsiv;}+\mathrm{\&xi;}\left(k\right)]\\ -\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\widetilde{\mathrm{\&alpha;}}\left(k\right)[\left({\left[f_{\mathrm{svm}}\left(n\right)\right]}^{2}y\left(k\right)\right)z_{\mathrm{svm}}\left(k\right)-R\left(k\right)+\mathrm{\&epsiv;}+\widetilde{\mathrm{\&xi;}}\left(k\right)]\end{array}---\left(6\right)$

WhereinIt is Lagrange multiplier vector；The original optimization problem in formula (1)~(5) is converted into convex quadratic programming problem, i.e.,

$\begin{array}{c}\max E_{\mathrm{svm}}^{\text{'}}\left(f_{\mathrm{svm}}\left(n\right)\right)=-\frac{1}{2}\underset{k,m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))(\widetilde{\mathrm{\&alpha;}}\left(k\right)-\mathrm{\&alpha;}\left(k\right))\left(z_{\mathrm{svm}}\left(m\right)z_{\mathrm{svm}}\left(k\right)\right)K<y_m,y_k>\\ -\mathrm{\&epsiv;}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)+\mathrm{\&alpha;}\left(m\right))+\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))\end{array}---\left(7\right)$

In formula, E '_svm() indicates the precision ε estimation of Support vector regression after convex quadratic programming；Its constraint condition is

$\left\{\begin{array}{c}\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(m\right)-\mathrm{\&alpha;}\left(m\right))=0\\ 0\&le;\widetilde{\mathrm{\&alpha;}}\left(m\right)\&le;C,m=1,...,N\end{array}\right.---\left(8\right)$

In formula, K < y_m,y_kThe inner product of > expression support vector machines；

By being compared to primal problem with dual problem, then the weight vector of balanced device can be expressed as

$f_{\mathrm{svm}}\left(n\right)=\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(\widetilde{\mathrm{\&alpha;}}\left(k\right)-\mathrm{\&alpha;}\left(k\right))z_{\mathrm{svm}}\left(k\right)y\left(k\right)---\left(9\right)$

In formula, Lagrange multiplier

It can be solved by formula (7) and (8) with α (k)；

By the above process, balanced device initial weight vector f can be calculated_svm(n), then loop iteration is carried out until meeting switching condition；f_svm(n) update is realized using following formula

f_svm(n)=λf_svm(n-1)+(1-λ)f_svm(n)    (10)

In formula, n is the number of iterations, and λ is iteration step length；

When meeting the switching condition of following formula

$\left\{\begin{array}{c}\mathrm{MSE}\left(n\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}({\left|z_{\mathrm{svm}}\left(k\right)\right|}^2-R\left(k\right))\\ |\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1)|\&le;\mathrm{\&eta;}\end{array}\right.---\left(11\right)$

The initialization weight vector f of global optimum can be obtained_svm(n), and using this weight vector as initialization weight vector, in formula (11), MSE (n) indicates the mean square error of n times iteration, and η is switching threshold.

2. the wavelet multi-mode blind balance method according to claim 1 for introducing immune optimization support vector machines, it is characterised in that support vector machines parameter selection method is as follows:

(1) initialization of population

It is randomly generated the antibody population of certain amount, each antibody therein respectively corresponds kernel function, one group of value in punishment parameter C and ε；

(2) affine angle value is calculated

Affine angle value between calculating antibody and antigen；

(3) Immune Clone Selection

Immune Clone Selection operation is the inverse operation of clone's increment operation；The operation is to select outstanding individual in the filial generation respectively cloned after rising in value from antibody, is an asexual selection course to form new antibody population；One antibody forms a sub- antibody population after clone's increment, realizes that the affinity of part increases using operating after the operation of affinity maturation by Immune Clone Selection；Antibody first in the antibody population described in second step is arranged by the sequence of affinity from small to large, is evaluated according to the size of affinity, and affinity refers to that an antibody generates the degree of identification to the antigen of an identical chain length；Optimum antibody is selected to carry out clonal expansion operation, it is directly proportional to affinity to clone number by the antibody population A after being expanded；

(4) king-crossover strategy

The principle of king-crossover is as follows: in the realization of immune algorithm, the probability P of a king-crossover given first_kc, wherein kc indicates king-crossover, i.e. king-crossover, the random number R between one [0,1] is generated for each individual a (t) for t in clonal antibody group described in third step, if R is less than king-crossover probability P_kcThen a (t) is selected intersects with the former generation elite individual b (t) that works as saved, its method is: a (t) and b (t) are put into a small mating pond, according to selected Crossover Strategy, crossover operation is carried out to a (t) and b (t), obtain a pair of of offspring individual a'(t) and b'(t), the Crossover Strategy includes single-point, two o'clock, multiple spot and consistent intersection；Then, it is then lost and is not had to a (t), b'(t in a'(t) substitution population)；

(5) high frequency closedown

High frequency closedown is carried out to clonal antibody each in antibody population A, generates variation group A^*；Primary operational operator of the high frequency closedown as Immune Clone Selection can prevent diversity that is precocious and increasing antibody of evolving；

(6) affine angle value is calculated

Each antibody after high frequency closedown described in (5) is recalculated into its corresponding affine angle value；

(7) it selects

From variation group A^*The low antibody of n affinity, n are inversely proportional to the average affine angle value of antibody population in the high antibody replacement initial antibodies group of n affinity of middle selection；

(8) whether judgement terminates

Judged according to the evolutionary generation of antibody, when evolutionary generation is less than maximum evolutionary generation, then go to (2), repeat the operating procedure of (2)~(5), until evolutionary generation is greater than maximum evolutionary generation, such as reach termination condition, then EP (end of program), exports global parameter optimal solution.

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