CN102299875A - 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 small echo multimode blind balance method of immune optimization SVMs

Technical field

The present invention relates to introduce in a kind of underwater sound communication of limited bandwidth the small echo multimode blind balance method of immune optimization SVMs.

Background technology

In the underwater sound communication of limited bandwidth, because intersymbol interference (the Inter-symbol Interference that channel fading and multipath transmission etc. are produced, ISI) have a strong impact on communication quality, reliability of data transmission and transmission rate have under water been reduced, therefore need to adopt effective channel equalization technique to eliminate and (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).Use constant mould blind balance method to replace traditional adaptive equilibrium method, need not send training sequence, can save massive band width, improve transmission of Information speed effectively.But for having the not high-order orthogonal amplitude-modulated signal (QAM) of isotype value, its convergence rate is slow, steady-state error (is seen 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 greatly; Document [3] Wu Di, Ge Lindong, Wang Bin. be applicable to the mixed type blind equalization algorithm [J] of high-order QAM signal. information engineering college journal .2010,1 (11): pp.45-48; Document [4] Xu Xiaodong, Dai Xuchu, Xu Peixia. be fit to the weighting multimode blind equalization algorithm [J] of high-order QAM signal. electronics and information journal, 2007.29 (6): pp.1352-1355.).In order to overcome this shortcoming, Yang has proposed multimode blind balance method (Multi-Modulus Algorithm, MMA), it mainly is applicable in the high-order QAM system, and the phase place of correcting planisphere when eliminating intersymbol interference is rotated, but its convergence rate is still slower, steady-state error also (is seen document [5] Yang J greatly, Werner JJ, 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, high pretty. be applicable to the multimode blind equalization new algorithm [J] of high-order QAM system. electronics and information journal .2008,2 (30): pp.388-391; 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.1-4; ).Document [9] [10] [11] (see document: [9] Han Yingge, Guo Yecai, Wu Zaolin, Zhou Qiaoxi. based on the design of multimode blind equalizer and algorithm simulating research [J] Chinese journal of scientific instrument, 2008,29 (7): pp.1441-1445 of orthogonal wavelet transformation; Document [10] Zhu jie, Guo Ye-cai, Yang Chao.Decision teedback blind equalization algorithm based on momentum and orthogonal wavelet packet transform.WiCOM ' 09Proceedings of the 5th International Conference on Wireless communications, networking and mobile computing, IEEE, 2009:pp.2161-2164; Document [11] Han Yingge, Guo Yecai. introduce orthogonal wavelet transformation blind equalization algorithm [J] the system emulation journal .2008 of momentum term, 20 (6): pp.1559～1562) studies show that, input signal to equalizer carries out wavelet transformation, and signal is carried out energy normalized handle, autocorrelation between each component is effectively reduced, accelerated convergence rate, but these blind equalization algorithms all are to adopt gradient descent algorithm to seek the equalizer optimal weight vector, it is relatively more responsive to the initialization of weight vector, initialization improperly easily makes algorithmic statement to local minimum, even disperses.Document [12] [13] [14] [15] (is seen 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] .2008 International 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, Wang Chen. based on the DFF [J] of non-single-point fuzzy support vector machine. electronics and information journal .2008,30 (1): pp.117～120) proposed a kind of algorithm of SVMs (SVM) being introduced the blind equalization problem, this algorithm is owing to utilize SVMs and the optimized characteristics of structure risk, makes convergence rate improve greatly and has globally optimal solution.But in the construction process of SVMs, the parameter of SVM is provided with has bigger influence to final classification accuracy.Reasonable parameter selects to make SVMs to have higher precision, better generalization ability (is seen: document [16] Yao Quanzhu, field unit. based on the supporting vector machine model selection algorithm [J] of artificial immunity. computer engineering .2008,15 (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

The present invention seeks to slowly and have the local convergence problem, invented a kind of small echo multimode blind balance method (CSA-SVM-WT-MMA) of introducing the immune optimization SVMs at orthogonal wavelet transformation multimode blind balance method (WT-MMA) convergence rate.This inventive method is carried out orthogonal wavelet transformation by the input signal to the multimode blind equalizer, to reduce the autocorrelation of signal, and utilize SVMs multimode blind equalization problem to be converted into the support vector regression problem of global optimum, by extracting a bit of primary data, weight vector to blind equalizer is carried out initialization, also utilizes immune algorithm that the parameter in the SVMs has been carried out optimized choice simultaneously.Theory analysis and underwater acoustic channel simulation result show that this inventive method obviously is better than multimode blind balance method, orthogonal wavelet multimode blind balance method and SVMs orthogonal wavelet multimode blind balance method.Therefore, has certain practical value.

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

The present invention introduces the small echo multimode blind balance method of immune optimization SVMs, it is characterized in that comprising the steps:

A.) a (k) that will transmit obtains channel output vector x (k) through impulse response channel c (k), and wherein k is a time series, down with;

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

C.) the input signal y (k) with the described equalizer of step b imports R (k) through the equalizer that arrives behind the orthogonal wavelet transformation, equalizer is imported R (k) upgrade the equalizer weight vector through the multimode blind balance method;

It is characterized in that:

When reflector transmits, get equalizer received signal y (k)=y _Re(k)+jy _Im(k) (k=1,2 ... N, y _Re(k) be the real part of y (k), y _Im(k) be the imaginary part of y (k), the similar expression formula in back, expressed implication is identical) preceding N group vector, utilize SVMs to come these N group data are carried out equilibrium.According to structural risk minimization and the statistical property that transmits, with the initial weight vector f of precision ε estimation balancing device _Svm(n).Set up following SVMs 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 the formula, E _Svm() expresses support for the precision ε estimation that vector machine returns.Constraint function is

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

In the formula (2), R (k)=R _Re(k)+jR _Im(k), parameter ε has determined the width in the insensitive zone of ε and the number of support vector.

For " softening " above-mentioned rigid ε-band SVMs, introducing slack variable ξ (k),

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

Constraints is

In formula (3) and (4), ξ (k) and

Be to weigh the distance size that sample peels off, punishment variable C has then embodied the attention degree to this outlier.

But because constraints is for equalizer weight vector f _Svm(n) contain quadratic term, top optimization problem can't be found the solution by the linear programming method that SVM adopted.So (Iterative Reweighted Quadratic Programming IRWQP) solves this problem, the quadratic constraints in the formula (4) can be rewritten as linear restriction according to a kind of iteration power quadratic programming algorithm.Promptly

In the formula, z _Svm(k)=z _Re.svm(k)+jz _{Im, svm}(k) for deriving the dual problem of primal problem, introduce the Lagrange function

Wherein

It is Lagrange multiplier vector.The original optimization problem of formula (1)～(5) is converted to convex quadratic programming problem (dual problem), promptly

In the formula, E ' _SvmThe precision ε that SVMs returns behind () expression convex quadratic programming estimates.Its constraints is

In the formula, K＜y _m, y _kExpress support for the inner product of vector machine;

By primal problem and dual problem are compared, then the weight vector of equalizer can be expressed as

In the formula, the Lagrange multiplier

And α (k) can through type (7) and (8) find the solution.

By said process, just can calculate equalizer initial weight vector f _Svm(n), carry out loop iteration again until satisfying switching condition.f _Svm(n) renewal adopts following formula to realize

f _svm(n)＝λf _svm(n-1)+(1-λ)f _svm(n) (10)

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

When satisfying the switching condition of following formula

$\left\{\begin{array}{c}\mathrm{MSE}\left(n\right)=\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\Σ}}}({\left|z_{\mathrm{svm}}\left(k\right)\right|}^2-R\left(k\right))\\ |\mathrm{MSE}\left(n\right)-\mathrm{MSE}(n-1)|\≤\mathrm{\η}\end{array}\right.---\left(11\right)$

Can obtain the initialization weight vector f of global optimum _Svm(n), and with this weight vector as the initialization weight vector, in the formula (11), the mean square error of n iteration of MSE (n) expression, η is a switching threshold.

The SVMs parameter selection method is as follows:

(1) initialization of population

Produce the antibody population of some at random, one group of value among wherein the corresponding kernel function of each antibody difference, punishment parameters C and the e;

(2) calculate the affinity value

Affinity value between calculating antibody and the antigen;

(3) Immune Clone Selection

The Immune Clone Selection operation is the inverse operation of clone's increment operation.This operation is to select outstanding individuality the filial generation after antibody is cloned increment separately, thereby forms new antibody population, is an asexual selection course.An antibody forms an inferior antibody population through clone's increment back, realizes that by the Immune Clone Selection operation local affinity raises through the ripe operation of affinity back again.At first the antibody in the described antibody population of second step is arranged by affinity order from small to large, according to the affinity size evaluation of (antibody is called affinity to the degree that the antigen of an identical chain length produces identification), select optimum antibody to carry out the clonal expansion operation, antibody population A after obtaining increasing, clone's number is directly proportional with affinity.

(4) elite's Crossover Strategy

The principle that the elite is intersected is as follows: in the realization of immune algorithm, and the probability P that an at first given elite is intersected _Kc(kc represents king-crossover, i.e. elite intersect), produce random number R between one [0,1] for t among the described clonal antibody group of the 3rd step for each individual a (t), if R is less than elite's crossover probability P _KcThen a (t) is selected intersects with the individual b of former generation elite (t) that works as that preserves, its method is: a (t) and b (t) are put into a little mating pond, according to selected Crossover Strategy (single-point, 2 points, multiple spot with consistent intersect etc.), a (t) and b (t) are carried out interlace operation, obtain a pair of offspring individual a ' (t) and b ' (t).Then, (t) substitute a (t) in the population with a ', b ' (t) then loses need not.

(5) high frequency variation

Each clonal antibody carries out the high frequency variation among the antagonist group A, produces variation group A ^*High frequency variation is as the main operation operator of Immune Clone Selection, and precocity and increase the diversity of antibody can prevent to evolve;

(6) calculate the affinity value

Each antibody after (5) described high frequency variation is recomputated its corresponding affinity value.

(7) select

From variation group A ^*The antibody that n affinity of middle selection is high is replaced n antibody that affinity is low among the initial antibodies group, and n is inversely proportional to the average affinity value of antibody population;

(8) whether judgement stops

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

The present invention utilizes the ability of searching optimum of immune clone selection algorithm, parameter in the SVMs blind equalization algorithm is selected to determine by manually choosing to become automatically, then SVMs is incorporated in the orthogonal wavelet multimode blind balance method, invented a kind of small echo multimode blind balance method (CSA-SVM-WT-MMA) of introducing the immune optimization SVMs, this inventive method is trained the initial weight of estimating blind equalizer by utilizing SVMs to a bit of initial data that extracts, utilize immune algorithm that the parameter among the SVM has been carried out optimized choice simultaneously, and the initial weight that SVM is estimated is as the weight vector of orthogonal wavelet multimode blind equalization algorithm (WT-MMA).The simulation result of underwater acoustic channel shows, compare with multimode blind balance method, orthogonal wavelet multimode blind balance method and SVMs orthogonal wavelet multimode blind balance method, this inventive method has convergence rate and steady-state error faster, thereby has better improved the performance of underwater sound communication.

Description of drawings

Fig. 1: the present invention: the small echo multimode blind balance method schematic diagram of introducing the immune optimization SVMs;

Fig. 2: implement experiment simulation figure as a result, (a) the mean square error curve of 5 kinds of methods, (b) interference curve between the residue code of 5 kinds of methods, (c) ISI of 5 kinds of methods and SNR comparison curves, (d) CMA output planisphere, (e) MMA output planisphere, (f) WT-MMA output planisphere, (g) SVM-WT-MMA output planisphere, (h) CSA-SVM-WT-MMA output planisphere of the present invention.

Embodiment

Introduce the small echo multimode blind balance method principle of immune optimization SVMs, as shown in Figure 1.Among Fig. 1, a (k) is expressed as a (k)=a for the letter in reply source transmits _Re(k)+ja _Im(k), a _Re(k) and a _Im(k) be respectively the real part and the imaginary part of source signal; C (k) is the channel impulse response vector, and length is M; Vector v (k) is an additive white Gaussian noise; Vector y (k) is the input complex signal of equalizer, and length is N, and it is divided into real part and imaginary part, i.e. y (k)=y _Re(k)+jy _Im(k), y _Re(k) be the real part of y (k), y _Im(k) be the imaginary part (the similar expression formula in back, expressed implication is identical) of y (k); Vector f (k) is that equalizer weight vector and length are L, i.e. f (k)=[f ₀(k), L, f _L(k)] ^T([*] ^TThe computing of expression transposition); Y (*) is memoryless nonlinear function, represents memoryless nonlinear estimator; Z (k) is the output complex signal sequence of equalizer.Among Fig. 1, the part that does not contain frame of broken lines is an orthogonal wavelet multimode blind equalization algorithm (WT-MMA); The part that comprises frame of broken lines is for introducing the orthogonal wavelet multimode blind equalization algorithm (CSA-SVM-WT-MMA) of immune optimization SVMs.Existing division is as follows:

Orthogonal wavelet multimode blind equalization algorithm (WT-MMA) utilizes orthogonal wavelet transformation that the reception complex signal of equalizer is carried out conversion, and carries out energy normalized and handle, and has reduced the autocorrelation of input complex signal.

Make a (k)=[a (k), L, a (k-N _c+ 1)] ^T, y (k)=[y (k+N), L, y (k), L, y (k-N)] ^T, as shown in Figure 1

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

According to wavelet transformation theory, equalizer f (k) is the FIR filter, can be expressed as:

In the formula, k=0,1, hair on the neck, N, j _{P, q}(k) the expression scale parameter is that p, translation parameters are the wavelet basis function of q; y _{P, q}(k) the expression scale parameter is that P, translation parameters are the scaling function of q,

k _p=N/2 ^p-1 (p=1,2, hair on the neck, J), P is the wavelet decomposition out to out, k _pBe the maximal translation under the yardstick p, because the characteristic of f (n) is by E _{P, q}=＜f (k), j _{P, q}(k)＞and F _{P, q}=＜f (k), y _{P, q}(k)＞reflect, so be called the equalizer weight coefficient.

Input signal through the orthogonal wavelet transformation post-equalizer divides real part and imaginary part to be expressed as respectively

R(k)＝R _Re(k)+jR _Im(k)＝Qy _Re(k)+j(Qy _Im(k))

(3)

Wherein, R _Re(k) and R _Im(k) be respectively R (k) real part and imaginary part, its representation is as follows,

$R_r\left(k\right)={[d_{\mathrm{Re}\mathrm{1,0}}\left(k\right),{\mathrm{<figure-callout\; id="1"\; label="d\; Re"\; filenames="HDA0000068377820000011.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{Re}}\left(k\right),L,d_{\mathrm{ReP},k_P}\left(k\right),s_{\mathrm{ReP},0}\left(k\right),L{s}_{\mathrm{ReP},k_p}\left(k\right)]}^T---\left(4\right)$

$\left\{\begin{array}{c}{d}_{\mathrm{Rep},q}\left(k\right)=\underset{n=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{y}_{\mathrm{Re}}(k-n)j_{p,q}\left(n\right)\\ s_{\mathrm{ReP},q}\left(k\right)=\underset{n=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{y}_{\mathrm{Re}}(k-n)y_{P,q}\left(n\right)\end{array}\right.---\left(5\right)$

$R_{\mathrm{Im}}\left(k\right)={[d_{\mathrm{<figure-callout\; id="1"\; label="Im"\; filenames="HDA0000068377820000011.png"\; state="\{\{state\}\}">Im</figure-callout>}\mathrm{1,0}}\left(k\right),{\mathrm{<figure-callout\; id="1"\; label="d\; Im"\; filenames="HDA0000068377820000011.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathrm{Im}}\left(k\right),L,d_{\mathrm{ImP}.k_p}\left(k\right),s_{\mathrm{ImP},0}\left(k\right),L{s}_{\mathrm{ImP},k_p}\left(k\right)]}^T---\left(6\right)$

$\left\{\begin{array}{c}{d}_{\mathrm{Imp},q}\left(k\right)=\underset{n=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{y}_{\mathrm{Im}}(k-n)j_{p,q}\left(n\right)\\ s_{\mathrm{ImP},q}\left(k\right)=\underset{n=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{y}_{\mathrm{Im}}(k-n)y_{P,q}\left(n\right)\end{array}\right.---\left(7\right)$

In the formula, k=0,1, L, L-1, L=2 ^PLength for equalizer; Re and Im represent to get real part and imaginary part respectively;

And y _{P, q}(n) represent wavelet function and scaling function, d respectively _{P, q}(k), s _{P, q}(k) be respectively corresponding small echo and change of scale coefficient, Q is the orthogonal wavelet transformation matrix.

Equalizer is output as

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

In the formula, With

(H represents conjugate transpose) is respectively the real part vector sum imaginary part vector of equalizer weight vector, z _Re(k) and z _Im(k) be respectively the real part and the imaginary part of equalizer output signal.

Cost function form by MMA is

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

Wherein $R_{\mathrm{Re},\mathrm{MMA}}^2=E\left\{\left(a_{\mathrm{Re}}^4\left(k\right)\right)\right\}/E\left\{\left(a_{\mathrm{Re}}^2\left(k\right)\right)\right\},$ $R_{\mathrm{Im},\mathrm{MMA}}^2=E\left\{\left(a_{\mathrm{Im}}^4\left(k\right)\right)\right\}/E\left\{\left(a_{\mathrm{Im}}^2\left(k\right)\right)\right\},$ The former represents the mould value of homophase direction, and the latter represents the mould value of orthogonal direction.

The error of equalizer is

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

The iterative formula of its corresponding equalizer 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 the formula, R ^*(k) be the conjugation of R (k);

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

In the formula,

Represent d respectively _{P, k}(k), s _{P, k}(k) average power is estimated,

For right

Estimated value is obtained by the following formula derivation:

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

Wherein, diag[] the expression diagonal matrix, β is a smoothing factor, and 0＜β＜1.d _{P, q}(k) q signal of expression wavelet space p layer decomposition, s _{P, q}Q signal when (k) maximum is decomposed number of plies P in the expression metric space.Formula (2)～formula (13) constitutes based on orthogonal wavelet multimode blind equalization side algorithm (WT-MMA).

Orthogonal wavelet multimode blind equalization algorithm is to utilize the cost function that constructs that the equalizer weight vector is asked gradient, thereby determine the iterative equation of equaliser weights, this method lacks ability of searching optimum, and unsuitable initialization makes algorithmic statement go to the lavatory to local pole easily.In order to overcome this shortcoming, this paper utilizes SVMs to search the optimization initial weight vector of WT-MMA algorithm, is used for remedying the defective of WT-MMA algorithm, solves the problem of sinking into local convergence in the search procedure better.

When reflector transmits, get equalizer received signal y (k)=y _Re(k)+jy _Im(k) (k=1,2 ... N, y _Re(k) be the real part of y (k), y _Im(k) be the imaginary part of y (k).) preceding N group vector, utilize SVMs to come these N group data are carried out equilibrium.According to structural risk minimization and the statistical property that transmits, with the initial weight vector f of precision ε estimation balancing device _Svm(n).Set up following SVMs 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 the formula, E _Svm() expresses support for the precision ε estimation that vector machine returns.Constraint function is

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

In the formula (15), R (k)=R _Re(k)+jR _Im(k), parameter ε has determined the width in the insensitive zone of ε and the number of support vector.

For " softening " above-mentioned rigid ε-band SVMs, introducing slack variable ξ (k),

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

Constraints is

In formula (16) and (17), ξ (k) and

Be to weigh the distance size that sample peels off, punishment variable C has then embodied the attention degree to this outlier.

But because constraints is for equalizer weight vector f _Svm(n) contain quadratic term, top optimization problem can't be found the solution by the linear programming method that SVM adopted.So (Iterative Reweighted Quadratic Programming IRWQP) solves this problem to a kind of iteration power quadratic programming algorithm that proposes according to document [13], the quadratic constraints in the formula (17) can be rewritten as linear restriction.Promptly

In the formula, z _Svm(k)=z _{Re, svm}(k)+jz _{Im, svm}(k) for deriving the dual problem of primal problem, introduce the Lagrange function

Wherein

It is Lagrange multiplier vector.The original optimization problem of formula (14)～(18) is converted to convex quadratic programming problem (dual problem), promptly

In the formula, E ' _SvmThe precision ε that SVMs returns behind () expression convex quadratic programming estimates.Its constraints is

In the formula, K＜y _m, y _kExpress support for the inner product of vector machine.

By primal problem and dual problem are compared, then the weight vector of equalizer can be expressed as

In the formula, the Lagrange multiplier

And α (k) can through type (20) and (21) find the solution.

By said process, just can calculate equalizer initial weight vector f _Svm(n), carry out loop iteration again until satisfying switching condition.f _Svm(n) renewal adopts following formula to realize

f _svm(n)＝λf _svm(n-1)+(1-λ)f _svm(n)

(23)

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

When satisfying the switching condition of following formula

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

Can obtain the initialization weight vector f of global optimum _Svm(n), and with the initialization weight vector of this weight vector as the WT-MMA algorithm.In the formula (24), the mean square error of n iteration of MSE (n) expression, η is a switching threshold.

In SVMs multimode blind equalization algorithm, need to determine the value of some parameters, as kernel function, punishment parameters C, e-insensitive loss function etc., different parameters the performance that can have a strong impact on the SVM machine learning is set, so mostly all be the experiment by repeatedly, and people's subjective experience selects the parameter that needs, and need pay more time cost.Wherein the e width of penalty C and e-insensitive loss function is the free parameter of control approximating function VC dimension (quantitative target of approximating function set sizes), because it must be adjusted when selecting simultaneously, has certain complexity.

Therefore, the present invention utilizes the characteristic of immune clone selection algorithm global optimizing, and the parameter in the SVMs has been carried out optimized choice.The training sample that mainly is SVM is set to antigen, parameters C and e are as antibody, at first determine the span of parameters C and e, principle by simulation Immune System antagonist Immune Clone Selection, variation, utilize antibody cloning to enlarge hunting zone, the multifarious characteristics of variation maintenance, search out the parametric optimal solution of target function, and as the punishment parameters C in the SVMs, e-insensitive loss function.When the immune clone selection algorithm was applied to the SVMs optimization of parameter choice, the basic step of algorithm was as follows:

(1) initialization of population

Produce the antibody population of some at random, one group of value among wherein the corresponding kernel function of each antibody difference, punishment parameters C and the e;

(2) calculate the affinity value

Affinity value between calculating antibody and the antigen;

(3) Immune Clone Selection

The Immune Clone Selection operation is the inverse operation of clone's increment operation.This operation is to select outstanding individuality the filial generation after antibody is cloned increment separately, thereby forms new antibody population, is an asexual selection course.An antibody forms an inferior antibody population through clone's increment back, realizes that by the Immune Clone Selection operation local affinity raises through the ripe operation of affinity back again.At first the antibody in the described antibody population of second step is arranged by affinity order from small to large, according to the affinity size evaluation of (antibody is called affinity to the degree that the antigen of an identical chain length produces identification), select optimum antibody to carry out the clonal expansion operation, antibody population A after obtaining increasing, clone's number is directly proportional with affinity.

(4) elite's Crossover Strategy

The principle that the elite is intersected is as follows: in the realization of immune algorithm, and the probability P that an at first given elite is intersected _Kc(kc represents king-crossover, i.e. elite intersect), produce random number R between one [0,1] for t among the described clonal antibody group of the 3rd step for each individual a (t), if R is less than elite's crossover probability P _KcThen a (t) is selected intersects with the individual b of former generation elite (t) that works as that preserves, its method is: a (t) and b (t) are put into a little mating pond, according to selected Crossover Strategy (single-point, 2 points, multiple spot with consistent intersect etc.), a (t) and b (t) are carried out interlace operation, obtain a pair of offspring individual a ' (t) and b ' (t).Then, (t) substitute a (t) in the population with a ', b ' (t) then loses need not.

(5) high frequency variation

Each clonal antibody carries out the high frequency variation among the antagonist group A, produces variation group A ^*High frequency variation is as the main operation operator of Immune Clone Selection, and precocity and increase the diversity of antibody can prevent to evolve;

(6) calculate the affinity value

Each antibody after (5) described high frequency variation is recomputated its corresponding affinity value.

(7) select

From variation group A ^*The antibody that n affinity of middle selection is high is replaced n antibody that affinity is low among the initial antibodies group, and n is inversely proportional to the average affinity value of antibody population;

(8) whether judgement stops

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

By above process, just can be optimized selection, thereby improve the performance of SVMs initialization weight vector parameter among the SVM.

Embodiment

In order to verify the validity of the inventive method CSA-SVM-WT-MMA,, carry out emulation experiment with CMA, MMA, WT-MMA and SVM-WT-MMA method object as a comparison.In the l-G simulation test, the antibody scale is 100, and clone's controlling elements are 0.6, and elite's crossover probability is 0.2, and the variation probability is 0.1, and the algorithm maximum iteration time is 200.Parameters C and e optimize span and be made as: 1#C 20, and 0.00001#e 0.1, the training sample number N=2000 that the SVMs initialization is extracted;

Mixed-phase underwater acoustic channel c=[0.3132-0.10400.89080.3134]; Transmitting is 128QAM, and equalizer power is long to be 16, signal to noise ratio 30dB.In SVM-WT-MMA, C=15, e=0.1; In CSA-SVM-WT-MMA of the present invention, it is C=17.8477 that immune optimization is selected optimized parameter, e=0.0765.Other parameter is provided with, and is as shown in table 1.1000 Meng Te Kano simulation results, as shown in Figure 2.In order to compare each algorithm performance, the intersymbol interference of definition residue is as follows:

$\mathrm{ISI}=10\lg ((\underset{i}{\mathrm{\&Sigma;}}{\left|h_i\right|}^2-{\left|h_{\max }\right|}^2)/{\left|h_{\max }\right|}^2)---\left(25\right)$

In the formula, h is a composite channel

In i element, and h _MaxExpression wherein has the element of maximum value.

The setting of table 1 simulation parameter

Fig. 2 (a) shows that (b) on convergence rate, CSA-SVM-WT-MMA of the present invention and SVM-WT-MMA are basic identical, but than MMA fast nearly 6000 the step, than WT-MMA fast nearly 3000 the step.In the residue intersymbol interference, CSA-SVM-WT-MMA of the present invention reduces nearly 0.8dB than WT-MMA and SVM-WT-MMA.By Fig. 2 (c) as can be known, along with the increase of signal to noise ratio, the residue intersymbol interference of five kinds of methods is all constantly reducing, and the amplitude maximum that CSA-SVM-WT-MMA of the present invention reduces, same signal to noise ratio more more can embody the superiority of this algorithm.Fig. 2 (e), (f), (g), (h) show that the planisphere of CSA-SVM-WT-MMA of the present invention is more clear, compact than CMA, MMA, WT-MMA and SVM-WT-MMA, and very strong anti-intersymbol interference (ISI) ability is arranged, and have certain practicality.

Claims (2)

1. a small echo multimode blind balance method of introducing the immune optimization SVMs is characterized in that comprising the steps:

A.) a (k) that will transmit obtains channel output vector x (k) through impulse response channel c (k), and wherein k is a time series, down with;

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

C.) the input signal y (k) with the described equalizer of step b imports R (k) through the equalizer that arrives behind the orthogonal wavelet transformation, equalizer is imported R (k) upgrade the equalizer weight vector through the multimode blind balance method;

It is characterized in that:

When reflector transmits, get equalizer received signal y (k)=y _Re(k)+jy _Im(k) (k=1,2 ... N, y _Re(k) be the real part of y (k), y _Im(k) be the imaginary part of y (k),

Be imaginary unit, the similar expression formula in back, expressed implication is identical) preceding N group vector, utilize SVMs to come these N group data are carried out equilibrium.According to structural risk minimization and the statistical property that transmits, with the initial weight vector f of precision ε estimation balancing device _Svm(n).Set up following SVMs 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 the formula, E _Svm() expresses support for the precision ε estimation that vector machine returns.Its constraint function is

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

In the formula (2), R (k)=R _Re(k)+jR _Im(k), parameter ε has determined the width in the insensitive zone of ε and the number of support vector.

For " softening " above-mentioned rigid ε-band SVMs, introducing slack variable ξ (k), With penalty C, the optimization problem of formula (1) and (2) just can be converted into finds the solution following constrained optimization problem:

Constraints is

In formula (3) and (4), ξ (k) and

Be to weigh the distance size that sample peels off, punishment variable C has then embodied the attention degree to this outlier.

But because constraints is for equalizer weight vector f _Svm(n) contain quadratic term, top optimization problem can't be found the solution by the linear programming method that SVM adopted.So (Iterative Reweighted Quadratic Programming IRWQP) solves this problem, the quadratic constraints in the formula (4) can be rewritten as linear restriction according to a kind of iteration power quadratic programming algorithm.Promptly

In the formula, z _Svm(k)=x _{Re, svm}(k)+jz _{Im, svm}(k) for deriving the dual problem of primal problem, introduce the Lagrange function

Wherein

It is Lagrange multiplier vector.The original optimization problem of formula (1)～(5) is converted to convex quadratic programming problem (dual problem), promptly

In the formula, E ' _SvmThe precision ε that SVMs returns behind () expression convex quadratic programming estimates.Its constraints is

In the formula, K＜y _m, y _kExpress support for the inner product of vector machine;

By primal problem and dual problem are compared, then the weight vector of equalizer can be expressed as

In the formula, the Lagrange multiplier

And α (k) can through type (7) and (8) find the solution.

By said process, just can calculate equalizer initial weight vector f _Svm(n), carry out loop iteration again until satisfying switching condition.f _Svm(n) renewal adopts following formula to realize

f _svm(n)＝λf _svm(n-1)+(1-λ)f _svm(n) (10)

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

When satisfying the switching condition of following formula

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

Can obtain the initialization weight vector f of global optimum _Svm(n), and with this weight vector as the initialization weight vector, in the formula (11), the mean square error of n iteration of MSE (n) expression, η is a switching threshold.

2. the small echo multimode blind balance method of introducing immune optimization SVMs according to claim 1 is characterized in that the SVMs parameter selection method is as follows:

(1) initialization of population

Produce the antibody population of some at random, one group of value among wherein the corresponding kernel function of each antibody difference, punishment parameters C and the e;

(2) calculate the affinity value

Affinity value between calculating antibody and the antigen;

(3) Immune Clone Selection

The Immune Clone Selection operation is the inverse operation of clone's increment operation.This operation is to select outstanding individuality the filial generation after antibody is cloned increment separately, thereby forms new antibody population, is an asexual selection course.An antibody forms an inferior antibody population through clone's increment back, realizes that by the Immune Clone Selection operation local affinity raises through the ripe operation of affinity back again.At first the antibody in the described antibody population of second step is arranged by affinity order from small to large, according to the affinity size evaluation of (antibody is called affinity to the degree that the antigen of an identical chain length produces identification), select optimum antibody to carry out the clonal expansion operation, antibody population A after obtaining increasing, clone's number is directly proportional with affinity.

(4) elite's Crossover Strategy

The principle that the elite is intersected is as follows: in the realization of immune algorithm, and the probability P that an at first given elite is intersected _Kc(kc represents king-crossover, i.e. elite intersect), produce random number R between one [0,1] for t among the described clonal antibody group of the 3rd step for each individual a (t), if R is less than elite's crossover probability P _KcThen a (t) is selected intersects with the individual b of former generation elite (t) that works as that preserves, its method is: a (t) and b (t) are put into a little mating pond, according to selected Crossover Strategy (single-point, 2 points, multiple spot with consistent intersect etc.), a (t) and b (t) are carried out interlace operation, obtain a pair of offspring individual a ' (t) and b ' (t).Then, (t) substitute a (t) in the population with a ', b ' (t) then loses need not.

(5) high frequency variation

Each clonal antibody carries out the high frequency variation among the antagonist group A, produces variation group A ^*High frequency variation is as the main operation operator of Immune Clone Selection, and precocity and increase the diversity of antibody can prevent to evolve;

(6) calculate the affinity value

Each antibody after (5) described high frequency variation is recomputated its corresponding affinity value.

(7) select

From variation group A ^*The antibody that n affinity of middle selection is high is replaced n antibody that affinity is low among the initial antibodies group, and n is inversely proportional to the average affinity value of antibody population;

(8) whether judgement stops

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

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