CN102299875A

CN102299875A - Wavelet multimode blind equalization method introducing immune-optimized SVM (Support Vector Machine)

Info

Publication number: CN102299875A
Application number: CN2011101601492A
Authority: CN
Inventors: 郭业才; 丁锐; 季童莹
Original assignee: Nanjing University of Information Science and Technology
Current assignee: Nanjing University of Information Science and Technology
Priority date: 2011-06-15
Filing date: 2011-06-15
Publication date: 2011-12-28
Anticipated expiration: 2031-06-15
Also published as: CN102299875B

Abstract

The invention discloses a wavelet multi-mode blind equalization method that introduces an immune optimization support vector machine, utilizes the global search ability of the immune clone selection algorithm, and changes the parameter selection in the support vector machine blind equalization method from manual selection to automatic determination, and then Introduce the support vector machine into the orthogonal wavelet multi-mode blind equalization method, and invent a wavelet multi-mode blind equalization method that introduces the immune optimization support vector machine. The initial weights of the blind equalizer are estimated by training the original data, and the parameters in the SVM are optimized by using the immune algorithm, and the initial weights estimated by the SVM are used as the weight vector of the orthogonal wavelet multi-mode blind equalization method. Compared with the multi-mode blind equalization method, the orthogonal wavelet multi-mode blind equalization method and the support vector machine orthogonal wavelet multi-mode blind equalization method, the present invention has fast convergence speed and small steady-state error, and better improves the level Acoustic communication quality.

Description

A Wavelet Multi-mode Blind Equalization Method Introducing Immune Optimization Support Vector Machine

技术领域 technical field

本发明涉及一种带宽受限的水声通信中引入免疫优化支持向量机的小波多模盲均衡方法。The invention relates to a wavelet multimode blind equalization method which introduces an immune optimization support vector machine into underwater acoustic communication with limited bandwidth.

背景技术 Background technique

在带宽受限的水声通信中，由于信道衰落和多径传输等所产生的码间干扰(Inter-symbol Interference，ISI)严重影响通信质量，降低了水下数据传输的可靠性和传输速率，因此需要采用有效的信道均衡技术来消除(见文献[1] Shafayat Abrar，Asoke K.Nandi.Blind equalization of square-QAM signals：a multi-modulusapproach.IEEE Trans.Commun.2010.6(58)：pp.1601-1604)。使用常数模盲均衡方法代替传统的自适应均衡方法，不需发送训练序列，可节省大量带宽，有效地提高信息的传输速率。但对于具有不同模值的高阶正交振幅调制信号(QAM)，其收敛速度慢、稳态误差大(见文献[2] Jenq-Tay Yuan，and Tzu-Chao Lin.Equalization andCarrier Phase Recovery of CMA and MMA in Blind Adaptive Receivers.IEEE Trans.Signal Process.2010.6(58)：pp.3206-3217；文献[3] 吴迪，葛临东，王彬.适用于高阶QAM信号的混合型盲均衡算法[J].信息工程大学学报.2010，1(11)：pp.45-48；文献[4] 许小东，戴旭初，徐佩霞.适合高阶QAM信号的加权多模盲均衡算法[J].电子与信息学报，2007.29(6)：pp.1352-1355.)。为了克服这一缺点，Yang提出了多模盲均衡方法(Multi-Modulus Algorithm，MMA)，其主要适用于高阶QAM系统中，并在消除码间干扰的同时纠正星座图的相位旋转，但其收敛速度仍然较慢、稳态误差也较大(见文献[5] Yang J，Werner JJ，Dumont G A.Themultimodulus blind equalization and its generalized algorithm [J].IEEE Journal OnSel.Areas in Commun，2002，20(5)：997-1015；文献[6] Jenq-Tay Yuan，Kun-DaTsai.Analysis of the Multimodulus Blind Equalization Algorithm in QAMCommunication Systems.IEEE Trans.Commun.2005.9(53)：pp.1427-1431；文献[7]窦高奇，高俊.适用于高阶QAM系统的多模盲均衡新算法[J].电子与信息学报.2008，2(30)：pp.388-391；文献[8] Gholami M R，Esfahani S N.Improving theconvergence rate of blind equalization using transform domain[C]//ISSPA，Shush，United Arab Emirates：University of Sharjah.2007；pp.1-4；)。文献[9][10][11](见文献：[9]韩迎鸽，郭业才，吴造林，周巧喜.基于正交小波变换的多模盲均衡器设计与算法仿真研究[J]仪器仪表学报，2008，29(7)：pp.1441-1445；文献[10]Zhu jie，Guo Ye-cai，Yang Chao.Decision teedback blind equalization algorithmbased 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；文献[11] 韩迎鸽，郭业才.引入动量项的正交小波变换盲均衡算法[J]系统仿真学报.2008，20(6)：pp.1559～1562)研究表明，对均衡器的输入信号进行小波变换，并对信号进行能量归一化处理，可以使各分量之间的自相关性得到有效降低，加快了收敛速度，但这些盲均衡算法都是采用梯度下降算法来寻找均衡器最优权向量的，它对权向量的初始化比较敏感，不当的初始化易使算法收敛至局部极小值，甚至发散。文献[12][13][14][15](见文献：[12]Feng Liu，Hu-cheng An，Jia-ming Li，and Lin-dongGe.Build Equalization Using v-Support Vector Regressor for Constant ModulusSignals [J].2008 International Joint Conference on Neural Networks(IJCNN2008)，IEEE，2008：pp.161～164；文献[13] Marcelino Lazaro，JonathanGonzalez-Olasola.Blind equalization using the IRWLS formulation of the SupportVector Machine[J].Signal Processing.2009，7(89)：pp.1265-1270；文献[14] Cooklev.T.An Efficient Architecture for Orthogonal Wavelet Transforms[J].IEEE SignalProcessing Letters，2006，13(2)：pp.77～79；文献[15] 宋恒，王晨.基于非单点模糊支持向量机的判决反馈均衡器[J].电子与信息学报.2008，30(1)：pp.117～120)提出了一种将支持向量机(SVM)引入盲均衡问题的算法，该算法由于利用支持向量机和结构风险最优化的特点，使得收敛速度大大提高并且具有全局最优解。但在支持向量机的构造过程中，SVM的参数设置对最终分类精确度有较大的影响。合理的参数选择可以使支持向量机具有更高的精度、更好的泛化能力(见：文献[16] 姚全珠，田元.基于人工免疫的支持向量机模型选择算法[J].计算机工程.2008，15(34)：pp.223～225.Yao Quan-zhu，Tian Yuan.Model Selection Algorithmof SVM Based on Artificial Immune[J].Computer Engineering.2008，15(34)：pp.223～225)。In underwater acoustic communication with limited bandwidth, the inter-symbol interference (ISI) caused by channel fading and multipath transmission seriously affects the communication quality and reduces the reliability and transmission rate of underwater data transmission. Therefore, effective channel equalization techniques need to be used to eliminate (see [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). Using the constant modulus blind equalization method instead of the traditional adaptive equalization method does not need to send training sequences, which can save a lot of bandwidth and effectively increase the transmission rate of information. However, for high-order quadrature amplitude modulation signals (QAM) with different modulus values, the convergence speed is slow and the steady-state error is large (see [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; literature [3] Wu Di, Ge Lindong, Wang Bin. Hybrid blind equalization algorithm for high-order QAM signals[J] .Journal of Information Engineering University. 2010, 1(11):pp.45-48; Literature [4] Xu Xiaodong, Dai Xuchu, Xu Peixia. Weighted multi-mode blind equalization algorithm suitable for high-order QAM signals[J]. Electronics and Information Science, 2007.29(6):pp.1352-1355.). In order to overcome this shortcoming, Yang proposed a multi-modulus blind equalization method (Multi-Modulus Algorithm, MMA), which is mainly suitable for high-order QAM systems, and corrects the phase rotation of the constellation diagram while eliminating inter-symbol interference, but its The convergence speed is still slow, and the steady-state error is also large (see literature [5] Yang J, Werner JJ, Dumont G A. The multimodulus blind equalization and its generalized algorithm [J]. IEEE Journal OnSel. Areas in Commun, 2002, 20 (5): 997-1015; Literature [6] Jenq-Tay Yuan, Kun-DaTsai.Analysis of the Multimodulus Blind Equalization Algorithm in QAMCommunication Systems.IEEE Trans.Commun.2005.9(53):pp.1427-1431; Literature [ 7] Dou Gaoqi, Gao Jun. A new multi-mode blind equalization algorithm suitable for high-order QAM systems [J]. Journal of Electronics and Information Technology. 2008, 2(30): pp.388-391; literature [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;). Literature [9][10][11] (see literature: [9] Han Yingge, Guo Yecai, Wu Zuolin, Zhou Qiaoxi. Design and Algorithm Simulation Research of Multi-mode Blind Equalizer Based on Orthogonal Wavelet Transform[J] Instrument and Apparatus , 2008, 29(7): pp.1441-1445; Literature [10] Zhu jie, Guo Ye-cai, Yang Chao. Decision teedback blind equalization algorithm based on momentum and orthogonal wavelet packet transform. WiCOM′09 Proceedings of the 5th International Conference on Wireless communications, networking and mobile computing, IEEE, 2009: pp.2161-2164; literature [11] Han Yingge, Guo Yecai. Orthogonal wavelet transform blind equalization algorithm with momentum term [J] Journal of System Simulation. 2008, 20 (6): pp.1559～1562) Research shows that wavelet transform is performed on the input signal of the equalizer, and energy normalization is performed on the signal, which can effectively reduce the autocorrelation between components and speed up the convergence However, these blind equalization algorithms use gradient descent algorithm to find the optimal weight vector of the equalizer, which is sensitive to the initialization of the weight vector, and improper initialization can easily make the algorithm converge to a local minimum or even diverge. Literature [12][13][14][15] (see literature: [12]Feng Liu, Hu-cheng An, Jia-ming Li, and Lin-dongGe.Build Equalization Using v-Support Vector Regressor for Constant ModulusSignals [ J].2008 International Joint Conference on Neural Networks (IJCNN2008), IEEE, 2008: pp.161～164; literature [13] Marcelino Lazaro, JonathanGonzalez-Olasola.Blind equalization using the IRWLS formulation of the SupportVector Machine[J].Signal Processing.2009, 7(89):pp.1265-1270; literature [14] Cooklev.T.An Efficient Architecture for Orthogonal Wavelet Transforms[J].IEEE Signal Processing Letters, 2006,13(2):pp.77～79 ; Literature [15] Song Heng, Wang Chen. Decision feedback equalizer based on non-single-point fuzzy support vector machine [J]. The support vector machine (SVM) is introduced into the algorithm of the blind equalization problem. Due to the use of the support vector machine and the characteristics of structural risk optimization, the algorithm greatly improves the convergence speed and has a global optimal solution. However, during the construction of the support vector machine, the parameter settings of the SVM have a greater impact on the final classification accuracy. Reasonable parameter selection can make the support vector machine have higher precision and better generalization ability (see: literature [16] Yao Quanzhu, Tian Yuan. Model selection algorithm for support vector machine based on artificial immunity [J]. 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).

发明内容 Contents of the invention

本发明目的是针对正交小波变换多模盲均衡方法(WT-MMA)收敛速度慢且存在局部收敛问题，发明了一种引入免疫优化支持向量机的小波多模盲均衡方法(CSA-SVM-WT-MMA)。该发明方法通过对多模盲均衡器的输入信号进行正交小波变换，以降低信号的自相关性，并利用支持向量机将多模盲均衡问题转化为全局最优的支持向量回归问题，通过提取一小段初始数据，对盲均衡器的权向量进行初始化，同时还利用免疫算法对支持向量机中的参数进行了优化选择。理论分析与水声信道仿真结果表明，该发明方法明显优于多模盲均衡方法、正交小波多模盲均衡方法和支持向量机正交小波多模盲均衡方法。因此，具有一定的实用价值。The purpose of the invention is to solve the slow convergence speed and local convergence problem of the orthogonal wavelet transform multi-mode blind equalization method (WT-MMA), and invent a wavelet multi-mode blind equalization method (CSA-SVM- WT-MMA). The inventive method performs orthogonal wavelet transform on the input signal of the multi-mode blind equalizer to reduce the autocorrelation of the signal, and uses the support vector machine to transform the multi-mode blind equalization problem into a globally optimal support vector regression problem, through A small piece of initial data is extracted, and the weight vector of the blind equalizer is initialized. At the same time, the parameters in the support vector machine are optimized by using the immune algorithm. Theoretical analysis and underwater acoustic channel simulation results show that the inventive method is obviously superior to the multi-mode blind equalization method, the orthogonal wavelet multi-mode blind equalization method and the support vector machine orthogonal wavelet multi-mode blind equalization method. Therefore, it has certain practical value.

本发明为实现上述目的，采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:

本发明引入免疫优化支持向量机的小波多模盲均衡方法，其特征在于包括如下步骤：The present invention introduces the wavelet multimode blind equalization method of immune optimization support vector machine, is characterized in that comprising the following steps:

a.)将发射信号a(k)经过脉冲响应信道c(k)得到信道输出向量x(k)，其中k为时间序列，下同；a.) Pass the transmitted signal a(k) through the impulse response channel c(k) to obtain the channel output vector x(k), where k is a time series, the same below;

b.)采用信道噪声v(k)和步骤a所述的信道输出向量x(k)得到正交小波变换器(WT)的输入信号：y(k)＝v(k)+x(k)；b.) Obtain the input signal of the orthogonal wavelet transformer (WT) by using the channel noise v(k) and the channel output vector x(k) described in step a: y(k)=v(k)+x(k) ;

c.)将步骤b所述的均衡器的输入信号y(k)经过正交小波变换后的到均衡器输入R(k)，将均衡器输入R(k)经过多模盲均衡方法更新均衡器权向量；c.) The input signal y(k) of the equalizer described in step b undergoes orthogonal wavelet transformation to the equalizer input R(k), and the equalizer input R(k) is updated and equalized by the multi-mode blind equalization method weight vector;

其特征在于：It is characterized by:

当发射器发射信号时，取均衡器接收信号y(k)＝y_Re(k)+jy_Im(k)(k＝1，2…N，y_Re(k)为y(k)的实部，y_Im(k)为y(k)的虚部，后面类似的表达式，所表达的含义相同)的前N组向量，利用支持向量机来对这N组数据进行均衡。根据结构风险最小化原则以及发射信号的统计特性，以精度ε估计均衡器的初始权向量f_svm(n)。建立如下支持向量机回归问题When the transmitter transmits a signal, take the equalizer received signal y(k)=y _Re (k)+jy _Im (k) (k=1, 2...N, y _Re (k) is the real part of y(k) , y _Im (k) is the imaginary part of y(k), the following similar expressions express the same meaning) of the first N groups of vectors, and use the support vector machine to balance the N groups of data. According to the principle of structural risk minimization and the statistical characteristics of the transmitted signal, the initial weight vector f _svm (n) of the equalizer is estimated with precision ε. Set up the following support vector machine regression problem

$min min {E E.}_{svm svm} (({f f}_{svm svm} ((n no)))) = = \frac{11}{22} {| | | | {f f}_{svm svm} ((n no)) | | | |}^{22} - - - - - - ((11))$

式中，E_svm(·)表示支持向量机回归的精度ε估计。约束函数为In the formula, E _svm (·) represents the precision ε estimation of support vector machine regression. The constraint function is

$\{\begin{matrix} R R ((k k)) - - {[[(({f f}_{svm svm} ((n no))]]}^{T T} y the y ((k k)) {))}^{22} \leq \leq ϵ ϵ \\ {[[(({f f}_{svm svm} ((n no))]]}^{T T} y the y ((k k)) {))}^{22} - - R R ((k k)) \leq \leq ϵ ϵ \end{matrix} - - - - - - ((22))$

式(2)中，R(k)＝R_Re(k)+jR_Im(k)，参数ε决定了ε不敏感区域的宽度和支持向量的数目。In formula (2), R(k)=R _Re (k)+jR _Im (k), parameter ε determines the width of ε insensitive region and the number of support vectors.

为了“软化”上述硬性ε-带支持向量机，引入松弛变量ξ(k)、

和惩罚函数C，式(1)和(2)的最优化问题就可以转化为求解以下约束最优化问题：In order to "soften" the above rigid ε-band SVM, the slack variable ξ(k),

and penalty function C, the optimization problems of formulas (1) and (2) can be transformed into solving the following constrained optimization problems:

约束条件为The constraints are

式(3)和(4)中，ξ(k)和

是衡量样本离群的距离大小，而惩罚变量C则体现了对该离群点的重视程度。In formulas (3) and (4), ξ(k) and

is to measure the distance of the sample outlier, and the penalty variable C reflects the importance of the outlier.

但是由于约束条件对于均衡器权向量f_svm(n)含有二次项，上面的最优化问题无法通过SVM所采用的线性规划方法求解。于是，根据一种迭代权二次规划算法(Iterative Reweighted Quadratic Programming，IRWQP)来解决这一问题，可以将式(4)中的二次约束改写为线性约束。即However, since the constraint condition contains a quadratic term for the equalizer weight vector f _svm (n), the above optimization problem cannot be solved by the linear programming method adopted by SVM. Therefore, according to an iterative reweighted quadratic programming algorithm (Iterative Reweighted Quadratic Programming, IRWQP) to solve this problem, the quadratic constraint in formula (4) can be rewritten as a linear constraint. Right now

式中，z_svm(k)＝z_Re.svm(k)+jz_Im，svm(k)为导出原始问题的对偶问题，引入Lagrange函数In the formula, z _svm (k) = z _Re.svm (k) + jz _{Im, svm} (k) is the dual problem derived from the original problem, and the Lagrange function is introduced

其中

是Lagrange乘子向量。将式(1)～(5)的原始最优化问题转换为凸二次规划问题(对偶问题)，即in

is the Lagrange multiplier vector. Transform the original optimization problem of formulas (1) to (5) into a convex quadratic programming problem (dual problem), namely

式中，E′_svm(·)表示凸二次规划后支持向量机回归的精度ε估计。其约束条件为In the formula, E′ _svm (·) represents the precision ε estimation of support vector machine regression after convex quadratic programming. Its constraints are

式中，K<y_m，y_k>表示表示支持向量机的内积；In the formula, K<y _m , y _k > represents the inner product of the support vector machine;

通过对原始问题与对偶问题进行比较，则均衡器的权向量可以表示为By comparing the original problem with the dual problem, the weight vector of the equalizer can be expressed as

式中，Lagrange乘子

和α(k)可以通过式(7)和(8)来求解。where the Lagrange multiplier

and α(k) can be solved by equations (7) and (8).

通过上述过程，便可以计算出均衡器初始权向量f_svm(n)，再进行循环迭代直至满足切换条件。f_svm(n)的更新采用下式进行实现Through the above process, the initial weight vector f _svm (n) of the equalizer can be calculated, and then loop iterations are performed until the switching condition is satisfied. The update of f _svm (n) is realized by the following formula

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

式中，n为迭代次数，λ为迭代步长；In the formula, n is the number of iterations, and λ is the iteration step size;

当满足下式的切换条件时When the switching conditions of the following formula are satisfied

$\{\begin{matrix} MSE MSE ((n no)) = = \frac{11}{N N} {Σ Σ}_{k k = = 11}^{N N} (({| | {z z}_{svm svm} ((k k)) | |}^{22} - - R R ((k k)))) \\ | | MSE MSE ((n no)) - - MSE MSE ((n no - - 11)) | | \leq \leq η η \end{matrix} - - - - - - ((1111))$

即可得到全局最优的初始化权向量f_svm(n)，并将这个权向量作为初始化权向量，式(11)中，MSE(n)表示n次迭代的均方误差，η为切换阈值。The global optimal initialization weight vector f _svm (n) can be obtained, and this weight vector is used as the initialization weight vector. In formula (11), MSE(n) represents the mean square error of n iterations, and η is the switching threshold.

支持向量机参数选择方法如下：The selection method of support vector machine parameters is as follows:

(1)种群初始化(1) Population initialization

随机产生一定数目的抗体群，其中的每个抗体分别对应核函数、惩罚参数C和e中的一组取值；Randomly generate a certain number of antibody groups, each of which corresponds to a set of values in the kernel function, penalty parameters C and e;

(2)计算亲和度值(2) Calculate the affinity value

计算抗体和抗原之间的亲和度值；Calculate the affinity value between the antibody and the antigen;

(3)克隆选择(3) Clone selection

克隆选择操作是克隆增值操作的逆操作。该操作是从抗体各自克隆增值后的子代中选择优秀的个体，从而形成新的抗体群，是一个无性选择过程。一个抗体经过克隆增值后形成一个亚抗体群，再经过亲和度成熟操作后通过克隆选择操作实现局部的亲和度升高。首先对第二步所述抗体群中的抗体按亲和度从小到大的顺序进行排列，根据亲和度(一个抗体对一个相同链长的抗原产生识别的程度称为亲和度)的大小评价，选择最佳抗体进行克隆扩增操作，得到扩增后的抗体群A，克隆数与亲和度成正比。The clone selection operation is the inverse of the clone increment operation. This operation is to select excellent individuals from the progeny of each antibody clone to form a new antibody group, which is a non-sexual selection process. An antibody forms a sub-antibody group after clonal proliferation, and then undergoes an affinity maturation operation to achieve a partial affinity increase through a clonal selection operation. First, arrange the antibodies in the antibody group described in the second step in ascending order of affinity, according to the degree of affinity (the degree to which an antibody recognizes an antigen with the same chain length is called affinity) Evaluation, select the best antibody for clonal expansion operation, and obtain the amplified antibody group A, the number of clones is directly proportional to the affinity.

(4)精英交叉策略(4) Elite Crossover Strategy

精英交叉的原理如下：在免疫算法的实现中，首先给定一个精英交叉的概率P_kc(kc表示king-crossover，即精英交叉)，对于第三步所述的克隆抗体群中第t代每个个体a(t)产生一个[0，1]之间的随机数R，如果R小于精英交叉概率P_kc，则a(t)被选中与保存的当前代精英个体b(t)进行交叉，其方法是：将a(t)和b(t)放入一个小的交配池中，根据选定的交叉策略(单点、两点、多点和一致交叉等)，对a(t)和b(t)进行交叉操作，得到一对子代个体a′(t)和b′(t)。然后，用a′(t)替代种群中的a(t)，b′(t)则丢失不用。The principle of elite crossover is as follows: In the implementation of the immune algorithm, firstly a probability P _kc of elite crossover is given (kc means king-crossover, i.e. elite crossover), for every An individual a(t) generates a random number R between [0, 1]. If R is less than the elite crossover probability P _kc , then a(t) is selected to crossover with the saved current generation elite individual b(t). The method is: put a(t) and b(t) into a small mating pool, according to the selected crossover strategy (single-point, two-point, multi-point and consistent crossover, etc.), a(t) and b(t) b(t) performs crossover operation to obtain a pair of offspring individuals a'(t) and b'(t). Then, replace a(t) in the population with a'(t), and b'(t) is lost.

(5)高频变异(5) High-frequency variation

对抗体群A中每个克隆抗体进行高频变异，产生变异群A^*；高频变异作为克隆选择的主要操作算子，可以防止进化早熟并增加抗体的多样性；High-frequency mutation is performed on each cloned antibody in antibody group A to generate mutant group A ^* ; high-frequency mutation is used as the main operator for clonal selection, which can prevent premature evolution and increase the diversity of antibodies;

(6)计算亲和度值(6) Calculate the affinity value

将(5)所述的高频变异后的各抗体重新计算其对应的亲和度值。Recalculate the corresponding affinity value of each antibody after the high-frequency mutation described in (5).

(7)选择(7) choose

从变异群A^*中选择n个亲和度高的抗体替换初始抗体群中n个亲和度低的抗体，n反比于抗体群的平均亲和度值；Select n antibodies with high affinity from the variant group A ^* to replace n antibodies with low affinity in the initial antibody population, and n is inversely proportional to the average affinity value of the antibody population;

(8)判断终止与否(8) Judging whether to terminate or not

根据抗体的进化代数进行判断，当进化代数小于最大进化代数，则转至(2)，重复进行(2)～(5)的操作步骤，直至进化代数大于最大进化代数，如达到终止条件，则程序结束，输出全局参数最优解。Judging according to the evolutionary generation of the antibody, if the evolutionary generation is less than the maximum evolutionary generation, then go to (2), and repeat the operation steps (2) to (5) until the evolutionary generation is greater than the maximum evolutionary generation, if the termination condition is met, then At the end of the program, the optimal solution of the global parameters is output.

本发明利用免疫克隆选择算法的全局搜索能力，对支持向量机盲均衡算法中的参数选择由人工选取变为自动确定，然后将支持向量机引入到正交小波多模盲均衡方法中，发明了一种引入免疫优化支持向量机的小波多模盲均衡方法(CSA-SVM-WT-MMA)，该发明方法通过利用支持向量机对提取的一小段起始数据训练来估计盲均衡器的初始权值，同时利用免疫算法对SVM中的参数进行了优化选择，并将SVM估计出的初始权值作为正交小波多模盲均衡算法(WT-MMA)的权向量。水声信道的仿真结果表明，与多模盲均衡方法、正交小波多模盲均衡方法和支持向量机正交小波多模盲均衡方法相比，该发明方法具有较快的收敛速度和稳态误差，从而更好的提高了水声通信的性能。The present invention utilizes the global search ability of the immune clone selection algorithm to change the parameter selection in the support vector machine blind equalization algorithm from manual selection to automatic determination, and then introduces the support vector machine into the orthogonal wavelet multi-mode blind equalization method, inventing A wavelet multi-mode blind equalization method (CSA-SVM-WT-MMA) that introduces an immune optimization support vector machine. The inventive method estimates the initial weight of the blind equalizer by using the support vector machine to train a small piece of initial data extracted. At the same time, the immune algorithm is used to optimize the parameters in the SVM, and the initial weight estimated by the SVM is used as the weight vector of the orthogonal wavelet multi-mode blind equalization algorithm (WT-MMA). The simulation results of the underwater acoustic channel show that, compared with the multi-mode blind equalization method, the orthogonal wavelet multi-mode blind equalization method and the support vector machine orthogonal wavelet multi-mode blind equalization method, the inventive method has faster convergence speed and steady state error, thereby better improving the performance of underwater acoustic communication.

附图说明 Description of drawings

图1：本发明：引入免疫优化支持向量机的小波多模盲均衡方法原理图；Fig. 1: The present invention: the schematic diagram of the wavelet multimode blind equalization method that introduces the immune optimization support vector machine;

图2：实施实验仿真结果图，(a)5种方法的均方误差曲线，(b)5种方法的剩余码间干扰曲线，(c)5种方法的ISI与SNR比较曲线，(d)CMA输出星座图，(e)MMA输出星座图，(f) WT-MMA输出星座图，(g)SVM-WT-MMA输出星座图，(h)本发明CSA-SVM-WT-MMA输出星座图。Figure 2: The graph of the simulation results of the implementation experiment, (a) the mean square error curve of the five methods, (b) the residual intersymbol interference curve of the five methods, (c) the ISI and SNR comparison curve of the five methods, (d) CMA outputs constellation, (e) MMA outputs constellation, (f) WT-MMA outputs constellation, (g) SVM-WT-MMA outputs constellation, (h) CSA-SVM-WT-MMA of the present invention outputs constellation .

具体实施方式 Detailed ways

引入免疫优化支持向量机的小波多模盲均衡方法原理，如图1所示。图1中，a(k)为复信源发射信号，表示为a(k)＝a_Re(k)+ja_Im(k)，a_Re(k)和a_Im(k)分别为信源信号的实部和虚部；c(k)为信道脉冲响应向量，长度为M；向量v(k)为加性高斯白噪声；向量y(k)为均衡器的输入复信号，长度为N，将其分为实部和虚部，即y(k)＝y_Re(k)+jy_Im(k)，y_Re(k)为y(k)的实部，y_Im(k)为y(k)的虚部(后面类似的表达式，所表达的含义相同)；向量f(k)为均衡器权向量且长度为L，即f(k)＝[f₀(k)，L，f_L(k)]^T([×]^T表示转置运算)；y(×)为无记忆非线性函数，表示无记忆非线性估计器；z(k)为均衡器的输出复信号序列。图1中，不含虚线框的部分为正交小波多模盲均衡算法(WT-MMA)；包含虚线框的部分为引入免疫优化支持向量机的正交小波多模盲均衡算法(CSA-SVM-WT-MMA)。现分述如下：The principle of the wavelet multi-mode blind equalization method that introduces the immune optimization support vector machine is shown in Figure 1. In Figure 1, a(k) is the signal transmitted by the complex source, expressed as a(k)=a _Re (k)+ja _Im (k), a _Re (k) and a _Im (k) are the source signals respectively c(k) is the channel impulse response vector, the length is M; the vector v(k) is the additive Gaussian white noise; the vector y(k) is the input complex signal of the equalizer, the length is N, Divide it into real part and imaginary part, that is, y(k)=y _Re (k)+jy _Im (k), y _Re (k) is the real part of y(k), y _Im (k) is y( The imaginary part of k) (the following similar expressions have the same meaning); the vector f(k) is the equalizer weight vector and the length is L, that is, f(k)=[f ₀ (k), L, f _L (k)] ^T ([×] ^T represents the transpose operation); y(×) is a memoryless nonlinear function, representing a memoryless nonlinear estimator; z(k) is the output complex signal sequence of the equalizer. In Figure 1, the part without the dotted box is the orthogonal wavelet multimode blind equalization algorithm (WT-MMA); the part containing the dotted box is the orthogonal wavelet multimode blind equalization algorithm (CSA-SVM -WT-MMA). Now it is described as follows:

正交小波多模盲均衡算法(WT-MMA)，利用正交小波变换对均衡器的接收复信号进行变换，并进行能量归一化处理，降低了输入复信号的自相关性。Orthogonal wavelet multimode blind equalization algorithm (WT-MMA) uses orthogonal wavelet transform to transform the received complex signal of the equalizer, and performs energy normalization processing to reduce the autocorrelation of the input complex signal.

令a(k)＝[a(k)，L，a(k-N_c+1)]^T，y(k)＝[y(k+N)，L，y(k)，L，y(k-N)]^T，由图1可知Let a(k)=[a(k), L, a(kN _c +1)] ^T , y(k)=[y(k+N), L, y(k), L, y(kN) ] ^T , we can see from Figure 1

$y the y ((k k)) = = {Σ Σ}_{i i = = 00}^{{N N}_{c c} - - 11} {c c}_{i i} a a ((k k - - i i)) + + v v ((k k)) = = {c c}^{T T} a a ((k k)) + + v v ((k k)) - - - - - - ((11))$

根据小波变换理论，均衡器f(k)为FIR滤波器，可表示为：According to the wavelet transform theory, the equalizer f(k) is a FIR filter, which can be expressed as:

式中，k＝0，1，鬃，□N，j_p，q(k)表示尺度参数为p、平移参数为q的小波基函数；y_P，q(k)表示尺度参数为P、平移参数为q的尺度函数，In the formula, k=0, 1, mane, □N, j _{p, q} (k) represents the wavelet basis function with scale parameter p and translation parameter q; y _{P, q} (k) represents the scale parameter P, translation A scaling function with parameter q,

k_p＝N/2^p-1(p＝1，2，鬃，□J)，P为小波分解最大尺度，k_p为尺度p下的最大平移，由于f(n)的特性由E_p，q＝＜f(k)，j_p，q(k)＞和F_P，q＝＜f(k)，y_P，q(k)＞反应出来，故称其为均衡器权系数。k _p =N/2 ^p -1(p=1, 2, mane, □J), P is the maximum scale of wavelet decomposition, k _p is the maximum translation under the scale p, due to the characteristics of f(n) by E _{p, q} = <f(k), j _{p, q} (k)> and F _{P, q} = <f(k), y _{P, q} (k)> are reflected, so it is called equalizer weight coefficient.

经过正交小波变换后均衡器的输入信号分实部和虚部分别表示为After the orthogonal wavelet transform, the input signal of the equalizer is divided into real part and imaginary part respectively expressed as

R(k)＝R_Re(k)+jR_Im(k)＝Qy_Re(k)+j(Qy_Im(k))R(k)＝R _Re (k)+jR _Im (k)＝Qy _Re (k)+j(Qy _Im (k))

(3)(3)

其中，R_Re(k)和R_Im(k)分别为R(k)实部和虚部，其表示形式如下，Among them, R _Re (k) and R _Im (k) are the real part and imaginary part of R(k) respectively, and their expressions are as follows,

${R R}_{r r} ((k k)) = = {[[{d d}_{Re Re 1,0 1,0} ((k k)),, {d d}_{Re Re 1,1 1,1} ((k k)),, L L,, {d d}_{ReP ReP,, {k k}_{P P}} ((k k)),, {s the s}_{ReP ReP,, 00} ((k k)),, L L {s the s}_{ReP ReP,, {k k}_{p p}} ((k k))]]}^{T T} - - - - - - ((44))$

$\{\begin{matrix} {d d}_{Rep rep,, q q} ((k k)) = = {Σ Σ}_{n no = = 00}^{L L - - 11} {y the y}_{Re Re} ((k k - - n no)) {j j}_{p p,, q q} ((n no)) \\ {s the s}_{ReP ReP,, q q} ((k k)) = = {Σ Σ}_{n no = = 00}^{L L - - 11} {y the y}_{Re Re} ((k k - - n no)) {y the y}_{P P,, q q} ((n no)) \end{matrix} - - - - - - ((55))$

${R R}_{Im Im} ((k k)) = = {[[{d d}_{Im Im 1,0 1,0} ((k k)),, {d d}_{Im Im 1,1 1,1} ((k k)),, L L,, {d d}_{ImP ImP . . {k k}_{p p}} ((k k)),, {s the s}_{ImP ImP,, 00} ((k k)),, L L {s the s}_{ImP ImP,, {k k}_{p p}} ((k k))]]}^{T T} - - - - - - ((66))$

$\{\begin{matrix} {d d}_{Imp Imp,, q q} ((k k)) = = {Σ Σ}_{n no = = 00}^{L L - - 11} {y the y}_{Im Im} ((k k - - n no)) {j j}_{p p,, q q} ((n no)) \\ {s the s}_{ImP ImP,, q q} ((k k)) = = {Σ Σ}_{n no = = 00}^{L L - - 11} {y the y}_{Im Im} ((k k - - n no)) {y the y}_{P P,, q q} ((n no)) \end{matrix} - - - - - - ((77))$

式中，k＝0，1，L，L-1，L＝2^P为均衡器的长度；Re和Im分别表示取实部和虚部；

和y_P，q(n)分别表示小波函数和尺度函数，d_p，q(k)、s_P，q(k)分别为相应的小波和尺度变换系数，Q为正交小波变换矩阵。In the formula, k=0,1, L, L-1, L=2 ^P is the length of equalizer; Re and Im represent to take real part and imaginary part respectively;

and y _{P, q} (n) represent the wavelet function and scaling function respectively, d _{p, q} (k), s _{P, q} (k) are the corresponding wavelet and scaling coefficients respectively, and Q is the orthogonal wavelet transformation matrix.

均衡器输出为The equalizer output is

$\{\begin{matrix} {z z}_{Re Re} ((k k)) = = {f f}_{Re Re}^{H h} ((k k)) {R R}_{Re Re} ((k k)) \\ {z z}_{Im Im} ((k k)) = = {f f}_{Im Im}^{H h} ((k k)) {R R}_{Im Im} ((k k)) \end{matrix} - - - - - - ((88))$

式中，和

(H表示共轭转置)分别为均衡器权向量的实部向量和虚部向量，z_Re(k)和z_Im(k)分别为均衡器输出信号的实部和虚部。In the formula, and

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

由MMA的代价函数形式为The form of the cost function by MMA is

${J J}_{MMA MMA} ((f f)) = = E E. {{{(({z z}_{Re Re}^{22} ((k k)) - - {R R}_{Re Re,, MMA MMA}^{22}))}^{22} + + {(({z z}_{Im Im}^{22} ((k k)) - - {R R}_{Im Im,, MMa M Ma}^{22}))}^{22}}} - - - - - - ((99))$

其中 $R_{Re, MMA}^{2} = E {(a_{Re}^{4} (k))} / E {(a_{Re}^{2} (k))},$ $R_{Im, MMA}^{2} = E {(a_{Im}^{4} (k))} / E {(a_{Im}^{2} (k))},$ 前者表示同相方向的模值，后者表示正交方向的模值。in $R_{Re, MMA}^{2} = E. {(a_{Re}^{4} (k))} / E. {(a_{Re}^{2} (k))},$ $R_{Im, MMA}^{2} = E. {(a_{Im}^{4} (k))} / E. {(a_{Im}^{2} (k))},$ The former represents the modulus value in the same phase direction, and the latter represents the modulus value in the orthogonal direction.

均衡器的误差为The error of the equalizer is

$\{\begin{matrix} {e e}_{Re Re,, MMA MMA} ((k k)) = = {z z}_{Re Re} ((k k)) (({z z}_{Re Re}^{22} ((k k)) - - {R R}_{Re Re,, MMA MMA}^{22})) \\ {e e}_{Im Im,, MMA MMA} ((k k)) = = {z z}_{Im Im} ((k k)) (({z z}_{Im Im}^{22} ((k k)) - - {R R}_{Im Im,, MMA MMA}^{22})) \end{matrix} - - - - - - ((1010))$

其相应的均衡器权向量的迭代公式为The iterative formula of the corresponding equalizer weight vector is

$\{\begin{matrix} {f f}_{Re Re} ((k k + + 11)) = = {f f}_{Re Re} ((k k)) - - μ μ {\overset{^^}{R R}}^{- - 11} ((k k)) {e e}_{Re Re,, MMA MMA} ((k k)) {R R}_{Re Re}^{* *} ((k k)) \\ {f f}_{Im Im} ((k k + + 11)) = = {f f}_{Im Im} ((k k)) - - μ μ {\overset{^^}{R R}}^{- - 11} ((k k)) {e e}_{Im Im,, MMA MMA} ((k k)) {R R}_{Im Im}^{* *} ((k k)) \end{matrix} - - - - - - ((1111))$

式中，R^＊(k)为R(k)的共轭；In the formula, R ^* (k) is the conjugate of R(k);

${\overset{^^}{R R}}^{- - 11} ((k k)) = = diag diag [[{σ σ}_{p p,, 00}^{22} ((k k)),, {σ σ}_{p p,, 11}^{22} ((k k)),, L L,, {σ σ}_{P P,, {k k}_{P P} - - 11}^{22} ((k k)),, {σ σ}_{P P + + 1,0 1,0}^{22} ((k k)),, L L,, {σ σ}_{P P + + 11,, {k k}_{P P} - - 11}^{22} ((k k))]] - - - - - - ((1212))$

式中，

分别表示对d_p，k(k)，s_P，k(k)平均功率估计，

为对

估计值，由下式推导得到：In the formula,

Respectively represent the average power estimation of d _{p, k} (k), s _{P, k} (k),

for right

Estimated value, derived from the following formula:

$\{\begin{matrix} {\overset{^^}{σ σ}}_{p p,, q q}^{22} ((k k + + 11)) = = β β {\overset{^^}{σ σ}}_{p p,, q q}^{22} ((k k)) + + ((11 - - β β)) {| | {d d}_{p p,, q q} ((k k)) | |}^{22} \\ {\overset{^^}{σ σ}}_{P P + + 11,, q q}^{22} ((k k + + 11)) = = β β {\overset{^^}{σ σ}}_{P P + + 11,, q q}^{22} ((k k)) + + ((11 - - β β)) {| | {s the s}_{P P,, q q} ((k k)) | |}^{22} \end{matrix} - - - - - - ((1313))$

其中，diag[]表示对角矩阵，β为平滑因子，且0＜β＜1。d_p，q(k)表示小波空间p层分解的第q个信号，s_P，q(k)表示尺度空间中最大分解层数P时的第q个信号。式(2)～式(13)构成基于正交小波多模盲均衡方算法(WT-MMA)。Among them, diag[] represents a diagonal matrix, β is a smoothing factor, and 0<β<1. d _{p, q} (k) represents the qth signal of wavelet space p-level decomposition, and s _{P, q} (k) represents the qth signal when the maximum number of decomposition layers P in the scale space. Equations (2) to (13) form an orthogonal wavelet-based multi-mode blind equalization algorithm (WT-MMA).

正交小波多模盲均衡算法是利用构造出的代价函数对均衡器权向量求梯度，从而确定均衡器权值的迭代方程，这种方法缺乏全局搜索能力，不适当的初始化容易使算法收敛到局部极小解。为了克服这一缺点，本文利用支持向量机来搜寻WT-MMA算法的最优化初始权向量，用来弥补WT-MMA算法的缺陷，更好地解决搜索过程中陷于局部收敛的问题。Orthogonal wavelet multi-mode blind equalization algorithm uses the constructed cost function to calculate the gradient of the equalizer weight vector, so as to determine the iterative equation of the equalizer weight. This method lacks the ability of global search, and improper initialization can easily make the algorithm converge to local minimum solution. In order to overcome this shortcoming, this paper uses the support vector machine to search for the optimal initial weight vector of the WT-MMA algorithm, which is used to make up for the defects of the WT-MMA algorithm and better solve the problem of local convergence in the search process.

当发射器发射信号时，取均衡器接收信号y(k)＝y_Re(k)+jy_Im(k)(k＝1，2…N，y_Re(k)为y(k)的实部，y_Im(k)为y(k)的虚部。)的前N组向量，利用支持向量机来对这N组数据进行均衡。根据结构风险最小化原则以及发射信号的统计特性，以精度ε估计均衡器的初始权向量f_svm(n)。建立如下支持向量机回归问题When the transmitter transmits a signal, take the equalizer received signal y(k)=y _Re (k)+jy _Im (k) (k=1, 2...N, y _Re (k) is the real part of y(k) , y _Im (k) is the imaginary part of y(k).) of the first N groups of vectors, use the support vector machine to balance the N groups of data. According to the principle of structural risk minimization and the statistical characteristics of the transmitted signal, the initial weight vector f _svm (n) of the equalizer is estimated with precision ε. Set up the following support vector machine regression problem

$min min {E E.}_{svm svm} (({f f}_{svm svm} ((n no)))) = = \frac{11}{22} {| | | | {f f}_{svm svm} ((n no)) | | | |}^{22} - - - - - - ((1414))$

$\{\begin{matrix} R R ((k k)) - - {[[(({f f}_{svm svm} ((n no))]]}^{T T} y the y ((k k)) {))}^{22} \leq \leq ϵ ϵ \\ {[[(({f f}_{svm svm} ((n no))]]}^{T T} y the y ((k k)) {))}^{22} - - R R ((k k)) \leq \leq ϵ ϵ \end{matrix} - - - - - - ((1515))$

式(15)中，R(k)＝R_Re(k)+jR_Im(k)，参数ε决定了ε不敏感区域的宽度和支持向量的数目。In formula (15), R(k)=R _Re (k)+jR _Im (k), parameter ε determines the width of ε insensitive region and the number of support vectors.

和惩罚函数C，式(14)和(15)的最优化问题就可以转化为求解以下约束最优化问题：In order to "soften" the above rigid ε-band SVM, the slack variable ξ(k),

and the penalty function C, the optimization problems of formulas (14) and (15) can be transformed into solving the following constrained optimization problems:

约束条件为The constraints are

式(16)和(17)中，ξ(k)和

是衡量样本离群的距离大小，而惩罚变量C则体现了对该离群点的重视程度。In formulas (16) and (17), ξ(k) and

但是由于约束条件对于均衡器权向量f_svm(n)含有二次项，上面的最优化问题无法通过SVM所采用的线性规划方法求解。于是，根据文献[13]提出的一种迭代权二次规划算法(Iterative Reweighted Quadratic Programming，IRWQP)来解决这一问题，可以将式(17)中的二次约束改写为线性约束。即However, since the constraint condition contains a quadratic term for the equalizer weight vector f _svm (n), the above optimization problem cannot be solved by the linear programming method adopted by SVM. Therefore, according to an Iterative Reweighted Quadratic Programming algorithm (IRWQP) proposed in literature [13] to solve this problem, the quadratic constraint in formula (17) can be rewritten as a linear constraint. Right now

式中，z_svm(k)＝z_Re，svm(k)+jz_Im，svm(k)为导出原始问题的对偶问题，引入Lagrange函数In the formula, z _svm (k) = z _{Re, svm} (k) + jz _{Im, svm} (k) is the dual problem derived from the original problem, and the Lagrange function is introduced

其中

是Lagrange乘子向量。将式(14)～(18)的原始最优化问题转换为凸二次规划问题(对偶问题)，即in

is the Lagrange multiplier vector. Transform the original optimization problem of formulas (14)~(18) into a convex quadratic programming problem (dual problem), namely

式中，K<y_m，y_k>表示表示支持向量机的内积。In the formula, K<y _m , y _k > represents the inner product of the support vector machine.

式中，Lagrange乘子

和α(k)可以通过式(20)和(21)来求解。where the Lagrange multiplier

and α(k) can be solved by equations (20) and (21).

f_svm(n)＝λf_svm(n-1)+(1-λ)f_svm(n)f _svm (n)＝λf _svm (n-1)+(1-λ)f _svm (n)

(23)(twenty three)

式中，n为迭代次数，λ为迭代步长。In the formula, n is the number of iterations, and λ is the iteration step size.

$\{\begin{matrix} MSE MSE ((n no)) = = \frac{11}{N N} {Σ Σ}_{k k = = 11}^{N N} (({| | {z z}_{svm svm} ((k k)) | |}^{22} - - R R ((k k)))) \\ | | MSE MSE ((n no)) - - MSE MSE ((n no - - 11)) | | \leq \leq η η \end{matrix} - - - - - - ((24 twenty four))$

即可得到全局最优的初始化权向量f_svm(n)，并将这个权向量作为WT-MMA算法的初始化权向量。式(24)中，MSE(n)表示n次迭代的均方误差，η为切换阈值。The global optimal initialization weight vector f _svm (n) can be obtained, and this weight vector is used as the initialization weight vector of the WT-MMA algorithm. In formula (24), MSE(n) represents the mean square error of n iterations, and η is the switching threshold.

在支持向量机多模盲均衡算法中，需要确定一些参数的取值，如核函数、惩罚参数C、e-不敏感损失函数等，不同参数的设置会严重影响SVM机器学习的性能，所以大多都是通过反复的实验，以及人的主观经验来选择需要的参数，并且需要付出较多的时间代价。其中惩罚函数C和e-不敏感损失函数的e宽度，是控制逼近函数VC维数(逼近函数集合大小的定量指标)的自由参数，由于其在选择时必须同时调整，具有一定的复杂性。In the support vector machine multi-mode blind equalization algorithm, it is necessary to determine the value of some parameters, such as kernel function, penalty parameter C, e-insensitive loss function, etc. The settings of different parameters will seriously affect the performance of SVM machine learning, so most The required parameters are selected through repeated experiments and human subjective experience, and it takes a lot of time. Among them, the penalty function C and the e-width of the e-insensitive loss function are free parameters to control the dimension of the approximation function VC (a quantitative indicator of the size of the approximation function set), which has certain complexity because it must be adjusted at the same time during selection.

因此，本发明利用免疫克隆选择算法全局寻优的特性，对支持向量机中的参数进行了优化选择。主要是将SVM的训练样本设置为抗原，参数C和e作为抗体，首先确定参数C和e的取值范围，通过模拟生物免疫系统对抗体克隆选择、变异的原理，利用抗体克隆扩大搜索范围、变异保持多样性的特点，寻找到目标函数的参数最优解，并作为支持向量机中的惩罚参数C、e-不敏感损失函数。将免疫克隆选择算法应用于支持向量机参数优化选择时，算法的基本步骤如下：Therefore, the present invention optimizes the parameters in the support vector machine by utilizing the global optimization characteristic of the immune clone selection algorithm. It mainly sets the training samples of SVM as antigens, parameters C and e as antibodies, firstly determine the value ranges of parameters C and e, and use antibody cloning to expand the search range by simulating the principle of biological immune system for antibody clone selection and variation. Mutation maintains the characteristics of diversity, finds the optimal solution of the parameters of the objective function, and uses it as the penalty parameter C and e-insensitive loss function in the support vector machine. When the immune clone selection algorithm is applied to the optimization selection of support vector machine parameters, the basic steps of the algorithm are as follows:

(1)种群初始化(1) Population initialization

(2)计算亲和度值(2) Calculate the affinity value

(3)克隆选择(3) Clone selection

(4)精英交叉策略(4) Elite Crossover Strategy

(5)高频变异(5) High-frequency variation

(6)计算亲和度值(6) Calculate the affinity value

(7)选择(7) choose

(8)判断终止与否(8) Judging whether to terminate or not

通过以上过程，就可对SVM中参数进行优化选择，从而改善支持向量机初始化权向量的性能。Through the above process, the parameters in the SVM can be optimally selected, thereby improving the performance of the initialization weight vector of the support vector machine.

实施实例Implementation example

为了验证本发明方法CSA-SVM-WT-MMA的有效性，以CMA、MMA、WT-MMA和SVM-WT-MMA方法作为比较对象，进行仿真实验。仿真试验中，抗体规模为100，克隆控制因子为0.6，精英交叉概率为0.2，变异概率为0.1，算法最大迭代次数为200。参数C和e优化取值范围设为：1#C 20，0.00001#e 0.1，支持向量机初始化所提取的训练样本个数N＝2000；In order to verify the effectiveness of the method CSA-SVM-WT-MMA of the present invention, a simulation experiment was carried out with the methods of CMA, MMA, WT-MMA and SVM-WT-MMA as comparison objects. In the simulation test, the antibody scale is 100, the cloning control factor is 0.6, the elite crossover probability is 0.2, the mutation probability is 0.1, and the maximum number of iterations of the algorithm is 200. The optimal value range of parameters C and e is set as: 1#C 20, 0.00001#e 0.1, and the number of training samples extracted by the support vector machine initialization is N=2000;

混合相位水声信道c＝[0.3132-0.10400.89080.3134]；发射信号为128QAM，均衡器权长均为16，信噪比30dB。在SVM-WT-MMA中，C＝15，e＝0.1；在本发明CSA-SVM-WT-MMA中，免疫优化选择最优参数为C＝17.8477，e＝0.0765。其它参数设置，如表1所示。1000次蒙特卡诺仿真结果，如图2所示。为了比较各算法性能，定义剩余码间干扰如下：Mixed-phase underwater acoustic channel c=[0.3132-0.10400.89080.3134]; the transmitted signal is 128QAM, the weight length of the equalizer is 16, and the signal-to-noise ratio is 30dB. In SVM-WT-MMA, C=15, e=0.1; in CSA-SVM-WT-MMA of the present invention, the optimal parameters for immune optimization selection are C=17.8477, e=0.0765. Other parameter settings are shown in Table 1. The results of 1000 Monte Cano simulations are shown in Figure 2. In order to compare the performance of each algorithm, the residual intersymbol interference is defined as follows:

$ISI ISI = = 1010 lg lg ((((\underset{i i}{Σ Σ} {| | {h h}_{i i} | |}^{22} - - {| | {h h}_{max max} | |}^{22})) / / {| | {h h}_{max max} | |}^{22})) - - - - - - ((2525))$

式中，h是合成信道

中的第i个元素，而h_max表示其中具有最大绝对值的元素。where h is the composite channel

The i-th element in , and h _max represents the element with the largest absolute value.

表1 仿真参数设置Table 1 Simulation parameter settings

图2(a)(b)表明，在收敛速度上，本发明CSA-SVM-WT-MMA与SVM-WT-MMA基本相同，但比MMA快了近6000步、比WT-MMA快了近3000步。剩余码间干扰上，本发明CSA-SVM-WT-MMA比WT-MMA和SVM-WT-MMA减小近0.8dB。由图2(c)可知，随着信噪比的增加，五种方法的剩余码间干扰都在不断减小，而本发明CSA-SVM-WT-MMA减小的幅度最大，同一信噪比比较更能体现该算法的优越性。图2(e)、(f)、(g)、(h)表明，本发明CSA-SVM-WT-MMA的星座图比CMA、MMA、WT-MMA和SVM-WT-MMA更加清晰、紧凑，有很强的抗码间干扰(ISI)能力，具有一定的实用性。Figure 2(a)(b) shows that, on the convergence speed, CSA-SVM-WT-MMA of the present invention is basically the same as SVM-WT-MMA, but it is nearly 6000 steps faster than MMA and nearly 3000 steps faster than WT-MMA step. In terms of residual intersymbol interference, the CSA-SVM-WT-MMA of the present invention is nearly 0.8dB less than WT-MMA and SVM-WT-MMA. It can be seen from Fig. 2(c) that with the increase of SNR, the residual intersymbol interference of the five methods is continuously decreasing, and the CSA-SVM-WT-MMA of the present invention has the largest reduction range, and the same SNR The comparison can better reflect the superiority of the algorithm. Fig. 2 (e), (f), (g), (h) shows that the constellation diagram of CSA-SVM-WT-MMA of the present invention is clearer and more compact than CMA, MMA, WT-MMA and SVM-WT-MMA, It has a strong ability to resist intersymbol interference (ISI), and has certain practicability.

Claims

1. a wavelet multimode blind equalization method introducing immune optimization support vector machine, is characterized in that comprising the steps:

a.) Pass the transmitted signal a(k) through the impulse response channel c(k) to obtain the channel output vector x(k), where k is a time series, the same below;

b.) Obtain the input signal of the orthogonal wavelet transformer (WT) by using the channel noise v(k) and the channel output vector x(k) described in step a: y(k)=v(k)+x(k) ;

c.) Input the equalizer input signal y(k) described in step b to the equalizer input R(k) after orthogonal wavelet transformation, and update the equalizer input R(k) through the multi-mode blind equalization method weight vector;

It is characterized by:

When the transmitter transmits a signal, take the equalizer received signal y(k)=y _Re (k)+jy _Im (k) (k=1, 2...N, y _Re (k) is the real part of y(k) , y _Im (k) is the imaginary part of y(k),

is the imaginary number unit, and the following similar expressions have the same meaning), and the support vector machine is used to balance the N sets of data. According to the principle of structural risk minimization and the statistical characteristics of the transmitted signal, the initial weight vector f _svm (n) of the equalizer is estimated with precision ε. Set up the following support vector machine regression problem

min min {E E.}_{svm svm} (({f f}_{svm svm} ((n no)))) = = \frac{11}{22} {| | | | {f f}_{svm svm} ((n no)) | | | |}^{22} - - - - - - ((11))

In the formula, E _svm (·) represents the precision ε estimation of support vector machine regression. Its constraint function is

\{\begin{matrix} R R ((k k)) - - {[[(({f f}_{svm svm} ((n no))]]}^{T T} y the y ((k k)) {))}^{22} \leq \leq ϵ ϵ \\ {[[(({f f}_{svm svm} ((n no))]]}^{T T} y the y ((k k)) {))}^{22} - - R R ((k k)) \leq \leq ϵ ϵ \end{matrix} - - - - - - ((22))

In formula (2), R(k)=R _Re (k)+jR _Im (k), parameter ε determines the width of ε insensitive region and the number of support vectors.

In order to "soften" the above rigid ε-band SVM, the slack variable ξ(k), and penalty function C, the optimization problems of formulas (1) and (2) can be transformed into solving the following constrained optimization problems:

The constraints are

In formulas (3) and (4), ξ(k) and

However, since the constraint condition contains a quadratic term for the equalizer weight vector f _svm (n), the above optimization problem cannot be solved by the linear programming method adopted by SVM. Therefore, according to an iterative reweighted quadratic programming algorithm (Iterative Reweighted Quadratic Programming, IRWQP) to solve this problem, the quadratic constraint in formula (4) can be rewritten as a linear constraint. Right now

In the formula, z _svm (k) = x _{Re, svm} (k) + jz _{Im, svm} (k) is the dual problem derived from the original problem, and the Lagrange function is introduced

in

In the formula, E′ _svm (·) represents the precision ε estimation of support vector machine regression after convex quadratic programming. Its constraints are

In the formula, K<y _m , y _k > represents the inner product of the support vector machine;

By comparing the original problem with the dual problem, the weight vector of the equalizer can be expressed as

where the Lagrange multiplier

and α(k) can be solved by equations (7) and (8).

Through the above process, the initial weight vector f _svm (n) of the equalizer can be calculated, and then loop iterations are performed until the switching condition is satisfied. The update of f _svm (n) is realized by the following formula

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

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

When the switching conditions of the following formula are satisfied

\{\begin{matrix} MSE MSE ((n no)) = = \frac{11}{N N} {Σ Σ}_{k k = = 11}^{N N} (({| | {z z}_{svm svm} ((k k)) | |}^{22} - - R R ((k k)))) \\ | | MSE MSE ((n no)) - - MSE MSE ((n no - - 11)) | | \leq \leq η η \end{matrix} - - - - - - ((1111))

The global optimal initialization weight vector f _svm (n) can be obtained, and this weight vector is used as the initialization weight vector. In formula (11), MSE(n) represents the mean square error of n iterations, and η is the switching threshold.

2. the wavelet multimode blind equalization method of introducing immune optimization support vector machine according to claim 1 is characterized in that support vector machine parameter selection method is as follows:

(1) Population initialization

Randomly generate a certain number of antibody groups, each of which corresponds to a set of values in the kernel function, penalty parameters C and e;

(2) Calculate the affinity value

Calculate the affinity value between the antibody and the antigen;

(3) Clone selection

The clone selection operation is the inverse of the clone increment operation. This operation is to select excellent individuals from the progeny of each antibody clone to form a new antibody group, which is a non-sexual selection process. An antibody forms a sub-antibody group after clonal proliferation, and then undergoes an affinity maturation operation to achieve a partial affinity increase through a clonal selection operation. First, arrange the antibodies in the antibody group described in the second step in ascending order of affinity, according to the degree of affinity (the degree to which an antibody recognizes an antigen with the same chain length is called affinity) Evaluation, select the best antibody for clonal expansion operation, and obtain the amplified antibody group A, the number of clones is directly proportional to the affinity.

(4) Elite Crossover Strategy

The principle of elite crossover is as follows: In the implementation of the immune algorithm, firstly a probability P _kc of elite crossover is given (kc means king-crossover, i.e. elite crossover), for every An individual a(t) generates a random number R between [0, 1]. If R is less than the elite crossover probability P _kc , then a(t) is selected to crossover with the saved current generation elite individual b(t). The method is: put a(t) and b(t) into a small mating pool, according to the selected crossover strategy (single-point, two-point, multi-point and consistent crossover, etc.), a(t) and b(t) b(t) performs crossover operation to obtain a pair of offspring individuals a'(t) and b'(t). Then, replace a(t) in the population with a'(t), and b'(t) is lost.

(5) High-frequency variation

High-frequency mutation is performed on each cloned antibody in antibody group A to generate mutant group A ^* ; high-frequency mutation is used as the main operator for clonal selection, which can prevent premature evolution and increase the diversity of antibodies;

(6) Calculate the affinity value

Recalculate the corresponding affinity value of each antibody after the high-frequency mutation described in (5).

(7) choose

Select n antibodies with high affinity from the variant group A ^* to replace n antibodies with low affinity in the initial antibody population, and n is inversely proportional to the average affinity value of the antibody population;

(8) Judging whether to terminate or not

Judgment is made according to the evolutionary algebra of the antibody. When the evolutionary algebra is less than the maximum evolutionary algebra, go to (2) and repeat steps (2) to (5) until the evolutionary algebra is greater than the maximum evolutionary algebra. If the termination condition is met, then At the end of the program, the optimal solution of the global parameters is output.