CN102184455B - Orthogonal wavelet super-exponential iteration blind equalization method based on self-adaptive immune clone - Google Patents

Abstract

The invention discloses an orthogonal wavelet super-exponential iteration blind equalization method based on self-adaptive immune clone. The orthogonal wavelet super-exponential iteration blind equalization method includes the steps as follows: population initialization, calculation of an affinity value, clonal selection, high frequency variation, calculation of an affinity value, selection, judgment of whether stopping is performed, and selection of an optimum weight vector individual. The multimodal optimizing characteristic of a self-adaptive immune clone selection algorithm is utilized in the method, the weight vector of an equalizer serves as an antibody, the autocorrelation of signals is lowered by adopting orthogonal wavelet transformation, and whitening is conducted on input data of the equalizer by utilizing a super-exponential iteration (SEI) method. The result of the embodiment of the invention shows that compared with an orthogonal wavelet super-exponential iteration (WTSEI) blind equalization method and an orthogonal wavelet super-exponential iteration blind equalization method of the immune clone (CSA-WTSEI), the orthogonal wavelet super-exponential iteration blind equalization method based on the self-adaptive immune clone has higher convergence speed and smaller steady-state errors.

Description

Orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone

Technical field

The present invention relates to the orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone in a kind of underwater sound communication system.

Background technology

In underwater sound communication system, blind equalization algorithm due to do not need to send training sequence (see document [1] Guo Yecai, work. adaptive blind equalization technology [M]. publishing house of HeFei University of Technology, 2007, P.1-153; ), can effectively save the underwater sound communication bandwidth, eliminate intersymbol interference, improve underwater sound communication efficiency and quality.Document (see document [2] O Shalvi, E Weinstein.Super-Exponential Methods for Blind Deconvolution[J] .IEEE Trans.Inform.Theory, 1993, vol.39, pp.504～519; ) a kind of super index blind balance method and super Exponential Iterative algorithm (Super-Exponential Iterative proposed, SEI), this algorithm calculates by increasing albefaction matrix Q, can play whitening action to the input signal of balanced device, and the equilibrium of underwater acoustic channel is had to certain effect.Document [3]～[5] (see: [3] Cooklev T An Efficient Architecture for Orthogonal Wavelet Transforms[J] .IEEE Signal Processing Letters, 2006,13 (2): pp.77-79; Document [4] Han Yingge, Guo Yecai etc. introduce the orthogonal wavelet transformation blind equalization algorithm [J] of momentum term. Journal of System Simulation; 2008,20 (6): pp.1559-1562; Document [5] Wang Feng. Blind equalization for underwater acoustic communication theory and algorithm [D] based on high-order statistic. the doctorate paper, the .2003 of Northwestern Polytechnical University) show, carry out wavelet transformation by the input signal to balanced device, can reduce the autocorrelation of signal, effectively convergence speedup speed.But these blind balance methods are all to adopt random gradient descent method search optimal weight vector, easily are absorbed in local minimum.And immunization method is the multi-peak searching method that the simulation Immune System designs the diversity recognition capability of germ.Its a kind of as in the global search method, there is larger hunting zone (having increased the diversity of antibody), effectively prevent from evolving precocious and search for the problem that is absorbed in local extremum and (see document [6] Ayara, Timmis, de Lemos, de Castro, Duncan..Negative Selection:How to Generate Detectors.Proceedings of 1 ^StInternational Conference of Artificial Immune Systems (ICARIS), University of Kent at Canterbury, UK, 2002,9; Document [7] Kim, Bentley.Immune Memory in the Dynamic Clonal Selection Algorithm.International Conference on Artificial Immune System (ICARIS), University of Kent at Canterbury, UK, 2002.9.University ofKent at Canterbury, UK, 2002.9).For standard Immune Clone Selection method, adopt fixing antibody cloning number and high frequency variation probability, incorrect if parameter is selected, just easily cause precocity and local convergence.For this problem, and employing self-adaptation Immune Clone Selection method (see that document [8] Wei is round, Tang Chaoli, Huang Yourui. self-adaptation clonal selection algorithm and simulation study thereof [J]. pattern-recognition and artificial intelligence .2009,2 (22): pp.202-207; Document [9] Huang Yourui work. intelligent optimization algorithm and application thereof [M]. Beijing: National Defense Industry Press, 2008; Document [10] Hu Jiangqiang, Guo Chen, Li Tieshan. heuristic self-adaptation immune clone algorithm [J]. Harbin Engineering University's journal; 2007,1 (28): pp.1-5) antagonist clone's number and high frequency variation probability carry out adaptively selected strategy, can improve ability of searching optimum, make antibody jump out Local Extremum, and the carrying out along with iteration, total aberration rate of antibody reduces gradually, can strengthen local search ability, thereby more is conducive to the search of balanced device optimal weight vector.

Summary of the invention

The present invention seeks to for super-exponential iteration (SEI) blind equalization algorithm (SEI) speed of convergence slow, the shortcoming of the large and local convergence of steady-state error, immune clonal selection method and orthogonal wavelet transformation theory are incorporated in super-exponential iteration (SEI) blind equalization algorithm, invented a kind of orthogonal wavelet super-exponential iteration blind equalization (an orthogonal wavelet transform super-exponential iterative blind equalization algorithm based on the optimization of adaptive immune clone algorithm based on the self-adaptation immune clone, ACSA-WTSEI).The embodiment result shows, the inventive method has speed of convergence and less steady-state error faster, thereby has improved better the performance of underwater sound communication.

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

The present invention is based on the orthogonal wavelet super-exponential iteration blind equalization of self-adaptation immune clone, comprise the steps:

The first step: initialization of population

The random antibody population that produces some, the weight vector of the respectively corresponding balanced device of each antibody wherein.

Second step: calculate the affinity value

By the antibody population of the described random generation of the first step, in conjunction with the cost function J of norm balanced device (CMA) _CMA(w), the function of definition affinity, i.e. the objective function of immune algorithm optimizing:

$J\left(w\right)=\frac{1}{1+J_{\mathrm{CMA}}\left(w\right)}$

In formula, w means the balanced device weight vector.The corresponding J of the maximal value of J (w) _CMA(w) minimum value, be about to the blind equalization problem and be converted into the coefficient that solves balanced device corresponding to the highest affinity value.

The 3rd step: Immune Clone Selection

Regulate clone's number of each antibody according to the affinity value, clone's number of each antibody is calculated as follows:

Wherein, C means the antibody cloning number that need to be cloned, C _MAXMean given maximum clone controlling elements, f means the antibody affinity value that need to be cloned, f _MINMean the poorest antibody affinity value in antibody population, f _avgThe average affinity value that means antibody population, Mean to round downwards.

The 4th step: high frequency variation

Regulate the high frequency aberration rate of antibody according to the algebraically of affinity value and evolution, being calculated as follows of adaptive high frequency aberration rate:

Wherein, P _m(m means Hypermutation, i.e. high frequency variation) mean to be made a variation high frequency aberration rate of antibody, P _{M_MAX}Mean given maximum high frequency aberration rate, P _{M_MIN}Mean given minimum high frequency aberration rate, t _MAXMean maximum algebraically, t means current algebraically, and f means the antibody affinity value that need to be cloned, f _avgThe average affinity value that means antibody population;

The 5th step: calculate the affinity value

Each antibody affinity value after the described high frequency variation of the 4th step is recalculated;

The 6th step: select

Regulate the renewal number in per generation according to affinity value and evolutionary generation, adaptively selected renewal is calculated as follows:

Wherein, d means the per generation renewal number calculated, d _MAXMean given maximum renewal number, d _MINMean given minimum renewal number, f _MAXAnd f _MINBe expressed as respectively optimum in antibody population and the poorest antibody affinity value, t _MAXMean maximum algebraically, t means current algebraically, f _avgThe average affinity value that means antibody population;

The 7th step: whether judgement stops

Judged according to the evolutionary generation of antibody, when evolutionary generation is less than maximum evolutionary generation, gone to second step, repeat the second operation steps to the 6th step, until evolutionary generation is greater than maximum evolutionary generation, as reach end condition, EOP (end of program), export globally optimal solution;

The 8th step: select the optimum right vector individuality

Ask for corresponding weight vector value while making objective function optimum, and the initialization weight vector using this weight vector as the described orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone, thereby the weight vector initialization procedure completed.

The present invention utilizes the ability of searching optimum of self-adaptation Immune Clone Selection method and contributes to prevent to search for the characteristic optimizing weight vector of sinking into local extremum, and the strong decorrelation of input signal to balanced device in conjunction with orthogonal wavelet transformation, invented a kind of orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone, the method has further been accelerated speed of convergence, has reduced steady-state error simultaneously.The embodiment result shows: with the orthogonal wavelet super-exponential iteration blind equalization (CSA-WTSEI) of orthogonal wavelet super-exponential iteration blind equalization (WTSEI) and standard Immune Clone Selection method, compare, the inventive method has better performance on speed of convergence and steady-state error.Therefore, the present invention has certain practical value.

The accompanying drawing explanation

Fig. 1: the super-exponential iteration (SEI) blind equalization algorithm schematic diagram of orthogonal wavelet transformation.

Fig. 2: the present invention: the orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm schematic diagram based on the self-adaptation immune clone.

Fig. 3: embodiment 1 simulation result figure, (a) the square error curve of three kinds of methods, (b) WTSEI output planisphere, (c) CSA-WTSEI output planisphere, (d) ACSA-WTSEI output planisphere of the present invention.

Fig. 4: embodiment 2 simulation result figure, (a) the square error curve of three kinds of methods, (b) WTSEI output planisphere, (c) CSA-WTSEI output planisphere, (d) ACSA-WTSEI output planisphere of the present invention.

Embodiment

Orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm

The schematic diagram of orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm, as shown in Figure 1.In Fig. 1, n is time series, and a (n) is for transmitting, c (n) is the channel impulse response vector, and v (n) is additive white Gaussian noise, and y (n) is equalizer input signal, w (n) is that balanced device weight vector and length are L, i.e. w (n)=[w ₀(n), hair on the neck, L, w _L(n)] ^T([*] ^TMean the transposition computing), y (*) is memoryless nonlinear function, for generation of error signal, means memoryless nonlinear estimator, the output sequence that z (n) is balanced device.

If V is the orthogonal wavelet transformation matrix, V=[P ₀P ₁H ₁P ₂H ₁H ₀L; P _J-1H _J-2LH ₁H ₀H _J-1H _J-2LH ₁H ₀], in formula, j is the wavelet decomposition number of plies, H _jAnd P _jBe respectively the matrix formed by wavelet filter coefficient h (n) and scaling filter coefficient p (n).H _jAnd P _jMean the split-matrix formed by wavelet filter coefficient h (n) and scaling filter coefficient p (n) in j layer wavelet decomposition, and H _jAnd P _jIn each element two be respectively infinite matrix H after extracting _j(l, n)=h (n-2l), P _j(l, n)=p (n-2l), l, n ∈ Z.L means the length of the weight vector of balanced device.J? [0, J 1] means the wavelet decomposition number of plies, and J means the maximum decomposition level number of wavelet decomposition.Process wavelet transformation post-equalizer being input as

R(n)＝y(n)V (1)

Balanced device is output as

z(n)＝w ^T(n)R(n) (2)

The calculating iterative formula of the albefaction matrix Q (n) of SEI is

In formula, m _mThe iteration step length that means Q (n) matrix computations, [*] ^TMean the transposition computing, [*] ^*Mean conjugation.

The iterative formula of weight vector is

$w(n+1)=w\left(n\right)+m{\hat{R}}^{-1}\left(n\right)Q\left(n\right)e\left(n\right)R\left(n\right)z\left(n\right)---\left(4\right)$

In formula,

And

Mean r respectively _{J, k}(n), s _{J, k}(n) average power is estimated,

For right

Estimated value, derive and obtain by following formula:

${\hat{s}}_{j,k}^2(n+1)=b{\hat{s}}_{j,k}^2\left(n\right)+(1-b){\left|r_{j,k}\left(n\right)\right|}^2---\left(5\right)$

${\hat{s}}_{J+1,k}^2(n+1)=b{\hat{s}}_{J+1,k}^2\left(n\right)+(1-b){\left|s_{J,k}\left(n\right)\right|}^2---\left(6\right)$

Wherein, diag[] mean diagonal matrix, b is smoothing factor, and 0<β<1.R _{J, k}(n) mean k the signal that wavelet space j layer decomposes, s _{J, k}(n) k signal when in the expression metric space, maximum decomposition level is counted J.Formula (1) to (6) forms the super-exponential iteration (SEI) blind equalization algorithm (WT-SEI) based on orthogonal wavelet transformation.

Orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone

Orthogonal wavelet super-exponential iteration blind equalization (WT-SEI) is to utilize quick Gradient Descent search procedure to be searched for the weight vector of balanced device, lacks ability of searching optimum, easily sinks into local minimum.And the immune clonal selection method is a kind of method of global random searching, be used for making up the defect of WT-SEI, solve better in search procedure the problem of sinking into local convergence, but in standard immunoassay Immune Clone Selection method, for different optimization problems, need repetition test to determine clone's number and the high frequency variation probability of antibody.And self-adaptation immune clonal selection method is a kind of clone's number and high frequency variation probability of adaptively selected definite antibody, at the initial stage of evolving, utilize operation operator assurance antibody to search on a large scale, carry out when the overall situation is evolved avoiding Premature Convergence.At later stage of evolution, when approaching globally optimal solution, antibody is just jumped out Local Extremum, and in subrange, search is evolved, and makes the precision of better raising solution.This just requires operation operator fibrous root during evolution according to the evolution situation of antibody, to change at any time the strategy of evolving.And the high frequency mutation operator is to determine constringent core operation in clonal selection algorithm.Therefore, the inventive method is incorporated into self-adaptation immune clonal selection method in orthogonal wavelet super-exponential iteration blind equalization, has invented a kind of orthogonal wavelet super-exponential iteration blind equalization of self-adaptation immune clone, and its specific implementation step is as follows:

The first step: initialization of population

The random antibody population that produces some, the weight vector of the respectively corresponding balanced device of each antibody wherein.

Second step: calculate the affinity value

By the antibody population of the described random generation of the first step, in conjunction with the cost function J of norm balanced device (CMA) _CMA(w), the function of definition affinity, i.e. the objective function of immune algorithm optimizing:

$J\left(w\right)=\frac{1}{1+J_{\mathrm{CMA}}\left(w\right)}---\left(7\right)$

In formula, w means the balanced device weight vector.The corresponding J of the maximal value of J (w) _CMA(w) minimum value, be about to the blind equalization problem and be converted into the coefficient that solves balanced device corresponding to the highest affinity value.

The 3rd step: Immune Clone Selection

Regulate clone's number of each antibody according to the affinity value, clone's number of each antibody is calculated as follows:

Wherein, C means the antibody cloning number that need to be cloned, C _MAXMean given maximum clone controlling elements, f means the antibody affinity value that need to be cloned, f _MINMean the poorest antibody affinity value in antibody population, f _avgThe average affinity value that means antibody population, Mean to round downwards.Formula (8) shows, clone's number of antibody is directly proportional to the affinity value of himself, realizes the survival of the fittest of antibody in the time of evolution.When antibody poor (the affinity value is less than average affinity value), this antibody is suppressed; When antibody more excellent (its affinity value is greater than average affinity value), this antibody will be cloned.

The 4th step: high frequency variation

Regulate the high frequency aberration rate of antibody according to the algebraically of affinity value and evolution, being calculated as follows of adaptive high frequency aberration rate:

Wherein, P _m(m means Hypermutation, i.e. high frequency variation) mean to be made a variation high frequency aberration rate of antibody, P _{M_MAX}Mean given maximum high frequency aberration rate, P _{M_MIN}Mean given minimum high frequency aberration rate, t _MAXMean maximum algebraically, t means current algebraically, and f means the antibody affinity value that need to be cloned, f _avgThe average affinity value that means antibody population.Formula (9) shows, when antibody poor (the affinity value is less than average affinity value), it has higher aberration rate; When antibody more excellent (its affinity value is greater than average affinity value), according to its iterative state, give that individual corresponding aberration rate---iteration algebraically approaches maximum algebraically, the aberration rate of antibody is just less.Therefore when optimizing starts, aberration rate is higher, thereby improved ability of searching optimum, make antibody jump out Local Extremum, and, along with the carrying out of iteration, total aberration rate of antibody reduces gradually, has strengthened local search ability, make antibody more approach globally optimal solution, effectively prevent from evolving precocious and increase the diversity of antibody.

The 5th step: calculate the affinity value

Each antibody affinity value after the described high frequency variation of the 4th step is recalculated;

The 6th step: select

Regulate the renewal number in per generation according to affinity value and evolutionary generation, adaptively selected renewal is calculated as follows:

Wherein, d means the per generation renewal number calculated, d _MAXMean given maximum renewal number, d _MINMean given minimum renewal number, f _MAXAnd f _MINBe expressed as respectively optimum in antibody population and the poorest antibody affinity value, t _MAXMean maximum algebraically, t means current algebraically, f _avgThe average affinity value that means antibody population.Formula (10) can find out, the average affinity value of antibody, optimum antibody, the poorest antibody and evolutionary process are all upgraded number to per generation and had a great impact.Because the average affinity value of d and antibody population is inversely proportional to, therefore when optimizing starts, antibody affinity value is less, d is larger, the probability that antibody is updated is just higher, and along with the continuous evolution of antibody, the average affinity value of antibody increases gradually, the rate that is updated reduces, and effectively prevents the phenomenon of the more excellent antibody of part degeneration antibody replacement.

The 7th step: whether judgement stops

Judged according to the evolutionary generation of antibody, when evolutionary generation is less than maximum evolutionary generation, gone to second step, repeat the second operation steps to the 6th step, until evolutionary generation is greater than maximum evolutionary generation, as reach end condition, EOP (end of program), export globally optimal solution;

The 8th step: select the optimum right vector individuality

Consider that self-adaptation Immune Clone Selection method need to meet the ZF condition at the real-time and the blind balance method that extract optimum antibody, ask for corresponding weight vector value while making objective function optimum, and the initialization weight vector using this weight vector as ACSA-WTSEI of the present invention, thereby complete the weight vector initialization procedure.

Embodiment

In order to check the validity of ACSA-WTSEI method of the present invention, take WTSEI method and CSA-WTSEI method is comparison other, carries out emulation experiment, and the parameter of emulation experiment arranges as follows:

(1) standard Immune Clone Selection method (CSA): the antibody scale is 100, and clone's controlling elements are 0.6, and the variation probability is 0.1, and maximum iteration time is 500.

(2) self-adaptation Immune Clone Selection method (ACSA): the antibody scale is 100, and maximum iteration time is 500.C _MAX＝2；P _{m_MAX}＝0.7，P _{m_MIN}＝0.05；d _MAX＝5，d _MIN＝1.

[embodiment 1] transmits as 8PSK, adopts two footpath underwater acoustic channel c=[-0.35 00 1] carry out emulation experiment; Signal to noise ratio (S/N ratio) is 20dB, and equalizer length is 16.In the WTSEI method, the 10th tap initialization is set to 1.Other parameter arranges, as shown in table 1,500 Meng Te Kano simulation results, as shown in Figure 3.

The setting of table 1 simulation parameter

Fig. 3 (a) shows: on speed of convergence, ACSA-WTSEI of the present invention and CSA-WTSEI are basic identical, but than WTSEI fast 700 steps.On steady-state error, ACSA-WTSEI of the present invention compares with CSA-WTSEI, has reduced nearly 1.5dB, with the WTSEI method, compares, and has reduced 3.5dB.Fig. 2 (b, c, d) shows: the output planisphere of ACSA-WTSEI of the present invention is more more clear, compact than CSA-WTSEI and WTSEI.

[embodiment 2] transmit as 4QAM, adopt mixed-phase underwater acoustic channel c=[0.3132-0.1040 0.8908 0.3134] carry out emulation experiment; Signal to noise ratio (S/N ratio) is 20dB, and equalizer length is 16.In the WTSEI method, the 10th tap initialization is set to 1.Other parameter arranges, as shown in table 2,500 Meng Te Kano simulation results, as shown in Figure 4.

The setting of table 2 simulation parameter

Fig. 3 (a) shows: on speed of convergence, ACSA-WTSEI of the present invention and CSA-WTSEI are basic identical, but than WTSEI fast 1000 steps.On steady-state error, ACSA-WTSEI of the present invention compares with CSA-WTSEI, has reduced nearly 2dB, with WTSEI, compares, and has reduced nearly 6dB.Fig. 3 (b, c, d) shows: the output planisphere of ACSA-WTSEI of the present invention is more more clear, compact than CSA-WTSEI and WTSEI.

Claims (1)

1. the orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone in a underwater sound communication system, is characterized in that comprising the steps:

The first step: initialization of population

The random antibody population that produces some, the weight vector of the respectively corresponding balanced device of each antibody wherein;

Second step: calculate the affinity value

By the antibody population of the described random generation of the first step, in conjunction with the cost function J of norm balanced device (CMA) _CMA(w), the function of definition affinity, i.e. the objective function of immune algorithm optimizing:

$J\left(w\right)\frac{1}{1+J_{\mathrm{CMA}}\left(w\right)}$

In formula, w means the balanced device weight vector;

The 3rd step: Immune Clone Selection

Regulate clone's number of each antibody according to the affinity value, clone's number of each antibody is calculated as follows:

Wherein, C means the antibody cloning number that need to be cloned, C _MAXMean given maximum clone controlling elements, f means the antibody affinity value that need to be cloned, f _MINMean the poorest antibody affinity value in antibody population, f _avgThe average affinity value that means antibody population, Mean to round downwards;

The 4th step: high frequency variation

Regulate the high frequency aberration rate of antibody according to the algebraically of affinity value and evolution, being calculated as follows of adaptive high frequency aberration rate:

$P_m=\left\{\begin{array}{c}{P}_{m\_\mathrm{MAX}}-\left(\frac{P_{m\_\mathrm{MAX}}-P_{m\_\mathrm{MIN}}}{t_{\mathrm{MAX}}}\right)t,f>f_{\mathrm{avg}}\\ P_{m\_\mathrm{MAX},}f\&le;f_{\mathrm{avg}}\end{array}\right.$

Wherein, P _m(m means Hypermutation, i.e. high frequency variation) mean to be made a variation high frequency aberration rate of antibody, P _{M_MAX}Mean given maximum high frequency aberration rate, P _{M_MIN}Mean given minimum high frequency aberration rate, t _MAXMean maximum algebraically, t means current algebraically, and f means the antibody affinity value that need to be cloned, f _avgThe average affinity value that means antibody population;

The 5th step: calculate the affinity value

Each antibody affinity value after the described high frequency variation of the 4th step is recalculated;

The 6th step: select

Regulate the renewal number in per generation according to affinity value and evolutionary generation, adaptively selected renewal is calculated as follows:

$d=\left\{\begin{array}{c}{d}_{\mathrm{MAX}}-\left(\frac{d_{\mathrm{MAX}}-d_{\mathrm{MIN}}}{t_{\mathrm{MAX}}}\right)t,f_{\mathrm{MAX}}-f_{\mathrm{MIN}}<\frac{f_{\mathrm{avg}}}{2}\\ d_{\mathrm{MAX}},f_{\mathrm{MAX}}-f_{\mathrm{MIN}}\&GreaterEqual;\frac{f_{\mathrm{avg}}}{2}\end{array}\right.$

Wherein, d means the per generation renewal number calculated, d _MAXMean given maximum renewal number, d _MINMean given minimum renewal number, f _MAXAnd f _MINBe expressed as respectively optimum in antibody population and the poorest antibody affinity value, t _MAXMean maximum algebraically, t means current algebraically, f _avgThe average affinity value that means antibody population;

The 7th step: whether judgement stops

Judged according to the evolutionary generation of antibody, when evolutionary generation is less than maximum evolutionary generation, gone to second step, repeat the second operation steps to the 6th step, until evolutionary generation is greater than maximum evolutionary generation, as reach end condition, EOP (end of program), export globally optimal solution;

The 8th step: select the optimum right vector individuality

Ask for corresponding weight vector value while making objective function optimum, and the initialization weight vector using this weight vector as the described orthogonal wavelet super-exponential iteration blind equalization based on the self-adaptation immune clone, thereby the weight vector initialization procedure completed.

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