CN103338170A - General multi-mode blind equalization method for chaotic artificial fish school optimization - Google Patents

Abstract

The invention discloses a general multi-mode blind equalization method for chaotic artificial fish school optimization. The method comprises the following steps: initializing the position vector of a group of chaotic artificial fish schools at random, taking the position vector as a decision variable of a chaotic artificial fish school optimization method, considering an input signal of an equalizer as an input signal of the chaotic artificial fish school optimization method, determining the food concentration of chaotic artificial fishes through the cost function of the general multi-mode blind equalization method, obtaining the optimal position vector of the chaotic artificial fish school by the chaotic artificial fish school optimization method, and taking the position vector as an initialized weight vector of the general multi-mode blind equalization method. When a high-order quadrature amplitude modulation signal is processed, the method has the characteristics of high convergence rate and small steady-state error, and has a certain practical value.

Description

Chaos artificial fish school optimization broad sense multimode blind balance method

Technical field

The present invention relates to a kind of underwater acoustic channel blind equalization field, especially relate to a kind of chaos artificial fish school optimization broad sense multimode blind balance method.

Background technology

Traditional adaptive equalization technique (is seen document [1] Zhao Haiquan, Zhang Jiashu. the neural FIR self adaptation amplitude Laguerre equalizer [J] of non-linear communication channel. (F collects Chinese science: information science) .2009 (39) 10:1095-1103.) need periodically send training sequence to equalizer, though do the reliability that has improved communication like this, but bandwidth resources have been wasted greatly, especially in the communication network of multicast.Do not need periodically to send the Blind Equalization Technique of training sequence, caused widely and paid close attention to.Constant mould blind balance method (Constant Modulus Algorithm by Sato and Godard invention, CMA) be that the technology of people's extensive use (is seen document [2] Sato Y.A Method of Self-recovering Equalization for Multilevel Amplitude Modulation Systems [J] .IEEE Translations on Communication.1975,23 (6): 679-682. document [3] GodardDN.Self-recovering Equalization and Carrier Tracking in Two-dimensional Data Communication Systems[J] .IEEE Translations on Communication.1980, (28) 11:1867-1875.).Constant mould blind balance method CMA is on the circle that to be balanced to a radius be R of the output signal with equalizer (wherein R is the statistics mould value that transmits) (seeing document [4] Shafayat A and Asoke K N.Blind Equalization of Square-QAM Signals:A Mul timdulus Approach [J] .IEEE Trans lations on Communication.2010 (58) 6:1674-1685.), has good portfolio effect for constant mould signal.And high-order orthogonal amplitude modulation(PAM) (Quadrature Amplitude Modulation, QAM) constellation point of signal is distributed on the circle of several different radiis, if adopt CMA to carry out equilibrium, then output signal is tending towards a certain fixedly circle, it is big to cause the equalizer weight vector to upgrade error, influence equalization performance (see document [5] Li X.L, Zhang X D.A Family of Generalized Constant Modulus Algorithm for Blind Equalization[J] .IEEE Trans.Comm.2006 (54) 11:1913-1917.).And traditional multimode blind balance method (Mul ti-modulus Algorithm, MMA), with the real part of equalizer input signal and imaginary part get respectively separately homophase and the mould value of quadrature component, utilize amplitude and phase information, can correct the phase place rotation of high-order QAM signal effectively, but when the exponent number of QAM signal was higher, traditional MMA portfolio effect was undesirable, and eye pattern is unintelligible even not to be opened.And broad sense multimode blind balance method (Generalized Multi-modulus Algorithm, GMMA) (see document [6] Xin L L and Wen J Z.Performance Analysis and Adaptive Newton Algorithms of Multi modulus Blind Equalization crieron[J] .Signal Process. document [7] Dou Gaoqi, high pretty. be suitable for the multimode blind equalization new method [J] of high-order QAM system. electronics and information are reported .2008 (30) 2:388-391.), the planisphere of high-order QAM signal is divided into several different subregions, each subregion is adjusted the mould value in the cost function by judging the input signal region in the weight vector renewal process; Revise the mould value adaptively in the equalizer weight vector is upgraded, GMMA has the better constringency performance than MMA, but convergence rate is slow, and steady-state error is bigger, still can not practical requirement.The artificial fish-swarm method (is seen document [8] Li Xiaolei, Shao Zhijiang River. a kind of based on the communal optimizing pattern of animal: fish-swarm algorithm [J]. the system engineering theory with put into practice .2002 (22) 11:32-38.) have characteristics such as fast convergence rate, ability of searching optimum are strong, but easily be absorbed in local optimum simultaneously, cause " precocity " phenomenon.Chaotic motion can not have according to the displacement rule within the specific limits and repeatedly travels through all states, has stronger local search ability.Chaos optimization method is embedded into the artificial fish-swarm method, can avoids artificial fish-swarm to be absorbed in " precocity " phenomenon effectively, make method jump out local optimum.

Summary of the invention

The present invention seeks to have invented a kind of chaos artificial fish school optimization broad sense multimode blind balance method CAFSA-GMMA in order effectively to improve the effect of balanced high-order orthogonal amplitude-modulated signal (QAM).This method is utilized the prior information of signal constellation (in digital modulation) figure, chaos artificial fish school optimization method CAFSA is incorporated in the broad sense multimode blind balance method, utilize the quick global optimizing ability of chaos artificial fish-swarm algorithm to come the weight coefficient of initialization equalizer, in equalizer weight vector iterative process, adjust the mould value in the cost function adaptively.Theory analysis and simulation result show, compare with artificial fish school optimization broad sense multimode blind balance method AFSA-GMMA with broad sense multimode blind balance method GMMA, CAFSA-GMMA of the present invention has littler steady-state error and convergence rate faster, more is applicable to balanced high-order QAM signal.

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

Chaos artificial fish school optimization broad sense multimode blind balance method of the present invention, described method is as follows:

The position vector of one group of artificial fish of chaos of random initializtion, and as the decision variable of chaos artificial fish school optimization method, with the input signal of the equalizer input signal as the chaos artificial fish school optimization method, determined the food concentration of the artificial fish of chaos by the cost function of broad sense multimode blind balance method, try to achieve the optimal location vector of chaos artificial fish-swarm by the chaos artificial fish school optimization method, and with the initialization weight vector of this position vector as broad sense multimode blind balance method.

Described chaos artificial fish school optimization broad sense multimode blind balance method, described chaos artificial fish school optimization weight vector method is as follows:

Step 1: the food concentration that defines artificial fish: with the inverse of the broad sense multimode blind balance method cost function food concentration as artificial fish;

Step 2: initialization artificial fish-swarm: the quantity of establishing artificial fish in the artificial fish-swarm is M, and M is positive integer; Produce the food concentration of position and the position of artificial fish at random;

Step 3: shoal of fish chaos initialization:

Set a threshold value, with the position vector X of the artificial fish of i bar _i=(X _I1, X _I2..., X _Iq) in q dimension position X _IqWith threshold ratio, q is positive integer; If X _IqLess than threshold value, then should keep the dimension position; Otherwise, with the q dimension position X of the artificial fish of i bar _IqCarry out the Logistic mapping, obtain the mapping position of artificial fish, this mapping position is

X _iq(n+1)=α·X _iq(n)·[1-X _iq(n)]

Wherein, X _Iq(n+1) the artificial fish position vector of expression n+1 moment i bar X _iQ dimension position; α is parameter, and the α ∈ that satisfies condition (2,4];

Step 4: the food concentration F (X that calculates the artificial fish of i bar position _i):

A position vector of depositing artificial fish is set reaches corresponding with it food concentration storeroom, this storeroom is called bulletin board; By looking for food, bunch and the position vector X of the artificial fish of i bar being upgraded in the behavior of knocking into the back _iWith food concentration F (X _i), with the food concentration maximum of artificial fish in the artificial fish-swarm and with it corresponding position vector deposit bulletin board in;

Step 5: the food concentration variances sigma of calculating artificial fish ²: the food concentration variance is defined as

${\mathrm{\σ}}^2=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{\left(\frac{F\left(X_i\right)-F_{\mathrm{avg}}}{F}\right)}^2$

In the formula, ε is very little positive number; F _AvgBe the average food concentration of current artificial fish-swarm, F is normalization factor, and its effect is restriction σ ²Size, the computing formula of F is

In the formula, M is the population scale of artificial fish; If σ ²＜ε illustrates artificial fish precocity, and it is moving to need that at this moment it is carried out the chaos perturbation, forwards step 6 to; Otherwise change step 7;

Step 6: chaotic disturbance:

With the position vector of artificial fish in [Visual, Visual] interior Chaos Search within sweep of the eye

X _i(n+1)=X _i(n)+Δ _i(n+1)*ones(1,q)

Obtain the reposition vector, forward step 7 then to; Wherein, X _i(n) expression i bar artificial fish is through the reposition vector after Chaos Search, and ones (1, the q) unit vector of expression 1 row q row; Δ _i(n+1)=-Visual+ ρ Visualp (n);

P (n) is through the Chaos Variable behind the chaos iteration; Visual is the size of field range; Δ _i(n+1) the chaotic disturbance variable of the artificial fish of expression n+1 moment i bar; ρ ∈ (2,4] be called as the Logistic parameter;

Step 7: upgrade bulletin board: food concentration in new food concentration and the bulletin board is compared; If new food concentration greater than food concentration in the bulletin board, then reaches corresponding with it reposition vector with new food concentration and replaces content in the bulletin board, this process is called the renewal bulletin board; Otherwise change step 3;

Step 8: stop upgrading bulletin board: if the bulletin board food concentration does not change, stop upgrading bulletin board, withdraw from circulation, the position vector corresponding with food concentration in the output bulletin board, this position vector is as the initialization weight vector of broad sense multimode blind balance method; Otherwise, jump procedure 3.

The present invention is merged broad sense multimode blind balance method and chaos artificial fish school optimization algorithm mutually, has invented a kind of broad sense multimode blind balance method CAFSA-GMMM based on the chaos artificial fish school optimization.Compare with the broad sense multimode blind balance method AFSA-GMMA of broad sense multimode blind balance method GMMA and artificial fish school optimization, CAFSA-GMMA of the present invention has littler steady-state error and convergence rate faster, more is applicable to balanced high-order QAM signal.

Description of drawings

Fig. 1 is broad sense multimode blind balance method schematic diagram;

Fig. 2 is 128-QAM signal constellation (in digital modulation) figure;

Fig. 3 is 256-QAM signal constellation (in digital modulation) figure;

Fig. 4 a is the mean square error curve chart of three kinds of methods;

Fig. 4 b is MSE and SNR comparative graph;

Fig. 4 c is the output planisphere of GMMA;

Fig. 4 d is the output planisphere of AFSA-GMMA;

Fig. 4 e is CAFSA-GMMA output planisphere of the present invention;

Fig. 5 a is the mean square error curve of three kinds of methods;

Fig. 5 b is MSE and SNR comparative graph;

Fig. 5 c is GMMA output planisphere;

Fig. 5 d is AFSA-GMMA output planisphere;

Fig. 5 e is CAFSA-GMMA output planisphere of the present invention.

GMMA among Fig. 4 a, Fig. 4 b, Fig. 5 a and Fig. 5 b represents broad sense multimode blind balance method, and AFSA-GMMA represents artificial fish school optimization broad sense multimode blind balance method, and CAFSA-GMMA represents chaos artificial fish school optimization broad sense multimode blind balance method.

Embodiment

Tradition multimode blind balance method

The planisphere of traditional high-order multimode blind balance method is divided into square and cross, and the cost function of square planisphere (seeing document [9] Jian Y and Jean J W.The Mul ti-modulus Equalization and Its Generalized Algorithm [J] .IEEE Journal on Selected Areas in Communications.2002 (20) 5:997-1015.) is

$J_{\mathrm{MMA}}=E[{({z_{\mathrm{Re}}}^2\left(n\right)-R_{\mathrm{MMA}}^2)}^2+{(z_{\mathrm{Im}}^2\left(n\right)-R_{\mathrm{MMA}}^2)}^2]---\left(1\right)$

$R_{\mathrm{MMA}}^2=\frac{E[a^4\left(n\right)+b^4\left(n\right)]}{E[a^2\left(n\right)+b^2\left(n\right)]}=\frac{E\left[a^4\left(n\right)\right]}{E\left[a^2\left(n\right)\right]}=\frac{E\left[b^4\left(n\right)\right]}{E\left[b^2\left(n\right)\right]}---\left(2\right)$

In the formula, E represents to peek and term hopes that n represents time series, and subscript Re, Im represent real part and imaginary part respectively, down together; R _MMABe the mould value of s emission signal s (n), a (n), b (n) represents real part and the imaginary part of independent identically distributed s emission signal s (n) respectively; z _Re(n), z _Im(n) represent real part and the imaginary part of equalizer output signal z (n) respectively; Therefore, formula (1) is expressed as with real part and imaginary part cost function sum

$J_{\mathrm{Re}}=E\left[{(z_{\mathrm{Re}}^2\left(n\right)-R_{\mathrm{MMA}}^2)}^2\right]---\left(3\right)$

$J_{\mathrm{Im}}=E\left[{(z_{\mathrm{Im}}^2\left(n\right)-R_{\mathrm{MMA}}^2)}^2\right]---\left(4\right)$

$J_{\mathrm{MMA}}=J_{\mathrm{Re}}+J_{\mathrm{Im}}=E\left[{(z_{\mathrm{Re}}^2\left(n\right)-R_{\mathrm{MMA}}^2)}^2\right]+E\left[{(z_{\mathrm{Im}}^2\left(n\right)-R_{\mathrm{MMA}}^2)}^2\right]---\left(5\right)$

By cost function J _ReAnd J _Im, get weight vector more new formula be

$f_{\mathrm{Re}}(n+1)=f_{\mathrm{Re}}\left(n\right)-\mathrm{\μ}(z_{\mathrm{Re}}^2\left(n\right)-R_{\mathrm{MMA}}^2)z_{\mathrm{Im}}\left(n\right)y\left(n\right)---\left(6\right)$

$f_{\mathrm{Im}}(n+1)=f_{\mathrm{Re}}\left(n\right)-\mathrm{\μ}(z_{\mathrm{Im}}^2\left(n\right)-R_{\mathrm{MMA}}^2)z_{\mathrm{Im}}\left(n\right)y\left(n\right)---\left(7\right)$

In the formula, f _Re(n) and f _Im(n) be respectively the real part vector sum imaginary part vector of equalizer weight vector f (n), μ is step-length, and y (n) is the input signal of equalizer.

For the cross planisphere, be example with 128-QAM, its planisphere is as shown in Figure 2.

As shown in Figure 2, the real part of signal and imaginary part all take from the QAM signal modulation point set ± 1, ± 3, ± 5, ± 7, ± 9, ± 11}, and each signal appears at modulation point ± 9, ± 11 probability less than appear at ± 1, ± 3, ± 5, ± 7 place.The cost function of square planisphere is revised, and the cost function that gets the cross planisphere is

$J_{\mathrm{Re}}=E\left[{(z_{\mathrm{Re}}^2\left(n\right)-{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003345274300021.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^2)}^2\right],\left|z_{\mathrm{Im}}\left(n\right)\right|<k---\left(8\right)$

$J_{\mathrm{Im}}=E\left[{(z_{\mathrm{Im}}^2\left(n\right)-{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HDA00003345274300021.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^2)}^2\right],\left|z_{\mathrm{Re}}\left(n\right)\right|<k---\left(9\right)$

$J_{\mathrm{Re}}=E\left[{(z_{\mathrm{Re}}^2\left(n\right)-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA00003345274300011.png,HDA00003345274300012.png"\; state="\{\{state\}\}">R</figure-callout>}}_2^2)}^2\right],\left|z_{\mathrm{Im}}\left(n\right)\right|>k---\left(10\right)$

$J_{\mathrm{Im}}=E\left[{(z_{\mathrm{Im}}^2\left(n\right)-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA00003345274300011.png,HDA00003345274300012.png"\; state="\{\{state\}\}">R</figure-callout>}}_2^2)}^2\right],\left|z_{\mathrm{Re}}\left(n\right)\right|<k---\left(11\right)$

In the formula, k is the cut off value of zone (A), (B) among Fig. 2, gets the number between 5 to 7.For mould value R ₁, only need to consider the first quartile of Fig. 2, a (n)=1,3,5,7,9,11 then, b (n)=1,3,5,7, the probability 1/24=1/6 that occurs of b (n) so.In like manner, for mould value R ₂, b (n)=1,3,5,7, a (n)=9,11, the probability 2/8=1/4 of b (n) appearance so.

Therefore, in (A) district,

$E\left[b^2\left(n\right)\right]=\frac{1}{6}(1^2+3^2+5^2+7^2+9^2{+11}^2)=46.67---\left(12\right)$

In (B) district,

$E\left[b^2\left(n\right)\right]=\frac{1}{6}(1^2+3^2+5^2+7^2)=21---\left(13\right)$

For the 128-QAM planisphere, by formula (2), (12) and (13) as can be known, R ₁≈ 9.2, R ₂≈ 6.1.

Broad sense multimode blind balance method

Fig. 1 is the system block diagram (removing in the frame of broken lines) of broad sense multimode blind balance method.

S among the figure (n) is that independent same distribution and average are zero transmitting, and c (n) is the impulse response vector of channel, and w (n) is additive white Gaussian noise, and y (n) is the input signal of equalizer and is y (n)=y _Re(n)+jy _Im(n), equalizer tap coefficient vector f (n)=[f ₀(n), f ₁(n) ..., f _N(n)], wherein, f _N(n) be N the coefficient of equalizer weight vector f (n), N is positive integer,

Be imaginary unit; Z (n) is the output complex signal of equalizer.

After the convergence of MMA stable state, the error correction function

Average go to zero, even but its variance is also non-vanishing under noise-free case, cause the excess mean square error (Mean Square Error, MSE) bigger.Have two kinds of methods control steady-state errors (see document [10] Xu Xiaodong, Dai Xuchu. be fit to the weighting multimode blind equalization algorithm [J] of high-order QAM signal. electronics and information journal .2007 (29) 6:1352-1355.): (1) reduces iteration step length μ; (2) reduce error function

Yet μ is subjected to the restriction of convergence rate and precision, can not infinitely reduce, and therefore reducing error function seems more effective.Along with the increase of signal order of modulation, error function is also increasing to the contribution of excess mean square error (MSE).

But utilize the prior information of planisphere, select suitable cost function and qam constellation figure coupling, just can further reduce mean square error (seeing document [11] T Yuan.Tsai K D.Analysis of The Multi modus Blind Equalization Algorithm in QAM Communication System.IEEE Trans.Comm.2005 (53) 4:1427-1431.).

Based on this thought, the 256-QAM planisphere is divided into several different area of space, as shown in Figure 3.To being in the input signal in different spaces zone, according to different mould values, to its equilibrium, obtained broad sense multimode blind balance method GMMA, the form of its cost function is

$J_{\mathrm{GMMA}}=E[{(z_{\mathrm{Re},l}^2\left(n\right)-R_{\mathrm{Re},l}^2)}^2+{(z_{\mathrm{Im},l}^2\left(n\right)-R_{\mathrm{Im},l}^2)}^2]---\left(14\right)$

In the formula, l=I, II, III.

Compare GMMA R with the cost function formula (3) of MMA _{Re, l}And R _{Im, l}Replaced R _MMAWherein, R _MMAIt is a constant relevant with the statistical property of information source; And R _{Re, l}And R _{Im, l}Not only the statistical property with information source is relevant, and is also relevant with the output of decision device.They are indicated respectively in regional l.In iterative process, as the real part z of output signal _{Re, l}(n) and imaginary part z _{Im, l}When (n) being in different l zones, R _{Re, l}And R _{Im, l}The adaptively modifying value, l=I, II, III;

When l=I, R _{Re, I}And R _{Im, I}Be respectively real part and the imaginary part of mould value RI among Fig. 3; When l=II, R _{Re, II}And R _{Im, II}Be respectively real part and the imaginary part of mould value RII among Fig. 3; When l=III, R _{Re, III}And R _{Im, III}Be respectively real part and the imaginary part of mould value RIII among Fig. 3.

The broad sense multimode blind balance method of chaos artificial fish school optimization

Artificial fish-swarm method (AFSA) is that a kind of global optimization method based on population intelligent search strategy (is seen document [13] Zhao Zhijing, Xu Shiyu, Zheng Shilian. based on the understanding radio decision engine [J] of binary particle swarm algorithm. Acta Physica Sinica .2009 (58) 7:5118-5125. document [14] Fang Wei, Sun Jun. quantum particle swarm is optimized Convergence Analysis and control parameter study [J]. Acta Physica Sinica .2010 (59) 6:2686-3694.).Every fish of artificial fish-swarm all has position and two features of food concentration, in searching process, the optimal value that other artificial fishes search in the historical optimal value that searches according to artificial fish and the colony, bring in constant renewal in the position of current artificial fish, select optimal value by the food concentration of judging artificial fish position.

For high-dimensional complicated optimum problem, AFSA easily goes into problems such as local extreme value and algorithm later stage optimizing efficient is low.The initialization of artificial fish-swarm has randomness, causes the artificial fish of part in the population away from optimal solution, if initial population is relatively good, then can improve the precision that optimizing efficient is conciliate.Chaos sequence has ergodic and regular characteristics, the chaos optimization algorithm utilizes this feature, utilize formula (2) that the position vector of artificial fish is mapped to Chaos Variable, produce chaos sequence by iteration, and obtain new position vector do inverse mapping, with the initial position vector of new position vector as artificial fish.

AFSA is in the search later stage, and a large amount of artificial fishes assemble at the Local Extremum place and cause algorithm " precocity " phenomenon.Therefore, bunch and the behavior of knocking into the back after utilize chaos traversal and perturbation is moving at random makes the shoal of fish break away from Local Extremum, improve the search efficiency in algorithm later stage.

The present invention utilizes chaos artificial fish-swarm method (CAFSA) to optimize the weight vector of equalizer, its principle as shown in Figure 1, determined the food concentration function of chaos artificial fish-swarm by the cost function of broad sense multimode blind balance method (GMMA), utilize chaos artificial fish-swarm method to find the solution the cost function of equalizer, seek the optimal location vector of artificial fish-swarm by chaos artificial fish-swarm method, and as the initial weight vector of broad sense multimode blind balance method, it is as follows to optimize step:

Step 1: the food concentration that defines artificial fish: with the inverse of the broad sense multimode blind balance method cost function food concentration as artificial fish;

Step 2: initialization artificial fish-swarm: the quantity of establishing artificial fish in the artificial fish-swarm is M, and M is positive integer; Produce the food concentration of position and the position of artificial fish at random;

Step 3: shoal of fish chaos initialization:

Set a threshold value, with the position vector X of the artificial fish of i bar _i=(X _I1, X _I2..., X _Iq) in q dimension position X _IqWith threshold ratio, q is positive integer; If X _IqLess than threshold value, then should keep the dimension position; Otherwise, with the q dimension position X of the artificial fish of i bar _IqCarry out the Logistic mapping, obtain the mapping position of artificial fish, this mapping position is

X _iq(n+1)=α·X _iq(n)·[1-X _iq(n)]

Wherein, X _Iq(n+1) the artificial fish position vector of expression n+1 moment i bar X _iQ dimension position; α is parameter, and the α ∈ that satisfies condition (2,4];

Step 4: the food concentration F (X that calculates the artificial fish of i bar position _i):

A position vector of depositing artificial fish is set reaches corresponding with it food concentration storeroom, this storeroom is called bulletin board; By looking for food, bunch and the position vector X of the artificial fish of i bar being upgraded in the behavior of knocking into the back _iWith food concentration F (X _i), with the food concentration maximum of artificial fish in the artificial fish-swarm and with it corresponding position vector deposit bulletin board in;

Step 5: the food concentration variances sigma of calculating artificial fish ²: the food concentration variance is defined as

${\mathrm{\&sigma;}}^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left(\frac{F\left(X_i\right)-F_{\mathrm{avg}}}{F}\right)}^2$

In the formula, ε is very little positive number; F _AvgBe the average food concentration function of current artificial fish-swarm, F is normalization factor, and its effect is restriction σ ²Size, the computing formula of F is

In the formula, M is the population scale of artificial fish; If σ ²＜ε illustrates artificial fish precocity, and it is moving to need that at this moment it is carried out the chaos perturbation, forwards step 6 to; Otherwise change step 7;

Step 6: chaotic disturbance:

With the position vector of artificial fish in [Visual, Visual] interior Chaos Search within sweep of the eye

X _i(n+1)=X _i(n)+Δ _i(n+1)*ones(1,q)

Obtain new position vector, forward step 7 then to; Wherein, X _i(n) expression i bar artificial fish is through reposition vector after Chaos Search, and ones (1, the q) unit vector of expression 1 row q row; Δ _i(n+1)=-Visual+ ρ Visualp (n);

P (n) is through the Chaos Variable behind the chaos iteration; Visual is the size of field range; Δ _i(n+1) the chaotic disturbance variable of the artificial fish of expression n+1 moment i bar; ρ ∈ (2,4] be called as the Logistic parameter;

Step 7: upgrade bulletin board: food concentration in new food concentration and the bulletin board is compared; If new food concentration greater than food concentration in the bulletin board, then reaches corresponding with it reposition vector with new food concentration and replaces content in the bulletin board, this process is called the renewal bulletin board; Otherwise change step 3;

Step 8: stop upgrading bulletin board: if the bulletin board food concentration does not change, stop upgrading bulletin board, withdraw from circulation, the position vector corresponding with food concentration in the output bulletin board, this position vector is as the initialization weight vector of broad sense multimode blind balance method; Otherwise, jump procedure 3.

Embodiment:

In order to verify the performance of CAFSA-GMMA of the present invention, be comparison other with GMMA and AFSA-GMMA, carry out emulation experiment.

[embodiment 1] adopts two footpath phase place underwater acoustic channel c=[-0.35001], transmitting is that 256-QAM, signal to noise ratio are 30dB.Equalizer power is long to be made as 8.In the l-G simulation test, GMMA adopts centre cap initialization, step-length 2 * 10 ^-6Population scale is 50, and the evolution number of times gets 20, AFSA-GMMA and the CAFSA-GMMA step-length is respectively 1.8 * 10 ^-6, 2.5 * 10 ^-6, field range 0.5.600 Monte Carlo simulation results, as shown in Figure 4.

Fig. 4 a to Fig. 4 e shows: CAFSA-GMMA convergence rate of the present invention is than fast about 12000 steps of GMMA, with the AFSA-GMMA basically identical; On steady-state error MSE, basic identical with GMMA, compare with AFSA-GMMA, reduced 3dB.And the output planisphere of CAFSA-GMMA of the present invention is more clear, compactness.

[embodiment 2] employing audio bandwidth channel (see document [16] G.Picchi and G.Prati.Blind Equalization and Carrier Recovery Using a ' Stop-and-go ' Decision Directed Algorithm[J] .IEEE Trans.Commun.1987, (35) 9:877-887.), GMMA, AFSA-GMMA and CAFSA-GMMA step-length are respectively 1.8 * 10 ^-6, 1 * 10 ^-6, other parameters are with experiment 1 unanimity.600 Monte Carlo simulation results are shown in Fig. 5 a to Fig. 5 e.

Fig. 5 shows: CAFSA-GMMA convergence rate of the present invention is than fast about 11000 steps of GMMA, with the AFSA-GMMA basically identical; On steady-state error MSE, basic identical with GMMA; Compare with AFSA-GMMA, reduced 1dB.And the output planisphere of the inventive method CAFSA-GMMA is more clear, compactness.

Above-mentioned case verification result shows, the inventive method CAFSA-GMMA has given full play to the advantage of broad sense multimode blind balance method and chaos artificial fish school optimization method, has fast convergence rate, steady-state error MSE is little, be particularly suitable for balanced high-order QAM signal, have certain practical value.

Claims (2)

1. chaos artificial fish school optimization broad sense multimode blind balance method is characterized in that described method is as follows:

The position vector of one group of artificial fish of chaos of random initializtion, and as the decision variable of chaos artificial fish school optimization method, with the input signal of the equalizer input signal as the chaos artificial fish school optimization method, determined the food concentration of the artificial fish of chaos by the cost function of broad sense multimode blind balance method, try to achieve the optimal location vector of chaos artificial fish-swarm by the chaos artificial fish school optimization method, and with the initialization weight vector of this position vector as broad sense multimode blind balance method.

2. chaos artificial fish school optimization broad sense multimode blind balance method according to claim 1 is characterized in that, described chaos artificial fish school optimization weight vector method is as follows:

Step 1: the food concentration that defines artificial fish: with the inverse of the broad sense multimode blind balance method cost function food concentration as artificial fish;

Step 2: initialization artificial fish-swarm: the quantity of establishing artificial fish in the artificial fish-swarm is M, and M is positive integer; Produce the food concentration of position and the position of artificial fish at random;

Step 3: shoal of fish chaos initialization:

Set a threshold value, with the position vector X of the artificial fish of i bar _I=(X _I1, X _I2..., X _Iq) in q dimension position X _IqWith threshold ratio, q is positive integer; If X _IqLess than threshold value, then should keep the dimension position; Otherwise, with the q dimension position X of the artificial fish of i bar _IqCarry out the Logistic mapping, obtain the mapping position of artificial fish, this mapping position is

X _iq(n+1)=α·X _iq(n)·[1-X _iq(n)]

Wherein, X _Iq(n+1) the artificial fish position vector of expression n+1 moment i bar X _iQ dimension position; α is parameter, and the α ∈ that satisfies condition (2,4];

Step 4: the food concentration F (X that calculates the artificial fish of i bar position _i): a position vector of depositing artificial fish is set reaches corresponding with it food concentration storeroom, this storeroom is called bulletin board; By looking for food, bunch and the position vector X of the artificial fish of i bar being upgraded in the behavior of knocking into the back _iWith food concentration F (X _i), with the food concentration maximum of artificial fish in the artificial fish-swarm and with it corresponding position vector deposit bulletin board in;

Step 5: the food concentration variances sigma of calculating artificial fish ²: the food concentration variance is defined as

${\mathrm{\&sigma;}}^2=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\left(\frac{F\left(X_i\right)-F_{\mathrm{avg}}}{F}\right)}^2$

In the formula, ε is very little positive number; F _AvgBe the average food concentration of current artificial fish-swarm, F is normalization factor, and its effect is restriction σ ²Size, the computing formula of F is

In the formula, M is the population scale of artificial fish; If σ ²＜ε illustrates artificial fish precocity, and it is moving to need that at this moment it is carried out the chaos perturbation, forwards step 6 to; Otherwise change step 7;

Step 6: chaotic disturbance: with the position vector of artificial fish in [Visual, Visual] interior Chaos Search within sweep of the eye

X _i(n+1)=X _i(n)+Δ _i(n+1)*ones(1,q)

Obtain the reposition vector, forward step 7 then to; Wherein, X _i(n) expression i bar artificial fish is through the reposition vector after Chaos Search, and ones (1, the q) unit vector of expression 1 row q row; Δ _i(n+1)=-Visual+ ρ Visualp (n);

P (n) is through the Chaos Variable behind the chaos iteration; Visual is the size of field range; Δ _i(n+1) the chaotic disturbance variable of the artificial fish of expression n+1 moment i bar; ρ ∈ (2,4] be called as the Logistic parameter;

Step 7: upgrade bulletin board: food concentration in new food concentration and the bulletin board is compared; If new food concentration greater than food concentration in the bulletin board, then reaches corresponding with it reposition vector with new food concentration and replaces content in the bulletin board, this process is called the renewal bulletin board; Otherwise change step 3;

Step 8: stop upgrading bulletin board: if the bulletin board food concentration does not change, stop upgrading bulletin board, withdraw from circulation, the position vector corresponding with food concentration in the output bulletin board, this position vector is as the initialization weight vector of broad sense multimode blind balance method; Otherwise, jump procedure 3.

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