CN101902417B - Orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm based on ant colony optimization - Google Patents

Abstract

The invention discloses an orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization method based on ant colony optimization. The method utilizes ant colony optimization to search the optimal weight vector as an initial weight vector value inputted by an equalizer so as to avoid local convergence of the algorithm. The method utilizes a positive feedback mechanism to increase convergence rate, utilizes the whitening action of the super-exponential iteration (SEI) method on data, utilizes orthogonal wavelet transformation to perform decorrelation on signals and fully utilizes the global convergence of ant colony optimization. Underwater acoustic channel simulation results show that compared with the orthogonal wavelet transformation super-exponential iteration constant modulus algorithm (WT-SEI-CMA), the method has higher convergence rate and smaller state error, and an equalized eye pattern is clearer and compacter. Thus, the method has certain practical valve.

Description

Orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm based on ant group optimization

Technical field

The present invention relates to a kind of orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm, relate in particular to a kind of orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm based on ant group optimization.

Background technology

Under water in the communication system, the intersymbol interference that multipath effect and finite bandwidth bring (Inter-Symbol Inter-ferences, ISI), it is the principal element that affects communication quality, need to adopt balancing technique to eliminate and (see document: Guo Yecai, Yang Chao. based on super Exponential Iterative blind equalizer design and the emulation [J] of orthogonal wavelet transformation. Journal of System Simulation, 2009,21 (20)-: 6556-6559).The blind equalization algorithm that does not need training sequence only utilizes the statistical property that receives signal itself to come equalizing signal, but its convergence rate is slow, steady-state error is also larger.Document (O Shalvi, E Weinstein.Super-Exponential Methods for Blind Deconvolution[J] .IEEE Trans.Inform.Theory, 1993, vol.39,504～519.) a kind of super index blind equalization algorithm (Super-Exponential that restrains to be close to super index speed has been proposed, SE) and iterative algorithm (Super-Exponential Iterative, SEI).Compare with the CMA algorithm, the SEI algorithm is introduced albefaction matrix Q, and this matrix plays whitening action to the input signal of equalizer, has accelerated convergence rate, but it still can not satisfy the requirement of engineering realizability.Document (Guo Yecai, Ding Xuejie, Guo Fudong, etc. based on the cascade adaptive blind equalization algorithm [J] of normaliztion constant modulo n arithmetic. Journal of System Simulation, 2008,20 (17): 4647-4650; Han Yingge, Guo Yecai, Li Baokun etc. introduce the orthogonal wavelet transformation blind equalization algorithm [J] of momentum term. Journal of System Simulation; 2008,20 (6): 1559-1562; Cooklev T An Efficient Architecture for Orthogonal Wavelet Transforms[J] .IEEESignal Processing Letters (S1070-9980), 2006,13 (2): 77～79.) show: the input signal to equalizer carries out wavelet transformation, and make energy normalized and process, can reduce the correlation of signal and noise, thereby convergence speedup speed effectively, but remaining by gradient direction, the small wave blind equalization algorithm seeks optimal weight vector, it is relatively more responsive to the initialization of weight vector, improperly initialization meeting makes algorithmic statement to local minimum, even disperses.And ant group algorithm (ACO) is on the Research foundation of true ant group's the collective behavior to occurring in nature, at first put forward by Italian scholar Dorigo M etc., it is the parallel intelligent evolution algorithm of a kind of heuristic bionical class based on population, have intelligent search, global optimization, robustness, positive feedback, Distributed Calculation, and being easy to the characteristics such as other algorithms combine, the situation of the harshness such as it is discontinuous to function, non-differentiability, Local Extremum are intensive also has good search capability.Evolutionary process by the colony that is comprised of candidate solution is sought optimal solution; By positive feedback mechanism, accelerate the searching process of algorithm, fast searching greatly reduces so that be absorbed in the possibility of local convergence to globally optimal solution.

Summary of the invention

The present invention seeks to slow for traditional constant mould blind balance method (CMA) convergence rate, steady-state error is large and the shortcoming of local convergence, this paper is analyzing ant group optimization, super Exponential Iterative (Super-Exponential Iterative, SEI) on the basis of method and orthogonal wavelet transformation theory, a kind of orthogonal wavelet super-exponential iteration blind equalization based on ant group optimization (ACO-WT-SEI) has been proposed.The method takes full advantage of the global random searching of ant group algorithm and the characteristics of positive feedback mechanism, and the weight vector of equalizer is carried out initialization, utilizes the SEI method to the whitening action of data, and adopts orthogonal wavelet transformation to reduce the autocorrelation of signal.

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

The present invention is based on the orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm of ant group optimization, comprise the steps:

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

B.) adopt interchannel noise n (k) and the described channel output vector of step a x (k) to obtain the input signal of equalizer: y (k)=x (k)+n (k);

C.) error signal e (k) is introduced albefaction matrix Q by the SEI algorithm, adopt albefaction matrix Q to input signal y (k) albefaction of equalizer;

D.) with step c) the input signal y (k) after the described albefaction obtains the output vector of orthogonal wavelet through orthogonal wavelet transformation: R (k)=y (k) V, wherein V is the orthogonal wavelet transformation matrix;

Also comprise the steps:

E.) produce at random initial population W=[W ₁, W ₂..., W _M], the individual W of i ant wherein _iI weight vector of corresponding equalizer, 0＜i≤M wherein, i and M are natural number, with its initialized location as ant;

F.) with the inverse of the cost function of the equalizer target function as the ant group algorithm optimizing:

$f\left(W_i\right)=\frac{1}{J\left(W_i\right)}$

In the formula, J (W _i)=J _CMAIt is the cost function of equalizer;

G.) every ant is adopted step f.) described one step of target function optimizing or finish optimizing to all M weight vector after, the residual risk element is upgraded processing:

f _ij(t+1)＝(1-ρ)f _ij(t)+Δf _ij，

In the formula,

Represent that k ant stay the pheromones on the path between i weight vector and j the weight vector in this circulation, ρ is the pheromones volatility coefficient, span be ρ ∈ [0,1), Δ f _IjThe expression ant pheromones that the path between i weight vector and j weight vector stays in this circulation, f _Ij(t) upgrade t for pheromones and go on foot corresponding pheromones;

H.) ask for corresponding weight vector value when making target function optimum, and the initialization weight vector of this weight vector as equalizer.

The present invention has announced a kind of orthogonal wavelet super-exponential iteration blind equalization of ant group optimization, and the method utilizes ant group algorithm to seek optimum weight vector as the initial weight vector value of equalizer input, thereby avoids algorithm the situation of local convergence to occur.The method has the positive feedback mechanism of convergence speedup speed, utilizes super Exponential Iterative (SEI) method to the whitening action of data, utilizes orthogonal wavelet transformation that signal is carried out decorrelation, and takes full advantage of the global convergence of ant group algorithm.The underwater acoustic channel simulation result shows that (WT-SEI-CMA) compares with orthogonal wavelet super-exponential iteration blind equalization, and the method has better convergence rate and steady-state error, and the eye pattern after the equilibrium is more clear, compact.Thereby the method has certain practical value.

Description of drawings

Fig. 1: based on the SEI Method And Principle block diagram of orthogonal wavelet transformation;

Fig. 2: the orthogonal wavelet transformation blind equalization schematic diagram of ant group optimization;

Fig. 3: (a) mean square error curve, (b) output signal of SEI, (c) WT-SEI output, (d) ACA-WT-SEI output;

Fig. 4: (a) mean square error curve, (b) output signal of SEI, (c) WT-SEI output, (d) ACA-WT-SEI output.

Embodiment

The super Exponential Iterative of orthogonal wavelet is incorporated into blind balance method (CMA), obtains orthogonal wavelet super-exponential iteration blind equalization (WT-SEI).Its schematic diagram, as shown in Figure 1.The method is introduced albefaction matrix Q by the SEI algorithm, this matrix plays whitening action to the input signal of equalizer, the recycling small echo carries out orthogonal wavelet transformation to signal, and make energy normalized and process, afterwards in transform domain, utilize the signal behind the wavelet transformation that the equalizer weight coefficient is adjusted, reduced the autocorrelation of these signals, accelerated convergence rate.

Among Fig. 1, a (k) expression transmitter transmits, and is that variance is 1 white i. i. d. random sequence; C (k) is the channel impulse response vector; N (k) is interchannel noise, generally is assumed to be Gaussian sequence, and independent with signal statistics.Y (k) is the list entries of equalizer, and y (k)=[y (k), y (k-1) ..., y (k-L+1)] ^TW (k) is the equalizer weight vector; ψ () is the nonlinear function that produces error e (k); Z (k) is the output sequence of equalizer.Equalizer input signal is

y(k)＝x(k)+n(k)＝c ^T(k)a(k)+n(k) (1)

If V is the orthogonal wavelet transformation matrix,

In the formula,

For wavelet conversion coefficient,

Be the change of scale coefficient,

With Be the weight coefficient of equalizer, J is out to out; k _J=N/2 ^j-1 (j=1,2 ..., J) be the maximal translation of wavelet function under the yardstick j.Then

R(k)＝y(k)V (2)

z(k)＝W ^H(k)R(k) (3)

H is conjugate transpose in the formula, and at this moment, the calculating iterative formula of Q matrix is

$Q(k+1)=\frac{1}{1-{\mathrm{\μ}}_m}[Q\left(k\right)-\frac{{\mathrm{\μ}}_{m}Q\left(k\right)R^{*}\left(k\right)R^T\left(k\right)Q\left(k\right)}{1-{\mathrm{\μ}}_m+{\mathrm{\μ}}_m{R}^T\left(k\right)Q\left(k\right)R^{*}\left(k\right)}]---\left(4\right)$

In the formula, μ _mThe iteration step length of expression Q matrix computations.The iterative formula of weight vector is

$W(k+1)=W\left(k\right)+\mathrm{\μ}{\hat{R}}^{-1}\left(k\right)Q\left(k\right)e\left(k\right)R\left(k\right)z\left(k\right)---\left(5\right)$

In the formula, e (k)=y (k) (| y (k) | ²-R) be error function, R=E[|a (k) | ⁴]/E[|a (k) | ²] be the mould of transmitting sequence a (k), μ is step-length.

Represent respectively wavelet conversion coefficient r _{J, n}(k), change of scale coefficient s _{J, n}(k) average power is estimated, can be obtained by the following formula recursion

${\mathrm{\σ}}_{J,n}^2(k+1)={\mathrm{\β\σ}}_{J,n}^2\left(k\right)+(1-\mathrm{\β}){\left|r_{j,n}\left(k\right)\right|}^2---\left(6\right)$

${\mathrm{\σ}}_{J+1,n}^2(k+1)={\mathrm{\β\σ}}_{J,n}^2\left(k\right)+(1-\mathrm{\β}){\left|s_{j,n}\left(k\right)\right|}^2---\left(7\right)$

In the formula, β is smoothing factor, r _{J, n}(k) be wavelet conversion coefficient, the s of n signal of wavelet space j layer decomposition _{J, n}The change of scale coefficient of n signal when (k) maximum decomposition level is counted j in the expression metric space.Formula (2)～(7) have just consisted of the super-exponential iteration (SEI) blind equalization algorithm (Super-Exponential Iterative Based onOrthogonal Wavelet Transform, WT-SEI) based on orthogonal wavelet transformation.

The super Exponential Iterative blind equalization algorithm of the orthogonal wavelet of ant group optimization of the present invention is as follows:

Traditional orthogonal wavelet super-exponential iteration blind equalization (WT-SEI-CMA) is to utilize super Exponential Iterative algorithm to calculate the Q matrix when the each iteration of weight vector, come the Optimal Step Size factor by this matrix, input signal to equalizer plays whitening action, and it is carried out orthogonal wavelet transformation, the signal autocorrelation approximate matrix become band distribution (see document: Guo Yecai, HanYingge.Orthogonal Wavelet Transform Based Sign Decision Dual-mode Blind EqualizationAlgorithm[C] // 2,008 9 ^ThInternational Conference on Signal ProcessingProceedings, Beijing, China.USA:The Institute of Electrical and Electronics EngineersInc.2009:80-83.Han Yingge, Guo Yecai, Wu Zaolin, etc. based on the design of multimode blind equalizer and the algorithm simulating research [J] of orthogonal wavelet. Chinese journal of scientific instrument, 2008,29 (7): 1441-1445), its autocorrelation descends.Traditional blind equalization algorithm is constructed first a cost function, and utilize this cost function that the equalizer weight vector is asked gradient, thereby determine the iterative equation of equaliser weights, but this method essence is a kind of the Gradient Descent search method of considering regional area, lack ability of searching optimum, easily converge to local pole and go to the lavatory.

The present invention adopts ant group algorithm to seek optimal solution, overcomes the defective of WT-SEI-CMA.With the ant group optimization blind balance method very little one section data are carried out equilibrium first, utilize positive feedback mechanism and the pheromones regeneration characteristics of ant group algorithm, weight vector when searching out the target function optimum, and with the initialization weight vector of this group weight vector as the orthogonal wavelet blind balance method.

As shown in Figure 2.The present invention produces one group of weight vector at random, every ant successively correspondence organized weight vector, the decision variable of this weight vector as ant group algorithm, the input of equalizer input signal as ant group algorithm, and in conjunction with the cost function of CMA algorithm, determine the evolution target function of ant group algorithm, utilize ant group algorithm to find the solution the cost function of equalizer, the equaliser weights that search is best.Like this, ant group algorithm is incorporated in the orthogonal wavelet super-exponential iteration blind equalization, is called the orthogonal wavelet super-exponential iteration blind equalization (ACO-WT-SEI) based on ant group optimization.In this method, utilize the characteristics of ant group algorithm search of overall importance and positive feedback mechanism, seek best equaliser weights, and unlike the CMA algorithm, equaliser weights is adjusted in the guidance that relies on gradient information.

The ant group algorithm optimizing process is as follows:

No matter be constant mould blind balance method or the cost function of orthogonal wavelet blind balance method, be:

$J_{\mathrm{CMA}}={({\left|z\left(k\right)\right|}^2-R_{\mathrm{CM}}^2)}^2---\left(8\right)$

In the formula, z (k) be equalizer output,

It is the mould value of equalizer.Existing convolution (8) formula illustrates optimizing process.The generation of 1 initialization weight vector

Ant group algorithm is that each ant optimizing to colony operates, want the initialization ant to all rise before the optimizing operation and begin to search for the primary data of point, i.e. the corresponding weight vector of every ant of initialization determines that its initial value is [1,1], and produce the weight vector of some with random device.A weight vector of the individual corresponding equalizer of each ant wherein, the number of weight vector is the scale of ant.If the initial population W=[W that produces at random ₁, W ₂..., W _M], the individual W of one of them ant _i(weight vector of corresponding equalizer of 0＜i≤M) is with its initialized location as ant.

The generation of 2 target functions

The purpose of blind balance method is to make the cost function iteration to minimum value, obtain best equaliser weights, and the purpose of ant group algorithm optimizing is corresponding individuality when obtaining the target function value maximum, for this reason, with the inverse of the cost function of the equalizer target function as the ant group algorithm optimizing, then have

$f\left(W_i\right)=\frac{1}{J\left(W_i\right)},i=\mathrm{1,2},\·\·\·,M---\left(9\right)$

In the formula, J (W _i)=J _CMAThe cost function of equalizer, W _iThe equalizer weight vector individuality that ant group algorithm produces, with its initial information element as the ant group algorithm optimizing.

The renewal of 3 pheromones

The each time optimizing of ant group algorithm all will receive certain input signal, these signals are provided by input signal, it enters at first to decide according to transition probability behind the ant group algorithm and carries out local optimal searching or global optimizing, and reposition is limited in the feasible zone (sees document: Zhou Jianxin, Yang Weidong, Li Qing. find the solution improvement ant group algorithm and the emulation [J] of continuous function optimization problem. Journal of System Simulation, 2009,21 (6): 1685-1688).Before ant whenever moves to a reposition, the position that it all can be newer, can make pheromones is to strengthen or weaken.Just move to reposition if strengthen, simultaneously to the pheromones of environment release new position, otherwise just continue to sound out other position (see document: Wang Lei, Wu Qidi. the application [J] of ant group algorithm in continuous space optimizing solution. control and decision-making, 2003,18 (1): 45-48).For avoiding the residual risk element to flood heuristic information, in one step of every ant optimizing or after finishing optimizing to all M weight vector, the residual risk element is upgraded processing, be shown below:

f _ij(t+1)＝(1-ρ)f _ij(t)+Δf _ij， (10)

In the formula,

Represent that k ant stay pheromones on the ij of path in this circulation, ρ is the pheromones volatility coefficient, span be ρ ∈ [0,1), Δ f _IjThe expression ant pheromones that the path between i weight vector and j weight vector stays in this circulation, f _Ij(t) upgrade t for pheromones and go on foot corresponding pheromones;

The selection of 4 optimum right vectors

Transition probability by ant group algorithm carries out local optimal searching and global optimizing, and optimizing result is limited in the feasible zone, keeping optimization, find the solution optimum weight vector through the renewal of pheromones again, with the weight vector individual choice of target function maximum in per generation out, consider that real-time and the blind equalization algorithm of algorithm when extracting optimized individual will satisfy the ZF condition, ask at last corresponding weight vector value when making target function optimum, and the initialization weight vector of this weight vector as ACO-WT-SEI.

The underwater acoustic channel emulation of 1 liang of footpath of embodiment

The unit impulse response of two footpath underwater acoustic channels is c=[-0.35,0,0,1], transmitting is 8PSK, equalizer power is long to be 16, and signal to noise ratio 25dB, in the SEI algorithm, the 4th tap coefficient is set to 1, and all the other are 0, step size mu _SEI=0.00015, μ _m=0.02; In the WT-SEI algorithm, the 11st tap coefficient is set to 1, and all the other are 0, step size mu _WT-SEI=0.01, μ _m=0.002; The step size mu of ACA-WT-SEI _ACA-WT-SEI=0.004, μ _m=0.004.Input signal to each channel adopts the DB4 orthogonal wavelet to decompose, and decomposition level is 2 layers, and the power initial value is set to 4, forgetting factor β=0.9999; 500 Meng Te Kano simulation results, as shown in Figure 3.

Fig. 3 (a) shows: on convergence rate, ACA-WT-SEI is than about fast 8000 steps of SEI, than about fast 4000 steps of WT-SEI.On steady-state error, ACA-WT-SEI compares with SEI, has reduced nearly 7dB, compares with WT-SEI, has reduced nearly 6dB.Fig. 3 (b, c, d) shows: the output planisphere of ACA-WT-SEI is more more clear, compact than SEIA and WT-SEI.

Embodiment 2 mixed-phase channels

The mixed-phase channel is c=[0.3132-0.1040 0.8908 0.3134], transmitting is 16QAM, equalizer power is long to be 16, signal to noise ratio 25dB, in the SEI algorithm, the 3rd tap coefficient is set to 1, and all the other are 0, step size mu _SEI=0.00005, μ _m=0.02; In the WT-SEI algorithm, the 4th tap coefficient is set to 1, and all the other are 0, step size mu _WT-SEI=0.0005, μ _m=0.02; The step size mu of ACA-WT-SEI _ACA-WT-SEI=0.0006, μ _m=0.0006.Input signal to each channel adopts the DB4 orthogonal wavelet to decompose, and decomposition level is 2 layers, and the power initial value is set to 4, forgetting factor β=0.9999; 500 Meng Te Kano simulation results, as shown in Figure 4.

Fig. 4 (a) shows: on convergence rate, ACA-WT-SEI than SEI and WT-SEI approximately fast 4000 steps.On steady-state error, ACA-WT-SEI compares with SEI, has reduced nearly 2.2dB, compares with WT-SEI, has reduced nearly 1.8dB.Fig. 4 (b, c, d) shows: the output planisphere of ACA-WT-SEI is more more clear, compact than SEI and WT-SEI.

Claims (1)

1. the orthogonal wavelet transformation super-exponential iteration (SEI) blind equalization algorithm based on ant group optimization comprises the steps:

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

B.) adopt interchannel noise n (k) and the described channel output vector of step a x (k) to obtain the input signal of equalizer: y (k)=x (k)+n (k);

C.) error signal e (k) is introduced albefaction matrix Q by super Exponential Iterative SEI method, adopt albefaction matrix Q to input signal y (k) albefaction of equalizer;

D.) with step c) the input signal y (k) after the described albefaction obtains the output vector of orthogonal wavelet through orthogonal wavelet transformation: R (k)=y (k) V, wherein V is the orthogonal wavelet transformation matrix;

It is characterized in that, also comprise the steps:

E.) produce at random initial population W=[W ₁, W ₂..., W _M], i weight vector of i ant corresponding equalizer of individual Wi wherein, 0＜i≤M wherein, i and M are natural number, with its initialized location as ant;

F.) with the inverse of the cost function of the equalizer target function as the ant group algorithm optimizing:

$f\left(W_i\right)=\frac{1}{J\left(W_i\right)}$

In the formula, J (W _i)=J _CMAThe cost function of equalizer, wherein

In the formula, z (k) is the output of equalizer, It is the mould value of equalizer;

G.) every ant is adopted step f.) described one step of target function optimizing or finish optimizing to all M weight vector after, the residual risk element is upgraded processing:

f _ij(t+1)＝(1-ρ)f _ij(t)+Δf _ij，

In the formula,

Represent that k ant stay the pheromones on the path between i weight vector and j the weight vector in this circulation; Δ f _IjThe expression ant pheromones that the path between i weight vector and j weight vector stays in this circulation, ρ is the pheromones volatility coefficient, span be ρ ∈ [0,1), f _Ij(t) upgrade t for pheromones and go on foot corresponding pheromones;

H.) ask for corresponding weight vector value when making target function optimum, and the initialization weight vector W (k) of this weight vector as equalizer, obtain equalizer output signal z (k)=W ^H(k) R (k), wherein H represents transpose conjugate.

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