CN101902417A - 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, intersymbol interference (the Inter-Symbol Inter-ferences that multipath effect and finite bandwidth are brought, ISI), it is the principal element that influences communication quality, need to adopt balancing technique to eliminate and (see document: Guo Yecai, Yang Chao. based on the super index iteration blind equalizer design and the emulation [J] of orthogonal wavelet transformation. the system emulation journal, 2009,21 (20)-: 6556-6559).The blind equalization algorithm that does not need training sequence only utilizes the statistical property of received signal itself to come equalizing signal, but its convergence rate is slow, steady-state error is also bigger.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 with intimate super index speed convergence 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. system emulation journal, 2008,20 (17): 4647-4650; Han Yingge, Guo Yecai, Li Baokun etc. introduce the orthogonal wavelet transformation blind equalization algorithm [J] of momentum term. the system emulation journal; 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 handle, can reduce the correlation of signal and noise, thereby accelerate convergence rate 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, initialization meeting improperly makes algorithmic statement to local minimum, even disperses.And ant group algorithm (ACO) is on the research basis of the collective behavior of the true ant group 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 characteristics such as other algorithms combine, the situation of harshness such as it is discontinuous to function, non-differentiability, Local Extremum are intensive also has good search capability.Seek optimal solution by the population evolution process of forming by candidate solution; By positive feedback mechanism, accelerate the searching process of algorithm, search out globally optimal solution fast, make the possibility that is absorbed in local convergence significantly reduce.

Summary of the invention

The present invention seeks to slow at traditional constant mould blind balance method (CMA) convergence rate, steady-state error is big and the shortcoming of local convergence, this paper is analyzing ant group optimization, super index iteration (Super-Exponential Iterative, SEI) on the basis of method and orthogonal wavelet transformation theory, a kind of orthogonal wavelet super-exponential iteration (SEI) blind equalization algorithm (ACO-WT-SEI) based on ant group optimization has been proposed.This method has made full use 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 whitening action of SEI method to 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 a time series, down 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 input signal y (k) albefaction of albefaction matrix Q 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 initial population W=[W at random 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 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 pheromones that the expression ant stays on the path between i weight vector and j the weight vector in this circulation, f _Ij(t) upgrade t for pheromones and go on foot pairing pheromones;

H.) ask for pairing 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 (SEI) blind equalization algorithm of ant group optimization, and this method utilizes ant group algorithm to seek the initial weight vector value of optimum weight vector as the equalizer input, thereby avoids algorithm the situation of local convergence to occur.This method has the positive feedback mechanism of accelerating convergence rate, utilizes the whitening action of super index iteration (SEI) method to data, utilizes orthogonal wavelet transformation that signal is carried out decorrelation, and has made full use of the global convergence of ant group algorithm.The underwater acoustic channel simulation result shows that (WT-SEI-CMA) compares with the orthogonal wavelet super-exponential iteration (SEI) blind equalization algorithm, and this method has better convergence rate and steady-state error, and the eye pattern after the equilibrium is more clear, compact.Thereby this method has certain practical value.

Description of drawings

Fig. 1: based on the SEI method theory 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 index iteration of orthogonal wavelet is incorporated into blind balance method (CMA), obtains orthogonal wavelet super-exponential iteration (SEI) blind equalization algorithm (WT-SEI).Its schematic diagram, as shown in Figure 1.This method is introduced albefaction matrix Q by the SEI algorithm, this matrix plays whitening action to the input signal of equalizer, utilize small echo that signal is carried out orthogonal wavelet transformation again, and make energy normalized and handle, 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 independent same distribution sequence; C (k) is the channel impulse response vector; N (k) is an interchannel noise, generally is assumed to be the white Gaussian noise 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 an 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 a 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 a 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 a 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 is decomposed number of plies j in the expression metric space.Formula (2)～(7) just constituted super-exponential iteration (SEI) blind equalization algorithm based on orthogonal wavelet transformation (Super-Exponential Iterative Based onOrthogonal Wavelet Transform, WT-SEI).

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

Traditional orthogonal wavelet super-exponential iteration (SEI) blind equalization algorithm (WT-SEI-CMA) is to utilize super index iterative algorithm to calculate the Q matrix when the each iteration of weight vector, optimize step 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 cost function of structure earlier, 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 decline 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.Earlier very little one section data are carried out equilibrium with the ant group optimization blind balance method, utilize more new feature of the positive feedback mechanism of ant group algorithm and pheromones, 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 correspondence successively 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 (SEI) blind equalization algorithm, is called orthogonal wavelet super-exponential iteration (SEI) blind equalization algorithm (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 the 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 of colony is operated, want the initialization ant to all rise before the optimizing operation and begin to search for the primary data of point, i.e. the pairing 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 of Chan Shenging 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 a pairing individuality when obtaining the target function value maximum, for this reason, with the inverse of the cost function of equalizer target function, then have as the ant group algorithm optimizing

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

In the formula, J (W _i)=J _CMABe the cost function of equalizer, W _iBe the 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 optimizing each time 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 the improvement ant group algorithm and the emulation [J] of continuous function optimization problem. system emulation journal, 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 problem is separated. 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, the residual risk element is upgraded processing to all M weight vector, 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 pheromones that the expression ant stays on the path between i weight vector and j the weight vector in this circulation, f _Ij(t) upgrade t for pheromones and go on foot pairing pheromones;

The selection of 4 optimum right vectors

Transition probability by ant group algorithm carries out local optimal searching and global optimizing, and the optimizing result is limited in the feasible zone, keep optimal solution, find the solution optimum weight vector through the renewal of pheromones again, the weight vector individual choice of target function maximum in per generation is come out, consider that real-time and the blind equalization algorithm of algorithm when extracting optimized individual will satisfy the ZF condition, ask for pairing weight vector value when making target function optimum at last, 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, 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 decomposing 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 decomposing 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 a time series, down 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 method, adopt input signal y (k) albefaction of albefaction matrix Q 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 initial population W=[W at random 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 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 pheromones that the expression ant stays on the path between i weight vector and j the weight vector in this circulation, f _Ij(t) upgrade t for pheromones and go on foot pairing pheromones;

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

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