CN101478509A - Orthogonal wavelet transform and time diversity technique fused blind equalizing method - Google Patents

Abstract

The invention discloses a blind equalization method with the integration of orthogonal wavelet transformation and time diversity technique. Integrated with time diversity technique, wavelet transformation technique, phase-lock ring technique and decision-directed (DD) algorithm, the blind equalization method can reduce the influences of multipath effect by using time diversity, can overcome the disadvantages of asymmetry of constant modulus error function by using a hyperbolic tangent error function, can lower the self-correlativity of input signals of a blind equalizer by using orthogonal wavelet transformation to improve the convergence speed, can reduce stable error by using DD algorithm, and can correct phase rotation by using digital phase-lock ring technique. The method has the advantages of high convergence speed and less mean square error, and can effectively suppress phase rotation.

Description

The blind balance method that orthogonal wavelet transformation and time diversity technique merge mutually

Technical field

The present invention relates to a kind of time diversity blind balance method, relate in particular to the blind balance method that a kind of orthogonal wavelet transformation and time diversity technique merge mutually.

Background technology

In underwater sound communication, because the existence of multipath fading and channel distortion, (Inter-Symbol Interference ISI), has reduced the rate of information throughput and reliability can to produce serious intersymbol interference at receiving terminal.Blind Equalization Technique is more suitable for the underwater acoustic channel of limited bandwidth owing to do not need training sequence to save bandwidth.Yet, the influence that the not fine solution channel multi-path decline of traditional Blind Equalization Technique is brought, diversity technique is one of effective way that overcomes multipath fading, therefore diversity technique is applied to will improve communication quality greatly in the blind equalization.Diversity technique commonly used mainly comprises space diversity, time diversity and frequency diversity etc.Wherein time diversity is meant signal to be sent is repeated to send in interval (Transmission Time Interval is more than or equal to coherence time) at regular intervals, forms diversity at receiving terminal, compares the number of having saved reception antenna with space diversity.

(Constant Modulus Algorithm CMA) because the asymmetry of error function curve, makes that its convergence rate is slow, steady-state error is big to the tradition constant modulus algorithm.Document [1] (Guo Yecai, Zhang Yanping. the double mode constant mould blind equalization algorithm [J] of employing judgement circle judgement. data acquisition and processing 2007,22 (3): 278-281) utilize odd symmetric tanh error function, the mean square error of blind equalization algorithm is reduced, but convergence rate is not accelerated; Document [2] (Mahmoud Hadef, Stephan Weiss.Concurrent Constant ModulusAlgorithm and Decision Directed Scheme for Synchronous DS-CDMAEqualization[J] .IEEE Statistical signal processing2005, vol.issue (17-20): 203-205) show, decision-directed (Decision Directed, DD) algorithm, can accelerate convergence rate and can reduce steady-state error again, but can not reduce the autocorrelation of input signal; Document [3] (Han Yingge, Guo Yecai, Wu Zaolin etc. based on the design of multimode blind equalizer and the algorithm simulating research [J] of orthogonal wavelet transformation. Chinese journal of scientific instrument, 2008,29 (7): 1441-1445) show, after the equalizer input carries out orthogonal wavelet transformation to input signal, can reduce the autocorrelation of signal, thereby improve convergence rate effectively.These several algorithms all can not be corrected the phase place rotation that causes because of Doppler frequency shift; Document [4] (Cooklev T.An efficientarchitecture for orthogonal wavelet transforms[J] .IEEE Signal Processing Letters (S1070-9980), 2006,13 (2): 77-79) show, in blind equalization algorithm, introduce digital phase-locked loop and corrected the phase place rotation preferably, realize that effectively carrier wave recovers.But convergence rate is slow, mean square error is big.

Summary of the invention

The technical problem to be solved in the present invention is to propose the blind balance method that a kind of orthogonal wavelet transformation and time diversity merge mutually at the defective that prior art exists.

The blind balance method that orthogonal wavelet transformation of the present invention and time diversity technique merge mutually, it is characterized in that the channel branch road that comprises that the D weight structure is identical, through time interval Tc second branch road receive a that transmits (n), through two time interval 2Tc the 3rd branch roads receive a that transmits (n), and the like receive a that transmits (n) through D-1 the time interval (D-1) Tc to the D branch road, D is a positive integer, and wherein the first branch road equalization methods comprises the steps:

1.) a (n) that will transmit obtains the first channel output vector x through the first impulse response channel c (n) ₁(n), wherein n is a time series, down together;

2.) adopt the first interchannel noise w ₁(n) and the described first channel output vector x of step 1 ₁(n) obtain the input vector of first equalizer: y ₁(n)=x ₁(n)+w ₁(n);

3.) with the input vector y of described first equalizer of step 2 ₁(n) obtain the output vector of the first orthogonal wavelet transformation device WT through first orthogonal wavelet transformation: R ₁(n)=Qy ₁(n), wherein Q is the orthogonal wavelet transformation matrix;

4.) by time diversity blind equalizer weight vector f based on the tanh error function _(HCMA)(n), decision-directed equalizer weight vector f _(DD)(n) and digital phase-locked loop obtain first via equalizer weight vector: $f_1\left(n\right)=f_{1\left(\mathrm{HCMA}\right)}\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)}+f_{1\left(\mathrm{DD}\right)}\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)},$ Wherein e is the nature truth of a matter, $i=\sqrt{-1}$ Be imaginary unit,

Be estimated value to the Chang Xiangwei rotation,

Be phase place rotation complex signal; The 1st branch of subscript 1 expression.

5.) the output vector R of the described first orthogonal wavelet transformation device WT of employing step 3 ₁(n) and the described first via equalizer of step 4 weight vector f ₁(n) obtain the output sequence of first via equalizer: z ₁(n)=f ₁(n) R ₁(n);

The output sequence that adopts D to weigh the equalizer of channel branch road obtains output signal and is: $z\left(n\right)=\underset{l=0}{\overset{D}{\mathrm{\Σ}}}{p}_l{z}_l\left(n\right),$ Z wherein _l(n) be the output sequence of l equalizer; p _lBe the weight coefficient of the output signal of l branch road equalizer, owing to adopt the equal gain combining method, so p _l=1.

Step 4 is described based on tanh error function time diversity blind equalizer weight vector f _{1 (HCMA)}(n) and decision-directed blind equalizer weight vector f _{1 (DD)}Asking for (n) comprises the steps:

6.) adopt phase place rotation complex signal

Obtain the decision device input signal with the output sequence z (n) of the described equalizer of step 5: $g\left(n\right)=z\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)};$

7.) A200910028459D0006085526QIETU.GIF is exported in the judgement that the described decision device input signal of step 6 g (n) is obtained the output sequence z (n) of equalizer through judgment device;

8.) the judgement output of the output sequence z (n) of the output sequence z (n) of the described equalizer of employing step 5 and the described equalizer of step 7

Obtain the judgement output of the output sequence z (n) of equalizer And the phase difference estimation value between the decision device input signal g (n):

$\widehat{\mathrm{\ϵ}}\left(n\right)={\sin }^{-1}\left\{\frac{\mathrm{Im}\left[\hat{a}\left(n\right)\hat{z}\left(n\right)\right]}{\left|\hat{a}\left(n\right)\right|\left|\hat{z}\left(n\right)\right|}\right\}\≈\mathrm{Im}\left[\hat{a}\left(n\right)\hat{z}\left(n\right)\right],$ Wherein

Estimated value for the output sequence z (n) of equalizer;

9.) adopt the judgement of the described equalizer output sequence z of step 8 (n) to export

And the phase difference estimation value between the decision device input signal g (n) Obtain estimated value to the Chang Xiangwei rotation $\widehat{\mathrm{\θ}}(n+1)=\widehat{\mathrm{\θ}}\left(n\right)+\mathrm{\η}\widehat{\mathrm{\ϵ}}\left(n\right),$ Wherein η is the iteration step length of phase-locked loop, and n+1 is the back moment of current time sequence n, down together;

10.) the judgement output of the output sequence z (n) of output sequence z (n), the decision device input signal g (n) of the described equalizer of employing, equalizer

With phase place rotation complex signal

Obtain the time diversity blind equalizer weight vector iterative formula of the 1st roadbed in the tanh error function:

$f_{1\left(\mathrm{HCMA}\right)}(n+1)=f_{1\left(\mathrm{HCMA}\right)}\left(n\right)-{\mathrm{\μ}}_{1\left(\mathrm{HCMA}\right)}{\hat{R}}_1^{-1}\left(n\right)\frac{\tanh \left(|g\left(n\right)-R|\right)}{{\cosh }^2(\left|g\left(n\right)\right|-R)}{R}_1^{*}\left(n\right)\mathrm{sign}\left[g\left(n\right)\right]e^{i\widehat{\mathrm{\θ}}\left(n\right)},$

The 1 tunnel decision-directed blind equalizer weight vector iterative formula:

$f_{1\left(\mathrm{DD}\right)}(n+1)=f_{1\left(\mathrm{DD}\right)}\left(n\right)+{\mathrm{\μ}}_{1\left(\mathrm{DD}\right)}{\hat{R}}_1^{-1}\left(n\right)\mathrm{\δ}[\hat{\tilde{a}}\left(n\right)-\hat{a}\left(n\right)]{[\hat{a}\left(n\right)-g\left(n\right)]}^{*}{R}_1^{*}\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)},$

μ wherein _{1 (HCMA)}Be the iteration step length of the first via based on tanh error function time diversity blind equalizer weight vector, μ _{1 (DD)}Be the iteration step length of the decision-directed blind equalizer weight vector of the first via,

Estimated value for the output sequence z (n) of equalizer

Judgement output Output vector R for first via orthogonal wavelet transformation device WT ₁(n) conjugation, unit impulse function $\mathrm{\δ}\left(n\right)=\left\{\begin{array}{c}1,n=0+i0\\ 0,n\≠0+i0\end{array}\right.,$ R is the mould of a (n) that transmit,

For Conjugation.

${\hat{R}}_1^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\σ}}_{1(j,0)}^2\left(n\right),{\mathrm{\σ}}_{1(j,1)}^2\left(n\right),\·\·\·{\mathrm{\σ}}_{1(J+1,K)}^2\left(n\right),{\mathrm{\σ}}_{1(J+\mathrm{1,0})}^2\left(n\right),\·\·\·{\mathrm{\σ}}_{1(J+1,K)}^2\left(n\right)],$ Expression is to r _{1 (j, k)}(n) average power estimation,

Expression is to s _{1 (j, k)}(n) average power estimation, For right

Estimated value,

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

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

Wherein, diag[] the expression diagonal matrix, β is the iteration coefficient, r _{1 (j, k)}(n) the j layer decomposes k signal, s in expression the 1 road wavelet space _{1 (j, k)}(n) the j layer decomposes k signal in expression the 1 road metric space, and k is that k wavelet filter is positive integer 0＜k≤K, and K is the wavelet filter number.

The present invention is applied to time diversity technique in the blind equalizer based on the tanh error function, in conjunction with the DD algorithm, and after the introducing digital phase-locked loop, input signal to blind equalization algorithm carries out orthogonal wavelet transformation, thereby obtains the blind equalization algorithm that a kind of orthogonal wavelet transformation and time diversity merge mutually.This algorithm the convergence speed is fast, mean square error is little, can overcome the phase place rotation effectively.

Description of drawings

Fig. 1: the fractional spaced blind equalization principle 1 of time diversity;

Fig. 2: principle of the invention Fig. 2;

Fig. 3: inventive embodiments simulation result figure, (a) input signal (c) TDE-CMA of mean square error curve (b) equalizer output planisphere (d) TDE-HCMA output planisphere (e) CTDE output planisphere (f) WT-CTDE output planisphere.

Embodiment

As shown in Figure 1.Time diversity repeats to send same signal with regard to being meant the time interval to surpass channel coherence time, makes receiving terminal receive a plurality of signals with independent fading environment, merge through suitable mode again, thereby improve receiving terminal signal to noise ratio, reduce the error rate.Have the heavy time diversity blind equalizer of D structure, in the time diversity blind equalizer, each route same channel is formed with different sub-equalizers.The output signal of each branch road merges through combiner again, in folding, though the equal gain combining performance is easy to realize not as high specific merges most.

Constant modulus algorithm (HCMA) based on hyperbolic tangent function has than traditional constant modulus algorithm more performance, combine with the mode of decision-directed (DD) algorithm after time diversity introduced this blind equalization algorithm with soft handover, can reduce mean square error, but can not correct the phase place rotation that time varying channel causes, cause the increase of DD algorithmic error judgement, can't restrain fast.Therefore, introduce first-order phase-locked loop technology (PLL), overcome the phase place rotation, at this moment will constitute time diversity associating blind equalization algorithm and be designated as CTDE to reduce the erroneous judgement of DD algorithm.

As shown in Figure 2.Orthogonal wavelet transformation of the present invention and the blind balance method that time diversity technique merges mutually is characterized in that the channel branch road that comprises that the D weight structure is identical, through a time interval T _cSecond branch road receives a that transmits (n), through two time interval 2T _cThe 3rd branch road receive a that transmits (n), and the like to the D branch road through D-1 the time interval (D-1) T _cReceive a that transmits (n), D is a positive integer, and wherein the first branch road equalization methods comprises the steps:

1.) a (n) that will transmit obtains the first channel output vector x through the first impulse response channel c (n) ₁(n), wherein n is a time series, down together;

2.) adopt the first interchannel noise w ₁(n) and the described first channel output vector x of step 1 ₁(n) obtain the input vector of first equalizer: y ₁(n)=x ₁(n)+w ₁(n);

3.) with the input vector y of described first equalizer of step 2 ₁(n) obtain the output vector of the first orthogonal wavelet transformation device WT through first orthogonal wavelet transformation: R ₁(n)=Qy ₁(n), wherein Q is the orthogonal wavelet transformation matrix;

4.) by time diversity blind equalizer weight vector f based on the tanh error function _(HCMA)(n), decision-directed equalizer weight vector f _(DD)(n) and digital phase-locked loop obtain first via equalizer weight vector: $f_1\left(n\right)=f_{1\left(\mathrm{HCMA}\right)}\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)}+f_{1\left(\mathrm{DD}\right)}\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)},$ Wherein e is the nature truth of a matter, $i=\sqrt{-1}$ Be imaginary unit,

Be estimated value to the Chang Xiangwei rotation,

Be phase place rotation complex signal; The 1st branch of subscript 1 expression.

5.) the output vector R of the described first orthogonal wavelet transformation device WT of employing step 3 ₁(n) and the described first via equalizer of step 4 weight vector f ₁(n) obtain the output sequence of first via equalizer: z ₁(n)=f ₁(n) R ₁(n);

The output sequence that adopts D to weigh the equalizer of channel branch road obtains output signal and is: $z\left(n\right)=\underset{l=0}{\overset{D}{\mathrm{\Σ}}}{p}_l{z}_l\left(n\right),$ Z wherein _l(n) be the output sequence of l equalizer; p _lBe the output signal weight coefficient of l branch road equalizer, owing to adopt the equal gain combining method, so p _l=1.

Step 4 is described based on tanh error function time diversity blind equalizer weight vector f _{1 (HCMA)}(n) and decision-directed blind equalizer weight vector f _{1 (DD)}Asking for (n) comprises the steps:

6.) adopt phase place rotation complex signal

Obtain the decision device input signal with the output sequence z (n) of the described equalizer of step 5: $g\left(n\right)=z\left(n\right)e^{i\widehat{\mathrm{\θ}}\left(n\right)};$

7.) A200910028459D0006085526QIETU.GIF is exported in the judgement that the described decision device input signal of step 6 g (n) is obtained the output sequence z (n) of equalizer through judgment device;

8.) the judgement output of the output sequence z (n) of the output sequence z (n) of the described equalizer of employing step 5 and the described equalizer of step 7

Obtain the judgement output of the output sequence z (n) of equalizer

And the phase difference estimation value between the decision device input signal g (n):

$\widehat{\mathrm{\ϵ}}\left(n\right)={\sin }^{-1}\left\{\frac{\mathrm{Im}\left[\hat{a}\left(n\right)\hat{z}\left(n\right)\right]}{\left|\hat{a}\left(n\right)\right|\left|\hat{z}\left(n\right)\right|}\right\}\≈\mathrm{Im}\left[\hat{a}\left(n\right)\hat{z}\left(n\right)\right],$ Wherein

Estimated value for the output sequence z (n) of equalizer;

9.) adopt the judgement of the described equalizer output sequence z of step 8 (n) to export

And the phase difference estimation value between the decision device input signal g (n)

Obtain estimated value to the Chang Xiangwei rotation $\widehat{\mathrm{\θ}}(n+1)=\widehat{\mathrm{\θ}}\left(n\right)+\mathrm{\η}\widehat{\mathrm{\ϵ}}\left(n\right),$ Wherein η is the iteration step length of phase-locked loop, and n+1 is the back moment of current time sequence n, down together;

10.) the judgement output A200910028459D0006085526QIETU.GIF of the output sequence z (n) of output sequence z (n), the decision device input signal g (n) of the described equalizer of employing, equalizer and phase place rotation complex signal

Obtain the time diversity blind equalizer weight vector iterative formula of the 1st roadbed in the tanh error function:

$f_{1\left(\mathrm{HCMA}\right)}(n+1)=f_{1\left(\mathrm{HCMA}\right)}\left(n\right)-{\mathrm{\&mu;}}_{1\left(\mathrm{HCMA}\right)}{\hat{R}}_1^{-1}\left(n\right)\frac{\tanh \left(|g\left(n\right)-R|\right)}{{\cosh }^2(\left|g\left(n\right)\right|-R)}{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A200910028458E00121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{*}\left(n\right)\mathrm{sign}\left[g\left(n\right)\right]e^{i\widehat{\mathrm{\&theta;}}\left(n\right)},$

The 1 tunnel decision-directed blind equalizer weight vector iterative formula:

$f_{1\left(\mathrm{DD}\right)}(n+1)=f_{1\left(\mathrm{DD}\right)}\left(n\right)+{\mathrm{\&mu;}}_{1\left(\mathrm{DD}\right)}{\hat{R}}_1^{-1}\left(n\right)\mathrm{\&delta;}[\hat{\tilde{a}}\left(n\right)-\hat{a}\left(n\right)]{[\hat{a}\left(n\right)-g\left(n\right)]}^{*}{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A200910028458E00121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^{*}\left(n\right)e^{i\widehat{\mathrm{\&theta;}}\left(n\right)},$

μ wherein _{1 (HCMA)}Be the iteration step length of the first via based on tanh error function time diversity blind equalizer weight vector, μ _{1 (DD)}Be the iteration step length of the decision-directed blind equalizer weight vector of the first via,

Estimated value for the output sequence z (n) of equalizer

Judgement output,

Output vector R for first via orthogonal wavelet transformation device WT ₁(n) conjugation, unit impulse function $\mathrm{\&delta;}\left(n\right)=\left\{\begin{array}{c}1,n=0+\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="A200910028458E00121.png"\; state="\{\{state\}\}">i</figure-callout>}0\\ 0,n\&NotEqual;0+\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="A200910028458E00121.png"\; state="\{\{state\}\}">i</figure-callout>}0\end{array}\right.,$ R is the mould of a (n) that transmit,

For

Conjugation.

${\hat{R}}_1^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\&sigma;}}_{1(j,0)}^2\left(n\right),{\mathrm{\&sigma;}}_{1(j,1)}^2\left(n\right),\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&sigma;}}_{1(J+1,K)}^2\left(n\right),{\mathrm{\&sigma;}}_{1(J+\mathrm{1,0})}^2\left(n\right),\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&sigma;}}_{1(J+1,K)}^2\left(n\right)],$

Expression is to r _{1 (j, k)}(n) average power estimation,

Expression is to s _{1 (j, k)}(n) average power estimation,

For right

Estimated value,

${\widehat{\mathrm{\&sigma;}}}_{1(j,k)}^2(n+1)=\mathrm{\&beta;}{\widehat{\mathrm{\&sigma;}}}_{1(j,k)}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|r_{1(j,k)}\left(n\right)\right|}^2$

${\widehat{\mathrm{\&sigma;}}}_{1(j+1,k)}^2(n+1)=\mathrm{\&beta;}{\widehat{\mathrm{\&sigma;}}}_{1(j+1,k)}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|s_{1(j,k)}\left(n\right)\right|}^2$

Wherein, diag[] the expression diagonal matrix, β is the iteration coefficient, r _{1 (j, k)}(n) the j layer decomposes k signal, s in expression the 1 road wavelet space _{1 (j, k)}(n) the j layer decomposes k signal in expression the 1 road metric space, and k is that k wavelet filter is positive integer 0＜k≤K, and K is the wavelet filter number.

The equalization methods of the 2nd to D branch road is quite analogous to the equalization methods of first branch road.

As shown in Figure 3.In order to verify the validity of WT-CTDE algorithm, adopt two serious footpath underwater acoustic channels of distortion to carry out emulation, its transfer function is c=[e ^-0.7j, 0,0,0.3e ^-1.8j]; Transmit to the 16QAM signal to noise ratio is 25dB, equalizer power length is 16 and all adopts the centre cap initialization; D=2 among Fig. 2; And the two-way parameter is provided with identical; Every road signal is adopted the DB2 wavelet decomposition, and decomposing level is 2 layers, and the power initial value is 4; β=0.999; TDE-CMA weight vector step-length is μ _CMA=0.001; TDE-HCMA weight vector step-length is μ _HCMA=0.005; The HCAM step-length is μ in the CTDE algorithm _HCMA=0.005; The DD step-length is μ _DD=0.0185; μ in the WT-CTDE algorithm _HCMA=0.0195; The DD step-length is μ _DD=0.0225; 500 Meng Te Kano simulation results.Fig. 3 (a) shows, under TDE-CMA and the much the same situation of TDE-HCMA convergence rate, TDE-HCMA is than the TDE-CMA error nearly 12dB that descended; The CTDE convergence rate than TDE-HCMA fast about 2000 the step and steady-state error reduced about 9dB; WT-CTDE is than fast about 1500 steps of CTDE convergence, the about 5dB of steady-state error decline.(c d) shows Fig. 3, and TDE-HCMA algorithm planisphere is more concentrated than TDE-CMA, but they all can't correct the phase place rotation; (e f) show that CTDE and WT-CTDE have overcome the phase place rotation, but the WT-CTDE planisphere is the most clear, compact for Fig. 3.

Claims (1)

1. orthogonal wavelet transformation and the blind balance method that time diversity technique merges mutually is characterized in that the channel branch road that comprises that the D weight structure is identical, through a time interval T _cSecond branch road receives a that transmits (n), through two time interval 2T _cThe 3rd branch road receive a that transmits (n), and the like to the D branch road through D-1 the time interval (D-1) T _cReceive a that transmits (n), D is a positive integer, and wherein the first branch road equalization methods comprises the steps:

1.) a (n) that will transmit obtains the first channel output vector x through the first impulse response channel c (n) ₁(n), wherein n is a time series, down together;

2.) adopt the first interchannel noise w ₁(n) and the described first channel output vector x of step 1 ₁(n) obtain the input vector of first equalizer: y ₁(n)=x ₁(n)+w ₁(n);

3.) with the input vector y of described first equalizer of step 2 ₁(n) obtain the output vector of the first orthogonal wavelet transformation device WT through first orthogonal wavelet transformation: R ₁(n)=Qy ₁(n), wherein Q is the orthogonal wavelet transformation matrix;

4.) by time diversity blind equalizer weight vector f based on the tanh error function _(HCMA)(n), decision-directed equalizer weight vector f _(DD)(n) and digital phase-locked loop obtain first via equalizer weight vector: $f_1\left(n\right)=f_{1\left(\mathrm{HCMA}\right)}\left(n\right)e^{i\widehat{\mathrm{\&theta;}}\left(n\right)}+f_{1\left(\mathrm{DD}\right)}\left(n\right)e^{i\widehat{\mathrm{\&theta;}}\left(n\right)},$ Wherein e is the nature truth of a matter, $i=\sqrt{-1}$ Be imaginary unit,

Be estimated value to the Chang Xiangwei rotation,

Be phase place rotation complex signal; The 1st branch of subscript 1 expression.

5.) the output vector R of the described first orthogonal wavelet transformation device WT of employing step 3 ₁(n) and the described first via equalizer of step 4 weight vector f ₁(n) obtain the output sequence of first via equalizer: z ₁(n)=f ₁(n) R ₁(n);

The output sequence that adopts D to weigh the equalizer of channel branch road obtains output signal and is: $z\left(n\right)=\stackrel{D}{\mathrm{\&Sigma;}}{p}_l{z}_l\left(n\right),$ Z wherein _l(n) be the output sequence of l equalizer; p _lBe the weight coefficient of the output signal of l branch road equalizer, owing to adopt the equal gain combining method, so p _l=1.

Step 4 is described based on tanh error function time diversity blind equalizer weight vector f _{1 (HcMA)}(n) and decision-directed blind equalizer weight vector f _{1 (DD)}Asking for (n) comprises the steps:

6.) adopt phase place rotation complex signal

Obtain the decision device input signal with the output sequence z (n) of the described equalizer of step 5: $g\left(n\right)=z\left(n\right)e^{i\widehat{\mathrm{\&theta;}}\left(n\right)};$

7.) judgement that the described decision device input signal of step 6 g (n) is obtained the output sequence z (n) of equalizer through judgment device is exported

8.) the judgement output of the output sequence z (n) of the output sequence z (n) of the described equalizer of employing step 5 and the described equalizer of step 7

Obtain the judgement output of the output sequence z (n) of equalizer

And the phase difference estimation value between the decision device input signal g (n):

$\widehat{\mathrm{\&epsiv;}}\left(n\right)={\sin }^{-1}\left\{\frac{\mathrm{Im}\left[\hat{a}\left(n\right)\hat{z}\left(n\right)\right]}{\left|\hat{a}\left(n\right)\right|\left|\hat{z}\left(n\right)\right|}\right\}\&ap;\mathrm{Im}\left[\hat{a}\left(n\right)\hat{z}\left(n\right)\right],$ Wherein

Estimated value for the output sequence z (n) of equalizer;

9.) adopt the judgement of the described equalizer output sequence z of step 8 (n) to export

And the phase difference estimation value between the decision device input signal g (n) Obtain estimated value to the Chang Xiangwei rotation $\widehat{\mathrm{\&theta;}}(n+1)=\widehat{\mathrm{\&theta;}}\left(n\right)+\mathrm{\&eta;}\widehat{\mathrm{\&epsiv;}}\left(n\right),$ Wherein η is the iteration step length of phase-locked loop, and n+1 is the back moment of current time sequence n, down together;

10.) the judgement output of the output sequence z (n) of output sequence z (n), the decision device input signal g (n) of the described equalizer of employing, equalizer

With phase place rotation complex signal

Obtain the time diversity blind equalizer weight vector iterative formula of the 1st roadbed in the tanh error function:

$f_{1\left(\mathrm{HCMA}\right)}(n+1)=f_{1\left(\mathrm{HCMA}\right)}\left(n\right)-{\mathrm{\&mu;}}_{1\left(\mathrm{HCMA}\right)}{\hat{R}}_1^{-1}\left(n\right)\frac{\tanh \left(|g\left(n\right)-R|\right)}{{\cosh }^2(\left|g\left(n\right)\right|-R)}{R}_1^{*}\left(n\right)\mathrm{sign}\left[g\left(n\right)\right]e^{i\widehat{\mathrm{\&theta;}}\left(n\right)},$

The 1 tunnel decision-directed blind equalizer weight vector iterative formula:

$f_{1\left(\mathrm{DD}\right)}(n+1)=f_{1\left(\mathrm{DD}\right)}\left(n\right)+{\mathrm{\&mu;}}_{1\left(\mathrm{DD}\right)}{\hat{R}}_1^{-1}\left(n\right)\mathrm{\&delta;}\left[\stackrel{\widehat{~}}{a}\left(n\right)-\hat{a}\left(n\right)\right]{[\hat{a}\left(n\right)-g\left(n\right)]}^{*}{R}_1^{*}\left(n\right)e^{i\widehat{\mathrm{\&theta;}}\left(n\right)},$

μ wherein _{1 (HCMA)}Be the iteration step length of the first via based on tanh error function time diversity blind equalizer weight vector, μ _{1 (DD)}Be the iteration step length of the decision-directed blind equalizer weight vector of the first via,

Estimated value for the output sequence z (n) of equalizer

Judgement output, Output vector R for first via orthogonal wavelet transformation device WT ₁(n) conjugation, unit impulse function $\mathrm{\&delta;}\left(n\right)=\left\{\begin{array}{c}1,n=0+i0\\ 0,n\&NotEqual;0+i0\end{array}\right.,$ R is the mould of a (n) that transmit,

For

Conjugation.

${\hat{R}}_1^{-1}\left(n\right)=\mathrm{diag}[{\mathrm{\&sigma;}}_{1(j,0)}^2\left(n\right),{\mathrm{\&sigma;}}_{1(j,1)}^2\left(n\right),\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&sigma;}}_{1(J+1,K)}^2\left(n\right),{\mathrm{\&sigma;}}_{1(J+\mathrm{1,0})}^2\left(n\right),\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&sigma;}}_{1(J+1,K)}^2\left(n\right)],$ Expression is to r _{1 (j, k)}(n) average power estimation, Expression is to s _{1 (j, k)}(n) average power estimation,

For right

Estimated value,

${\widehat{\mathrm{\&sigma;}}}_{1(j,k)}^2(n+1)=\mathrm{\&beta;}{\widehat{\mathrm{\&sigma;}}}_{1(j,k)}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|r_{1(j,k)}\left(n\right)\right|}^2,$

${\widehat{\mathrm{\&sigma;}}}_{1(j+1,k)}^2(n+1)=\mathrm{\&beta;}{\widehat{\mathrm{\&sigma;}}}_{1(j+1,k)}^2\left(n\right)+(1-\mathrm{\&beta;}){\left|s_{1(j,k)}\left(n\right)\right|}^2$

Wherein, diag[] the expression diagonal matrix, β is the iteration coefficient, r _{1 (j, k)}(n) the j layer decomposes k signal, s in expression the 1 road wavelet space _{1 (j, k)}(n) the j layer decomposes k signal in expression the 1 road metric space, and k is that k wavelet filter is positive integer 0＜k≤K, and K is the wavelet filter number.

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