Blind equalization method for wavelet neural network based on space diversity

Technical Field

The invention relates to a space diversity-based wavelet neural network blind equalization method, which belongs to the overcoming underwater acoustic channel multi-path fading caused by the intersymbol interference (  Interference Inter-Symbol, ISI) technical field of blind equalization method.

Background Art

In underwater communication system, the multipath fading and channel distortion caused by the intersymbol interference (Inter-Symbol Inter-ference, ISI), the transmission signal of the distortion occurs, and producing the error at the receiving end, a serious impact on the communication quality. To reduce intersymbol interference is an effective means of equalizing technology. Balanced itself may be viewed as the mode classification problems, and neural network has the characteristics of good pattern classification, neural network used for the equalizer designs blindly is the subject of the study (see literature CHENG   Hai-qing, ZHANG   Li-yi. Blind   Equalization   Algorithm   Using   Feed-forward Neural   Network   Based   on   a   Modified   Target   Function[J] .Journal   Of   Tai   yuan   University   Of Technology, 2006, 37:39-41). Because the wavelet analysis has good zooming characteristic and the time-frequency local characteristic, the self-learning neural network has, self-adaptability, strong robustness and spreading ability, therefore a wavelet neural network is the problem of concern. Wavelet neural network has the ability to relatively strong, but also the mutual influence between the neurons is reduced, can accelerate the convergence speed of the training algorithm (see literature : WANG   Jun-feng .Study   on   adaptive   equalization algorithms   based   on   wavelets   and   neural   networks[D] .Ph.D.Thesis, Xidian   Universtiy, Xi ' an, China, 2003). Traditionally equalization technology need to periodically send training sequence, a waste of the limited bandwidth resources, but does not need to send blind equalization of a known training sequence technology, can save bandwidth, improve the communication efficiency. Through the equalization technology, the characteristics can be designed completely opposite the channel equalizer, in order to offset the effects of channel distortion (see literature : E.G. Larsson,   the   combination   of   spatial   diversity On   multi-user   diversity[J   and] .IEEE Communications   Letters, 2004, 8 : 517-519), but the traditional blind equalization method is directed to the study of single channel, a new generation of high-speed underwater communication system will be based on the multi-path balancing method, therefore, diversity technology, the design of the equalizer blind has proposed a kind of new ideas (see literature : Sung-Hoon   Moon, Ju-Yeun   Kim   and Dong-Seog .Han.Spatial   diversity   technique   for   Improvement   of   DTV   reception performance[J] .IEEE   Transactions   on   consumer   electronics, 2003, 49 (4): 958-964). In many diversity technology, because the space diversity is not sacrifice the advantage of the bandwidth of the signal, the most used as the diversity of forms (see literature : Cybeako   G.Approximations   by   superposition   of   a   sigmoidal   function[J] .Math   Contr Syst   Signals, 1989, 2 : 303-314. Conference   Record   of   the   Twenty-Ninth   Asilomar   Conference   on Signals, Systems   and   Computers, 1995 : 1694-1647). Space diversity of the received signal using a plurality of array elements to reduce the effects of multi-path fading, so as to improve the reliability of information transmission.

Content of the invention

The purpose of this invention is for the defects of the prior art, the use of space diversity technology is introduced in the wavelet neural network blind equalization method, based on the space diversity technique is wavelet neural network blind equalization method. The method fully utilize the space diversity techniques and wavelet neural network the advantages of blind equalization method, has accelerated the convergence speed, reduces the mean square error.

To achieve the above-mentioned purposes of the present invention, adopts the following technical scheme:

The invention is based on the space diversity blind equalization method wavelet neural network, which is characterized by comprising the following steps:

1st step: the transmitted signal sequence s (k) D heavy branch section through the impulse response channel in other words c⁽¹⁾ (k) to c^(D) (k) D obtained is heavy branch channel output vector x⁽¹⁾ (k) to x^(D) (k), wherein k as the time sequence, D is a natural number expressing diversity heavy few, with;

2nd step: D heavy branch of the channel noise w⁽¹⁾ (k) to w^(D) (k) and 1st step D heavy branch of the received channel output vector D heavy branch equalizer input signal: y⁽¹⁾ (k) to y^(D) (k);

3rd step: the 2nd step D heavy branch of the equalizer input signal respectively through D heavy branch of a wavelet neural network equalizer, f⁽¹⁾ (k) to f^(D) (k) D heavy branch by a wavelet neural network a signal, the equalizer output z⁽¹⁾ (k) to z^(D) (k);

4th step: the 3rd step D heavy branch of the wavelet neural network output signal through the combiner are combined by combiner output signal z (k).

The space diversity-based wavelet neural network blind equalization method, characterized in that the stated states the wavelet neural network adopts a three-layer feed-forward wavelet neural network WNN, the input layer sequentially, and an output layer concealed level , each branch of a wavelet neural network method are the same, wherein the section d of the branch in a wavelet neural network method is as follows:

(A) the 2nd step D heavy branch of the equalizer section in the input signal of the input signal d branch equalizer y^(d) (k) by the input layer is hidden layer input signal: ul(d)(k)=Σi=1Ifil(d)(k)yi(d)(k),I=1, 2, the   I, the number of input layer neurons that I, l=1, 2, the [...] , L, the number of hidden layer neurons expressed L, f_il^(d) (k) in subsection d branch section the input layer and the hidden layer neurons i section l is connected with the weight of the neurons, d=1, 2, 3..., D, the diversity renumbers D is a natural number expressed;

(B) the step (a) the hidden layer input signal u_l^(d) (k) after implied layer is hidden layer output signal: vl(d)(k)=ψ(ul,R(d)(k))+jψ(ul,I(d)(k))The input signal and an output layer up(d)(k)=Σl=1Lflp(d)(k)vl(d)(k),Implicit layer ψ (·) is the transfer function of the Morlet wavelet transformed function, u_l,R^(d) (k), u_l,I^(d) (k) hidden layer input signal are respectively said u_l^(d) (k) of the real and imaginary parts, f_lp^(d) (k) section l to connote layer neuron of the output layer neuron is connected with the weight section p, p=1, 2, the   P, the number of output neurons expressed P;

(C) the step (b) of the input signal of the output layer u_p^(d) (k) obtained by a wavelet neural network output equalizer output signal z(d)(k)=F(up,R(d)(k))+jF(up,I(d)(k)),The transfer function of output layer F (·), u_p,R^(d) (k), u_p,I^(d) (k) respectively representing the input signal of the output layer u_p^(d) (k) of the real and the imaginary part.

3, space diversity-based wavelet neural network blind equalization method according to Claim 2, characterized in that the output signal of the combiner z (k) to the branch d blind equalizer section i the input layer and a hidden layer neurons neurons section l connection weight f_il^(d) (k) section l hidden layer and the output layer neurons neurons section p connection weight f_lp^(d) (k), wherein i=1, 2, the   I, the number of input layer neurons that I, l=1, 2, the [...] , L, the number of hidden layer neurons expressed L, d=1, 2, 3..., D, that is the natural number D the diversity renumbers , p=1, 2, the   P, the number of output neurons expressed P; f_il^(d) (k), f_lp^(d) (k) and f^(d) (k) strike a comprises the following steps of:

D) z by the combiner output signal (k) and transmitting signal sequence s (k), defining the cost function J(k)=12[|z(k)|2-R2]2;

E) according to the method of steepest descent, in step d) to the gradient of the cost function, can branch d wavelet neural network output layer neurons section l with the hidden layer neurons section p adaptive weight f_lp^(d) (k), section d branch of a wavelet neural network input layer section i with the hidden layer neurons neurons section l adaptive weight f_il^(d) (k); can branch d wavelet neural network adaptive wavelet function expansion factor a^(d) (k) and scale factor b^(d) (k);

F) from step e) the section d branch of a wavelet neural network output layer neurons section p with the hidden layer neurons section l adaptive weight f_lp^(d) (k) and d branch of a wavelet neural network input layer section i with the hidden layer neurons neurons section l adaptive weight f_il^(d) (k) can branch d wavelet neural net winds blindly equalizer vector f^(d) (k).

Because the space diversity techniques can reduce the sound of the multi-path fading channel, and can improve the output signal-to-noise ratio; and of a wavelet neural network has stronger and more quickly approaching the capacity of the learning speed, for this reason, based on the small space diversity technique (SDE-WNN) blind equalization method wavelet neural network. The method to fully utilize space diversity technology and the advantages of a wavelet neural network, with a wavelet neural network (WNN) compared with blind equalization method, the convergence speed and the mean square error performance aspect, demonstrated the superiority of the more obvious, has accelerated the convergence speed, greatly reduce the mean square error. Underwater acoustic channel simulation result to verify the effectiveness of the method of the invention. Therefore, the method of the invention can effectively realize the separation of the signal and the noise signal and the real-time recovery.

Description of drawings

Figure 1: section d branch wavelet neural net winds blindly equalizer chart;

Figure 2: space diversity equalizer chart;

Figure 3: the invention: the space diversity technique-based wavelet neural net winds blindly equalizer chart

Figure 4: the embodiment of the invention 1 simulation chart , (a) error curve (b) WNN1 output constellation (c) WNN2 output constellation (d) the output constellation SDE-WNN;

Figure 5: the embodiment of the invention 2 simulation chart , (a) error curve (b) WNN1 output constellation (c) WNN2 output constellation (d) the output constellation map SDE-WNN.

Mode of execution

In conjuction with the following technical scheme of the invention to carry out a detailed description:

As shown in Figure 1, section d branch wavelet neural net winds blindly equalizer.

A wavelet neural network as a front to the neural network, the model is simple, and of general neural network simulation accuracy is difficult to achieve and the learning speed is fast, have proved Cybenc: concealed level containing a feed-forward neural network with arbitrary precision can be approximate any continuous function, therefore, the invention adopts a three-layer wavelet neural network (WNN), its structure is shown in Figure 2, graph, f_il^(d) (k) in subsection d branch section the input layer and the hidden layer neurons i section l of neurons is connected with the weight, the number of input layer neurons that I, i=1, 2, the [...] , I; L the number of hidden layer neurons expressed, l=1, 2,     L; f_lp^(d) (k) in subsection d branch section l hidden layer and the output layer neurons neurons section p is connected with the weight of, the number of output neurons expressed P p=1, 2, the [...] , P; the input of the section d branch input layer for y^(d) (k) = x^(d) (k) + w^(d) (k) = {y^(d) (k-1), y^(d) (k-2), …, y^(d) (k-i)}^T; section d is input into the hidden layer branch u_l^(d) (k); section d branch implied for output layer v_l^(d) (k); section d branch of the input to the output layer unit u_p^(d) (k), total output of the neural network for z (k). Implied layer transfer function adopts the Morlet mother wavelet transformation to obtain the formula is

ψ([!CenterDot!])=|a|-12ψ(x-ba)=|a|-12x-bae-(x-b)22a2---(1)

In the formula, a, respectively b-factor for the expansion factor. The transfer function of output layer

F (x) = x+αsin (πx)     (2)

In the formula, -∞ <x <∞, 0<α <1, x representative is u_l^(d) (k) and u_p^(d) (k), the function to the input signal has a good recognition ability.

Such QAM through the complex signal to a wavelet neural network, will inevitably produce phase deflection phenomenon, that takes into account the signal transmission in the network to the real part and the imaginary part is divided into two paths for transmission. Furthermore, section d branch of a wavelet neural network input signal, input layer is connected with the weight of the hidden layer, hidden layer and the output layer is connected with a weight for plural form can be expressed as

y(d)(k)=yR(d)(k)+jyI(d)(k)---(3)

fil(d)(k)=fil,R(d)(k)+jfil,I(d)(k)---(4)

flp(d)(k)=flp,R(d)(k)+jflp,I(d)(k)---(5)

In this way, a wavelet neural network's equation of state equation as

ul(d)(k)=Σi=1Ifil(d)(k)yi(d)(k)---(6)

vl(d)(k)=ψ(ul,R(d)(k))+jψ(ul,I(d)(k))---(7)

up(d)(k)=Σl=1Lflp(d)(k)vl(d)(k)---(8)

z(k)=F(up,R(d)(k))+jF(up,I(d)(k))---(9)

A digital-to-analog (CMA) the cost function

J(k)=12[|z(k)|2-R2]2---(10)

In the formula, z (k) to the output signal of the wavelet neural network, R² =E [|s (k) |⁴]/ E[s (k) |²] transmit the analog signal sequence. According to the descent fastest , the weights of the network can be obtained for the iterative formula

f(k+1)=f(k)-η[!PartialD!]J(k)[!PartialD!]f(k)---(11)

Network of implicit layer neuron using wavelet transform as a transfer function, the weight coefficient of the network and wavelet transform translation factor flexible factor obtained through the network training.

Therefore, section d wavelet neural network branch section the output layer neurons of the hidden layer l section p the weights of the neurons for the iterative formula

flp(d)(k+1)=flp(d)(k)-ρ[!PartialD!]J(k)[!PartialD!]flp(d)(k)---(12)

[!PartialD!]J(k)[!PartialD!]flp(d)(k)=[!PartialD!]J(k)[!PartialD!]z(k)[!CenterDot!][!PartialD!]z(k)[!PartialD!]flp(d)(k)---(13)

[!PartialD!]J(k)[!PartialD!]z(k)=2[!CenterDot!]|z(k)|[!CenterDot!][|z(k)|2-R2]---(14)

[!PartialD!]z(k)[!PartialD!]flp(d)(k)=[!PartialD!]|z(k)|[!PartialD!]flp(d)(k)[!CenterDot!]+j[!PartialD!]|z(k)|[!PartialD!]flp(d)(k)

=1|z(k)|{F[vR(d)(k)]F′[vR(d)(k)]Il,R(d)(k)+F[vI(d)(k)]F′[vI(d)(k)]Il,I(d)(k)}

+j1|z(k)|{-F[vR(d)(k)]F′[vR(d)(k)]Il,I(d)(k)+F[vI(d)(k)]F′[vI(d)(k)]Il,R(d)(k)}---(15)

flp(d)(k+1)=flp(d)(k)-2[!CenterDot!]ρ[!CenterDot!][|z(k)|2-R2][!CenterDot!]{F[vR(d)(k)][!CenterDot!]F′[vR(d)(k)]+jF[vI(d)(k)][!CenterDot!]F′[vI(d)(k)]}Il*(k)---(16)

The same can be, section d branch of a wavelet neural network section leaves the level i the input of the neuron of the hidden layer neurons section l the weight value of the iterative formula

fil(d)(k+1)=fil(d)(k)-ρ[!PartialD!]J(k)[!PartialD!]z(k)[!CenterDot!][!PartialD!]z(k)[!PartialD!]fil(d)(k)---(17)

[!PartialD!]z(k)[!PartialD!]fil(d)(k)=[!PartialD!]z(k)[!PartialD!]fil,R(d)(k)+j[!PartialD!]z(k)[!PartialD!]fil,I(d)(k)---(18)

=1|z(k)|{[F′[ul,R(d)(k)]Re{{F[vR(d)(k)]F′[vR(d)(k)]+jF[vI(d)(k)]F′[vI(d)(k)]}flp*(d)(k)}[yR(d)(k)-jyI(d)(k)]

+j[F′[ul,I(d)(k)]Im{{F[vR(d)(k)]F′[vR(d)(k)]+jF[vI(d)(k)]F′[vI(d)(k)]}flp*(d)(k)[yR(d)(k)-jyI(d)(k)]}---(19)

A flexible factor of the network after training for the iterative formula

a(d)(k+1)=a(d)(k)-μ[!PartialD!]J(k)[!PartialD!]|z(k)|[!CenterDot!][!PartialD!]|z(k)|[!PartialD!]a(d)(k)=a(d)(k)-2μ[!CenterDot!]|z(k)|[!CenterDot!][|z(k)|2-R2][!CenterDot!][!PartialD!]|z(k)|[!PartialD!]a(d)(k)---(20)

[!PartialD!]|z(k)|[!PartialD!]a(d)(k)=1|z(k)|{F(vR(d)(k))F′(vR(d)(k))[flp,R(d)(k)[!PartialD!]ψ[ul,R(d)(k)][!PartialD!]a(d)(k)---(21)

-flp,I(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]a(d)(k)]+F(vI(d)(k))F′(vI(d)(k))[flp,I(d)(k)[!PartialD!]ψ[ul,R(d)(k)][!PartialD!]a(d)(k)+flp,R(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]a(d)(k)]}---(22)

By the same token, the iterative formula b translation factor

b(d)(k+1)=b(d)(k)-μ[!PartialD!]J(k)[!PartialD!]|z(k)|[!CenterDot!][!PartialD!]|z(k)|[!PartialD!]b(d)(k)=b(d)(k)-2μ[!CenterDot!]|z(k)|[!CenterDot!][|z(k)|2-R2][!CenterDot!][!PartialD!]|z(k)|[!PartialD!]b(d)(k)---(23)

[!PartialD!]|z(k)|[!PartialD!]b(d)(k)=1|z(k)|{F(vR(d)(k))F′(vR(d)(k))[flp,R(d)(k)[!PartialD!]ψ[ul,R(d)(k)][!PartialD!]b(d)(k)---(24)

-flp,I(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]b(d)(k)]+F(vI(d)(k))F′(vI(d)(k))[flp,I(d)(k)[!PartialD!]ψ[ul,R(d)(k)][!PartialD!]b(d)(k)+flp,R(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]b(d)(k)]}---(25)

As shown in Figure 2, such as space diversity gain to balance the system.

Decay of the signal channel of the multi-way characteristics of underwater acoustic digital communication is more difficult, in the past, most underwater acoustic communication research has focused mainly on single-channel technology, space diversity processing will focus on selection or combination technology. In the underwater acoustic communication, space diversity combined to improve channel condition is a technical people's attention. At the receiving end of the appropriate, these signals are combined, thereby improving the receiving end of the signal-to-noise ratio, bit error rate is reduced. D path with the space of the system model the diversity is blind balanced, as shown in Figure 2. {S (k)} is transmitting signal sequence; c^(d) (k) is the impulse response of the tributary channel d ; {w^(d) (k)} of the branch section d is white Gaussian noise sequence; y^(d) (k) = [y^(d) (k), y^(d) (k-1), …, y^(d) (k-M_f + 1)]^T branch section d is the input signal of the equalizer; f^(d) (k) = [f^(d) (k), f^(d) (k+ 1), …, f^(d) (k+M_f -1)] is the weight vector of the equalizer; wherein M_f the length of the equalizer; z^(d) (k) is an output of the equalizer branch d; wherein d=1, the 2   D, z (k) is the output signal after the merger.

The basic idea is the space diversity on the space through a plurality of transmission characteristics of the different channel received signal, then the combined manner through appropriate effectively combined signal, thereby improving signal-to-noise ratio of the receiver, reducing the error rate. Diversity combined processing method is one of the key technologies of the equalizer, as the gain to be combined to realize the most simple, therefore, the invention adopts the gain combining technique. The so-called gain combining (  Combining   Gain Equal, EGC), that is, at the receiving end of a diversity branch D, after the phase adjustment, the gain factor in accordance with the same, in-phase addition, is then sent to a combiner a joint. The average gain combining such as the output signal-to-noise ratio:

SNRE=[1+(D-1)π4][!CenterDot!]SNR---(26)

The combined gain:

KE=SNRESNR=1+(D-1)π4---(27)

In the formula, SNR_E the average output signal-to-noise ratio of the merged, SNR expressed premerger each branch of the average signal-to-noise ratio, the number of diversity branches said D.

As shown in Figure 3, space diversity technique based on a wavelet neural network blind equalization method.

Space diversity can improve signal-to-noise ratio of the receiver, reducing the error rate, and with a wavelet neural network simulation of very high precision and very fast training speed, the space diversity technology is introduced in the wavelet neural network blind equalization method, based on the space diversity technique is wavelet neural network blind equalization method. Its principle structure, as shown in Figure 3.

To introduce spatial diversity techniques after the branch d wavelet neural network weight of the hidden layer and the output layer for the iterative formula

flp(d)(k+1)=flp(d)(k)-ρ[!CenterDot!][!PartialD!]J(k)[!PartialD!]flp(d)(k)---(28)

[!PartialD!]J(k)[!PartialD!]flp(d)(k)=[!PartialD!]J(k)[!PartialD!]z(k)[!CenterDot!][!PartialD!]z(k)[!PartialD!]flp(d)(k)---(29)

[!PartialD!]J(k)[!PartialD!]z(k)=2[!CenterDot!]|z(k)|[!CenterDot!][|z(k)|2-R2]---(30)

[!PartialD!]z(k)[!PartialD!]flp(d)(k)=[!PartialD!]|z(k)|[!PartialD!]flp(d)(k)+j[!PartialD!]|z(k)|[!PartialD!]flp(d)(k)

=1|z(k)|{F[vR(d)(k)]F′[vR(d)(k)]Il,R(d)(k)+F[vI(d)(k)]F′[vI(d)(k)]Il,I(d)(k)}

+j1|z(k)|{-F[vR(d)(k)]F′[vR(d)(k)]Il,I(d)(k)+F[vI(d)(k)]F′[vI(d)(k)]Il,R(d)(k)}---(31)

flp(d)(k+1)=flp(d)(k)-2[!CenterDot!]ρ[!CenterDot!][|z(k)|2-R2][!CenterDot!]{F[vR(d)(k)][!CenterDot!]F′[vR(d)(k)]+jF[vI(d)(k)]F′[vI(d)(k)]}Il*(k)---(32)

The same can be, the input layer to the iterative formula weight

fil(d)(k+1)=fil(d)(k)-ρ[!CenterDot!][!PartialD!]J(k)[!PartialD!]z(k)[!CenterDot!][!PartialD!]z(k)[!PartialD!]fil(d)(k)---(33)

[!PartialD!]z(k)[!PartialD!]fil(d)(k)=[!PartialD!]z(k)[!PartialD!]fil,R(d)(k)+j[!PartialD!]z(k)[!PartialD!]fil,I(d)(k)

=1|z(k)|{[F′[ul,R(d)(k)]Re{{F[vR(d)(k)]F′[vR(d)(k)]+jF[uI(d)(k)]F′[uI(d)(k)]}flp*(k)}[yR(d)(k)-jyI(d)(k)]

+j[F′[ul,I(d)(k)]Im{{F[uR(d)(k)]F′[uR(d)(k)]+jF[vI(d)(k)]F′[vI(d)(k)]}flp*(k)[yR(d)(k)-jyI(d)(k)]}---(34)

In the formula, ρ is a step size.

After introducing the space diversity, expansion factor a^(d) after wavelet neural network training iteration formula is:

a(d)(k+1)=a(d)(k)-μ1[!CenterDot!][!PartialD!]J(k)[!PartialD!]|z(k)|[!CenterDot!][!PartialD!]|z(k)|[!PartialD!]a(d)(k)=a(d)(k)-2[!CenterDot!]μ1[!CenterDot!]|z(k)|[!CenterDot!][|z(k)|2-R2][!CenterDot!][!PartialD!]|z(k)|[!PartialD!]a(d)(k)---(35)

[!PartialD!]|z(k)|[!PartialD!]a(d)(k)=1|z(k)|{F(vR(d)(k))F′(vR(d)(k))[flp,R(d)(k[!CenterDot!])[!PartialD!]ψ[ul,R(d)(k)][!PartialD!]a(d)(k)

-flp,I(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]a(d)(k)]+F(vI(d)(k))F′(vI(d)(k))[!CenterDot!][flp,I(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]a(d)(k)+flp,R(d)(k)[!PartialD!]ψ[ul,I(d)(k)][!PartialD!]a(d)(k)]---(36)

In the formula, μ₁ iterative step for the expansion factor.

By the same token, the translation factor b^(d) to iterative formula

b(d)(k+1)=b(d)(k)-μ2[!CenterDot!][!PartialD!]J(k)[!PartialD!]|z(k)|[!CenterDot!][!PartialD!]|z(k)|[!PartialD!]b(d)(k)=b(d)(k)-2[!CenterDot!]μ2[!CenterDot!]|z(k)|[!CenterDot!][|z(k)|2-R2][!CenterDot!][!PartialD!]|z(k)|[!PartialD!]b(d)(k)---(37)

[!PartialD!]|z(k)|[!PartialD!]b(d)(k)=1|z(k)|{F(vR(d)(k))F′(vR(d)(k))[flp,R(d)(k)[!PartialD!]ψ[ul,R(d)(k)][!PartialD!]b(d)(k)