CN101316158A - Additive waveshape pretreatment method in digital communication modulation - Google Patents

Abstract

The invention provides an additive waveform pretreatment method in the digital communication modulation, which superposes an additive wave f(t) that is selected, constructed and adjusted in advance to an initial signal g(t) of a transmitting end to form a reshaped wave g1(t) which has different waveform from the initial signal g(t), then the reshaped wave g1(t) is transmitted from the transmitting end; the reshaped wave signal received at a receiving end is that g1 (t) is equal to p(t)*g1(t) and is equal to g11(t) plus g12(t), wherein the '*' is a convolution operation sign, p(t) is the impulse response of a filter which can replace the transmission channel equivalently, g11(t)and g12(t) are the principal wave and trailing wave of the reshaped wave respectively. The reshaped wave g1(t) is characterized in that the waveform of the principal wave g11(t) of the receiving end signal g1(t) is led to be more approximate to the waveform of the initial signal g(t) at the transmitting end after passing the transmission channel, at the same time, the amplitude value of the trailing wave g12(t) waveform at the receiving end can be reduced effectively; and/ or the principal wave g11(t) of the receiving end signal g1(t) can meet the decoding requirement of the data transmission. The invention overcomes the defects of the traditional method that the signal spectrum form cannot meet the transmission performance requirement and the effect of removing the trailing wave is not distinct after the code element waveform is windowed.

Description

Additive waveshape pretreatment method in the digital communication modulation

Technical field

The present invention relates to a kind of modulator approach of signal of communication, exactly, relate to the additive waveshape pretreatment method in a kind of digital communication modulation, belong to digital communication technology field.

Background technology

In digital communication, binary message is converted to the signal waveform that can on transmission channel, transmit by modulation technique.By the principle of signal processing as can be known, on the one hand, each signal all has its specific frequency spectrum, but its spectral characteristic can not satisfy the requirement of signal transmission performances sometimes; On the other hand, on frequency domain, during limited bandwidth (be called for short limit band), on time domain, will cause distorted signals and produce the hangover ripple when transmission signals; Distorted signals can influence demodulation accuracy, and the hangover ripple then causes intersymbol interference (Inter-SymbolInterference is hereinafter to be referred as ISI) and the inter-carrier interference (Inter-Carrier Interference is hereinafter to be referred as ICI) between each signal element.Transmission network or transmission channel (in order to narrate conveniently, the below unified transmission channel that abbreviates as) produce bigger restriction in the restriction meeting aspect frequency domain and the time domain two to the transmission performance of digital communication to transmission signals.This physical phenomenon can be described with following mathematical formulae:

If the initialize signal of transmitting terminal is g (t), be through the signal that arrives receiving terminal of communication system (being designated hereinafter simply as receiving terminal) after the transmission channel

, be to simplify narration, transmission channel is equivalent to a filter (band is logical, low pass or high pass), the impulse response of this filter is represented it with p (t), then have:

$\tilde{g}\left(t\right)=p\left(t\right)*g\left(t\right),$ * be the convolution algorithm symbol; (1)

$\tilde{G}\left(u\right)=P\left(u\right)G\left(u\right)$ (2)

In the above-mentioned formula (1)

Be the time-domain representation of receiving terminal received signal, it is equivalent to the impulse response p (t) and the convolution that sends signal g (t) of filter, in the formula (2) It is the frequency domain representation of receiving terminal received signal, it is equivalent to the product of P (u) and G (u), P (u) is the frequency domain representation of p (t), G (u) is the frequency domain representation of g (t), convolution in the formula (1) is converted to product in formula (2), this formula is used for the pretreated method of waveform of the present invention and result are analyzed on frequency domain and compare.Received signal

Can be divided into main ripple With the hangover ripple

Two parts, main ripple

It is receiving end signal

Signal in a code-element period, the shape of the shape of main ripple and transmitting terminal initialize signal g (t) is unequal but approaching, the hangover ripple

It is receiving end signal

Behind code-element period one decay concussion waveform, it can cause the interference (ISI) between symbol signal and the interference (ICI) of intercarrier, and then the signal to noise ratio of reduction receiving terminal.For this reason, people develop the pretreated method of waveform, are used to reduce wave distortion, ISI and ICI.

Traditional waveform preprocess method starting point is to concentrate on the frequency domain performance of improving transmission signals, and concrete grammar is that the code element waveform is carried out windowing process, changing the spectral shape (Spectral Shaping) of signal, thereby improves the frequency domain characteristic of transmission signals.Spectral shape generally shows as periodic damping vibration deltoid (referring to Figure 12), and the cycle of curve below area maximum is called main lobe, and the frequency separation that main lobe occupies is called spectrum bandwidth at zero point.This windowing method can be described with following formula: $\hat{g}\left(t\right)=f\left(t\right)g\left(t\right),$ Wherein, the span of time variable t is: the T of kT≤t＜(k+1), T is the signal element cycle, g (t) is the initialize signal before communication system transmitting terminal (being designated hereinafter simply as transmitting terminal) windowing, f (t) is the windowing waveform, f (t) can be various waveforms, adopts square wave, Gaussian waveform or raised cosine waveform usually

Be the signal that at transmitting terminal initialize signal g (t) is carried out with traditional windowing method changing after the waveform preliminary treatment.This method is a kind of property taken advantage of waveform preprocess method.In many cases, windowing process can make secondary lobe (claiming that again band is outer) decay accelerate, and this helps reducing ICI and ISI, but can strengthen the main lobe interval width, increases the consumption of band resource.Therefore, only the spectral shape that changes signal by windowing can not satisfy the transmission performance requirement, and is particularly more not obvious to the effect of eliminating the hangover ripple.Therefore, how traditional waveform preprocess method is improved, just become and need the new problem that solves in this field to reduce wave distortion, ICI and ISI.

Summary of the invention

In view of this, the purpose of this invention is to provide the additive waveshape pretreatment method in a kind of digital communication modulation, this method is on the initialize signal of the transmitting terminal that on the time domain additional wave is added to, and by this waveform is carried out the additivity preliminary treatment, promptly is called for short what is called and adds ripple and handle; With overcome traditional the code element waveform is carried out windowing process after, the spectral shape of signal still can not satisfy the transmission performance requirement, especially eliminate the defective of the DeGrain of hangover ripple, can between spectral shape and time domain distortion, obtain better compromise and balance, reach the purpose that reduces ICI and ISI simultaneously.

In order to achieve the above object, the invention provides the additive waveshape pretreatment method in a kind of digital communication modulation, it is characterized in that: the additional wave f (t) that will select in advance, construct, adjust and obtain is added on the initialize signal g (t) of transmitting terminal, makes up a shaping ripple g different with initialize signal g (t) waveform ₁(t), i.e. g ₁(t)=g (t)+f (t), and send this shaping ripple g at transmitting terminal ₁(t); G (t) and g ₁(t) all being is the burst that chronomere divides with the code element, and Baud Length represents with period T, i.e. the T of kT≤t＜(k+1), k are zero or positive integer, and the waveform between each code element is separate; Signal arrives the receiving terminal procedural representation: ${\tilde{g}}_1\left(t\right)=p\left(t\right)*g_1\left(t\right)={\tilde{g}}_{11}\left(t\right)+{\tilde{g}}_{12}\left(t\right),$ In the formula,

Be the shaping ripple signal that receives at receiving terminal, * is the convolution algorithm symbol, and p (t) is defined as and is used for impulse response of replacing the filter of transmission channel of equal value, received signal

Can be decomposed into two parts: main ripple

With the hangover ripple

Its span is respectively: ${\tilde{g}}_{11}\left(t\right)=\left\{\begin{array}{cc}{\tilde{g}}_1\left(t\right),& \mathrm{kT}\&le;t<(K+1)T)\\ 0,& [(k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3)\end{array}\right.,$ ${\tilde{g}}_{12}\left(t\right)=\left\{\begin{array}{cc}0,& \mathrm{kT}\&le;t<(k+1)T)\\ {\tilde{g}}_1\left(t\right),& (k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3)\end{array}\right.;$ In the formula, T is the code-element period length of transmitting terminal initialize signal g (t), τ ₃Length be infinitely great in theory, depend on the attenuation of the wave amplitude that trail during enforcement, concrete numerical value depends on training algorithm, k is zero or positive integer; Behind above-mentioned preliminary treatment and transmission channel, received shaping ripple

Shape be different from received signal

Shape, can realize following technique effect: make receiving end signal

Main ripple

Waveform more near the waveform of transmitting terminal initialize signal g (t), and satisfy the requirement of transfer of data to decoding, effectively reduce receiving terminal hangover ripple simultaneously

The amplitude of waveform.

Described method is applied to each signal element when being made up of single waveform, further comprises following to the pretreated content of operation of additive waveshape:

The shaping ripple signal that transmitting terminal sends is g ₁(t)=g (t)+f (t), $f\left(t\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ M is a positive integer, i.e. shaping ripple g ₁(t) be the signal that forms and send behind initialize signal g (t) the stack additional wave f (t) of transmitting terminal by transmitting terminal, wherein additional wave f (t) is then by positive integer m sub-additional wave f _i(t) be combined to form sub-additional wave f _i(t) be training algorithm and the waveform that comprises triangular wave, trapezoidal wave, square wave or other Any shape selecting for use, construct and adjust according to the present invention, the position of additional wave is in time interval [kT-τ ₁, (k+1) T+ τ ₂] in the scope, wherein T is the code-element period of initialize signal g (t), τ ₁Be time section at the additional wave of initialize signal code-element period front end, τ ₂Be time section at the additional wave of initialize signal code-element period rear end, t=kT-τ ₁Expression from an initial moment of initialize signal code-element period to previous τ ₁The moment, t=(k+1) T+ τ ₂Expression is from this initialize signal code-element period finish time of τ backward ₂The moment, τ ₁, τ ₂The shape and the position of numerical value, sub-additional wave or additional wave are obtained by training algorithm respectively.

Take into account wave distortion and the hangover wave amplitude all enough little, be distortion and the hangover minimization method principle under, by training, structure corresponding sub-additional wave, additional wave and shaping ripple, the waveform of receiving end signal master ripple is tried one's best near the waveform of transmitting terminal initialize signal, and the waveform distortion of reduction received signal, reduce receiving end signal hangover wave amplitude simultaneously as far as possible; Described training algorithm further comprises following concrete operations content:

(1) make sequence number i=1 ..., m, m are positive integer, selected a series of sub-additional wave f _i(t), the additional wave structure of this series, shape and position are according to the ε in following step (3) and (5) ₁And ε ₂Constraints make up, construct the shaping ripple again $g_1\left(t\right)=g\left(t\right)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ In the formula, g (t) is the initialize signal of transmitting terminal, g ₁(t) be the shaping ripple that g (t) sends out after transmitting terminal is through the additive waveshape preliminary treatment;

(2) make shaping ripple g ₁(t) by with the filter of transmission channel equivalence after, receive the shaping ripple signal that obtains at receiving terminal Use formula ${\tilde{g}}_1\left(t\right)=g_1\left(t\right)*p\left(t\right)$ Represent it, in the formula, * is the convolution algorithm symbol, and p (t) is the impulse response of filter;

(3) choose signal at receiving terminal

Be positioned at time interval [kT, (k+1) T) main ripple Judge then whether following formula is set up: ${|g^2\left(t\right)-{\tilde{g}}_{11}^2|}^{1/2}\&le;{\mathrm{\&epsiv;}}_1,$ In the formula, ε ₁Be an enough little threshold value, be used to be illustrated in the shaping ripple that receiving terminal receives

Main ripple With respect to the requirement of the distortion level of transmitting terminal initialize signal g (t) waveform, this ε ₁Numerical value depend in the design performance under the given signal transmission conditions and require: the error rate is not more than a certain set point under the transmission rate of setting, and perhaps satisfies the requirement of transmission rate under the error rate of setting; If ε ₁Numerical value can satisfy this designing requirement, just thinks enough little; If above-mentioned formula is set up, then order is carried out subsequent operation; Otherwise, return step (1), continue the repetition training process, till the additional wave or sub-additional wave that are met above-mentioned formula establishment;

(4) choose shaping ripple signal at receiving terminal Be positioned at time interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple In the formula, τ ₃＞τ ₂, τ ₂Be time span at the additional wave of transmitting terminal initialize signal code-element period rear end, τ ₃Be to be a period of time length of the hangover ripple that intercepted of calculating hangover ripple signal at receiving terminal, this τ ₃Time span be infinite length in theory, during enforcement, τ ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then is decided by the judgment criterion of step (5);

(5) respectively interval [kT, (k+1) T) go up the main ripple of intercepting

With at interval [(k+1) T, (k+1) T+ τ ₃) last intercepting hangover ripple

And do following computing: in the interval [kT, (k+1) T) interior to main ripple calculating $G_{}$ ${}_1={\&Integral;}_{\mathrm{kT}}^{(k+1)T}{\tilde{g}}_{11}^2\left(t\right)\mathrm{dt},$ At interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple is calculated $G_2={\&Integral;}_{(k+1)T}^{(k+1)T+{\mathrm{\&tau;}}_3}{\tilde{g}}_{11}(t-(k+1)T){\tilde{g}}_{12}\left(t\right)d\left(t\right);$ Definition

Main ripple with the hangover Bob $\mathrm{MIR}=10{\log }_{10}\frac{G_1}{G_2},$ Judge whether following formula is set up: MTR 〉=ε ₂, in the formula, ε ₂Be an enough big threshold value, be used to reflect that the hangover phase of wave is for the influence degree of main ripple to transmission performance, this ε ₂Numerical value depends in the design performance under the given signal transmission conditions and requires: the error rate is not more than a certain set point under the transmission rate of setting, and perhaps satisfies the requirement of transmission rate under the error rate of setting; If ε ₂Numerical value can satisfy this designing requirement, just thinks enough big; If above-mentioned formula is set up, finish training process; Otherwise return step (1), continue the repetition training process,, finish additive waveshape preliminary treatment with distortion and hangover minimization method until being met sub-additional wave, additional wave and the shaping ripple that above-mentioned formula is set up.

Take into account signal to noise ratio enough big and the hangover wave amplitude is enough little, be under the principle of maximum signal to noise ratio method, by training, structure corresponding sub-additional wave, additional wave and shaping ripple, make the signal to noise ratio between receiving end signal and the transmission channel noise enough big, reduce the amplitude of receiving end signal hangover ripple simultaneously as far as possible; Described training algorithm further comprises following concrete operations content:

(1) make sequence number i=1 ..., m, m are positive integer, selected a series of sub-additional wave f _i(t), the additional wave structure of this series, shape and position are according to the ε in following step (3) and (5) ₁And ε ₂Constraints make up, construct the shaping ripple again $g_1\left(t\right)=g\left(t\right)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ In the formula, g (t) is the initialize signal of transmitting terminal, shaping ripple g ₁(t) be the signal that primary wave g (t) sends out after transmitting terminal is through the additive waveshape preliminary treatment;

(2) make shaping ripple g ₁(t) by with the filter of transmission channel equivalence after, receive the shaping ripple signal that obtains at receiving terminal

Use formula ${\tilde{g}}_1\left(t\right)=g_1\left(t\right)*p\left(t\right)$ Represent it, in the formula, * is the convolution algorithm symbol, and p (t) is the impulse response of filter;

(3) choose the shaping ripple signal that receives at receiving terminal

Be positioned at the interval [kT, (k+1) T) main ripple

Part, judge again whether the signal to noise ratio of receiving terminal satisfies formula: $\mathrm{SNR}=10{\log }_{10}\frac{{\tilde{g}}_{11}^2\left(t\right)}{{\mathrm{\&sigma;}}^2}\&GreaterEqual;{\mathrm{\&epsiv;}}_1,$ In the formula, σ ²Represent noise energy, ε ₁Be an enough big threshold value, its numerical value depend under the given signal transmission conditions to the requirement of design performance: the error rate is not more than a certain set point under the transmission rate of setting, or possesses sufficiently high transmission rate under the error rate of setting, if ε ₁Numerical value makes the noise specific energy of main ripple satisfy this designing requirement, just thinks enough big; If satisfy above-mentioned formula, then order is carried out subsequent operation; Otherwise, return step (1), continue the repetition training process, till the sub-additional wave that is met above-mentioned formula establishment, additional wave;

(4) choose shaping ripple signal at receiving terminal Be positioned at time interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple

In the formula, τ ₃＞τ ₂, τ ₂Be time section at the additional wave of transmitting terminal initialize signal code-element period rear end, τ ₃Be to be a period of time length of the hangover ripple that intercepted of calculating hangover ripple signal at receiving terminal, this τ ₃Time span be infinite length in theory, during enforcement, τ ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then depends on the judgment criterion of step (5);

(5) respectively interval [kT, (k+1) T) go up the main ripple of intercepting With at interval [(k+1) T, (k+1) T+ τ ₃) last intercepting hangover ripple And do following computing: in the interval [kT, (k+1) T) interior to main ripple calculating $G_{}$ ${}_1={\&Integral;}_{\mathrm{kT}}^{(k+1)T}{\tilde{g}}_{11}^2\left(t\right)\mathrm{dt},$ At interval [(k+1) T, (k+1) T+ τ ₃) interior to the calculating of hangover ripple $G_2={\&Integral;}_{(k+1)T}^{(k+1)T+{\mathrm{\&tau;}}_3}{\tilde{g}}_{11}(t-(k+1)T){\tilde{g}}_{12}\left(t\right)d\left(t\right);$ Definition Main ripple with the hangover Bob $\mathrm{MTR}=10{\log }_{10}\frac{G_1}{G_2},$ Judge whether following formula is set up: MTR 〉=ε ₂, in the formula, ε ₂Be an enough big threshold value, be used to reflect that the hangover phase of wave is for the influence degree of main ripple to transmission performance, this ε ₂Numerical value depends in the design performance under the given signal transmission conditions and requires: the error rate is not more than a certain set point under the transmission rate of setting, or has sufficiently high transmission rate under the error rate of setting; If ε ₂Numerical value can satisfy this designing requirement, just thinks enough big; If above-mentioned formula is set up, finish training process; Otherwise return step (1), continue the repetition training process,, finish the additive waveshape preliminary treatment of maximum signal to noise ratio method until being met sub-additional wave, additional wave and the shaping ripple that above-mentioned formula is set up.

When adopting one by one recurrence method, the ripple that will trail is divided into plurality of sections, and claim every section to be a son hangover ripple, construct each the sub-additional wave that to eliminate every cross-talk hangover ripple then repeatedly, at last this a little additional wave being stacked up constitutes the additional wave can eliminate whole hangover ripple, this additional wave and primary wave is synthesized the shaping ripple of transmitting terminal again; Described training algorithm further comprises following concrete operations content:

(1) with interval [(k+1) T, (k+1) T+ τ ₃) in the hangover wavelength-division be the L section, and be expressed as ${\tilde{g}}_{12}\left(t\right)={\tilde{g}}_{121}\left(t\right)+\&CenterDot;\&CenterDot;\&CenterDot;{\tilde{g}}_{12j}\left(t\right)+\&CenterDot;\&CenterDot;\&CenterDot;+{\tilde{g}}_{12L}\left(t\right),$ Be to have added shaping ripple behind the additional wave of top by the hangover part behind the filter p (t), wherein, j section hangover ripple

(k+1) T≤φ _j＜(k+1) T+ τ ₃), φ _j＜φ _J+1, j=1 ..., L, [φ _j, φ _J+1) be son hangover ripple

The interval;

(2) establishing v is cycle index counter, and makes v=1;

(3) make j=1;

(4) sub-additional wave f of structure _j(t), this sub-additional wave by filter after distortion and produce prolong and the new hangover ripple in whole hangover ripple interval, be formulated as: ${\tilde{f}}_j\left(t\right)={\tilde{f}}_1\left(t\right)*p\left(t\right),(k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3);$ Therefore the hangover ripple of present segment can be subjected to the influence of the new hangover ripple that additional wave produced of other section, is formulated as: ${\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{g}}_{12j}\left(t\right)={\tilde{g}}_{12j}\left(t\right)+\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{\tilde{f}}_k\left(t\right)+\underset{k=j+1}{\overset{{\mathrm{\&tau;}}_3}{\mathrm{\&Sigma;}}}{\tilde{f}}_k\left(t\right);$ Additional wave is trained, it is met the requirements of according to being: satisfy following inequality ${\&Integral;}_{{\mathrm{\&phi;}}_j}^{{\mathrm{\&phi;}}_{j+1}}{({\tilde{f}}_j\left(t\right)-{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{g}}_{12j}\left(t\right))}^2\mathrm{dt}<{\mathrm{\&epsiv;}}_4;$ ε ₄Be an enough little threshold value, so that

With

Approaching as far as possible, ε ₄Concrete numerical value determine in requiring in the design performance under the given signal transmission conditions: the error rate is not more than a certain setting numerical value under the transmission rate of setting, or has sufficiently high transmission rate under the error rate of setting; If ε ₄Numerical value can satisfy this designing requirement, just thinks enough little;

(5) make j=j+1, if j＞L then finishes the structure of additional wave in the v time circulation, otherwise returns step (4); Continue the repetition training process, until the sub-additional wave of the every cross-talk hangover ripple that is met above-mentioned formula establishment;

(6) check whether the hangover ripple of all each sections enough little? if reach enough little, then finish the training of additional wave, continue to carry out subsequent operation; Otherwise, establish v=v+1, and return execution in step (3);

(7) all sub-additional waves are stacked up formation additional wave stacks up additional wave and primary wave and synthesizes the shaping ripple, finishes one by one the additive waveshape preliminary treatment of recurrence method.

When adopting the liftering method, receive ripple and recover the transmission ripple from receiving ripple or part, or send ripple and recover required additional wave from part, this additional wave and primary wave are synthesized the shaping ripple of transmitting terminal, described training algorithm further comprises following concrete operations content:

Earlier with transmitting terminal initialize signal g (t) by with the filter of transmission channel equivalence after

Signal waveform be divided into two parts: interval [kT, (k+1) T) in main ripple signal

With at interval [(k+1) T, (k+1) T+ τ ₃) interior hangover ripple signal

T is the code-element period length of transmitting terminal initialize signal g (t), τ ₃Length be infinitely great in theory, τ during enforcement ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then depends on training algorithm, k is zero or positive integer, main ripple signal and hangover ripple signal are respectively: ${\tilde{g}}_M\left(t\right)=\left\{\begin{array}{cc}\tilde{g}\left(t\right),& \mathrm{kT}\&le;t<(k+1)T\\ 0,& (k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3)\end{array}\right.,$ ${\tilde{g}}_T\left(t\right)=\left\{\begin{array}{cc}0,& \mathrm{kT}\&le;t<(k+1)T\\ {\tilde{g}}_1\left(t\right),& (k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3\end{array}\right.;$ Ripple signal again will trail

As additional wave, described formula with liftering structure additional wave is by the waveform that obtains after the liftering: $F\left(u\right){=\tilde{G}}_T\left(u\right)/P\left(u\right);$ In the formula, F (u) is the frequency domain representation of required additional wave of finding the solution,

It is the hangover ripple Frequency domain representation, P (u) is the frequency domain representation that is used for the impulse response p (t) of the filter of replacing transmission channel of equal value; Then, F (u) is converted to time-domain signal f (t) with contrary fast fourier transform, perhaps according to following formula, directly will be with the hangover ripple signal of time-domain representation Through the time-frequency domain conversion, obtain the additional wave signal f (t) of time-domain representation: $f\left(t\right)=\mathrm{REAL}\left[\mathrm{IFFT}[\mathrm{FFT}\left[{\tilde{g}}_T\left(t\right)\right]/\mathrm{FFT}\left[p\left(t\right)\right]]\right],$ In the formula, f (t) representative is through the signal after the liftering, and p (t) is the impulse response of filter, FFT[] represent fast fourier transform, IFFT[] the contrary fast fourier transform of representative, REAL[] represent to get real; At last, will after initialize signal g (t) stack, pass through filter again, can reduce hangover, finish the additive waveshape preliminary treatment of liftering method through the signal f (t) after the liftering as additional wave.

It is by two or two above wavelet g that described method is applied to each signal element _i(t) the composite wave signal that waveform linear superposition forms $g\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_i\left(t\right)$ The time, being called the multiple wavelet code element, in the formula, natural number i is the wavelet sequence number, span is [1, N]; Select various dissimilar ripples, promptly the different ripple of shape, frequency, phase place, position or amplitude is used as wavelet g _i(t), and adopt aforementioned additive waveshape pretreatment method that each wavelet in the composite wave is handled to the signal element formed by single waveform, promptly select following method respectively for use: distortion and hangover minimization method or maximum signal to noise ratio method or recurrence method or liftering method are made the additive waveshape pretreatment operation to the waveform of each wavelet in the composite wave one by one, obtain pretreated composite wave, to satisfy the requirement of transmission channel and transmission performance.

Described select for use distortion and hangover minimization method or maximum signal to noise ratio method or one by one recurrence method or liftering method the waveform of composite wave made preprocess method further comprise following concrete operations step:

(1) makes wavelet sequence number i=1;

(2) to wavelet g _i(t) implement the pretreatment operation of " distortion and hangover minimization method " or " maximum signal to noise ratio method " or " recurrence method one by one " or " liftering method ", obtain pretreated sub-shaping ripple g _1i(t);

(3) make i=i+1 again, and judge that i＞N sets up? if then order is carried out subsequent operation; Otherwise, return step (2), continue to repeat pretreatment operation;

(4) with all sub-shaping ripple g _1i(t), i=1,2 ..., N, N are positive integer, carry out linear superposition according to following formula: $g_1\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_{1i}\left(t\right),$ Get the pretreated composite wave that is used for transmitting terminal to the end, i.e. the shaping ripple of the synthetic code element of multiple wavelet.

It is by two or two above wavelet g that described method is applied to each signal element _i(t) the composite wave signal that waveform linear superposition forms $g\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_i\left(t\right)$ The time, in the formula, natural number i is the wavelet sequence number, span is [1, N]; Select following method respectively for use: the carrier transmission of multiple width of cloth phase modulating baseband transmission or multiple width of cloth phase modulating baseband sign indicating number or the multiple width of cloth are modulated direct carrier transmission mutually waveform are made the additive waveshape pretreatment operation, obtain pretreated composite wave, to satisfy the requirement of transmission channel and transmission performance.

Carrier transmission, the multiple width of cloth of described multiple width of cloth phase modulating baseband transmission, multiple width of cloth phase modulating baseband sign indicating number are modulated three kinds of common features that are used for the coded system of circuit transfer encoding of direct carrier transmission mutually and are:

A, their code element all are made up of the identical wavelet of a plurality of frequencies, and each wavelet is got the amplitude of different brackets, and each grade amplitude is corresponding to a binary coding;

B, their all available following equation group form of Code And Decode are represented: encoding equtions group: AX=G, decoding equation group: X=A ^-1G, in the formula,

$X=\left[\begin{array}{c}{X}_1\\ X_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ X_h\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ X_H\end{array}\right],$ $G=\left[\begin{array}{c}{G}_1\\ G_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ G_h\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ G_H\end{array}\right]$

Wherein, X is the wavelet amplitude vector, and G is the vector that obtains behind a series of coherent computings of the process of receiving terminal code element, and A is the coefficient matrix of encoding equtions group, A ^-1Be the contrary of A, K _HjBe the element of coefficient matrix, span is a real number field, solving equation group X=A ^-1G promptly gets separating of each wavelet.

Three kinds of line codings that the carrier transmission and the multiple width of cloth of described multiple width of cloth phase modulating baseband transmission, multiple width of cloth phase modulating baseband sign indicating number modulated direct carrier transmission mutually are referred to as nonopiate amplitude Multiple Modulation coding, promptly abbreviate the NMAM coding as, when this NMAM coding is carried out the additive waveshape preliminary treatment, if encoding equtions group AX=G is an ill-condition equation, then according to minimum ill principle structure additional wave, its concrete operations step is as described below:

(1) from composite wave, takes out a wavelet, select for use a kind of in distortion and hangover minimization method or maximum signal to noise ratio method or successive approximation method or four kinds of methods of liftering method that this wavelet is carried out preliminary treatment respectively;

(2) judge whether to satisfy following formula: ‖ A ^-1‖＜γ, in the formula, ‖ A ^-1‖ is the contrary norm of equation group coefficient matrix, and γ is an enough little threshold value, and through the training decision, the foundation that training finishes is that coding or decoding solution of equations can reach desirable precision to its value by the designer; If ‖ is A ^-1The value of ‖ meets the demands, and finishes the additive waveshape preprocessing process; Otherwise, return step (1), continue to select new additional wave, sub-additional wave, till the sub-additional wave and additional wave that are met above-mentioned formula establishment.

Multiple width of cloth phase modulating baseband Digital Transmission in the additive waveshape pretreatment method of the present invention is with code element transmission one by one, each code element all is made up of a composite wave, described composite wave is made up of identical monocyclic sine wave of some cycles, and each sine wave moves a phase place in succession, its cycle is less than synthetic wave period, its amplitude is got a value from the quantification set of regulation, thereby realizes multiple width of cloth phase modulating baseband Digital Transmission.

The carrier transmission of the multiple width of cloth phase modulating baseband sign indicating number in the additive waveshape pretreatment method is that described multiple width of cloth phase modulating baseband sign indicating number carrier wave is formed carrier signal in a certain passband that is higher than base band, at receiving terminal, use the carrier wave in the received signal of band pass filter elimination earlier, decode again, realize the carrier wave Digital Transmission of multiple width of cloth phase modulating baseband sign indicating number.

It is with code element transmission one by one that the multiple width of cloth in the additive waveshape pretreatment method is modulated direct carrier transmission mutually, each code element is made up of a composite wave, each cycle of described composite wave is made up of the identical sine wave of some terms of validity, and the time span of this term of validity is the integral multiple of sine wave period, and less than synthetic wave period, each sine wave moves a phase place in succession, its amplitude is chosen a value arbitrarily from the quantification set of regulation, thereby realizes that the multiple width of cloth modulates direct carrier wave Digital Transmission mutually.

The good effect that the present invention brings is: usually, the finite value that the bandwidth of communication system is always set, this will make transmission signals deform on time domain and reduce the signal to noise ratio of separating timing, and then reduce transfer rate, or be called the increase error rate.The solution of prior art has three kinds: (1) does the waveform processing of windowing to sending signal, the frequency spectrum of transmission signals is done certain adjustment, to improve transmission performance; (2) isolation strip is set on frequency domain, with the phase mutual interference of the interchannel that reduces nearby frequency bands; (3) on time domain, for each code element adds a Cyclic Prefix (or insert several zero) between two code elements, to lower intersymbol interference.The first two kind method is be the requirement that cost satisfies transfer rate to increase frequency bandwidth (frequency domain resource), and the third method then is to be that cost satisfies the requirement to transmission error rates with reduction code element efficiency of transmission (time-domain resource).The pretreated method of additive waveshape of the present invention can be used frequency domain and time-domain resource cost than above-mentioned three kinds of method cost less, and keep higher demodulation performance.In windowing waveform preprocess method, the window function that finds so far is limited.Wherein commonly used is raised cosine, and it can accelerate the decay (it is little to show as " secondary lobe " on spectrogram) of the outer energy of signal band.But, the bandwidth that its main energy occupies but double (on spectrogram, show as " main lobe " and widen) referring to accompanying drawing 12.And the pretreated method of additive waveshape of the present invention can reduce secondary lobe under the situation that does not increase main lobe width, referring to accompanying drawing 3,5,7 and 10 (C), therefore can reduce ICI; Simultaneously, can on time domain, reduce the hangover of waveform and change the shape of main ripple again.Like this, both satisfied demodulation requirement, reduced ICI and ISI again,, can also reduce the pathosis of equation group effectively, and, can increase the morbid state of equation group as the method for the raised cosine windowing of Figure 12 for the NMAM coding to main ripple.In a word, the pretreated method of additive waveshape of the present invention has following advantage: the frequency spectrum of transmission signals can be adjusted in the scope that satisfies the transmission performance requirement, the pretreated signal of process waveform is by behind the transmission channel, not only reduce the outer energy of band (reducing ICI) of signal and the hangover (reducing ISI) of time domain, and reducing the pathosis of equation group effectively, this is a unexistent waveform preprocess method in the existing communication system.

Description of drawings

Fig. 1 is the operating procedure flow chart of the additive waveshape pretreatment method in the digital communication modulation of the present invention.

Fig. 2 (A), (B), (C), (D) be respectively according to the inventive method carry out the additional wave (single trapezoidal wave) of primary wave (sine wave), the transmitting terminal of the pretreated transmitting terminal of additive waveshape, through the waveform (solid line) of the primary wave that receives at receiving terminal behind the transmission channel and the waveform (dotted line) of additional wave, and pass through behind the transmission channel schematic diagram at the composite wave of the primary wave of receiving terminal and additional wave.

Fig. 3 is that the spectral shape (dotted line) of the initialize signal among Fig. 2 and the spectral shape (solid line) of the shaping ripple behind the stack additional wave compare schematic diagram.

Fig. 4 (A), (B), (C) be respectively according to the inventive method carry out the additional wave of the initialize signal sine wave (solid line) of the pretreated transmitting terminal of additive waveshape and cycle square wave (chain-dotted line), through (wherein solid line waveform is a primary wave in the signal waveform of receiving terminal behind the transmission channel, dotted line waveform is an additional wave), and through behind the transmission channel at the schematic diagram of the signal waveform (wherein solid line waveform is the shaping ripple, and dotted line waveform is a primary wave) of receiving terminal.

Fig. 5 is that the spectral shape (chain-dotted line) of the initialize signal among Fig. 4 and the spectral shape (solid line) of the shaping ripple behind the stack additional wave compare schematic diagram.

Fig. 6 (A), (B), (C) be respectively according to the inventive method carry out the additional wave of the initialize signal sine wave (solid line) of the pretreated transmitting terminal of additive waveshape and single triangular wave (chain-dotted line), through (wherein solid line waveform is a primary wave in the signal waveform of receiving terminal behind the transmission channel, dotted line waveform is an additional wave), and through behind the transmission channel at the schematic diagram of the signal waveform (wherein solid line waveform is the shaping ripple, and dotted line waveform is an initialize signal) of receiving terminal.

Fig. 7 is that the spectral shape (chain-dotted line) of the initialize signal among Fig. 6 and the spectral shape (solid line) of the shaping ripple behind the stack additional wave compare schematic diagram.

Fig. 8 (A), (B), (C), (D), (E), (F) be the waveform of initialize signal waveform (solid line) and first additional wave (dotted line) when adopting recurrence method one by one of the present invention to carry out the additive waveshape preliminary treatment respectively, shaping ripple after initialize signal and the stack of first additional wave is at the waveform (dotted line) of receiving terminal, the partial enlarged drawing of hangover ripple among Fig. 8 (B) figure, at transmitting terminal initialize signal (solid line), first additional wave (dotted line), second additional wave (one one line), the waveform of the 3rd additional wave (two standardized dotted lines), signal waveform (dotted line) after receiving terminal initialize signal and the stack of first additional wave, receiving terminal initialize signal and first, signal waveform after the stack of two additional waves (one one line), receiving terminal initialize signal and first, two, signal waveform after the stack of three additional waves (two two line), and the schematic diagram of the partial enlarged drawing of the ripple that trails among Fig. 8 (E) figure.

Fig. 9 (A), (B), (C) be respectively adopt liftering method of the present invention carry out the initialize signal sine wave of the pretreated transmitting terminal of additive waveshape, be equivalent to transmission channel filter frequency domain characteristic and with the schematic diagram of primary wave by the waveform behind the filter.

Figure 10 (A), (B), (C) be respectively the additional wave waveform that carries out obtaining after liftering is handled of the hangover ripple with the primary wave of Fig. 9 (C) figure, the shaping ripple after being added to this additional wave on the primary wave is by the waveform behind the filter, and the spectral shape schematic diagram of additional wave.

Figure 11 (A), (B), (C) are respectively that employing liftering method of the present invention is to improve the contrary norm ‖ A of equation group coefficient matrix ^-1‖ and NMAM coding is realized the pretreated various waveforms of additive waveshape.Figure 11 (A) is a wavelet in the initialize signal code element in the transmitting terminal NMAM coding, and its waveform is the multicycle sine wave.Figure 11 (B) for the waveform among Figure 11 (A) be applied through behind the additional wave that obtains after the liftering again by with the filter of channel equivalence after waveform, thus as the ‖ A of the NMAM of wavelet composition ^-1‖ is very big.Figure 11 (C) for after adding additional wave on the basis of Figure 11 (B) again by with the filter of channel equivalence after waveform, the ‖ A of the NMAM that forms as wavelet thus ^-1‖ reduces greatly.

Dotted line among Figure 12 is represented the frequency spectrum of square wave, and solid line is represented the frequency spectrum through the square wave of raised cosine windowing process, illustrates that raised cosine windowing process meeting strengthens the main lobe width of frequency spectrum, and accelerates the decay of secondary lobe.

Embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, the present invention is described in further detail below in conjunction with accompanying drawing.

The present invention is a kind of digital communication modulated waveform preprocess method that is used for, and with respect to the pretreated windowing method of the traditional property taken advantage of waveform, this method additive waveshape pretreatment method that is otherwise known as specifies it below:

If the initialize signal of transmitting terminal is g (t), be through the signal that arrives receiving terminal after the transmission channel

Be to simplify narration, transmission channel is equivalent to a filter (band is logical, low pass or high pass), the impulse response of this filter is p (t) (for easy, below directly be called p (t)), then has:

$\tilde{g}\left(t\right)=p\left(t\right)*g\left(t\right),$ * be the convolution algorithm symbol; (3)

$\tilde{G}\left(u\right)=P\left(u\right)G\left(u\right)$ (4)

In the above-mentioned formula (3)

Be the time-domain representation of receiving terminal received signal, its implication is the impulse response p (t) and the convolution that sends signal g (t) of filter.In the formula (4)

It is the frequency domain representation of receiving terminal received signal, it is the product of P (u) and G (u), P (u) and G (u) are respectively the frequency domain representations of p (t) and g (t), convolution in the formula (3) is converted to product in formula (4), formula (4) is used for the pretreated method of waveform of the present invention and result are analyzed on frequency domain and compare.Received signal

Can be divided into main ripple

With the hangover ripple

Two parts, main ripple It is receiving end signal Signal in a code-element period, the shape of the shape of main ripple and transmitting terminal initialize signal g (t) is unequal but approaching, the hangover ripple

It is receiving end signal

A decay concussion waveform behind code-element period, it can cause ICI and ISI, and then reduces the signal to noise ratio of receiving terminal.

Waveform preprocess method of the present invention be will be in advance through selecting, structure, adjust and the additional wave set is added on the initialize signal g (t) of transmitting terminal, make up one different with initialize signal g (t) waveform and be defined as g ₁(t) shaping ripple is then with this shaping ripple g ₁(t) send from transmitting terminal; And at receiving terminal, be the shaping ripple signal definition that receives And be expressed as ${\tilde{g}}_1\left(t\right)=p\left(t\right)*g_1\left(t\right),$ In the formula, * is the convolution algorithm symbol,

Be the receiving terminal received signal with time-domain representation, p (t) is used for impulse response of replacing the filter of transmission channel of equal value, and the received signal of this receiving terminal

Can divide the main ripple of serving as reasons equally With the hangover ripple

Two parts are formed.Key of the present invention is by selecting, construct and adjusting additional wave, to obtain suitable shaping ripple g at transmitting terminal ₁(t), make receiving end signal

Shape obtain certain and change, thereby reach following two or the goal of the invention of one of them:

(1) makes receiving end signal

Main ripple

Waveform more near the waveform of transmitting terminal initialize signal g (t), and reduce receiving terminal hangover ripple signal as far as possible

The amplitude of waveform;

(2) make receiving end signal

Main ripple

Satisfy the requirement of transfer of data to decoding.

Referring to Fig. 1, introduce the operating process and the realization principle of additive waveshape pretreatment method of the present invention:

One, the waveform preprocess method of the signal of forming by single waveform for each code element:

If signal-shaping ripple that transmitting terminal sends is g ₁(t)=g (t)+f (t), $f\left(t\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ In the formula, g (t) is the initialize signal of transmitting terminal, and f (t) is an additional wave, g ₁(t) be to add the shaping ripple that forms and send out behind the additional wave f (t), f by initialize signal g (t) at transmitting terminal _i(t) be sub-additional wave, m is a positive integer, additional wave f (t) can be made up of m sub-additional wave, sub-additional wave is the waveform that comprises triangular wave, trapezoidal wave, square wave or other Any shape that training algorithm according to the present invention is selected for use, constructed and adjusts, and the position of additional wave can be positioned at time interval [kT-τ ₁, (k+1) T+ τ ₂] in the scope, T is the code-element period of initialize signal g (t), τ ₁Be time section at the additional wave of initialize signal code-element period front end, τ ₂Be time section at the additional wave of initialize signal code-element period rear end, t=kT-τ ₁Expression from an initial moment of initialize signal code-element period to previous τ ₁The moment, t=(k+1) T+ τ ₂Expression is from this initialize signal code-element period finish time of τ backward ₂The moment, τ ₁, τ ₂And the shape of additional wave or sub-additional wave and position all be to be obtained by training, and training algorithm is divided into following four kinds of briefings:

A, distortion and hangover minimization method-take into account wave distortion and all enough little training algorithm of ripple that trails:

This training algorithm is by training, construct suitable sub-additional wave, additional wave and shaping ripple, the waveform of receiving end signal master ripple is tried one's best near the waveform of transmitting terminal initialize signal, and reduce the waveform distortion of received signal, reduce receiving end signal hangover ripple simultaneously as far as possible.Concrete training algorithm is as follows:

Step 1: make i=1 ..., m, m are positive integer, selected a series of sub-additional wave f _i(t), the additional wave structure of this series, shape and position are according to ε in the following step 3 ₁With ε in the step 5 ₂Constraints make up, construct the shaping ripple again $g_1\left(t\right)=g\left(t\right)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ In the formula, g (t) is the initialize signal of transmitting terminal, g ₁(t) be the shaping ripple that g (t) sends out after transmitting terminal is through the waveform preliminary treatment;

Step 2: make shaping ripple g ₁(t) by with the filter p (t) of transmission channel equivalence, obtain by the shaping ripple signal behind the transmission channel at receiving terminal

Use formula ${\tilde{g}}_1\left(t\right)=g_1\left(t\right)*p\left(t\right)$ Expression, * is the convolution symbol;

Step 3: choose at receiving terminal

Interval [kT, (k+1) T) main ripple

Judge whether to satisfy formula then: ${|g^2\left(t\right)-{\tilde{g}}_{11}^2|}^{1/2}\&le;{\mathrm{\&epsiv;}}_1,$ (ε ₁Be an enough little threshold value, be used to be illustrated in the shaping ripple of receiving terminal

Main ripple

With respect to the requirement of the distortion level of transmitting terminal initialize signal g (t) waveform, this ε ₁Value depend on that the error rate is not more than a certain set point under the transmission rate of setting satisfying under the given signal transmission conditions, perhaps satisfies the requirement to transmission rate under the error rate of setting; As long as ε ₁Numerical value can satisfy this designing requirement, just think enough little.If) satisfy above-mentioned condition, carry out subsequent operation; Otherwise, return step 1, and the repetition training process, till sub-additional wave that is met above-mentioned condition or additional wave;

Step 4: choose shaping ripple signal at receiving terminal

Be positioned at time interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple

In the formula, τ ₃＞τ ₂, τ ₂Be time span at the additional wave of transmitting terminal initialize signal code-element period rear end, τ ₃Be to be a period of time length of the hangover ripple that intercepted of calculating hangover ripple signal at receiving terminal, this τ ₃Time span be infinite length in theory, during enforcement, τ ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then is decided by the judgment criterion of step (5);

Step 5: respectively in the interval [kT, (k+1) T) the main ripple of last intercepting

With at interval [(k+1) T, (k+1) T+ τ ₃) last intercepting hangover ripple

And do following computing: in the interval [kT, (k+1) T) interior to main ripple calculating $G_1={\&Integral;}_{\mathrm{kT}}^{(k+1)T}{\tilde{g}}_{11}^2\left(t\right)\mathrm{dt},$ In interval, the hangover ripple is calculated $G_2={\&Integral;}_{(k+1)T}^{(k+1)T+{\mathrm{\&tau;}}_3}{\tilde{g}}_{11}(t-(k+1)T){\tilde{g}}_{12}\left(t\right)d\left(t\right);$ Definition $\mathrm{MTR}=10{\log }_{10}\frac{G_1}{G_2}$ For

Main ripple with the hangover Bob, judge whether to satisfy formula: MTR 〉=ε ₂, (ε ₂It is an enough big threshold value.Because main ripple is the carrier of transmission information, and the hangover ripple is a kind of unwanted interference; ε ₂Reflected that the hangover phase of wave is to the influence degree of main ripple to transmission performance.ε ₂Value depend on that the error rate is not more than a certain set point under the transmission rate of setting satisfying under the given signal transmission conditions, perhaps satisfies the requirement to transmission rate under the error rate of setting.As long as ε ₂Value can meet design requirement, just think enough big.If) satisfy above-mentioned formula, finish training process; Otherwise, return above-mentioned steps 1, continue the repetition training process, till additional wave that is met above-mentioned condition and shaping ripple, finish the waveform preliminary treatment of distortion and hangover minimization method.

B, maximum signal to noise ratio method-take into account the enough big and enough little training algorithm of hangover wave amplitude of signal to noise ratio: this training algorithm is by training, construct suitable sub-additional wave, additional wave and shaping ripple, make the signal to noise ratio between the noise of receiving end signal and transmission channel enough big, reduce the amplitude of receiving end signal hangover ripple simultaneously, concrete training algorithm is as follows as far as possible:

Step 1: make i=1 ..., m, m are positive integer, selected a series of sub-additional wave f _i(t), the additional wave structure of this series, shape and position are according to ε in the following step 3 ₁With ε in the step 5 ₂Constraints make up, construct the shaping ripple again $g_1\left(t\right)=g\left(t\right)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ G (t) is the initialize signal of transmitting terminal, g ₁(t) be the shaping ripple signal that after transmitting terminal primary wave g (t) is through the waveform preliminary treatment, sends;

Step 2: make shaping ripple g ₁(t) by with the filter p (t) of transmission channel equivalence, pass through shaping ripple signal behind the transmission channel what receiving terminal got

Use formula ${\tilde{g}}_1\left(t\right)=g_1\left(t\right)*p\left(t\right)$ Expression, * is the convolution symbol;

Step 3: choose the shaping ripple signal that receiving terminal receives

Time interval [kT, (k+1) T) main ripple

Whether the signal to noise ratio of judging receiving terminal satisfies condition $\mathrm{SNR}=10{\log }_{10}\frac{{\tilde{g}}_{11}^2\left(t\right)}{{\mathrm{\&sigma;}}^2}\&GreaterEqual;{\mathrm{\&epsiv;}}_1$ (σ ²Represent noise energy, ε ₁It is an enough big threshold value.ε ₁Value depend on that the error rate is not more than a certain set point under the transmission rate of setting satisfying under the given signal transmission conditions, perhaps satisfies the requirement to transmission rate under the error rate of setting.As long as ε ₁Numerical value can meet design requirement, just think enough big.If) satisfy above-mentioned condition, then carry out subsequent operation; Otherwise, return above-mentioned steps 1, continue the repetition training process, till sub-additional wave that is met above-mentioned condition or additional wave;

Step 4: choose shaping ripple signal at receiving terminal

Be positioned at time interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple

In the formula, τ ₃＞τ ₂, τ ₂Be time section at the additional wave of transmitting terminal initialize signal code-element period rear end, τ ₃Be to be a period of time length of the hangover ripple that intercepted of calculating hangover ripple signal at receiving terminal, this τ ₃Time span be infinite length in theory, during enforcement, τ ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then depends on the judgment criterion of step (5);

Step 5: respectively in the interval [kT, (k+1) T) the main ripple of last intercepting

With at interval [(k+1) T, (k+1) T+ τ ₃) last intercepting hangover ripple

And do following computing: in the interval [kT, (k+1) T) interior to main ripple calculating $G_1={\&Integral;}_0^T{\tilde{g}}_{11}^2\left(t\right)\mathrm{dt},$ At interval [(k+1) T, (k+1) T+ τ ₃) interior to the calculating of hangover ripple $G_2={\&Integral;}_T^{T+{\mathrm{\&tau;}}_3}{\tilde{g}}_{11}(t-(k+1)T){\tilde{g}}_{12}\left(t\right)d\left(t\right);$ Definition

Main ripple with the hangover Bob $\mathrm{MTR}=10{\log }_{10}\frac{G_1}{G_2},$ Judge whether to satisfy formula: MTR 〉=ε ₂, (ε ₂Be an enough big threshold value, its concrete numerical value depends on that the error rate is not more than a certain set point under the transmission rate of setting satisfying under the given signal transmission conditions, perhaps satisfies the requirement to transmission rate under the error rate of setting.As long as ε ₂Numerical value can satisfy the designing requirement of the error rate or transfer rate, just think enough big.If) satisfy above-mentioned condition, finish training process; Otherwise, return step 1, continue the repetition training process, till the sub-additional wave that is met above-mentioned condition, additional wave and shaping ripple, finish the waveform preliminary treatment of maximum signal to noise ratio method.

C, recurrence method-adopt the one by one training algorithm of recurrence method one by one, the ripple that will trail is divided into the L section, claim every section to be a son hangover ripple, construct each the sub-additional wave that to eliminate every cross-talk hangover ripple then repeatedly, at last this a little additional wave is stacked up and constitute the additional wave that to eliminate whole hangover ripple, with the shaping ripple of additional wave and primary wave stack formation transmitting terminal, described training algorithm further comprises following concrete operations content again:

(1) with interval [(k+1) T, (k+1) T+ τ ₃) in the hangover wavelength-division be the L section, and be expressed as: ${\tilde{g}}_{12}\left(t\right)={\tilde{g}}_{121}\left(t\right)+\&CenterDot;\&CenterDot;\&CenterDot;{\tilde{g}}_{12j}\left(t\right)+\&CenterDot;\&CenterDot;\&CenterDot;+{\tilde{g}}_{12L}\left(t\right),$ Be to have added the shaping ripple of part additional wave by the hangover ripple behind the filter p (t), wherein, j section hangover ripple

[(k+1) T≤φ _j＜(k+1) T+ τ ₃, φ _j＜φ _J+1, j=1 ..., L, [φ _j, φ _J+1) be son hangover ripple

The interval;

(2) establishing v is cycle index counter, and makes v=1;

(3) make j=1;

(4) sub-additional wave f of structure _j(t), this sub-additional wave by filter after distortion and produce the new hangover ripple involve whole hangover ripple interval, be formulated as: ${\tilde{f}}_j\left(t\right)={\tilde{f}}_1\left(t\right)*p\left(t\right),t\&Element;[T,{\mathrm{\&tau;}}_3);$ Therefore the hangover ripple of present segment can be subjected to the influence of the new hangover ripple that the additional wave of other section produces, and is formulated as: ${\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{g}}_{12j}\left(t\right)={\tilde{g}}_{12j}\left(t\right)+\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{\tilde{f}}_k\left(t\right)+\underset{k=j+1}{\overset{{\mathrm{\&tau;}}_3}{\mathrm{\&Sigma;}}}{\tilde{f}}_k\left(t\right);$ Additional wave trained it is met the requirements of according to being satisfied ${\&Integral;}_{{\mathrm{\&phi;}}_j}^{{\mathrm{\&phi;}}_{j+1}}{({\tilde{f}}_j\left(t\right)-{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{g}}_{12j}\left(t\right))}^2\mathrm{dt}<{\mathrm{\&epsiv;}}_4;$ ε ₄Be an enough little threshold value so that

With

Approaching as far as possible, concrete ε ₄Value determine under the given signal transmission conditions to the requirement of design performance: the error rate is not more than a certain setting numerical value under the transmission rate of setting, or has sufficiently high transmission rate under the error rate of setting; If ε ₄Numerical value can satisfy this designing requirement, just thinks enough little;

(5) make j=j+1,, otherwise return step (4) if j＞L finishes the structure of additional wave in the v time circulation; Continue the repetition training process, until the sub-additional wave of the every cross-talk hangover ripple that is met above-mentioned formula establishment;

(6) check whether the hangover ripple of all sections enough little? if reach enough little, then finish the training of additional wave and do next step, otherwise be v=v+1 and return (3),

(7) all sub-additional waves are stacked up formation additional wave, additional wave and primary wave stacked up synthesizes the shaping ripple, finishes one by one the ripple that adds of method and handles.

The training algorithm of D, liftering method-employing liftering method receives and recovers the transmission ripple the ripple from receiving ripple or part, or receives ripple from part and recover required additional wave, this additional wave and primary wave is synthesized the shaping ripple of transmitting terminal.Concrete training algorithm is as follows:

Can release the formula of general liftering by aforementioned formula (2): $G\left(u\right)=\tilde{G}\left(u\right)/P\left(u\right)$ (5)

Earlier with transmitting terminal initialize signal g (t) by with the filter of transmission channel equivalence after

Signal waveform be divided into interval [kT, (k+1) T) in main ripple signal

With at interval [(k+1) T, (k+1) T+ τ ₃) interior hangover ripple signal

Two parts, T, τ ₃Definition identical with related definition in the maximum signal to noise ratio method, ripple signal again will trail

By the waveform that obtains after the liftering as additional wave; Described formula with liftering structure additional wave is:

$F\left(u\right)={\tilde{G}}_T\left(u\right)/P\left(u\right)$ (6)

In the formula (6), F (u) is the frequency domain representation of the additional wave that will construct,

It is the hangover ripple

Frequency domain representation, P (u) is the frequency domain representation that is used for the impulse response p (t) of the filter of replacing transmission channel of equal value; Then, F (u) is converted to time-domain signal f (t) with contrary fast fourier transform (IFFT[]), perhaps according to following formula, directly will be with the hangover ripple signal of time-domain representation

Through the time-frequency domain conversion, the formula that obtains additional wave f (t) is: $f\left(t\right)=\mathrm{REAL}\left[\mathrm{IFFT}[\mathrm{FFT}\left[{\tilde{g}}_T\left(t\right)\right]/\mathrm{FFT}\left[p\left(t\right)\right]]\right],$ In the formula, f (t) representative is through the signal after the liftering, and p (t) representative is equivalent to the impulse response of the filter of transmission channel, FFT[] represent fast fourier transform, IFFT[] the contrary fast fourier transform of representative, REAL[] represent to get real; At last, will after initialize signal g (t) stack, just can reduce hangover as additional wave through the signal f (t) after the liftering, thereby finish the waveform preliminary treatment of liftering method by filter.

Two, the waveform preprocess method of the composite wave signal of being made up of two or two above wavelets for each code element (the present invention is called the multiple wavelet code element with this code element) mainly contains two kinds of methods, and it is described respectively:

First method: to the commonsense method of carrying out the waveform preliminary treatment of multiple wavelet code element:

The waveform of multiple wavelet code element is by a plurality of composite waves that form after the waveform linear superposition of wavelet that are called as.The wavelet waveform can be the ripple of various dissimilar (differences that comprise shape, frequency, phase place or amplitude), and selecting the principle of wavelet type is to satisfy the requirement of transmission channel and transmission performance; Be formulated as: $g\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_i\left(t\right);$ Wherein, g _i(t) be wavelet; Just can be converted into problem of pretreatment to the waveform problem of pretreatment of composite wave g (t) like this to each wavelet.That is to say,, more pretreated wavelet is done linear superposition, just obtain pretreated composite wave as long as each wavelet is implemented preliminary treatment.And the preliminary treatment that each wavelet is carried out can be realized according to four kinds of methods that the front is introduced.Below it is carried out comprehensive description-promptly composite wave implemented according to the preprocess method of " distortion and hangover minimization method " or " maximum signal to noise ratio method " or " recurrence method one by one " or " liftering method " handled:

Step 1: make wavelet sequence number i=1;

Step 2: to wavelet g _i(t) implement the pretreatment operation of " distortion and hangover minimization method " or " maximum signal to noise ratio method " or " recurrence method one by one " or " liftering method " respectively, obtain pretreated sub-shaping ripple g _1i(t);

Step 3: make i=i+1 again, and judge i＞N? if carry out subsequent operation; Otherwise, return step 2, continue to repeat pretreatment operation;

Step 4: with all sub-shaping ripple g _1i(t) (i=1 ..., N) carry out linear superposition according to following formula: $g_1\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_{1i}\left(t\right),$ Be used for to the end transmitting terminal through pretreated composite wave, i.e. the shaping ripple of multiple wavelet code element.

Second method: to the waveform preprocess method of " the multiple width of cloth phase modulating baseband transmission " described in applicant's the international patent application " a kind of Multiple Modulation transmission method " (application number is PCT/CN03/00321), " carrier transmission of multiple width of cloth phase modulating baseband sign indicating number ", " the multiple width of cloth is modulated direct carrier transmission mutually " three kinds of coded systems.Specify it below respectively:

A, " multiple width of cloth phase modulating baseband Digital Transmission " are with code element transmission one by one, each code element is made up of a composite wave, each cycle of this composite wave is made up of identical monocyclic sine wave of some cycles, each sine wave moves a phase place in succession, its cycle is less than synthetic wave period, its amplitude is at random got a value from the quantification set of regulation, thereby realizes multiple width of cloth phase modulating baseband Digital Transmission.

B, " carrier transmission of multiple width of cloth phase modulating baseband sign indicating number " are that multiple width of cloth phase modulating baseband sign indicating number carrier wave is formed carrier signal in a certain passband that is higher than base band, right at receiving terminal, use the carrier signal in the received signal of band pass filter elimination earlier, decode then, realize the carrier wave Digital Transmission of multiple width of cloth phase modulating baseband sign indicating number.

C, " the multiple width of cloth is modulated direct carrier transmission mutually " are with code element transmission one by one, each code element is made up of a composite wave, should form by the identical sinusoidal wave institute of some terms of validity synthetic wave period, the length of the term of validity is the integral multiple of sine wave period, and less than synthetic wave period, each sine wave moves a phase place in succession, and its amplitude is at random got a value from the quantification set of regulation; Realized that the multiple width of cloth modulates direct carrier wave Digital Transmission mutually.

" multiple the width of cloth phase modulating baseband transmission ", " carrier transmission of multiple width of cloth phase modulating baseband sign indicating number ", when " the multiple width of cloth is modulated direct carrier transmission mutually " three kinds of coded systems are used for line coding, mainly utilize its following two common features:

(1) their code element all is made up of the identical a plurality of wavelets of frequency, and each wavelet is got the amplitude of different brackets, and each grade amplitude is corresponding to a binary coding;

(2) all available following equation group form of their Code And Decode is represented:

The equation group of coding: AX=G (7); The equation group of decoding: X=A ^-1G (8);

In the formula,

$X=\left[\begin{array}{c}{X}_1\\ X_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ X_h\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ X_H\end{array}\right],$ $G=\left[\begin{array}{c}{G}_1\\ G_2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ G_h\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ G_H\end{array}\right]$

X is the wavelet amplitude vector, and G is the vector that obtains behind a series of coherent computings of the process of receiving terminal code element, and A is the coefficient matrix of encoding equtions group, K _HjBe the element of coefficient matrix, span is a real number field, and solving equation group (8) promptly gets separating of each wavelet.

Above-mentioned three kinds of line codings are collectively referred to as nonopiate amplitude Multiple Modulation coding (abbreviating the NMAM coding as), when the NMAM coding is carried out the waveform preliminary treatment, if equation group (8) is an ill-condition equation, just need according to minimum ill principle structure additional wave, its arthmetic statement is as follows:

The first step: from composite wave, take out a wavelet, select for use a kind of in " distortion and hangover minimization method " or " maximum signal to noise ratio method ", " liftering method " or " recurrence method one by one " four kinds of methods that this wavelet is implemented preliminary treatment respectively;

Second step: judge whether to satisfy ‖ A ^-1‖＜γ, (‖ A ^-1‖ is the contrary norm of equation group coefficient matrix, and through the training decision, the foundation whether training finishes is that separating of this equation can reach desirable precision to the value of γ by the designer), if ‖ is A ^-1The value of ‖ meets the demands, and then finishes the waveform preprocessing process; Otherwise, return the first step, continue to select new additional wave or additional wavelet, till additional wave that is met above-mentioned condition or sub-additional wave.

The present invention has tested enforcement, has obtained the invention effect of expection.Introduce the situation of several embodiments of the present invention below:

Referring to Fig. 2 and Fig. 3, introduce the 1st embodiment: initialize signal is for sinusoidal wave, and additional wave is single trapezoidal wave, and transmission channel has the waveform preprocess method of pass band filter characteristic:

The transmitting terminal initialize signal of this embodiment is sinusoidal wave, referring to Fig. 2 (A), additional wave is single trapezoidal wave, referring to Fig. 2 (B), the signal waveform that receiving terminal receives is initialize signal and the additional wave signal composite wave by waveform behind the transmission channel, referring to Fig. 2 (C).Among Fig. 2 C, solid line waveform is the waveform behind the primary wave process transmission channel, and dotted line waveform is that additional wave is through the waveform behind the transmission channel.Through behind the transmission channel, variation has all taken place in the waveform of primary wave and additional wave, and produces the hangover ripple; Additional wave is less relatively in the amplitude and the amplitude variation in the main ripple interval of primary wave, and the amplitude of the amplitude of additional wave hangover ripple and primary wave hangover ripple is approaching, but phase place is opposite.Again referring to passing through primary wave behind the transmission channel and additional wave composite wave shown in Fig. 2 (D) at receiving terminal, compare with the waveform of Fig. 2 (C), additional wave is little to the influence of the main wave of primary wave, but the hangover ripple of primary wave is effectively reduced, and the main ripple of receiving terminal composite wave is MTR=57.1735dB with the hangover Bob in this example.

So the result after the initialize signal waveform of receiving terminal and the stack of additional wave waveform is little to the influence of receiving terminal initialize signal master wave-wave shape, but can effectively reduce the hangover ripple of receiving terminal initialize signal, thereby the signal to noise ratio of receiving terminal is effectively improved.

Referring to Fig. 3, dotted line waveform, solid line waveform are respectively the initialize signal among Fig. 2 and the spectral shape of shaping ripple among the figure, the spectral shape of the two is basic identical in the main lobe interval, but in the interval outside main lobe, the frequency spectrum of shaping ripple descends rapidly, and near 0, and the frequency spectrum of initialize signal is present in the entire spectrum section, obviously, the spectral shape of shaping ripple is significantly better than the spectral shape of initialize signal.

Referring to Fig. 4 and Fig. 5, introduce the 2nd embodiment: initialize signal is for sinusoidal wave, and additional wave is the cycle square wave, and transmission channel has the waveform preprocess method of low-pass filter characteristic:

Earlier referring to Fig. 4 (A), the transmitting terminal initialize signal of this embodiment and additional wave are respectively sinusoidal wave (solid line) and cycle square wave (chain-dotted line), primary wave (solid line) and the additional wave (dotted line) that receives referring to the receiving terminal shown in Fig. 4 (B) again, through behind the transmission channel, the ripple that trails has all taken place to change and produce in the shape of primary wave and additional wave.Also be the signal waveform of receiving terminal shown in Fig. 4 (C), at the shaping ripple (solid line) of receiving terminal and the waveform of initialize signal (dotted line), relatively two waveforms as can be known, the waveform of the main ripple of shaping ripple and initialize signal master ripple is very approaching, but the hangover ripple of shaping ripple is very little, and initialize signal then has bigger hangover ripple.So the waveform preliminary treatment can effectively reduce the hangover wave amplitude of receiving terminal primary wave, in the present embodiment, the main ripple of receiving terminal shaping ripple is MTR=61.8673dB with the hangover Bob.

Referring to Fig. 5, this is the comparison diagram of initialize signal frequency spectrum (chain-dotted line) and shaping ripple frequency spectrum (solid line) in the present embodiment, the spectral shape of the two is basic identical in the main lobe interval, but in the interval outside main lobe, the frequency spectrum of shaping ripple descends rapidly and near 0, and the frequency spectrum of initialize signal is present in the entire spectrum section, and obviously, the spectral shape of shaping ripple is significantly better than the spectral shape of initialize signal.

Referring to Fig. 6 and Fig. 7, introduce the 3rd embodiment: initialize signal is for sinusoidal wave, and additional wave is single triangular wave, and transmission channel has the waveform preprocess method of low-pass filter characteristic:

Among Fig. 6 (A), the transmitting terminal initialize signal of present embodiment and additional wave are respectively sinusoidal wave (solid line) and single triangular wave (chain-dotted line), compare with the signal of transmitting terminal, receiving terminal primary wave (solid line) and additional wave (dotted line) are all changing through waveform behind the transmission channel and are producing the hangover ripple among Fig. 6 (B).The waveform of the shaping ripple (solid line) of receiving terminal and initialize signal (dotted line) as can be known in the comparison diagram 6 (C), the waveform of the main ripple of shaping ripple and the main ripple of initialize signal is very approaching, but the hangover ripple of shaping ripple is very little, initialize signal then has bigger hangover ripple, so, the waveform preliminary treatment can effectively reduce the amplitude of hangover ripple, and main ripple is MTR=79.0158dB with the hangover Bob in the present embodiment.

From above-mentioned figure as can be seen, the additional wave of the single triangular wave of being constructed changes less relatively by waveforms amplitude and the amplitude in initialize signal master ripple interval behind the transmission channel, and the amplitude of the amplitude of the hangover ripple of the additional wave that occurs in initialize signal hangover ripple interval and initialize signal hangover ripple is approaching, but phase place is opposite.So, result after initialize signal waveform that receiving terminal receives and the stack of additional wave waveform, influence to receiving terminal initialize signal master wave-wave shape is little, but can effectively reduce the hangover ripple of receiving terminal initialize signal, thereby the signal to noise ratio of receiving terminal received signal is effectively improved.

Referring to Fig. 7, solid line waveform and chain-dotted line waveform are respectively the shaping ripple among Fig. 6 (C) and the spectral shape of initialize signal among the figure, the spectral shape of the two is basic identical in the main lobe interval, but in the interval outside main lobe, the frequency spectrum of shaping ripple descends rapidly near 0, and the frequency spectrum of initialize signal is present in the entire spectrum section, and obviously, the spectral shape of shaping ripple is significantly better than the spectral shape of initialize signal.

Referring to Fig. 8, introduce the 4th embodiment: the waveform preprocess method that adopts one by one recurrence method.

Carrying out the pretreated process of waveform with recurrence method one by one is: the ripple that will trail is divided into the L section, claim every section to be a son hangover ripple, construct each the sub-additional wave that to eliminate every cross-talk hangover ripple then repeatedly, at last this a little additional wave being stacked up constitutes the additional wave eliminate whole hangover ripple, the shaping ripple of the formation transmitting terminal that again additional wave and primary wave superposeed; Expression initialize signal (solid line) and first additional wave (dotted line) among Fig. 8 (A); Shaping ripple after first additional wave that is illustrated in receiving terminal among Fig. 8 (B) and the beginning signal stack (dotted line claims the first shaping ripple, below roughly the same) and initialize signal (solid line); Fig. 8 (C) is the partial enlarged drawing of Fig. 8 (B) waveform hangover ripple part, from Fig. 8 (B), (C) as can be known, main wave-wave shape at the main ripple of the first shaping ripple of receiving terminal and initialize signal is very approaching, but the amplitude of first section hangover ripple of the first shaping ripple is more much smaller than the amplitude of first section hangover ripple of initialize signal; Fig. 8 (D) is the waveform of initialize signal (solid line), first (dotted line), second (one one line) and the 3rd additional wave (two standardized dotted lines) at transmitting terminal; Fig. 8 (E) is the waveform of the 3rd shaping ripple (two standardized dotted lines) after initialize signal (solid line), the first shaping ripple (dotted line), initialize signal at receiving terminal and the second shaping ripple after the stack of first, second additional wave (one one line) and initialize signal superpose with first, second, third additional wave; Fig. 8 (F) is the partial enlarged drawing of hangover ripple among Fig. 8 (E); The result of present embodiment shows, the first hangover ripple (one one line) of the second shaping ripple is bigger than the amplitude of the first hangover ripple (dotted line) of the first shaping ripple, but the amplitude of each section hangover ripple of the 3rd shaping ripple in whole hangover ripple is all effectively reduced (two standardized dotted lines).

Referring to Fig. 9 and Figure 10, introduce the 5th embodiment: that adopts liftering adds the ripple processing method.

The process that adds the ripple processing with the liftering method is: the hangover ripple with primary wave carries out the liftering processing earlier, and with resulting waveform as additional wave, the amplitude of this additional wave is with the hangover wave amplitude of primary wave is approaching but phase place is opposite, and in primary wave master ripple section no signal, then that additional wave is superimposed with initialize signal, behind the filter that is equivalent to transmission channel, just can reduce hangover.Fig. 9 has showed the initialize signal sine wave that adopts liftering method of the present invention to add the transmitting terminal of ripple processing respectively, referring to Fig. 9 (A), be equivalent to the frequency domain characteristic of the filter of transmission channel, referring to Fig. 9 (B), with primary wave by the waveform behind the filter, the main ripple of this primary wave changes and produces the hangover ripple, referring to Fig. 9 (C).Referring to Figure 10 (A), this figure has showed that the hangover ripple with primary wave among Fig. 9 (C) carries out the waveform that obtains after liftering is handled, the hangover ripple of this waveform and primary wave on amplitude near but phase place is opposite, this waveform is in the main ripple section no signal of primary wave, this waveform is exactly the additional wave that constructs.Figure 10 (B) showed be added to additional wave on the primary wave after, this shaping ripple is by the waveform behind the filter, the situation that the hangover ripple of its initialize signal is effectively eliminated.Figure 10 (C) then is the spectral shape of this additional wave.

Referring to Figure 11, introduce the 6th embodiment: improve the contrary norm ‖ A of equation group coefficient matrix by the liftering method ^-1It is primary wave wavelet in this embodiment transmitting terminal NMAM coding that ‖ realizes adding the method that ripple is handled: Figure 11 (A) to the NMAM coding, Figure 11 (B) is applied through behind the additional wave that obtains after the liftering for the waveform among Figure 11 (A), again by the waveform later with the filter of channel equivalence, the ‖ A of the NMAM that forms as wavelet thus ^-1‖ is very big, is 2.8978e+006.Figure 11 (C) is after adding additional wave on the basis of Figure 11 (B), and again by the waveform later with the filter of channel equivalence, this makes the ‖ A of NMAM ^-1‖ is reduced to 4.4313, obviously reduces by the matrix norm that adds after ripple is handled.

Claims (11)

1, the additive waveshape pretreatment method in a kind of digital communication modulation, it is characterized in that: the additional wave f (t) that will select in advance, construct, adjust and obtain is added on the initialize signal g (t) of transmitting terminal, makes up a shaping ripple g different with initialize signal g (t) waveform ₁(t), i.e. g ₁(t)=g (t)+f (t), and send this shaping ripple g at transmitting terminal ₁(t); G (t) and g ₁(t) all being is the burst that chronomere divides with the code element, and Baud Length represents with period T, i.e. the T of kT≤t＜(k+1), k are zero or positive integer, and the waveform between each code element is separate; Signal arrives the receiving terminal procedural representation: ${\tilde{g}}_1\left(t\right)=p\left(t\right)*g_1\left(t\right)={\tilde{g}}_{11}\left(t\right)+{\tilde{g}}_{12}\left(t\right),$ In the formula,

Be the shaping ripple signal that receives at receiving terminal, * is the convolution algorithm symbol, and p (t) is defined as and is used for impulse response of replacing the filter of transmission channel of equal value, received signal

Can be decomposed into two parts: main ripple

With the hangover ripple

, its span is respectively: ${\tilde{g}}_{11}\left(t\right)=\left\{\begin{array}{cc}{\tilde{g}}_1\left(t\right),& \mathrm{kT}\&le;t<(k+1)T)\\ 0,& (k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3\end{array}\right.,$ ${\tilde{g}}_{12}\left(t\right)=\left\{\begin{array}{cc}0,& \mathrm{kT}\&le;t<(k+1)T)\\ {\tilde{g}}_1\left(t\right),& (k+1)T\&le;(k+1)T{+\mathrm{\&tau;}}_3\end{array}\right.;$ In the formula, T is the code-element period length of transmitting terminal initialize signal g (t), τ ₃Length be infinitely great in theory, depend on the attenuation of the wave amplitude that trail during enforcement, concrete numerical value depends on training algorithm, k is zero or positive integer; Behind above-mentioned preliminary treatment and transmission channel, received shaping ripple

Shape be different from received signal

Shape, can realize following technique effect: make receiving end signal

Main ripple Waveform more near the waveform of transmitting terminal initialize signal g (t), and satisfy the requirement of transfer of data to decoding, effectively reduce receiving terminal hangover ripple simultaneously

The amplitude of waveform.

2, additive waveshape pretreatment method according to claim 1 is characterized in that: described method is applied to each signal element when being made up of single waveform, further comprises following to the pretreated content of operation of additive waveshape:

The shaping ripple signal that transmitting terminal sends is g ₁(t)=g (t)+f (t), $f\left(t\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ M is a positive integer, i.e. shaping ripple g ₁(t) be the signal that forms and send behind initialize signal g (t) the stack additional wave f (t) of transmitting terminal by transmitting terminal, wherein additional wave f (t) is then by positive integer m sub-additional wave f _i(t) be combined to form sub-additional wave f _i(t) be training algorithm and the waveform that comprises triangular wave, trapezoidal wave, square wave or other Any shape selecting for use, construct and adjust according to the present invention, the position of additional wave is in time interval [kT-τ ₁, (k+1) T+ τ ₂] in the scope, wherein T is the code-element period of initialize signal g (t), τ ₁Be time section at the additional wave of initialize signal code-element period front end, τ ₂Be time section at the additional wave of initialize signal code-element period rear end, t=kT-τ ₁Expression from an initial moment of initialize signal code-element period to previous τ ₁The moment, t=(k+1) T+ τ ₂Expression is from this initialize signal code-element period finish time of τ backward ₂The moment, τ ₁, τ ₂The shape and the position of numerical value, sub-additional wave or additional wave are obtained by training algorithm respectively.

3, additive waveshape pretreatment method according to claim 2, it is characterized in that: take into account wave distortion and the hangover wave amplitude all enough little, be distortion and the hangover minimization method principle under, by training, structure corresponding sub-additional wave, additional wave and shaping ripple, the waveform of receiving end signal master ripple is tried one's best near the waveform of transmitting terminal initialize signal, and the waveform distortion of reduction received signal, reduce receiving end signal hangover wave amplitude simultaneously as far as possible; Described training algorithm further comprises following concrete operations content:

(1) make sequence number i=1 ..., m, m are positive integer, selected a series of sub-additional wave f _i(t), the additional wave structure of this series, shape and position are according to the ε in following step (3) and (5) ₁And ε ₂Constraints make up, construct the shaping ripple again $g_1\left(t\right)=g\left(t\right)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ In the formula, g (t) is the initialize signal of transmitting terminal, g ₁(t) be the shaping ripple that g (t) sends out after transmitting terminal is through the additive waveshape preliminary treatment;

(2) make shaping ripple g ₁(t) by with the filter of transmission channel equivalence after, receive the shaping ripple signal that obtains at receiving terminal

, use formula ${\tilde{g}}_1\left(t\right)=g_1\left(t\right)*p\left(t\right)$ Represent it, in the formula, * is the convolution algorithm symbol, and p (t) is the impulse response of filter;

(3) choose signal at receiving terminal

Be positioned at time interval [kT, (k+1) T) main ripple

, judge then whether following formula is set up: ${|g^2\left(t\right)-{\tilde{g}}_{11}^2|}^{1/2}\&le;{\mathrm{\&epsiv;}}_1,$ In the formula, ε ₁Be an enough little threshold value, be used to be illustrated in the shaping ripple that receiving terminal receives

Main ripple

With respect to the requirement of the distortion level of transmitting terminal initialize signal g (t) waveform, this ε ₁Numerical value depend in the design performance under the given signal transmission conditions and require: the error rate is not more than a certain set point under the transmission rate of setting, and perhaps satisfies the requirement of transmission rate under the error rate of setting; If ε ₁Numerical value can satisfy this designing requirement, just thinks enough little; If above-mentioned formula is set up, then order is carried out subsequent operation; Otherwise, return step (1), continue the repetition training process, till the additional wave or sub-additional wave that are met above-mentioned formula establishment;

(4) choose shaping ripple signal at receiving terminal

Be positioned at time interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple

, in the formula, τ ₃＞τ ₂, τ ₂Be time span at the additional wave of transmitting terminal initialize signal code-element period rear end, τ ₃Be to be a period of time length of the hangover ripple that intercepted of calculating hangover ripple signal at receiving terminal, this τ ₃Time span be infinite length in theory, during enforcement, τ ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then is decided by the judgment criterion of step (5);

(5) respectively interval [kT, (k+1) T) go up the main ripple of intercepting

With at interval [(k+1) T, (k+1) T+ τ ₃) last intercepting hangover ripple

, and do following computing: in the interval [kT, (k+1) T) interior to main ripple calculating $G_1={\&Integral;}_{\mathrm{kT}}^{(k+1)T}{\tilde{g}}_{11}^2\left(t\right)\mathrm{dt},$ At interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple is calculated $G_2={\&Integral;}_{(k+1)T}^{(k+1)T+{\mathrm{\&tau;}}_3}{\tilde{g}}_{11}(t-(k+1)T){\tilde{g}}_{12}\left(t\right)d\left(t\right);$ Definition

Main ripple with the hangover Bob $\mathrm{MTR}=10{\log }_{10}\frac{G_1}{G_2},$ Judge whether following formula is set up: MTR 〉=ε ₂, in the formula, ε ₂Be an enough big threshold value, be used to reflect that the hangover phase of wave is for the influence degree of main ripple to transmission performance, this ε ₂Numerical value depends in the design performance under the given signal transmission conditions and requires: the error rate is not more than a certain set point under the transmission rate of setting, and perhaps satisfies the requirement of transmission rate under the error rate of setting; If ε ₂Numerical value can satisfy this designing requirement, just thinks enough big; If above-mentioned formula is set up, finish training process; Otherwise return step (1), continue the repetition training process,, finish additive waveshape preliminary treatment with distortion and hangover minimization method until being met sub-additional wave, additional wave and the shaping ripple that above-mentioned formula is set up.

4, additive waveshape pretreatment method according to claim 2, it is characterized in that: take into account signal to noise ratio enough big and the hangover wave amplitude is enough little, be under the principle of maximum signal to noise ratio method, by training, structure corresponding sub-additional wave, additional wave and shaping ripple, make the signal to noise ratio between receiving end signal and the transmission channel noise enough big, reduce the amplitude of receiving end signal hangover ripple simultaneously as far as possible; Described training algorithm further comprises following concrete operations content:

(1) make sequence number i=1 ..., m, m are positive integer, selected a series of sub-additional wave f _i(t), the additional wave structure of this series, shape and position are according to the ε in following step (3) and (5) ₁And ε ₂Constraints make up, construct the shaping ripple again $g_1\left(t\right)=g\left(t\right)+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i\left(t\right),$ In the formula, g (t) is the initialize signal of transmitting terminal, shaping ripple g ₁(t) be the signal that primary wave g (t) sends out after transmitting terminal is through the additive waveshape preliminary treatment;

(2) make shaping ripple g ₁(t) by with the filter of transmission channel equivalence after, receive the shaping ripple signal that obtains at receiving terminal

, use formula ${\tilde{g}}_1\left(t\right)=g_1\left(t\right)*p\left(t\right)$ Represent it, in the formula, * is the convolution algorithm symbol, and p (t) is the impulse response of filter;

(3) choose the shaping ripple signal that receives at receiving terminal

Be positioned at the interval [kT, (k+1) T) main ripple

Part, judge again whether the signal to noise ratio of receiving terminal satisfies formula: $\mathrm{SNR}=10{\log }_{10}\frac{{\tilde{g}}_{11}^2\left(t\right)}{{\mathrm{\&sigma;}}^2}\&GreaterEqual;{\mathrm{\&epsiv;}}_1,$ In the formula, σ ²Represent noise energy, ε ₁Be an enough big threshold value, its numerical value depend under the given signal transmission conditions to the requirement of design performance: the error rate is not more than a certain set point under the transmission rate of setting, or possesses sufficiently high transmission rate under the error rate of setting, if ε ₁Numerical value makes the noise specific energy of main ripple satisfy this designing requirement, just thinks enough big; If satisfy above-mentioned formula, then order is carried out subsequent operation; Otherwise, return step (1), continue the repetition training process, till the sub-additional wave that is met above-mentioned formula establishment, additional wave;

(4) choose shaping ripple signal at receiving terminal Be positioned at time interval [(k+1) T, (k+1) T+ τ ₃) the hangover ripple

, in the formula, τ ₃＞τ ₂, τ ₂Be time section at the additional wave of transmitting terminal initialize signal code-element period rear end, τ ₃Be to be a period of time length of the hangover ripple that intercepted of calculating hangover ripple signal at receiving terminal, this τ ₃Time span be infinite length in theory, during enforcement, τ ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then depends on the judgment criterion of step (5);

(5) respectively interval [kT, (k+1) T) go up the main ripple of intercepting

With at interval [(k+1) T, (k+1) T+ τ ₃) last intercepting hangover ripple

, and do following computing: in the interval [kT, (k+1) T) interior to main ripple calculating $G_1={\&Integral;}_{\mathrm{kT}}^{(k-1)T}{\tilde{g}}_{11}^2\left(t\right)\mathrm{dt},$ At interval [(k+1) T, (k+1) T+ τ ₃) interior to the calculating of hangover ripple $G_2={\&Integral;}_{(k+1)T}^{(k+1)T+{\mathrm{\&tau;}}_3}{\tilde{g}}_{11}(t-(k+1)T){\tilde{g}}_{12}\left(t\right)d\left(t\right);$ Definition

Main ripple with the hangover Bob $\mathrm{MTR}=10\mathrm{lo}{g}_{10}\frac{G_1}{G_2},$ Judge whether following formula is set up: MTR 〉=ε ₂, in the formula, ε ₂Be an enough big threshold value, be used to reflect that the hangover phase of wave is for the influence degree of main ripple to transmission performance, this ε ₂Numerical value depends in the design performance under the given signal transmission conditions and requires: the error rate is not more than a certain set point under the transmission rate of setting, or has sufficiently high transmission rate under the error rate of setting; If ε ₂Numerical value can satisfy this designing requirement, just thinks enough big; If above-mentioned formula is set up, finish training process; Otherwise return step (1), continue the repetition training process,, finish the additive waveshape preliminary treatment of maximum signal to noise ratio method until being met sub-additional wave, additional wave and the shaping ripple that above-mentioned formula is set up.

5, additive waveshape pretreatment method according to claim 2, it is characterized in that: when adopting one by one recurrence method, the ripple that will trail is divided into plurality of sections, and claim every section to be a son hangover ripple, construct each the sub-additional wave that to eliminate every cross-talk hangover ripple then repeatedly, at last this a little additional wave being stacked up constitutes the additional wave can eliminate whole hangover ripple, this additional wave and primary wave is synthesized the shaping ripple of transmitting terminal again; Described training algorithm further comprises following concrete operations content:

(1) with interval [(k+1) T, (k+1) T+ τ ₃) in the hangover wavelength-division be the L section, and be expressed as ${\tilde{g}}_{12}\left(t\right)={\tilde{g}}_{12l}\left(t\right)+\&CenterDot;\&CenterDot;\&CenterDot;{\tilde{g}}_{12j}\left(t\right)+\&CenterDot;\&CenterDot;\&CenterDot;{\tilde{g}}_{12L}\left(t\right),$ Be to have added the shaping ripple of part additional wave by the hangover ripple behind the filter p (t), wherein, j section hangover ripple

(k+1) T≤φ _j＜(k+1) T+ τ ₃, φ _j＜φ _J+1, j=1 ..., L, [φ _j, φ _J+1) be son hangover ripple

The interval;

(2) establishing v is cycle index counter, and makes v=1;

(3) make j=1;

(4) sub-additional wave f of structure _j(t), this sub-additional wave by filter after distortion and produce prolong and the new hangover ripple in whole hangover ripple interval, be formulated as: ${\tilde{f}}_j\left(t\right)=f_j\left(t\right)*p\left(t\right),(k+1)T\&le;t<{\mathrm{\&tau;}}_3);$ Therefore the hangover ripple of present segment can be subjected to the influence of the new hangover ripple that additional wave produced of other section, is formulated as: ${\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{g}}_{12j}\left(t\right)={\tilde{g}}_{12j}\left(t\right)+\underset{k=1}{\overset{j}{\mathrm{\&Sigma;}}}{\tilde{f}}_k\left(t\right)+\underset{k=j+1}{\overset{{\mathrm{\&tau;}}_3}{\mathrm{\&Sigma;}}}{\tilde{f}}_k\left(t\right);$ Additional wave is trained, it is met the requirements of according to being: satisfy following inequality ${\&Integral;}_{{\mathrm{\&phi;}}_j}^{{\mathrm{\&phi;}}_{h+1}}{({\tilde{f}}_j\left(t\right)-{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{g}}_{12j}\left(t\right))}^2\mathrm{dt}<{\mathrm{\&epsiv;}}_4;$ ε ₄Be an enough little threshold value, so that

With

Approaching as far as possible, ε ₄Concrete numerical value determine in requiring in the design performance under the given signal transmission conditions: the error rate is not more than a certain setting numerical value under the transmission rate of setting, or has sufficiently high transmission rate under the error rate of setting; If ε ₄Numerical value can satisfy this designing requirement, just thinks enough little;

(5) make j=j+1, if j＞L then finishes the structure of additional wave in the v time circulation, otherwise returns step (4); Continue the repetition training process, until the sub-additional wave of the every cross-talk hangover ripple that is met above-mentioned formula establishment;

(6) check whether the hangover ripple of all each sections enough little? if reach enough little, then finish the training of additional wave, continue to carry out subsequent operation; Otherwise, establish v=v+1, and return execution in step (3);

(7) all sub-additional waves are stacked up formation additional wave stacks up additional wave and primary wave and synthesizes the shaping ripple, finishes one by one the additive waveshape preliminary treatment of recurrence method.

6, additive waveshape pretreatment method according to claim 2, it is characterized in that: when adopting the liftering method, receive ripple and recover the transmission ripple from receiving ripple or part, or from partly sending ripple recovers required additional wave, this additional wave and primary wave are synthesized the shaping ripple of transmitting terminal, and described training algorithm further comprises following concrete operations content:

Earlier with transmitting terminal initialize signal g (t) by with the filter of transmission channel equivalence after

Signal waveform be divided into two parts: interval [kT, (k+1) T) in main ripple signal

With at interval [(k+1) T, (k+1) T+ τ ₃) interior hangover ripple signal

, T is the code-element period length of transmitting terminal initialize signal g (t), τ ₃Length be infinitely great in theory, τ during enforcement ₃Length depend on the attenuation of the wave amplitude that trails, concrete numerical value then depends on training algorithm, k is zero or positive integer, main ripple signal and hangover ripple signal are respectively: ${\tilde{g}}_M\left(t\right)=\left\{\begin{array}{cc}\tilde{g}\left(t\right),& \mathrm{kT}\&le;t<(k+1)T)\\ 0,& (k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3\end{array}\right.,$ ${\tilde{g}}_T\left(t\right)=\left\{\begin{array}{cc}0,& \mathrm{kT}\&le;t<(k+1)T)\\ \tilde{g}\left(t\right),& (k+1)T\&le;t<(k+1)T+{\mathrm{\&tau;}}_3\end{array}\right.;$ Ripple signal again will trail

As additional wave, described formula with liftering structure additional wave is by the waveform that obtains after the liftering: $F\left(u\right)={\tilde{G}}_T\left(u\right)/P\left(u\right);$ In the formula, F (u) is the frequency domain representation of required additional wave of finding the solution,

It is the hangover ripple

Frequency domain representation, P (u) is the frequency domain representation that is used for the impulse response p (t) of the filter of replacing transmission channel of equal value; Then, F (u) is converted to time-domain signal f (t) with contrary fast fourier transform, perhaps according to following formula, directly will be with the hangover ripple signal of time-domain representation

Through the time-frequency domain conversion, obtain the additional wave signal f (t) of time-domain representation: $f\left(t\right)=\mathrm{REAL}\left[\mathrm{IFFT}\right[\mathrm{FFT}\left[{\tilde{g}}_T\left(t\right)\right]/\mathrm{FFT}\left[p\left(t\right)\right]\left]\right],$ In the formula, f (t) representative is through the signal after the liftering, and p (t) is the impulse response of filter, FFT[] represent fast fourier transform, IFFT[] the contrary fast fourier transform of representative, REAL[] represent to get real; At last, will after initialize signal g (t) stack, pass through filter again, can reduce hangover, finish the additive waveshape preliminary treatment of liftering method through the signal f (t) after the liftering as additional wave.

7, according to claim 1 or 2 or 3 or 4 or 5 or 6 described additive waveshape pretreatment methods, it is characterized in that: it is by two or two above wavelet g that described method is applied to each signal element _i(t) the composite wave signal that waveform linear superposition forms $g\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_i\left(t\right)$ The time, being called the multiple wavelet code element, in the formula, natural number i is the wavelet sequence number, span is [1, N]; Select various dissimilar ripples, promptly the different ripple of shape, frequency, phase place, position or amplitude is used as wavelet g _i(t), and adopt aforementioned additive waveshape pretreatment method that each wavelet in the composite wave is handled to the signal element formed by single waveform, promptly select following method respectively for use: distortion and hangover minimization method or maximum signal to noise ratio method or recurrence method or liftering method are made the additive waveshape pretreatment operation to the waveform of each wavelet in the composite wave one by one, obtain pretreated composite wave, to satisfy the requirement of transmission channel and transmission performance.

8, according to claim 3 or 4 or 5 or 6 described additive waveshape pretreatment methods, it is characterized in that: described select for use distortion and hangover minimization method or maximum signal to noise ratio method or one by one recurrence method or liftering method the waveform of composite wave made preprocess method further comprise following concrete operations step:

(1) makes wavelet sequence number i=1;

(2) to wavelet g _i(t) implement the pretreatment operation of " distortion and hangover minimization method " or " maximum signal to noise ratio method " or " recurrence method one by one " or " liftering method ", obtain pretreated sub-shaping ripple g _1i(t);

(3) make i=i+1 again, and judge that i＞N sets up? if then order is carried out subsequent operation; Otherwise, return step (2), continue to repeat pretreatment operation;

(4) with all sub-shaping ripple g _1i(t), i=1,2 ..., N, N are positive integer, carry out linear superposition according to following formula: $g_1\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_{1i}\left(t\right),$ Get the pretreated composite wave that is used for transmitting terminal to the end, i.e. the shaping ripple of the synthetic code element of multiple wavelet.

9, additive waveshape pretreatment method according to claim 7 is characterized in that: it is by two or two above wavelet g that described method is applied to each signal element _i(t) the composite wave signal that waveform linear superposition forms $g\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{g}_i\left(t\right)$ The time, in the formula, natural number i is the wavelet sequence number, span is [1, N]; Select following method respectively for use: the carrier transmission of multiple width of cloth phase modulating baseband transmission or multiple width of cloth phase modulating baseband sign indicating number or the multiple width of cloth are modulated direct carrier transmission mutually waveform are made the additive waveshape pretreatment operation, obtain pretreated composite wave, to satisfy the requirement of transmission channel and transmission performance.

10, additive waveshape pretreatment method according to claim 9 is characterized in that: carrier transmission, the multiple width of cloth of described multiple width of cloth phase modulating baseband transmission, multiple width of cloth phase modulating baseband sign indicating number are modulated three kinds of common features that are used for the coded system of circuit transfer encoding of direct carrier transmission mutually and are:

A, their code element all are made up of the identical wavelet of a plurality of frequencies, and each wavelet is got the amplitude of different brackets, and each grade amplitude is corresponding to a binary coding;

B, their all available following equation group form of Code And Decode are represented: encoding equtions group: AX=G, decoding equation group: X=A ^-1G, in the formula,

$A=\left[\begin{array}{ccccccc}{K}_{11}& K_{12}& ...& ...& ...& ...& K_{1H}\\ & & & & .& & .\\ K_{21}& & & & .& & .\\ & & & & .& & .\\ .& & & & .& & .\\ .& & & & .& & .\\ .& & & & .& & .\\ .& & & & & & .\\ .& & & & K_{\mathrm{hj}}& & .\\ .& & & & & & .\\ .& & & & .& & .\\ .& & & & .& & .\\ .& & & & .& & .\\ .& & & & .& & .\\ .& & & & .& & .\\ .& & & & .& & .\\ K_{H1}& ...& ...& ...& ...& ...& K_{\mathrm{HH}}\end{array}\right],$ $X=\left[\begin{array}{c}{X}_1\\ X_2\\ .\\ .\\ .\\ X_h\\ .\\ .\\ .\\ .\\ .\\ .\\ X_H\end{array}\right],G=\left[\begin{array}{c}{G}_1\\ G_2\\ .\\ .\\ .\\ G_h\\ .\\ .\\ .\\ .\\ .\\ .\\ G_H\end{array}\right]$

Wherein, X is the wavelet amplitude vector, and G is the vector that obtains behind a series of coherent computings of the process of receiving terminal code element, and A is the coefficient matrix of encoding equtions group, A ^-1Be the contrary of A, K _HjBe the element of coefficient matrix, span is a real number field, solving equation group X=A ^-1G promptly gets separating of each wavelet.

11, additive waveshape pretreatment method according to claim 9, it is characterized in that: three kinds of line codings that the carrier transmission and the multiple width of cloth of described multiple width of cloth phase modulating baseband transmission, multiple width of cloth phase modulating baseband sign indicating number modulated direct carrier transmission mutually are referred to as nonopiate amplitude Multiple Modulation coding, promptly abbreviate the NMAM coding as, when this NMAM coding is carried out the additive waveshape preliminary treatment, if encoding equtions group AX=G is an ill-condition equation, then according to minimum ill principle structure additional wave, its concrete operations step is as described below:

(1) from composite wave, takes out a wavelet, select for use a kind of in distortion and hangover minimization method or maximum signal to noise ratio method or successive approximation method or four kinds of methods of liftering method that this wavelet is carried out preliminary treatment respectively;

(2) judge whether to satisfy following formula: || A ^-1||＜γ, in the formula, || A ^-1|| be the contrary norm of equation group coefficient matrix, γ is an enough little threshold value, and through the training decision, the foundation that training finishes is that coding or decoding solution of equations can reach desirable precision to its value by the designer; If || A ^-1|| value meet the demands, finish the additive waveshape preprocessing process; Otherwise, return step (1), continue to select new additional wave, sub-additional wave, till the sub-additional wave and additional wave that are met above-mentioned formula establishment.

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