CN105279349A - Simplification order reduction method for Volterra series behavior model - Google Patents

Abstract

The invention discloses a simplification order reduction method for a Volterra series behavior model. The method comprises steps that, a general Volterra series behavior model in a discrete mode is established, unknown Volterra nucleuses are simplified according to physical characteristics of a to-be-described circuit, and Volterra series interception is further carried out; the Volterra nucleuses at each order are trimmed by employing a preset trimming method; input signals are recombined according to the trimmed Volterra nucleuses, and an input signal matrix is established; a simplified Volterra series behavior model is acquired through identification by utilizing a preset identification method. Through the method, a problem of curse of dimensionality existing in a general Volterra series behavior model is solved, so the general Volterra series behavior model can be applied to strong non-linear and memory length nonlinear circuit modeling, and application to system-grade electromagnetic compatibility simulation of a nonlinear circuit is convenient.

Description

A kind of simplification order reducing method of Volterra progression behavior model

Technical field

The present invention relates to technical field of electromagnetic compatibility, be specifically related to a kind of simplification order reducing method of Volterra progression behavior model.

Background technology

Behavior model is the mathematical model describing circuit input and output behavioural characteristic, it can ignore parameter and the function of internal transistor level element, only depend on the inputoutput data of circuit or system, make originally complicated and the electronic system emulation that there is a large amount of undecidable decision problem becomes possibility, improve analysis efficiency.In EMC analysis, the special status of nonlinear problem makes non-linear behavior model also become the focus of research.Particularly in the field such as wireless communication system, Navigation Control, transmitter will use a large amount of nonlinear devices and strong nonlinearity circuit, by introducing the behavior model describing nonlinear characteristic, thus set up emission coefficient interferer models accurately, for system-level Emulation of EMC.

Volterra progression provides the general behavior model of a kind of non-linear circuit or system, and in theory, it can approach non-linear continuous function with arbitrary accuracy.But, because the number of identified parameters in Volterra progression increases along with the index that increases to of model order and memory span, easily cause the dimension disaster problem of Function identification.In order to reduce the complexity of Volterra progression behavior model, occur that simplified partial model is as memory polynomial model, Wiener model etc.Application number be 201110380468.4 patent document discloses a kind of power amplifier analogy method based on Volterra model, simplify classical Volterra model, but its polynomial expression number is only reduced to 1/2, unknown quantity is still along with the index that increases to of exponent number and memory span increases.Application number be 201310694910.X patent document discloses a kind of power amplifier predistortion device and method based on simplifying Volterra progression, single order is adopted to block the method for dynamic deflection reduction Volterra progression behavior model, but owing to only considering the first order component of memory term in Volterra progression, when multistage memory term has larger contribution to model output, the short-cut method precision of proposition reduces.

Therefore, need the simplification order reducing method proposing a kind of Volterra progression behavior model, obtain the compromise of unknown-model parameter amount and precision, the number of Volterra core to be identified can be reduced, the behavioural characteristic of circuit or system can be described again exactly, Volterra progression behavior model is enable to be applied to the non-linear circuit modeling of strong nonlinearity and memory span, for the electromagnetic compatibility analysis of complicated circuit domain system and assessment provide effective means.

Summary of the invention

The object of the present invention is to provide a kind of simplification order reducing method of Volterra progression behavior model, solve the problem of dimension disaster in general Volterra progression behavior model, the non-linear circuit modeling of strong nonlinearity and memory span can be applied to, conveniently be applied to the system-level Emulation of EMC of non-linear circuit.

In order to achieve the above object, the present invention is achieved through the following technical solutions: a kind of simplification order reducing method of Volterra progression behavior model, is characterized in, comprises following steps:

S1, set up the Volterra progression behavior model of general discrete form, the physical features according to circuit to be described, simplifies unknown Volterra core, and intercepts Volterra progression;

The Volterra core of pruning method to each rank that S2, employing are preset is pruned;

S3, check input signal recombinate according to the Volterra after pruning, set up input signal matrix;

S4, the Volterra progression behavior model utilizing the discrimination method identification preset to be simplified.

A step S5 is also comprised after described step S4,

S5, employing are preset determination methods and are judged whether the Volterra progression behavior model simplified meets accuracy requirement;

If not, then step S2 is returned;

If so, the simplification depression of order to Volterra progression behavior model is then completed.

Presetting determination methods in described step S5 is normalized mean squared error method.

The Volterra progression behavior model of discrete form general in described step S1 adopts following relational expression:

$y\left(k\right)=\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{i_1=0}{\overset{\mathrm{\∞}}{\Σ}}\mathrm{...}\underset{i_n=0}{\overset{\mathrm{\∞}}{\Σ}}{h}_n(i_1,i_2,\mathrm{...},i_n)\underset{j=1}{\overset{n}{\Π}}x(k-i_j)$

Wherein: y (k) is output signal, and x (k) is input signal, h _n(i ₁, i ₂..., i _n) be n rank Volterra core.

Specifically following steps are comprised in described step S1:

S1.1, set up the Volterra progression behavior model of general discrete form;

S1.2, the Volterra core symmetry utilizing the bandpass characteristics of circuit and signal combination to produce simplify;

S1.3, the exponent number in Volterra progression and memory span are set to finite value.

The pruning method preset in described step S2 is radial pruning method.

Specifically following steps are comprised in described step S2:

S2.1, to simplify from Cartesian coordinates direction of principal axis, the variable i of all n rank Volterra kernel functions _j(1≤j≤n) has a value non-vanishing, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,\mathrm{...},i_j,\mathrm{...},0)\≠0.$

S2.2, to simplify from two dimensional surface diagonal, the variable i of all n rank Volterra kernel functions _j(1≤j≤n) has two value is non-vanishing and value is equal, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,\mathrm{...},i_j,\mathrm{...},i_j,\mathrm{...},0)\≠0.$

S2.3, tie up hypercube diagonal from n and simplify, only when the variable i of n rank Volterra kernel function _jwhen (1≤j≤n) value is all equal, corresponding plural n rank Volterra core meets ${\tilde{h}}_n(i_1,i_2,\mathrm{...},i_n)\≠0.$

The input signal matrix set up in described step S3 comprises:

The element that Cartesian coordinates direction of principal axis Volterra checks the input signal matrix X answered comprises X _{n, 1,1}{ x (k), i _jand X _{n, 1,2}{ x (k), i _j, be expressed as,

X _{n, 1,1}{ x (k), i _j}=x ²(k) | x (k) | ^n-3x ^*(k-i _j) and X _{n, 1,2}{ x (k), i _j}=| x (k) | ^n-1x (k-i _j);

The element that two dimensional surface diagonal Volterra checks the input signal matrix X answered comprises X _{n, 2,1}{ x (k), i _j, X _{n, 2,2}{ x (k), i _jand X _{n, 2,3}{ x (k), i _j, be expressed as,

X _{n, 2,1}{ x (k), i _j}=x ²(k-i _j) | x (k) | ^n-3x ^*(k), X _{n, 2,2}{ x (k), i _j}=| x (k-i _j) | ²| x (k) | ^n-3x (k) and

X _n,2,3{x(k),i _j}＝x ^*2(k-i _j)|x(k)| ^n-5x ³(k)；

The element that n dimension hypercube diagonal Volterra checks the input signal matrix X answered comprises X _{n, n, 1}{ x (k), i _j, be expressed as, X _{n, n, 1}{ x (k), i _j}=| x (k-i _j) | ^n-1x (k-i _j).

The discrimination method preset in described step S4 is least square method, and Gather and input output signal data, more than the number of Volterra core to be identified, adopts following relational expression when estimating Volterra core:

$\hat{H}={\left(X^{\′}X\right)}^{-1}{X}^{\′}Y$

Wherein: for the Volterra core vector estimated, X input signal matrix, X' is the associate matrix of X, and Y is output signal matrix.

Normalized mean squared error ENMSE in described normalized mean squared error method meets following relational expression:

$E_{NMSE}=10log\left(\frac{\underset{s=1}{\overset{S}{\Σ}}\left(\right|{\tilde{y}}_s-{\tilde{y}}_s^{\mathrm{mod}}{|}^2)}{\underset{s=1}{\overset{S}{\Σ}}|{\tilde{y}}_s{|}^2}\right)$

Wherein: S is sampled point number, for Volterra progression behavior model output signal, for output signal complex envelope.

The simplification order reducing method of a kind of Volterra of the present invention progression behavior model compared with prior art has the following advantages: the problem solving dimension disaster in general Volterra progression behavior model, the number of Volterra core to be identified and exponent number and memory span linear, the non-linear circuit modeling of strong nonlinearity and memory span can be applied to; The behavioural characteristic describing circuit or system is exactly ensured while reducing the number of Volterra core to be identified in Volterra progression behavior model; Adopt radial pruning method to avoid high exponent arithmetic(al) in Volterra progression behavior model, the input signal matrix of foundation and output matrix meet linear equation, can directly use least square method to carry out System Discrimination, simple and convenient; The Volterra progression behavior model inner parameter simplified after depression of order easily adjusts, convenient System Level Electromagnetic Compatibility analysis and the assessment being used for non-linear circuit and system.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the simplification order reducing method of a kind of Volterra progression of the present invention behavior model;

Fig. 2 is that the radial direction of Volterra progression the 3rd rank item prunes direction schematic diagram;

Fig. 3 is part time domain complex envelope comparison of wave shape (N=5, M=4) that embodiment intermediate power amplifier exports;

Fig. 4 is part time domain complex envelope comparison of wave shape (N=7, M=2) that embodiment intermediate power amplifier exports.

Embodiment

Below in conjunction with accompanying drawing, by describing a preferably specific embodiment in detail, the present invention is further elaborated.

As shown in Figure 1, a kind of simplification order reducing method of Volterra progression behavior model, comprises following steps:

S1, set up the Volterra progression behavior model of general discrete form, the physical features according to circuit to be described, simplifies unknown Volterra core, and intercepts Volterra progression.

Specifically following steps are comprised in described step S1:

S1.1, set up the Volterra progression behavior model of general discrete form;

S1.2, the Volterra core symmetry utilizing the bandpass characteristics of circuit and signal combination to produce simplify;

S1.3, the exponent number in Volterra progression and memory span are set to finite value.

Wherein, the Volterra progression behavior model of general discrete form adopts following relational expression:

$y\left(k\right)=\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{i_1=0}{\overset{\mathrm{\∞}}{\Σ}}\mathrm{...}\underset{i_n=0}{\overset{\mathrm{\∞}}{\Σ}}{h}_n(i_1,i_2,\mathrm{...},i_n)\underset{j=1}{\overset{n}{\Π}}x(k-i_j)---\left(1\right)$

Wherein: y (k) is output signal, and x (k) is input signal, h _n(i ₁, i ₂..., i _n) be n rank Volterra core.

In the present embodiment, considering input, exporting is all modulation signal, y (k) and x (k) is respectively the complex envelope form of output and input signal, the bandpass characteristics of circuit is by the even order terms in filtering Volterra progression, utilize Volterra core symmetry simultaneously, and Volterra progression is intercepted as after exponent number N and memory span M, discrete-time complex baseband Volterra progression behavior model can be expressed as:

$\begin{array}{c}\tilde{y}\left(k\right)=\underset{i=0}{\overset{M}{\Σ}}{\tilde{h}}_1\left(i\right)\×(k-i)+\underset{i_1=0}{\overset{M}{\Σ}}\underset{i_2=i_1}{\overset{M}{\Σ}}\underset{i_3=0}{\overset{M}{\Σ}}{\tilde{h}}_3(i_1,i_2,i_3)\tilde{x}(k-i_1)\tilde{x}(k-i_i)\tilde{x}(k-i_2){\tilde{x}}^{*}(k-i_3)\\ +\underset{i_1=0}{\overset{M}{\Σ}}\underset{i_2=i_1}{\overset{M}{\Σ}}\underset{i_3=i_2}{\overset{M}{\Σ}}\underset{i_4=0}{\overset{M}{\Σ}}\underset{i_5=i_4}{\overset{M}{\Σ}}{\tilde{h}}_5(i_1,i_2,i_3,i_4,i_5)\tilde{x}(k-i_1)\tilde{x}(k-i_2)\tilde{x}(k-i_3){\tilde{x}}^{*}(k-i_4){\tilde{x}}^{*}(k-i_5)+\mathrm{...}\end{array}---\left(2\right)$

In formula, the multiple Volterra core in n rank for system; () ^*represent the complex conjugate of signal; with be respectively input and output complex envelope discrete signal.

The Volterra core of pruning method to each rank that S2, employing are preset is pruned.

In the present embodiment, the pruning method preset is radial pruning method, and described radial pruning method ties up hypercube diagonal simplify Volterra core from Cartesian coordinates direction of principal axis, two dimensional surface diagonal, n respectively.

Particularly, specifically following steps are comprised in described step S2:

S2.1, to simplify from Cartesian coordinates direction of principal axis, the variable i of all n rank Volterra kernel functions _j(1≤j≤n) has a value non-vanishing, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,\mathrm{...},i_j,\mathrm{...},0)\≠0.$

S2.2, to simplify from two dimensional surface diagonal, the variable i of all n rank Volterra kernel functions _j(1≤j≤n) has two value is non-vanishing and value is equal, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,\mathrm{...},i_j,\mathrm{...},i_j,\mathrm{...},0)\≠0.$

S2.3, tie up hypercube diagonal from n and simplify, only when the variable i of n rank Volterra kernel function _jwhen (1≤j≤n) value is all equal, corresponding plural n rank Volterra core meets ${\tilde{h}}_n(i_1,i_2,\mathrm{...},i_n)\≠0.$

S3, check input signal recombinate according to the Volterra after pruning, set up input signal matrix.

Particularly, the input signal matrix set up in described step S3 comprises:

The element that Cartesian coordinates direction of principal axis Volterra checks the input signal matrix X answered comprises X _{n, 1,1}{ x (k), i _jand X _{n, 1,2}{ x (k), i _j, be expressed as,

X _n,1,1{x(k),i _j}＝x ²(k)|x(k)| ^n-3x ^*(k-i _j)(3)

And X _{n, 1,2}{ x (k), i _j}=| x (k) | ^n-1x (k-i _j) (4);

The element that two dimensional surface diagonal Volterra checks the input signal matrix X answered comprises X _{n, 2,1}{ x (k), i _j, X _{n, 2,2}{ x (k), i _jand X _{n, 2,3}{ x (k), i _j, be expressed as,

X _n,2,1{x(k),i _j}＝x ²(k-i _j)|x(k)| ^n-3x ^*(k)(5)

X _n,2,2{x(k),i _j}＝|x(k-i _j)| ²|x(k)| ^n-3x(k)(6)

X _n,2,3{x(k),i _j}＝x ^*2(k-i _j)|x(k)| ^n-5x ³(k)(7)；

The element that n dimension hypercube diagonal Volterra checks the input signal matrix X answered comprises X _{n, n, 1}{ x (k), i _j, be expressed as,

X _n,n,1{x(k),i _j}＝|x(k-i _j)| ^n-1x(k-i _j)(8)。

S4, the Volterra progression behavior model utilizing the discrimination method identification preset to be simplified.

In the present embodiment, the discrimination method preset is least square method.

Particularly, least square method carries out identification and the Gather and input output signal data number more than Volterra core to be identified, adopts following relational expression when estimating Volterra core:

$\hat{H}={\left(X^{\′}X\right)}^{-1}{X}^{\′}Y---\left(9\right)$

Wherein: for the Volterra core vector estimated, X input signal matrix, X' is the associate matrix of X, and Y is output signal matrix.

S5, employing are preset determination methods and are judged whether the Volterra progression behavior model simplified meets accuracy requirement;

If not, then step S2 is returned;

If so, the simplification depression of order to Volterra progression behavior model is then completed.

In the present embodiment, presetting determination methods in described step S5 is normalized mean squared error method.

Normalized mean squared error ENMSE in described normalized mean squared error method meets following relational expression:

$E_{NMSE}=10log\left(\frac{\underset{s=1}{\overset{S}{\Σ}}\left(\right|{\tilde{y}}_s-{\tilde{y}}_s^{\mathrm{mod}}{|}^2)}{\underset{s=1}{\overset{S}{\Σ}}|{\tilde{y}}_s{|}^2}\right)---\left(10\right)$

Wherein: S is sampled point number, for Volterra progression behavior model output signal, for output signal complex envelope.

The normalized mean squared error ENMSE obtained is less, illustrates that the Volterra progression behavior model after simplifying is more accurate, if the normalized mean squared error ENMSE calculated meets accuracy requirement, illustrates that the Volterra progression behavior model after simplifying is more accurate.

Embody rule:

Step one: the Volterra progression behavior model setting up general discrete form, the physical features according to described circuit simplifies unknown Volterra core, and intercepts Volterra progression.

Certain power amplifier circuit is for amplifying the WCDMA signal that input bit rate is 3.84Mcps, carrier frequency is 2.14GHz, power is 10W, carry out identification of Model Parameters and validation verification in about 4000 the input/output signal data points of real power amplifier circuit input and output port collection, require that the normalized mean squared error ENMSE of Volterra progression behavior model is less than-40dB.

In the present embodiment, the input/output signal of consideration power amplifier is all modulation signal, even order terms can be carried out filtering by the bandpass characteristics of power amplifier circuit, Volterra progression is intercepted for exponent number N=5, memory span M=4, consider Volterra core symmetry, the expression formula obtaining discrete-time complex baseband Volterra progression behavior model according to formula (2) is simultaneously:

$\begin{array}{c}\tilde{y}\left(k\right)=\underset{i=0}{\overset{4}{\Σ}}{\tilde{h}}_1\left(i\right)\×\tilde{x}(k-i)+\underset{i_1=0}{\overset{4}{\Σ}}\underset{i_2=i_1}{\overset{4}{\Σ}}\underset{i_3=0}{\overset{4}{\Σ}}{\tilde{h}}_3(i_1,i_2,i_3)\tilde{x}(k-i_1)\tilde{x}(k-i_2){\tilde{x}}^{*}(k-i_3)\\ +\underset{i_1=0}{\overset{4}{\Σ}}\underset{i_2=i_1}{\overset{4}{\Σ}}\underset{i_3=i_2}{\overset{4}{\Σ}}\underset{i_4=0}{\overset{4}{\Σ}}\underset{i_5=i_4}{\overset{4}{\Σ}}{\tilde{h}}_5(i_1,i_2,i_3,i_4,i_5)\tilde{x}(k-i_1)\tilde{x}(k-i_2)\tilde{x}(k-i_3){\tilde{x}}^{*}(k-i_4){\tilde{x}}^{*}(k-i_5)\end{array}---\left(11\right)$

Step 2: adopt radial pruning method, then the Volterra core on each rank is pruned.

In the present embodiment, simplify from Cartesian coordinates direction of principal axis, the variable i of all n rank Volterra kernel functions _j(0≤i _j≤ 4,1≤j≤n) there is a value non-vanishing, other is all zero, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,\mathrm{...},i_j,\mathrm{...},0)\≠0.$

Simplify from two dimensional surface diagonal, the variable i of all n rank Volterra kernel functions _j(0≤i _j≤ 4,1≤j≤n) there are two value is non-vanishing and value is equal, corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,\mathrm{...},i_j,\mathrm{...},i_j,\mathrm{...},0)\≠0.$

Tie up hypercube diagonal from n to simplify, only when the variable i of n rank Volterra kernel function _jwhen (1≤j≤n) value is all equal, corresponding plural n rank Volterra core meets

In the present embodiment, the Volterra nuclear matrix H obtained is:

$\begin{array}{c}H=\[{\tilde{h}}_1\left(1\right),\mathrm{...},{\tilde{h}}_1\left(4\right),{\tilde{h}}_3(0,0,1),{\tilde{h}}_3(0,1,0),\mathrm{...},{\tilde{h}}_3(0,4,4){\tilde{h}}_5(0,0,0,0,1),\mathrm{...},\\ {\tilde{h}}_5(0,0,0,4,4),{\tilde{h}}_1\left(0\right),\mathrm{...},{\tilde{h}}_3(4,4,4),\mathrm{...},{\tilde{h}}_5(4,4,4,4,4){\]}^T\end{array}---\left(12\right)$

In the present embodiment, the Volterra core to be identified of general Volterra progression behavior model is 3905, and after step one in the present invention, Volterra core to be identified is 605, and after step 2 in the present invention, Volterra core to be identified is only 51.Can find out that Volterra nuclear volume to be identified greatly reduces.

Step 3: check input signal according to the Volterra after pruning and recombinate, set up input signal matrix.

In the present embodiment, if start sampling from the k moment, obtain 4000 sampled datas, according to pruning the Volterra core obtained, input signal is recombinated, utilizes formula (6) ~ formula (8) to obtain input signal submatrix X (k) in k moment to be:

$\begin{array}{c}X\left(k\right)=\[\tilde{x}(k-1),\mathrm{...},\tilde{x}(k-4),{\tilde{x}}^2\left(k\right){\tilde{x}}^{*}(k-1),|\tilde{x}\left(k\right){|}^2\tilde{x}(k-1),\mathrm{...},|\tilde{x}(k-4){|}^2\tilde{x}\left(k\right),\\ |\tilde{x}\left(k\right){|}^2{\tilde{x}}^2\left(k\right){\tilde{x}}^{*}(k-1),\mathrm{...},|\tilde{x}\left(k\right){|}^2\tilde{x}\left(k\right){\tilde{x}}^{*2}(k-4),\tilde{x}\left(k\right),\mathrm{...},\\ |\tilde{x}(k-4){|}^2\tilde{x}(k-4),\mathrm{...},|\tilde{x}(k-4){|}^4\tilde{x}(k-4)\]\end{array}---\left(13\right)$

The input signal matrix X in all sampled point moment is:

X＝[X(k),X(k+1),…,X(k+3999)] ^T(14)

Step 4: the Volterra progression behavior model utilizing least square method to carry out identification to be simplified.

In the present embodiment, output signal matrix Y is:

$Y={\[\tilde{y}\left(k\right),\tilde{y}(k+1),\mathrm{...},\tilde{y}(k+3999)\]}^T---\left(15\right)$

Utilize formula (9) to carry out identification, obtain the Volterra nuclear matrix estimated

Step 5: adopt normalized mean squared error ENMSE judgment models whether to meet accuracy requirement, the exponent number intercepted as satisfied continuation adjustment Volterra progression and memory span are until meet accuracy requirement.Utilize the Volterra nuclear matrix of input signal matrix X and estimation be multiplied the output matrix obtaining estimating then utilize formula (10) to calculate normalized mean squared error ENMSE=-39.2dB, do not meet accuracy requirement.As shown in Figure 3, the Output rusults and the acquired original that simplify Volterra progression behavior model export Data Comparison to the time domain complex envelope waveform that Partial Power amplifier exports, and do not fit like a glove.

Continue exponent number N=7, memory span M=2 that adjustment Volterra progression intercepts.Repeat step 2 ~ step 4, the Volterra core to be identified of general Volterra progression behavior model is 3279, after step one in the present invention, Volterra core to be identified is 231, and after step 2 in the present invention, Volterra core to be identified is only 40.The normalized mean squared error ENMSE=-45.1dB obtained, meets accuracy requirement.The time domain complex envelope waveform that Partial Power amplifier exports as shown in Figure 4, can find out simplify Volterra progression behavior model can the behavior of accurate description power amplifier circuit.

Although content of the present invention has done detailed introduction by above preferred embodiment, will be appreciated that above-mentioned description should not be considered to limitation of the present invention.After those skilled in the art have read foregoing, for multiple amendment of the present invention and substitute will be all apparent.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (10)

1. a simplification order reducing method for Volterra progression behavior model, is characterized in that, comprise following steps:

S1, set up the Volterra progression behavior model of general discrete form, the physical features according to circuit to be described, simplifies unknown Volterra core, and intercepts Volterra progression;

The Volterra core of pruning method to each rank that S2, employing are preset is pruned;

S3, check input signal recombinate according to the Volterra after pruning, set up input signal matrix;

S4, the Volterra progression behavior model utilizing the discrimination method identification preset to be simplified.

2. simplify order reducing method as claimed in claim 1, it is characterized in that, after described step S4, also comprise a step S5,

S5, employing are preset determination methods and are judged whether the Volterra progression behavior model simplified meets accuracy requirement;

If not, then step S2 is returned;

If so, the simplification depression of order to Volterra progression behavior model is then completed.

3. simplify order reducing method as claimed in claim 2, it is characterized in that, presetting determination methods in described step S5 is normalized mean squared error method.

4. simplify order reducing method as claimed in claim 1, it is characterized in that, the Volterra progression behavior model of discrete form general in described step S1 adopts following relational expression:

$y\left(k\right)=\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{i_1=0}{\overset{\mathrm{\∞}}{\Σ}}...\underset{i_n=0}{\overset{\mathrm{\∞}}{\Σ}}{h}_n(i_1,i_2,...,i_n)\underset{j=1}{\overset{n}{\Π}}x(k-i_j)$

Wherein: y (k) is output signal, and x (k) is input signal, h _n(i ₁, i ₂..., i _n) be n rank Volterra core.

5. simplify order reducing method as claimed in claim 1, it is characterized in that, in described step S1, specifically comprise following steps:

S1.1, set up the Volterra progression behavior model of general discrete form;

S1.2, the Volterra core symmetry utilizing the bandpass characteristics of circuit and signal combination to produce simplify;

S1.3, the exponent number in Volterra progression and memory span are set to finite value.

6. simplify order reducing method as claimed in claim 1, it is characterized in that, the pruning method preset in described step S2 is radial pruning method.

7. the simplification order reducing method as described in claim 1 or 6, is characterized in that, specifically comprises following steps in described step S2:

S2.1, to simplify from Cartesian coordinates direction of principal axis, the variable i of all n rank Volterra kernel functions _j(1≤j≤n) has a value non-vanishing, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,...,i_j,...,0)\≠0.$

S2.2, to simplify from two dimensional surface diagonal, the variable i of all n rank Volterra kernel functions _j(1≤j≤n) has two value is non-vanishing and value is equal, and corresponding plural n rank Volterra core meets ${\tilde{h}}_n(0,...,i_j,...,i_j,...,0)\≠0.$

S2.3, tie up hypercube diagonal from n and simplify, only when the variable i of n rank Volterra kernel function _jwhen (1≤j≤n) value is all equal, corresponding plural n rank Volterra core meets ${\tilde{h}}_n(i_1,i_2,...,i_n)\≠0.$

8. simplify order reducing method as claimed in claim 1, it is characterized in that, the input signal matrix set up in described step S3 comprises:

The element that Cartesian coordinates direction of principal axis Volterra checks the input signal matrix X answered comprises X _{n, 1,1}{ x (k), i _jand X _{n, 1,2}{ x (k), i _j, be expressed as,

X _{n, 1,1}{ x (k), i _j}=x ²(k) | x (k) | ^n-3x ^*(k-i _j) and X _{n, 1,2}{ x (k), i _j}=| x (k) | ^n-1x (k-i _j);

The element that two dimensional surface diagonal Volterra checks the input signal matrix X answered comprises X _{n, 2,1}{ x (k), i _j, X _{n, 2,2}{ x (k), i _jand X _{n, 2,3}{ x (k), i _j, be expressed as,

X _{n, 2,1}{ x (k), i _j}=x ²(k-i _j) | x (k) | ^n-3x ^*(k), X _{n, 2,2}{ x (k), i _j}=| x (k-i _j) | ²| x (k) | ^n-3x (k) and

X _n，2，3{x(k)，i _j}＝x ^*2(k-i _j)x(k)| ^n-5x ³(k)；

The element that n dimension hypercube diagonal Volterra checks the input signal matrix X answered comprises X _{n, n, 1}{ x (k), i _j, be expressed as, X _{n, n, 1}{ x (k), i _j}=| x (k-i _j) | ^n-1x (k-i _j).

9. simplify order reducing method as claimed in claim 1, it is characterized in that, the discrimination method preset in described step S4 is least square method, and Gather and input output signal data, more than the number of Volterra core to be identified, adopts following relational expression when estimating Volterra core:

$\hat{H}={\left(X^{\′}X\right)}^{-1}{X}^{\′}Y$

Wherein: for the Volterra core vector estimated, X input signal matrix, the associate matrix that X ' is X, Y is output signal matrix.

10. simplify order reducing method as claimed in claim 3, it is characterized in that, the normalized mean squared error ENMSE in described normalized mean squared error method meets following relational expression:

$E_{NMSE}=10log\left(\frac{\underset{s=1}{\overset{S}{\Σ}}\left(\right|{\tilde{y}}_s-{\tilde{y}}_s^{\mathrm{mod}}{|}^2)}{\underset{s=1}{\overset{S}{\Σ}}|{\tilde{y}}_s{|}^2}\right)$

Wherein: S is sampled point number, for Volterra progression behavior model output signal, for output signal complex envelope.