CN106100717A - Method and system are analyzed in a kind of linearization of nonlinear system - Google Patents

Abstract

The invention discloses a kind of linearization of nonlinear system and analyze method, including: utilize Bussgang theory to obtain transfer characteristic function h (y corresponding to source signal x time at the first via node at transmitting node_sr)；Utilize linear amplification theoretical to described transfer characteristic function h (y_sr) carry out linear amplification, obtain the first relay process function f_r(y_sr′)；The first reception signal y corresponding by source signal described time at the first via node to receiving node is obtained according to described first relay process function_rd.As can be seen here, in above process, it is possible to power attenuation factor and noise factor are combined so that first receives the character of the more real reaction source signal of signal.Additionally, invention additionally discloses a kind of linearization of nonlinear system to analyze system, effect is described above.

Description

Method and system are analyzed in a kind of linearization of nonlinear system

Technical field

The present invention relates to communication technical field, particularly relate to a kind of linearization of nonlinear system and analyze method and be System.

Background technology

In in the past few decades, wireless communication technology has obtained rapid development, and the most also obtains Huge progress.In technological revolution each time, communication technology all can obtain development at full speed, communication equipment in size, Cost and transmission reliability aspect are all greatly improved.

We are analyzed according to linear system, because our general Study mainly considers the system of research at present Be idealization linear amplifier, but the system in reality is all a nonlinear system, in signals transmission not only There is noise, but also have the factors such as power attenuation, prior art does not combine power attenuation factor and noise factor, Cause the analysis result cannot the character of more real reaction signal.

As can be seen here, the verity of the analysis result how improving signal is that those skilled in the art ask urgently to be resolved hurrilyly Topic.

Summary of the invention

It is an object of the invention to provide a kind of linearization of nonlinear system and analyze method and system, for improving signal The verity of analysis result.

For solving above-mentioned technical problem, the present invention provides a kind of linearization of nonlinear system to analyze method, including:

Bussgang theory is utilized to obtain transfer characteristic corresponding to source signal x time at the first via node at transmitting node Function h (y_sr)；

Wherein, y_sr'=h (y_sr)=α_sry_sr+d_sr,α_srIt is the first power factor, d_srFor First distortion noise, P_sFor the power of described transmitting node, h_srChannel for described transmitting node to described first via node Parameter, n_srNoise for described transmitting node to described first via node；

Utilize linear amplification theoretical to described transfer characteristic function h (y_sr) carry out linear amplification, obtain the first relay process Function f_r(y_sr'), f_r(y_sr')=α_srβ_sry_sr+β_srd_sr；

Wherein, β_srIt it is the first power normalization factor；

Obtain by source signal described time at the first via node to receiving node according to described first relay process function The first corresponding reception signal y_rd；

Wherein,Represent at described transmitting node, the first relaying Under the transmission path that node and described receiving node are constituted, average is the Gaussian noise of zero, P_rFor described first via node Launch power, h_rdChannel parameter for described first via node to described receiving node.

Preferably, also include: utilize Bussgang theory to obtain at transmitting node to described source time at the second via node Transfer characteristic function h (y corresponding for signal x_st)；

Wherein, y_st'=h (y_st)=α_sty_st+d_st,α_stIt is the second power factor, d_st It is the second distortion noise, P_sFor the power of described transmitting node, h_stLetter for described transmitting node to described second via node Road parameter, n_stNoise for described transmitting node to described second via node；

Utilize linear amplification theoretical to described transfer characteristic function h (y_st) carry out linear amplification, obtain the second relay process Function f_t(y_st'), f_t(y_st')=α_stβ_sty_st+β_std_st；

Wherein, β_stIt it is the second power normalization factor；

Obtain by source signal described time at the second via node to receiving node according to described second relay process function The second corresponding reception signal y_td；

Wherein,Represent described transmitting node, described the Under the transmission path that two via nodes and described receiving node are constituted, average is the Gaussian noise of zero, P_tFor described second relaying The transmitting power of node, h_tdChannel parameter for described second via node to described receiving node.

Preferably, described first power exponentα_srWith described first distortion noise d_srObtain according to equation below:

${\mathrm{\α}}_{sr}=\frac{{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)}{{\mathrm{\δ}}_x^2},$

${\mathrm{\δ}}_{d_{sr}}^2={\mathrm{\δ}}_x^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})-{\mathrm{\α}}_{sr}\[{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)\],$

Wherein, A is the saturated output amplitude of preferable soft limiting power amplifier,For compensating error letter Number, δ_x ²Variance yields for described source signal.

Preferably, described first power normalization factor-beta_srObtained by equation below:

Wherein, N₀For described first via node or the white noise of the second via node receiving terminal Power.

Preferably, noiseObtained by equation below:

${\tilde{n}}_{rd}={\mathrm{\α}}_{sr}\sqrt{\frac{P_r}{P_s{h}_{sr}^2+N_0}}\·h_{rd}{n}_{sr}+n_{rd}+\sqrt{\frac{P_r}{P_s{h}_{sr}^2+N_0}}{\mathrm{dh}}_{rd}.$

Preferably, described second power exponentα_stWith described second distortion noise d_stObtain according to equation below:

${\mathrm{\α}}_{st}=\frac{{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)}{{\mathrm{\δ}}_x^2},$

${\mathrm{\δ}}_{d_{st}}^2={\mathrm{\δ}}_x^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})-{\mathrm{\α}}_{st}\[{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)\],$

Wherein, A is the saturated output amplitude of preferable soft limiting power amplifier,For compensating error letter Number, δ_x ²Variance yields for described source signal.

Preferably, described second power normalization factor-beta_stObtained by equation below:

Wherein, N₀White for described first via node or described second via node receiving terminal Noise power.

Preferably, noiseObtained by equation below:

${\tilde{n}}_{td}={\mathrm{\α}}_{st}\sqrt{\frac{P_t}{P_s{h}_{st}^2+N_0}}\·h_{td}{n}_{st}+n_{td}+\sqrt{\frac{P_r}{P_s{h}_{st}^2+N_0}}{\mathrm{dh}}_{td}.$

A kind of linearization of nonlinear system analyzes system, including transmitting node, the first via node and receiving node；

Described transmitting node, for emission source signal；

Described first via node, for analyzing method to described source according to linearization of nonlinear system described above Signal carries out being calculated the first reception signal, and receives signal transmission by described first to described receiving node.

Preferably, also include: the second via node；

Described second via node, for analyzing method to described source according to linearization of nonlinear system described above Signal carries out being calculated the second reception signal, and receives signal transmission by described second to described receiving node.

Method and system are analyzed in linearization of nonlinear system provided by the present invention, obtain first with Bussgang theory Take the transfer characteristic function that source signal is corresponding, then utilize linear amplification theory that transfer characteristic function is carried out linear amplification, To the first relay process function f_r(y_sr'), obtain by the first via node extremely finally according to described first relay process function The first reception signal that time at receiving node, source signal is corresponding.As can be seen here, in above process, it is possible to by power attenuation factor Combine with noise factor so that first receives the character of the more real reaction source signal of signal.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention, the accompanying drawing used required in embodiment will be done simply below Introduction, it should be apparent that, below describe in accompanying drawing be only some embodiments of the present invention, for ordinary skill From the point of view of personnel, on the premise of not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 analyzes the flow chart of method for a kind of linearization of nonlinear system that the present invention provides；

Fig. 2 analyzes the structure chart of method for a kind of linearization of nonlinear system that the present invention provides；

Fig. 3 analyzes the flow chart of method for the another kind of linearization of nonlinear system that the present invention provides.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Describe, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiment wholely.Based on this Embodiment in invention, those of ordinary skill in the art are not under making creative work premise, and obtained is every other Embodiment, broadly falls into scope.

The core of the present invention is to provide a kind of linearization of nonlinear system and analyzes method and system.

In order to make those skilled in the art be more fully understood that the present invention program, below in conjunction with the accompanying drawings and detailed description of the invention The present invention is described in further detail.

Fig. 1 analyzes the flow chart of method for a kind of linearization of nonlinear system that the present invention provides.As it is shown in figure 1, it is non- The analysis by Linearization method of linear system includes:

S10: utilize Bussgang theory obtain at transmitting node s to the first via node r locate time source signal x corresponding turn Move characterisitic function.

Step S10 can be regarded as transmitting node s and sent by source signal to the first via node r source signal during this One conversion process of x.Theoretical, if input signal x (t) is gaussian signal, then through non-linear according to Bussgang After systemic effect, the transfer characteristic function of power amplifier just can be decomposed into: h (x (t))=α x (t)+d (t).

Fig. 2 analyzes the structure chart of method for a kind of linearization of nonlinear system that the present invention provides.In this application, source Signal x transmission is h to the channel parameter corresponding to the first via node r_srThat is, h_srFor transmitting node s to first via node r Channel parameter, and P_sFor the power of transmitting node s, then, in this transmitting procedure, source signal x just becomes y_sr,n_srNoise for transmitting node s to first via node r.y_srCorresponding transfer characteristic function It is exactly h (y_sr).Wherein, transfer characteristic function y_sr'=h (y_sr)=α_sry_sr+d_sr, α_srIt is the first power factor, d_srIt is first abnormal Become noise, n_srNoise for transmitting node s to first via node r.

In being embodied as, the first power exponentα_srWith the first distortion noise d_srObtain according to equation below:

${\mathrm{\α}}_{sr}=\frac{{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)}{{\mathrm{\δ}}_x^2},$

${\mathrm{\δ}}_{d_{sr}}^2={{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})-{\mathrm{\α}}_{sr}\[{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)\],$

Wherein, A is the saturated output amplitude of preferable soft limiting power amplifier,For compensating error letter Number, δ_x ²Variance yields for source signal.

S11: utilize linear amplification theory that transfer characteristic function is carried out linear amplification, obtain the first relay process function.

First relay process function f_r(y_sr')=α_srβ_sry_sr+β_srd_sr；Wherein, β_srIt it is the first power normalization factor.

In this step, it is by h (y_sr) carry out linear amplification, the most the above β_srTimes.It is being embodied as In, the first power normalization factor-beta_srObtained by equation below:

Wherein, N₀For described first via node or the white noise of the second via node receiving terminal Power.It is to be understood that the white noise power of the first via node receiving terminal and the white noise of the second via node receiving terminal Power is identical.

S12: obtain by source signal pair time at the first via node r to receiving node d according to the first relay process function The the first reception signal answered.

Wherein,Represent at transmitting node s, the first relaying joint Under the transmission path that some r and receiving node d is constituted, average is the Gaussian noise of zero, P_rIt it is the transmitting merit of the first via node r Rate, h_rdIt it is the channel parameter of the first via node r to receiving node d.

Be equivalent to the signal change procedure by the first via node r transmission to signal during receiving node d in this step, Signal at receiving node d is set to the first reception signal y_rd, now,

$y_{rd}={\mathrm{\α}}_{sr}\sqrt{\frac{P_s{P}_r}{P_s{h}_{sr}^2+N_0}}\·h_{sr}{h}_{rd}\·x+{\tilde{n}}_{rd}$

Said process is exactly that source signal x is transferred to receiving node d by the first via node r and obtains by transmitting node s First receives signal y_rd。

In being embodied as, noiseObtained by equation below:

${\tilde{n}}_{rd}={\mathrm{\α}}_{sr}\sqrt{\frac{P_r}{P_s{h}_{sr}^2+N_0}}\·h_{rd}{n}_{sr}+n_{rd}+\sqrt{\frac{P_r}{P_s{h}_{sr}^2+N_0}}{\mathrm{dh}}_{rd}.$

Method is analyzed in the linearization of nonlinear system that the present embodiment provides, and obtains source letter first with Bussgang theory Number corresponding transfer characteristic function, then utilizes linear amplification theory that transfer characteristic function is carried out linear amplification, obtains first Relay process function f_r(y_sr'), obtain by the first via node to receiving joint finally according to described first relay process function The first reception signal that time at Dian, source signal is corresponding.As can be seen here, in above process, it is possible to by power attenuation factor and noise Factor combines so that first receives the character of the more real reaction source signal of signal.

Owing to signal is in transmitting procedure, affected by various factors, caused the letter of the signal that receiving node d receives Making an uproar ratio may be the lowest, therefore, higher in order to increase the signal to noise ratio of the signal received, or improves the reliability of receiving node d, Therefore, in the present invention it is possible to a via node, the second via node t the most as shown in Figure 2 are set again.Understandably It is that the second via node t and the first via node r is only belonging to two different channels, and remaining signals transmission is phase With.Fig. 3 analyzes the flow chart of method for the another kind of linearization of nonlinear system that the present invention provides.Accordingly, as one Being preferably carried out mode, method is analyzed in linearization of nonlinear system, also includes:

S30: utilize Bussgang theory obtain at transmitting node s to the second via node t locate time source signal x corresponding turn Move characterisitic function.

As in figure 2 it is shown, in this application, source signal x transmission is h to the channel parameter corresponding to the first via node r_st That is, h_stFor the channel parameter of transmitting node s to second via node t, and P_sFor the power of transmitting node s, then in this transmission During, source signal x just becomes y_st。

n_stNoise for transmitting node s to second via node t.y_stCorresponding turns Moving characterisitic function is exactly h (y_st).Wherein, transfer characteristic function f_t(y_st')=α_stβ_sty_st+β_std_st, α_stIt is the second power factor, d_stIt is the second distortion noise, n_stNoise for transmitting node s to second via node t.

In being embodied as, the second power exponentα_stWith the second distortion noise d_stObtain according to equation below:

${\mathrm{\α}}_{st}=\frac{{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)}{{\mathrm{\δ}}_x^2},$

${\mathrm{\δ}}_{d_{st}}^2={{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})-{\mathrm{\α}}_{st}\[{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)\],$

Wherein, A is the saturated output amplitude of preferable soft limiting power amplifier,For compensating error letter Number, δ_x ²Variance yields for source signal.

S31: utilize linear amplification theory that transfer characteristic function is carried out linear amplification, obtain the second relay process function.

Second relay process function f_t(y_st')=α_stβ_sty_st+β_std_st；Wherein, β_stIt it is the second power normalization factor.

In this step, it is by h (y_st) carry out linear amplification, the most the above β_stTimes.It is being embodied as In, the first power normalization factor-beta_stObtained by equation below:

Wherein, N₀White for described first via node or described second via node receiving terminal Noise power.

S32: obtain by source signal pair time at the second via node t to receiving node d according to the second relay process function The the second reception signal answered.

Wherein,Represent at transmitting node s, the second relaying joint Under the transmission path that some t and receiving node d is constituted, average is the Gaussian noise of zero, P_tIt it is the transmitting merit of the second via node t Rate, h_tdIt it is the channel parameter of the second via node t to receiving node d.

Be equivalent to the signal change procedure by the second via node t transmission to signal during receiving node d in this step, Signal at receiving node d is set to the second reception signal y_td, now, $y_{td}={\mathrm{\α}}_{st}\sqrt{\frac{P_s{P}_t}{P_s{h}_{st}^2+N_0}}\·h_{st}{h}_{td}\·x+{\tilde{n}}_{td}$

Said process is exactly that source signal x is transferred to receiving node d by the second via node t and obtains by transmitting node s Second receives signal y_td。

In being embodied as, noiseObtained by equation below:

${\tilde{n}}_{td}={\mathrm{\α}}_{st}\sqrt{\frac{P_t}{P_s{h}_{st}^2+N_0}}\·h_{td}{n}_{st}+n_{td}+\sqrt{\frac{P_t}{P_s{h}_{st}^2+N_0}}{\mathrm{dh}}_{td}.$

It should be noted that in said process, step S10-step S12 and step S30-step S32 are independently of each other, Can there is sequencing, it is also possible to carry out simultaneously, not have strict order to specify.

As in figure 2 it is shown, system is analyzed in linearization of nonlinear system, including transmitting node s, the first via node r with connect Receive node d；

Transmitting node s, for emission source signal；

First via node r, for being calculated the first reception according to above-mentioned steps S10-step S12 to source signal Signal, and the first reception signal is sent to receiving node d.

As in figure 2 it is shown, system is analyzed in linearization of nonlinear system, also include: the second via node t；

Second via node t, for being calculated the second reception according to above-mentioned steps S30-step S32 to source signal Signal, and the second reception signal is sent to receiving node d.

Above linearization of nonlinear system provided by the present invention is analyzed method and system to be described in detail.Say In bright book, each embodiment uses the mode gone forward one by one to describe, and what each embodiment stressed is different from other embodiments Part, between each embodiment, identical similar portion sees mutually.For device disclosed in embodiment, due to its with Disclosed in embodiment, method is corresponding, so describe is fairly simple, relevant part sees method part and illustrates.Should refer to Go out, for those skilled in the art, under the premise without departing from the principles of the invention, it is also possible to the present invention Carrying out some improvement and modification, these improve and modify in the protection domain also falling into the claims in the present invention.

Professional further appreciates that, in conjunction with the unit of each example that the embodiments described herein describes And algorithm steps, it is possible to electronic hardware, computer software or the two be implemented in combination in, in order to clearly demonstrate hardware and The interchangeability of software, the most generally describes composition and the step of each example according to function.These Function performs with hardware or software mode actually, depends on application-specific and the design constraint of technical scheme.Specialty Technical staff specifically should can be used for using different methods to realize described function to each, but this realization should not Think beyond the scope of this invention.

The method described in conjunction with the embodiments described herein or the step of algorithm can direct hardware, processor be held The software module of row, or the combination of the two implements.Software module can be placed in random access memory (RAM), internal memory, read-only deposit Reservoir (ROM), electrically programmable ROM, electrically erasable ROM, depositor, hard disk, moveable magnetic disc, CD-ROM or technology In any other form of storage medium well known in field.

Claims (10)

1. method is analyzed in a linearization of nonlinear system, it is characterised in that including:

Bussgang theory is utilized to obtain transfer characteristic function corresponding to source signal x time at the first via node at transmitting node h(y_sr)；

Wherein, y_sr'=h (y_sr)=α_sry_sr+d_sr,α_srIt is the first power factor, d_srIt is first Distortion noise, P_sFor the power of described transmitting node, h_srFor the channel parameter of described transmitting node to described first via node, n_srNoise for described transmitting node to described first via node；

Utilize linear amplification theoretical to described transfer characteristic function h (y_sr) carry out linear amplification, obtain the first relay process function f_r(y_sr'), f_r(y_sr')=α_srβ_sry_sr+β_srd_sr；

Wherein, β_srIt it is the first power normalization factor；

Obtain by described source signal time at the first via node to receiving node corresponding according to described first relay process function First reception signal y_rd；

Wherein, Represent described transmitting node, the first via node and Under the transmission path that described receiving node is constituted, average is the Gaussian noise of zero, P_rTransmitting merit for described first via node Rate, h_rdChannel parameter for described first via node to described receiving node.

Method is analyzed in linearization of nonlinear system the most according to claim 1, it is characterised in that also include:

Bussgang theory is utilized to obtain at transmitting node to described transfer characteristic corresponding for source signal x time at the second via node Function h (y_st)；

Wherein, y_st'=h (y_st)=α_sty_st+d_st,α_stIt is the second power factor, d_stIt is Two distortion noises, P_sFor the power of described transmitting node, h_stChannel for described transmitting node to described second via node is joined Number, n_stNoise for described transmitting node to described second via node；

Utilize linear amplification theoretical to described transfer characteristic function h (y_st) carry out linear amplification, obtain the second relay process function f_t(y_st'), f_t(y_st')=α_stβ_sty_st+β_std_st；

Wherein, β_stIt it is the second power normalization factor；

Obtain by described source signal time at the second via node to receiving node corresponding according to described second relay process function Second reception signal y_td；

Wherein, Represent at described transmitting node, described second relaying Under the transmission path that node and described receiving node are constituted, average is the Gaussian noise of zero, P_tFor described second via node Launch power, h_tdChannel parameter for described second via node to described receiving node.

Linearization of nonlinear system the most according to claim 1 analyze method, it is characterised in that described first power because of Sub-α_srWith described first distortion noise d_srObtain according to equation below:

${\mathrm{\α}}_{sr}=\frac{{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)}{{\mathrm{\δ}}_x^2},$

${\mathrm{\δ}}_{d_{sr}}^2={\mathrm{\δ}}_x^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})-{\mathrm{\α}}_{sr}\[{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)\],$

Wherein, A is the saturated output amplitude of preferable soft limiting power amplifier,For complementary error function, δ_x ² Variance yields for described source signal.

Method is analyzed in linearization of nonlinear system the most according to claim 3, it is characterised in that described first power is returned One changes factor-beta_srObtained by equation below:

Wherein, N₀For described first via node or the white noise power of the second via node receiving terminal.

Method is analyzed in linearization of nonlinear system the most according to claim 4, it is characterised in that noiseBy as follows Formula obtains:

${\tilde{n}}_{rd}={\mathrm{\α}}_{sr}\sqrt{\frac{P_r}{P_s{h}_{sr}^2+N_0}}\·h_{rd}{n}_{sr}+n_{rd}+\sqrt{\frac{P_r}{P_s{h}_{sr}^2+N_0}}{\mathrm{dh}}_{rd}.$

Linearization of nonlinear system the most according to claim 2 analyze method, it is characterised in that described second power because of Sub-α_stWith described second distortion noise d_stObtain according to equation below:

${\mathrm{\α}}_{st}=\frac{{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)}{{\mathrm{\δ}}_x^2},$

${\mathrm{\δ}}_{d_{st}}^2={\mathrm{\δ}}_x^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})-{\mathrm{\α}}_{st}\[{{\mathrm{\δ}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\δ}}_x}^2}})+\frac{\sqrt{\mathrm{\π}}}{2}{\mathrm{A\δ}}_{x}Erfc\left(\frac{A}{{\mathrm{\δ}}_x}\right)\],$

Wherein, A is the saturated output amplitude of preferable soft limiting power amplifier,For complementary error function, δ_x ² Variance yields for described source signal.

Method is analyzed in linearization of nonlinear system the most according to claim 6, it is characterised in that described second power is returned One changes factor-beta_stObtained by equation below:

Wherein, N₀For described first via node or the white noise of described second via node receiving terminal Power.

Method is analyzed in linearization of nonlinear system the most according to claim 7, it is characterised in that noiseBy as follows Formula obtains:

${\tilde{n}}_{td}={\mathrm{\α}}_{st}\sqrt{\frac{P_t}{P_s{h}_{st}^2+N_0}}\·h_{td}{n}_{st}+n_{td}+\sqrt{\frac{P_t}{P_s{h}_{st}^2+N_0}}{\mathrm{dh}}_{td}.$

9. system is analyzed in a linearization of nonlinear system, it is characterised in that includes transmitting node, the first via node and connects Receive node；

Described transmitting node, for emission source signal；

Described first via node, for according to the linearization of nonlinear system analysis described in claim 1-4 any one Method is calculated the first reception signal to described source signal, and receives signal transmission by described first to the most described reception joint Point.

System is analyzed in linearization of nonlinear system the most according to claim 9, it is characterised in that also include: in second Continue node；

Described second via node, for according to the nonlinear system described in claim 2 or claim 6-8 any one Analysis by Linearization method is calculated the second reception signal to described source signal, and receives signal transmission by described second extremely Described receiving node.