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

Abstract

Translated fromChinese

本发明公开了一种非线性系统的线性化分析方法，包括：利用Bussgang理论获取发射节点处至第一中继节点处时源信号x对应的转移特性函数h(y_sr)；利用线性放大理论对所述转移特性函数h(y_sr)进行线性放大，得到第一中继处理函数f_r(y_sr′)；根据所述第一中继处理函数获取由第一中继节点处至接收节点处时所述源信号对应的第一接收信号y_rd。由此可见，在上述过程中，能够将功率衰减因素和噪音因素结合起来，使得第一接收信号更加真实的反应源信号的性质。此外，本发明还公开一种非线性系统的线性化分析系统，效果如上所述。

The invention discloses a linearization analysis method of a nonlinear system, comprising: using the Bussgang theory to obtain the transfer characteristic function h(y_sr ) corresponding to the source signal x from the transmitting node to the first relay node; using the linear amplification theory Linearly amplify the transfer characteristic function h(y_sr ) to obtain a first relay processing function f_r (y_sr '); according to the first relay processing function, obtain is the first received signal y_rd corresponding to the source signal. It can be seen that, in the above process, the power attenuation factor and the noise factor can be combined, so that the first received signal more truly reflects the nature of the source signal. In addition, the invention also discloses a linearized analysis system of a nonlinear system, and the effect is as above.

Description

Translated fromChinese

一种非线性系统的线性化分析方法及系统A linearization analysis method and system for a nonlinear system

技术领域technical field

本发明涉及通信技术领域，特别是涉及一种非线性系统的线性化分析方法及系统。The invention relates to the field of communication technology, in particular to a linearization analysis method and system for a nonlinear system.

背景技术Background technique

在过去的几十年里，无线通信技术得到了迅速的发展，并且在实际应用中也取得了巨大的进步。在每一次的技术革命中，通信技术都会得到飞速的发展，通信设备在尺寸，造价和传输可靠性方面都有了很大的提升。In the past few decades, wireless communication technology has developed rapidly, and has also made great progress in practical applications. In every technological revolution, communication technology will develop rapidly, and communication equipment has been greatly improved in terms of size, cost and transmission reliability.

我们目前研究的系统都是按照线性系统进行分析的，因为我们一般研究主要考虑的是理想化线性放大器，但是实际中的系统都是一个非线性系统，在信号传输过程中不仅有噪音，而且还有功率衰减等因素，现有技术中没有把功率衰减因素和噪音因素结合起来，导致分析结果无法更真实的反应信号的性质。The systems we are currently studying are all analyzed according to linear systems, because our general research mainly considers idealized linear amplifiers, but the actual system is a nonlinear system, and there are not only noises in the signal transmission process, but also There are factors such as power attenuation. In the prior art, the power attenuation factor and the noise factor are not combined, so that the analysis result cannot reflect the nature of the signal more realistically.

由此可见，如何提高信号的分析结果的真实性是本领域技术人员亟待解决地问题。It can be seen that how to improve the authenticity of the signal analysis results is an urgent problem to be solved by those skilled in the art.

发明内容Contents of the invention

本发明的目的是提供一种非线性系统的线性化分析方法及系统，用于提高信号的分析结果的真实性。The purpose of the present invention is to provide a linear analysis method and system for nonlinear systems, which are used to improve the authenticity of signal analysis results.

为解决上述技术问题，本发明提供一种非线性系统的线性化分析方法，包括：In order to solve the above-mentioned technical problems, the present invention provides a linearization analysis method of a nonlinear system, comprising:

利用Bussgang理论获取发射节点处至第一中继节点处时源信号x对应的转移特性函数h(y_sr)；Using the Bussgang theory to obtain the transfer characteristic function h(y_sr ) corresponding to the source signal x from the transmitting node to the first relay node;

其中，y_sr′＝h(y_sr)＝α_sry_sr+d_sr，α_sr为第一功率因子，d_sr为第一畸变噪声，P_s为所述发射节点的功率，h_sr为所述发射节点到所述第一中继节点的信道参数，n_sr为所述发射节点到所 述第一中继节点的噪声；Among them, y_sr ′=h(y_sr )=α_sr y_sr +d_sr , α_sr is the first power factor, d_sr is the first distortion noise, P_s is the power of the transmitting node, h_sr is the channel parameter from the transmitting node to the first relay node, n_sr is the noise from a transmitting node to said first relay node;

利用线性放大理论对所述转移特性函数h(y_sr)进行线性放大，得到第一中继处理函数f_r(y_sr′)，f_r(y_sr′)＝α_srβ_sry_sr+β_srd_sr；The transfer characteristic function h(y_sr ) is linearly amplified using the linear amplification theory to obtain the first relay processing function f_r (y_sr ′), f_r (y_sr ′)=α_sr β_sr y_sr +β_sr d_sr ;

其中，β_sr为第一功率归一化因子；Wherein, β_sr is the first power normalization factor;

根据所述第一中继处理函数获取由第一中继节点处至接收节点处时所述源信号对应的第一接收信号y_rd；Obtaining a first received signal y_rd corresponding to the source signal when traveling from the first relay node to the receiving node according to the first relay processing function;

其中，表示在所述发射节点、第一中继节点和所述接收节点构成的传输路径下，均值为零的高斯噪声，P_r为所述第一中继节点的发射功率，h_rd为所述第一中继节点到所述接收节点的信道参数。in, Represents Gaussian noise with a mean value of zero under the transmission path formed by the transmitting node, the first relay node, and the receiving node, P_r is the transmit power of the first relay node, h_rd is the first relay node A channel parameter from the relay node to the receiving node.

优选地，还包括：利用Bussgang理论获取发射节点处至第二中继节点处时所述源信号x对应的转移特性函数h(y_st)；Preferably, it also includes: using the Bussgang theory to obtain the transfer characteristic function h(y_st ) corresponding to the source signal x from the transmitting node to the second relay node;

其中，y_st′＝h(y_st)＝α_sty_st+d_st，α_st为第二功率因子，d_st为第二畸变噪声，P_s为所述发射节点的功率，h_st为所述发射节点到所述第二中继节点的信道参数，n_st为所述发射节点到所述第二中继节点的噪声；Among them, y_st '=h(y_st )=α_st y_st +d_st , α_st is the second power factor, d_st is the second distortion noise, P_s is the power of the transmitting node, h_st is the channel parameter from the transmitting node to the second relay node, n_st is the noise from a transmitting node to said second relay node;

利用线性放大理论对所述转移特性函数h(y_st)进行线性放大，得到第二中继处理函数f_t(y_st′)，f_t(y_st′)＝α_stβ_sty_st+β_std_st；The transfer characteristic function h(y_st ) is linearly amplified using the linear amplification theory to obtain the second relay processing function f_t (y_st ′), f_t (y_st ′)=α_st β_st y_st +β_st d_st ;

其中，β_st为第二功率归一化因子；Wherein, β_st is the second power normalization factor;

根据所述第二中继处理函数获取由第二中继节点处至接收节点处时所述源信号对应的第二接收信号y_td；Obtaining a second received signal y_td corresponding to the source signal when traveling from the second relay node to the receiving node according to the second relay processing function;

其中，表示在所述发射节点、所述第二中继节点和所述接收节点构成的传输路径下，均值为零的高斯噪声，P_t为所述第二中继节点的发射功率，h_td为所述第二中继节点到所述接收节点的信道参数。in, Represents Gaussian noise with a mean value of zero under the transmission path formed by the transmitting node, the second relay node, and the receiving node, P_t is the transmit power of the second relay node, h_td is the Channel parameters from the second relay node to the receiving node.

优选地，所述第一功率因子α_sr和所述第一畸变噪声d_sr依据如下公式得到：Preferably, the first power factor α_sr and the first distortion noise d_sr are obtained according to the following formula:

${\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}<span><span>=</span>=</span>\frac{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span>}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>,</span>,</span>$

${\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}<span><span>\&lsqb;</span>\&lsqb;</span>{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span><span><span>\&rsqb;</span>\&rsqb;</span><span><span>,</span>,</span>$

其中，A为理想软限幅功放的饱和输出幅度，为互补误差函数，δ_x²为所述源信号的方差值。Among them, A is the saturated output amplitude of the ideal soft-limiting power amplifier, is the complementary error function, and δ_x² is the variance value of the source signal.

优选地，所述第一功率归一化因子β_sr通过如下公式得到：Preferably, the first power normalization factor β_sr is obtained by the following formula:

其中，N₀为所述第一中继节点或第二中继节点接收端的白噪声功率。 Wherein, N₀ is the white noise power of the receiving end of the first relay node or the second relay node.

优选地，噪声通过如下公式得到：Preferably, the noise Obtained by the following formula:

${\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>n</span>no</span>}}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>r</span>r</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}<span><span>\&CenterDot;</span>\&CenterDot;</span>{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>r</span>r</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}{\mathrm{<span><span>dh</span>d\; h</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>.</span>.</span>$

优选地，所述第二功率因子α_st和所述第二畸变噪声d_st依据如下公式得到：Preferably, the second power factor α_st and the second distortion noise d_st are obtained according to the following formula:

${\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}<span><span>=</span>=</span>\frac{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span>}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>,</span>,</span>$

${\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}<span><span>\&lsqb;</span>\&lsqb;</span>{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span><span><span>\&rsqb;</span>\&rsqb;</span><span><span>,</span>,</span>$

其中，A为理想软限幅功放的饱和输出幅度，为 互补误差函数，δ_x²为所述源信号的方差值。Among them, A is the saturated output amplitude of the ideal soft-limiting power amplifier, is the complementary error function, and δ_x² is the variance value of the source signal.

优选地，所述第二功率归一化因子β_st通过如下公式得到：Preferably, the second power normalization factor_βst is obtained by the following formula:

其中，N₀为所述第一中继节点或所述第二中继节点接收端的白噪声功率。 Wherein, N₀ is the white noise power of the receiving end of the first relay node or the second relay node.

优选地，噪声通过如下公式得到：Preferably, the noise Obtained by the following formula:

${\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>n</span>no</span>}}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>t</span>t</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}<span><span>\&CenterDot;</span>\&CenterDot;</span>{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>r</span>r</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}{\mathrm{<span><span>dh</span>d\; h</span>}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>.</span>.</span>$

一种非线性系统的线性化分析系统，包括发射节点、第一中继节点和接收节点；A linearization analysis system for a nonlinear system, comprising a transmitting node, a first relay node and a receiving node;

所述发射节点，用于发射源信号；The transmitting node is configured to transmit a source signal;

所述第一中继节点，用于按照上述所述的非线性系统的线性化分析方法对所述源信号进行计算得到第一接收信号，并将所述第一接收信号发送至所述接收节点。The first relay node is configured to calculate the source signal according to the linearization analysis method of the above-mentioned nonlinear system to obtain a first received signal, and send the first received signal to the receiving node .

优选地，还包括：第二中继节点；Preferably, it also includes: a second relay node;

所述第二中继节点，用于按照上述所述的非线性系统的线性化分析方法对所述源信号进行计算得到第二接收信号，并将所述第二接收信号发送至所述接收节点。The second relay node is configured to calculate the source signal according to the linearization analysis method of the above-mentioned nonlinear system to obtain a second received signal, and send the second received signal to the receiving node .

本发明所提供的非线性系统的线性化分析方法及系统，首先利用Bussgang理论获取源信号对应的转移特性函数，然后利用线性放大理论对转移特性函数进行线性放大，得到第一中继处理函数f_r(y_sr′)，最后根据所述第一中继处理函数获取由第一中继节点处至接收节点处时源信号对应的第一接收信号。由此可见，在上述过程中，能够将功率衰减因素和噪音因素结合起来，使得第一接收信号更加真实的反应源信号的性质。In the linear analysis method and system of the nonlinear system provided by the present invention, first, the transfer characteristic function corresponding to the source signal is obtained by using the Bussgang theory, and then the transfer characteristic function is linearly amplified by using the linear amplification theory to obtain the first relay processing function f_r (y_sr '), and finally obtain the first received signal corresponding to the source signal from the first relay node to the receiving node according to the first relay processing function. It can be seen that, in the above process, the power attenuation factor and the noise factor can be combined, so that the first received signal more truly reflects the nature of the source signal.

附图说明Description of drawings

为了更清楚地说明本发明实施例，下面将对实施例中所需要使用 的附图做简单的介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to illustrate the embodiments of the present invention more clearly, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. As far as people are concerned, other drawings can also be obtained based on these drawings on the premise of not paying creative work.

图1为本发明提供的一种非线性系统的线性化分析方法的流程图；Fig. 1 is the flowchart of the linearization analysis method of a kind of nonlinear system provided by the present invention;

图2为本发明提供的一种非线性系统的线性化分析方法的结构图；Fig. 2 is the structural diagram of the linearization analysis method of a kind of nonlinear system provided by the present invention;

图3为本发明提供的另一种非线性系统的线性化分析方法的流程图。Fig. 3 is a flowchart of another linearization analysis method for a nonlinear system provided by the present invention.

具体实施方式detailed description

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下，所获得的所有其他实施例，都属于本发明保护范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

本发明的核心是提供一种非线性系统的线性化分析方法及系统。The core of the present invention is to provide a linear analysis method and system for nonlinear systems.

为了使本技术领域的人员更好地理解本发明方案，下面结合附图和具体实施方式对本发明作进一步的详细说明。In order to enable those skilled in the art to better understand the solution of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

图1为本发明提供的一种非线性系统的线性化分析方法的流程图。如图1所示，非线性系统的线性化分析方法包括：Fig. 1 is a flowchart of a linearization analysis method for a nonlinear system provided by the present invention. As shown in Figure 1, linearization analysis methods for nonlinear systems include:

S10：利用Bussgang理论获取发射节点s处至第一中继节点r处时源信号x对应的转移特性函数。S10: Obtain a transfer characteristic function corresponding to the source signal x from the transmitting node s to the first relay node r by using the Bussgang theory.

步骤S10可以看作是发射节点s将源信号发送至第一中继节点r这个过程中源信号x的一个变换过程。根据Bussgang理论，如果一个输入信号x(t)是高斯信号，则经过非线性系统作用后，功放的转移特性函数就可以分解为：h(x(t))＝αx(t)+d(t)。Step S10 can be regarded as a conversion process of the source signal x in the process of the transmitting node s sending the source signal to the first relay node r. According to the Bussgang theory, if an input signal x(t) is a Gaussian signal, the transfer characteristic function of the power amplifier can be decomposed into: h(x(t))=αx(t)+d(t ).

图2为本发明提供的一种非线性系统的线性化分析方法的结构图。在本申请中，源信号x传输至第一中继节点r所对应的信道参数 为h_sr即，h_sr为发射节点s到第一中继节点r的信道参数，而P_s为发射节点s的功率，则在这一传输过程中，源信号x就变为y_sr，n_sr为发射节点s到第一中继节点r的噪声。y_sr对应的转移特性函数就是h(y_sr)。其中，转移特性函数y_sr′＝h(y_sr)＝α_sry_sr+d_sr，α_sr为第一功率因子，d_sr为第一畸变噪声，n_sr为发射节点s到第一中继节点r的噪声。Fig. 2 is a structural diagram of a linearization analysis method for a nonlinear system provided by the present invention. In this application, the channel parameter corresponding to the transmission of the source signal x to the first relay node r is h_sr , that is, h_sr is the channel parameter from the transmitting node s to the first relay node r, and P_s is the transmitting node s power, then in this transmission process, the source signal x becomes y_sr , n_sr is the noise from the transmitting node s to the first relay node r. The transfer characteristic function corresponding to y_sr is h(y_sr ). Among them, transfer characteristic function y_sr ′=h(y_sr )=α_sr y_sr +d_sr , α_sr is the first power factor, d_sr is the first distortion noise, n_sr is the transmission node s to the first relay Noise at node r.

在具体实施中，第一功率因子α_sr和第一畸变噪声d_sr依据如下公式得到：In a specific implementation, the first power factor α_sr and the first distortion noise d_sr are obtained according to the following formula:

${\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}<span><span>=</span>=</span>\frac{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span>}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>,</span>,</span>$

${\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}<span><span>\&lsqb;</span>\&lsqb;</span>{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span><span><span>\&rsqb;</span>\&rsqb;</span><span><span>,</span>,</span>$

其中，A为理想软限幅功放的饱和输出幅度，为互补误差函数，δ_x²为源信号的方差值。Among them, A is the saturated output amplitude of the ideal soft-limiting power amplifier, is the complementary error function, and δ_x² is the variance value of the source signal.

S11：利用线性放大理论对转移特性函数进行线性放大，得到第一中继处理函数。S11: Linearly amplify the transfer characteristic function by using the linear amplification theory to obtain a first relay processing function.

第一中继处理函数f_r(y_sr′)＝α_srβ_sry_sr+β_srd_sr；其中，β_sr为第一功率归一化因子。The first relay processing function f_r (y_sr ′)=α_sr β_sry y_sr +β_sr d_sr ; where β_sr is the first power normalization factor.

在这一步骤中，只是将h(y_sr)进行线性放大，即上文中所述的β_sr倍。在具体实施中，第一功率归一化因子β_sr通过如下公式得到：In this step, only h(y_sr ) is linearly amplified, that is, the β_sr times mentioned above. In a specific implementation, the first power normalization factor β_sr is obtained by the following formula:

其中，N₀为所述第一中继节点或第二中继节点接收端的白噪声功率。可以理解地是，第一中继节点接收端的白噪声功率与第二中继节点接收端的白噪声功率是相同的。 Wherein, N₀ is the white noise power of the receiving end of the first relay node or the second relay node. It can be understood that the white noise power at the receiving end of the first relay node is the same as the white noise power at the receiving end of the second relay node.

S12：根据第一中继处理函数获取由第一中继节点r处至接收节点d处时源信号对应的第一接收信号。S12: Obtain a first received signal corresponding to the source signal when traveling from the first relay node r to the receiving node d according to the first relay processing function.

其中，表示在发射节点s、第一中继节点r和接收节点d构成的传输路径下，均值为零的高斯噪声，P_r为第一中继节点r的发射功率，h_rd为第一中继节点r到接收节点d的信道参数。in, Indicates the Gaussian noise with a mean value of zero under the transmission path composed of the transmitting node s, the first relay node r and the receiving node d, P_r is the transmission power of the first relay node r, and h_rd is the first relay node The channel parameters from r to receiving node d.

在本步骤中相当于信号由第一中继节点r传输至接收节点d时的信号的变化过程，将接收节点d处的信号定为第一接收信号y_rd，此时，This step is equivalent to the signal change process when the signal is transmitted from the first relay node r to the receiving node d, and the signal at the receiving node d is defined as the first received signal y_rd , at this time,

${\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>r</span>r</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}<span><span>\&CenterDot;</span>\&CenterDot;</span>{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\mathrm{<span><span>x</span>x</span>}<span><span>+</span>+</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>n</span>no</span>}}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}$

上述过程就是发射节点s将源信号x通过第一中继节点r传输到接收节点d得到的第一接收信号y_rd。The above process is the first received signal y_rd obtained by the transmitting node s transmitting the source signal x to the receiving node d through the first relay node r.

在具体实施中，噪声通过如下公式得到：In a specific implementation, the noise Obtained by the following formula:

${\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>n</span>no</span>}}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>r</span>r</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>r</span>r</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>r</span>r</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}{\mathrm{<span><span>dh</span>d\; h</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>.</span>.</span>$

本实施例提供的非线性系统的线性化分析方法，首先利用Bussgang理论获取源信号对应的转移特性函数，然后利用线性放大理论对转移特性函数进行线性放大，得到第一中继处理函数f_r(y_sr′)，最后根据所述第一中继处理函数获取由第一中继节点处至接收节点处时源信号对应的第一接收信号。由此可见，在上述过程中，能够将功率衰减因素和噪音因素结合起来，使得第一接收信号更加真实的反应源信号的性质。The linearization analysis method of the nonlinear system provided in this embodiment first uses the Bussgang theory to obtain the transfer characteristic function corresponding to the source signal, and then uses the linear amplification theory to linearly amplify the transfer characteristic function to obtain the first relay processing function f_r ( y_sr ′), and finally obtain the first received signal corresponding to the source signal from the first relay node to the receiving node according to the first relay processing function. It can be seen that, in the above process, the power attenuation factor and the noise factor can be combined, so that the first received signal more truly reflects the nature of the source signal.

由于信号在传输过程中，受到各种因素的影响，导致接收节点d接收到的信号的信噪比可能很低，因此，为了增加接收到的信号的信噪比较高，或者提高接收节点d的可靠性，因此，在本发明中，可以 再设置一个中继节点，即如图2所示的第二中继节点t。可以理解地是，第二中继节点t和第一中继节点r只是属于两个不同的信道，其余的信号传输过程是相同的。图3为本发明提供的另一种非线性系统的线性化分析方法的流程图。因此，作为一种优选地实施方式，非线性系统的线性化分析方法，还包括：Because the signal is affected by various factors during the transmission process, the signal-to-noise ratio of the signal received by the receiving node d may be very low. Therefore, in order to increase the signal-to-noise ratio of the received signal, or improve the signal-to-noise ratio of the receiving node d Therefore, in the present invention, another relay node can be set, that is, the second relay node t shown in FIG. 2 . It can be understood that the second relay node t and the first relay node r only belong to two different channels, and the rest of the signal transmission process is the same. Fig. 3 is a flowchart of another linearization analysis method for a nonlinear system provided by the present invention. Therefore, as a preferred embodiment, the linearization analysis method of nonlinear system also includes:

S30：利用Bussgang理论获取发射节点s处至第二中继节点t处时源信号x对应的转移特性函数。S30: Using the Bussgang theory to obtain a transfer characteristic function corresponding to the source signal x from the transmitting node s to the second relay node t.

如图2所示，在本申请中，源信号x传输至第一中继节点r所对应的信道参数为h_st即，h_st为发射节点s到第二中继节点t的信道参数，而P_s为发射节点s的功率，则在这一传输过程中，源信号x就变为y_st。As shown in Figure 2, in this application, the channel parameter corresponding to the transmission of the source signal x to the first relay node r is h_st , that is, h_st is the channel parameter from the transmitting node s to the second relay node t, and P_s is the power of the transmitting node s, and in this transmission process, the source signal x becomes y_st .

n_st为发射节点s到第二中继节点t的噪声。y_st对应的转移特性函数就是h(y_st)。其中，转移特性函数f_t(y_st′)＝α_stβ_sty_st+β_std_st，α_st为第二功率因子，d_st为第二畸变噪声，n_st为发射节点s到第二中继节点t的噪声。 n_st is the noise from the transmitting node s to the second relay node t. The transfer characteristic function corresponding to y_st is h(y_st ). Among them, the transfer characteristic function f_t (y_st ′)=α_st β_st y_st +β_st d_st , α_st is the second power factor, d_st is the second distortion noise, n_st is the transmission node s to the second The noise of relay node t.

在具体实施中，第二功率因子α_st和第二畸变噪声d_st依据如下公式得到：In a specific implementation, the second power factor α_st and the second distortion noise d_st are obtained according to the following formula:

${\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}<span><span>=</span>=</span>\frac{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span>}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>,</span>,</span>$

${\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}<span><span>\&lsqb;</span>\&lsqb;</span>{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}^{<span><span>-</span>-</span>\frac{{\mathrm{<span><span>A</span>A</span>}}^{\mathrm{<span><span>2</span>2</span>}}}{{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\sqrt{\mathrm{<span><span>\&pi;</span>\&pi;</span>}}}{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A\&delta;</span>A\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}\mathrm{<span><span>E</span>E.</span>}\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>f</span>f</span>}\mathrm{<span><span>c</span>c</span>}<span><span>(</span>(</span>\frac{\mathrm{<span><span>A</span>A</span>}}{{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}_{\mathrm{<span><span>x</span>x</span>}}}<span><span>)</span>)</span><span><span>\&rsqb;</span>\&rsqb;</span><span><span>,</span>,</span>$

其中，A为理想软限幅功放的饱和输出幅度，为互补误差函数，δ_x²为源信号的方差值。Among them, A is the saturated output amplitude of the ideal soft-limiting power amplifier, is the complementary error function, and δ_x² is the variance value of the source signal.

S31：利用线性放大理论对转移特性函数进行线性放大，得到第 二中继处理函数。S31: Using the linear amplification theory to linearly amplify the transfer characteristic function to obtain a second relay processing function.

第二中继处理函数f_t(y_st′)＝α_stβ_sty_st+β_std_st；其中，β_st为第二功率归一化因子。The second relay processing function f_t (y_st ′)=α_st β_st y_st +β_st d_st ; where β_st is the second power normalization factor.

在这一步骤中，只是将h(y_st)进行线性放大，即上文中所述的β_st倍。在具体实施中，第一功率归一化因子β_st通过如下公式得到：In this step, only h(y_st ) is linearly amplified, that is, the β_st times described above. In a specific implementation, the first power normalization factor_βst is obtained by the following formula:

其中，N₀为所述第一中继节点或所述第二中继节点接收端的白噪声功率。 Wherein, N₀ is the white noise power of the receiving end of the first relay node or the second relay node.

S32：根据第二中继处理函数获取由第二中继节点t处至接收节点d处时源信号对应的第二接收信号。S32: Obtain a second received signal corresponding to the source signal when traveling from the second relay node t to the receiving node d according to the second relay processing function.

其中，表示在发射节点s、第二中继节点t和接收节点d构成的传输路径下，均值为零的高斯噪声，P_t为第二中继节点t的发射功率，h_td为第二中继节点t到接收节点d的信道参数。in, Indicates the Gaussian noise with a mean value of zero under the transmission path composed of the transmitting node s, the second relay node t and the receiving node d, P_t is the transmission power of the second relay node t, h_td is the second relay node The channel parameters from t to receiving node d.

在本步骤中相当于信号由第二中继节点t传输至接收节点d时的信号的变化过程，将接收节点d处的信号定为第二接收信号y_td，此时，$y_{td}={\mathrm{\&alpha;}}_{st}\sqrt{\frac{P_s{P}_t}{P_s{h}_{st}^2+N_0}}\&CenterDot;h_{st}{h}_{td}\&CenterDot;x+{\tilde{n}}_{td}$This step is equivalent to the signal change process when the signal is transmitted from the second relay node t to the receiving node d, and the signal at the receiving node d is defined as the second received signal y_td , at this time,${\mathrm{the\; y}}_{td}={\mathrm{\&alpha;}}_{\mathrm{the\; s}t}\sqrt{\frac{P_{\mathrm{the\; s}}{P}_t}{P_{\mathrm{the\; s}}{h}_{\mathrm{the\; s}t}^2+N_0}}\&Center\; Dot;h_{\mathrm{the\; s}t}{h}_{td}\&Center\; Dot;x+{\widetilde{\mathrm{no}}}_{td}$

上述过程就是发射节点s将源信号x通过第二中继节点t传输到接收节点d得到的第二接收信号y_td。The above process is the second received signal y_td obtained by the transmitting node s transmitting the source signal x to the receiving node d through the second relay node t.

在具体实施中，噪声通过如下公式得到：In a specific implementation, the noise Obtained by the following formula:

${\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>n</span>no</span>}}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>t</span>t</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}<span><span>\&CenterDot;</span>\&CenterDot;</span>{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>+</span>+</span>\sqrt{\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>t</span>t</span>}}}{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}{\mathrm{<span><span>h</span>h</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}\mathrm{<span><span>t</span>t</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>N</span>N</span>}}_{\mathrm{<span><span>0</span>0</span>}}}}{\mathrm{<span><span>dh</span>d\; h</span>}}_{\mathrm{<span><span>t</span>t</span>}\mathrm{<span><span>d</span>d</span>}}<span><span>.</span>.</span>$

需要说明的是，上述过程中，步骤S10-步骤S12与步骤S30-步骤S32是相互独立地，可以有先后顺序，也可以同时进行，没有严格的顺序规定。It should be noted that, in the above process, step S10-step S12 and step S30-step S32 are independent of each other, and may be performed sequentially or simultaneously, and there is no strict order requirement.

如图2所示，非线性系统的线性化分析系统，包括发射节点s、第一中继节点r和接收节点d；As shown in Figure 2, the linearization analysis system of the nonlinear system includes a transmitting node s, a first relay node r and a receiving node d;

发射节点s，用于发射源信号；The transmitting node s is used to transmit the source signal;

第一中继节点r，用于按照上述步骤S10-步骤S12对源信号进行计算得到第一接收信号，并将第一接收信号发送至接收节点d。The first relay node r is configured to calculate the source signal according to the above step S10-step S12 to obtain the first received signal, and send the first received signal to the receiving node d.

如图2所示，非线性系统的线性化分析系统，还包括：第二中继节点t；As shown in Figure 2, the linearization analysis system of the nonlinear system also includes: a second relay node t;

第二中继节点t，用于按照上述步骤S30-步骤S32对源信号进行计算得到第二接收信号，并将第二接收信号发送至接收节点d。The second relay node t is configured to calculate the source signal according to the above step S30-step S32 to obtain the second received signal, and send the second received signal to the receiving node d.

以上对本发明所提供的非线性系统的线性化分析方法及系统进行了详细介绍。说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。对于实施例公开的装置而言，由于其与实施例公开的方法相对应，所以描述的比较简单，相关之处参见方法部分说明即可。应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以对本发明进行若干改进和修饰，这些改进和修饰也落入本发明权利要求的保护范围内。The linearization analysis method and system of the nonlinear system provided by the present invention have been introduced in detail above. Each embodiment in the description is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and for the related information, please refer to the description of the method part. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, some improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

专业人员还可以进一步意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、计算机软件或者二者的结合来实现，为了清楚地说明硬件和软件的可互换性，在上述说明中已经按照功能一般性地描述了各示例的组成及步骤。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本发明的范围。Professionals can further realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software or a combination of the two. In order to clearly illustrate the possible Interchangeability, in the above description, the components and steps of each example have been generally described according to their functions. Whether these functions are executed by hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art may use different methods to implement the described functions for each specific application, but such implementation should not be regarded as exceeding the scope of the present invention.

结合本文中所公开的实施例描述的方法或算法的步骤可以直接用硬件、处理器执行的软件模块，或者二者的结合来实施。软件模块可以置于随机存储器(RAM)、内存、只读存储器(ROM)、电可编程 ROM、电可擦除可编程ROM、寄存器、硬盘、可移动磁盘、CD-ROM、或技术领域内所公知的任意其它形式的存储介质中。The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be directly implemented by hardware, software modules executed by a processor, or a combination of both. Software modules can be placed in random access memory (RAM), internal memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other Any other known storage medium.

Claims (10)

1. A linearization analysis method for a nonlinear system, comprising:

acquiring a transfer characteristic function h (y) corresponding to a source signal x from a transmitting node to a first relay node by using a Bussgang theory_sr)；

Wherein, y_sr′＝h(y_sr)＝α_sry_sr+d_sr，α_srIs firstPower factor, d_srIs a first distortion noise, P_sIs the power of the transmitting node, h_srIs a channel parameter, n, of the transmitting node to the first relay node_srNoise for the transmitting node to the first relay node;

using linear amplification theory to transfer characteristic function h (y)_sr) Linear amplification is carried out to obtain a first relay processing function f_r(y_sr′)，f_r(y_sr′)＝α_srβ_sry_sr+β_srd_sr；

Wherein, β_srIs a first power normalization factor;

obtaining a first receiving signal y corresponding to the source signal from a first relay node to a receiving node according to the first relay processing function_rd；

Wherein,representing a Gaussian noise with a mean value of zero, P, in a transmission path formed by the transmitting node, the first relay node and the receiving node_rIs the transmission power, h, of the first relay node_rdChannel parameters for the first relay node to the receiving node.

2. The linearization analysis method of a nonlinear system of claim 1, further comprising:

obtaining a transfer characteristic function h (y) corresponding to the source signal x from the transmitting node to the second relay node by using a Bussgang theory_st)；

Wherein, y_st′＝h(y_st)＝α_sty_st+d_st，α_stIs a second power factor, d_stAs second distortion noise, P_sIs the power of the transmitting node, h_stIs a channel parameter, n, of the transmitting node to the second relay node_stNoise for the transmitting node to the second relay node;

using linear amplification theory to transfer characteristic function h (y)_st) Linear amplification is carried out to obtain a second relay processing function f_t(y_st′)，f_t(y_st′)＝α_stβ_sty_st+β_std_st；

Wherein, β_stIs a second power normalization factor;

obtaining a second receiving signal y corresponding to the source signal from a second relay node to a receiving node according to the second relay processing function_td；

Wherein,representing a Gaussian noise with a mean value of zero, P, in a transmission path formed by the transmitting node, the second relay node and the receiving node_tIs the transmission power, h, of the second relay node_tdChannel parameters for the second relay node to the receiving node.

3. The linearization analysis method of claim 1, wherein the first power factor α_srAnd the first distortion noise d_srObtained according to the following formula:

${\mathrm{\&alpha;}}_{sr}=\frac{{{\mathrm{\&delta;}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\&delta;}}_x}^2}})+\frac{\sqrt{\mathrm{\&pi;}}}{2}{\mathrm{A\&delta;}}_{x}Erfc\left(\frac{A}{{\mathrm{\&delta;}}_x}\right)}{{\mathrm{\&delta;}}_x^2},$

${\mathrm{\&delta;}}_{d_{sr}}^2={\mathrm{\&delta;}}_x^2(1-e^{-\frac{A^2}{{{\mathrm{\&delta;}}_x}^2}})-{\mathrm{\&alpha;}}_{sr}\&lsqb;{{\mathrm{\&delta;}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\&delta;}}_x}^2}})+\frac{\sqrt{\mathrm{\&pi;}}}{2}{\mathrm{A\&delta;}}_{x}Erfc\left(\frac{A}{{\mathrm{\&delta;}}_x}\right)\&rsqb;,$

wherein A is the saturation output amplitude of the ideal soft limiting power amplifier,in order to complement the function of the error,_x²is the variance value of the source signal.

4. The method of claim 3The method for analyzing linearity of a nonlinear system of (1), wherein the first power normalization factor β_srObtained by the following formula:

wherein N is₀And the white noise power is the white noise power of the receiving end of the first relay node or the second relay node.

5. The linearization analysis method of claim 4, wherein the noise is noiseObtained by the following formula:

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

6. the linearization analysis method of claim 2, wherein the second power factor α_stAnd the second distortion noise d_stObtained according to the following formula:

${\mathrm{\&alpha;}}_{st}=\frac{{{\mathrm{\&delta;}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\&delta;}}_x}^2}})+\frac{\sqrt{\mathrm{\&pi;}}}{2}{\mathrm{A\&delta;}}_{x}Erfc\left(\frac{A}{{\mathrm{\&delta;}}_x}\right)}{{\mathrm{\&delta;}}_x^2},$

${\mathrm{\&delta;}}_{d_{st}}^2={\mathrm{\&delta;}}_x^2(1-e^{-\frac{A^2}{{{\mathrm{\&delta;}}_x}^2}})-{\mathrm{\&alpha;}}_{st}\&lsqb;{{\mathrm{\&delta;}}_x}^2(1-e^{-\frac{A^2}{{{\mathrm{\&delta;}}_x}^2}})+\frac{\sqrt{\mathrm{\&pi;}}}{2}{\mathrm{A\&delta;}}_{x}Erfc\left(\frac{A}{{\mathrm{\&delta;}}_x}\right)\&rsqb;,$

wherein A is the saturation output amplitude of the ideal soft limiting power amplifier,in order to complement the function of the error,_x²is the variance value of the source signal.

7. The linearization analysis method of claim 6, wherein the second power normalization factor β_stObtained by the following formula:

wherein N is₀And the white noise power is the white noise power of the receiving end of the first relay node or the second relay node.

8. The linearization analysis method of claim 7, wherein the noise is noiseBy passingThe following equation is obtained:

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

9. a linearization analysis system of a nonlinear system is characterized by comprising a transmitting node, a first relay node and a receiving node;

the transmitting node is used for transmitting a source signal;

the first relay node is configured to calculate the source signal according to the linearization analysis method of the nonlinear system as claimed in any one of claims 1 to 4 to obtain a first received signal, and send the first received signal to the receiving node.

10. The linearization analysis system of claim 9, further comprising: a second relay node;

the second relay node is configured to calculate the source signal according to the linearization analysis method of the nonlinear system as set forth in claim 2 or any one of claims 6 to 8 to obtain a second received signal, and send the second received signal to the receiving node.