CN113141222B - Asymptotic approach error rate performance analysis method - Google Patents

Asymptotic approach error rate performance analysis method Download PDF

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CN113141222B
CN113141222B CN202110448980.1A CN202110448980A CN113141222B CN 113141222 B CN113141222 B CN 113141222B CN 202110448980 A CN202110448980 A CN 202110448980A CN 113141222 B CN113141222 B CN 113141222B
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徐磊
王兆瑞
常静
方红雨
李晓辉
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Anhui University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
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Abstract

The invention discloses a method for analyzing the performance of asymptotic close approximation error rate, which comprises the following steps: step S1, constructing an intelligent reflector auxiliary communication system model, and calculating the signal-to-noise ratio gamma output by the maximum ratio combiner; step S2, performing bit error rate analysis on the intelligent reflector assisted communication system, and converting γ into γ ═ γ1+γ2Form of (1) each constituting γ1And gamma2A moment mother function of; step S3, according to gamma1And gamma2Moment mother function of
Figure DDA0003038057770000011
And
Figure DDA0003038057770000012
and obtaining the asymptotic approach error rate. The invention reasonably constructs the reflection coefficient and the intelligent reflecting surface link coefficient, so that the signal-to-noise ratio on the intelligent reflecting surface forwarding link satisfies the harmonic mean value form, deduces a system asymptotic close approximation formula with a simple structure, and performs performance analysis on the intelligent reflecting surface auxiliary communication system by using a control variable method, thereby performing performance analysis on the error rate performance of the intelligent reflecting surface auxiliary communication system and the single-time-slot amplify-and-forward multi-relay systemAnd (6) performing line comparison analysis.

Description

一种渐近紧逼近误码率性能分析方法An Asymptotic Tight Approximation Bit Error Rate Performance Analysis Method

技术领域technical field

本发明涉及智能反射面辅助通信领域，尤其涉及一种智能反射面辅助通信系统的渐近紧逼近误码率性能分析方法。The invention relates to the field of intelligent reflective surface auxiliary communication, in particular to an asymptotic tight approximation bit error rate performance analysis method of an intelligent reflective surface auxiliary communication system.

背景技术Background technique

在未来无线通信系统中，智能反射面技术为解决需要更大带宽、更高频谱效率和更智能传输技术等难题提供了一种潜在的途径。智能反射面技术是一种由大量低成本无源反射元件组成的平面，并可以通过软件控制每个元件实现对入射信号振幅和相位的调整。智能反射面技术具有可扩展性强、实现成本低、工作频段宽、能够实现无线传播环境配置等诸多优点。In future wireless communication systems, smart reflector technology provides a potential way to solve difficult problems that require larger bandwidth, higher spectral efficiency, and smarter transmission technology. Smart reflective surface technology is a plane composed of a large number of low-cost passive reflective elements, and each element can be controlled by software to adjust the amplitude and phase of the incident signal. Intelligent reflector technology has many advantages, such as strong scalability, low implementation cost, wide operating frequency band, and the ability to realize wireless propagation environment configuration.

智能反射面辅助通信系统被认为是一种没有转发功率的单时隙放大转发多中继系统，但两者的误码率性能比较还没有量化分析和理论依据。The intelligent reflector-assisted communication system is considered to be a single-slot amplification-and-forward multi-relay system without forwarding power, but there is no quantitative analysis and theoretical basis for the comparison of the bit error rate performance between the two.

发明内容SUMMARY OF THE INVENTION

为解决智能反射面辅助通信系统和单时隙放大转发多中继系统的的误码率性能进行比较分析的技术问题，本发明提供一种智能反射面辅助通信系统的渐近紧逼近误码率性能分析方法。In order to solve the technical problem of comparing and analyzing the bit error rate performance of the intelligent reflector-assisted communication system and the single-slot amplification-and-forward multi-relay system, the present invention provides an asymptotic tight approximation bit error rate of the intelligent reflector-assisted communication system. performance analysis methods.

本发明采用以下技术方案实现：一种渐近紧逼近误码率性能分析方法，其针对智能反射面辅助通信系统和单时隙放大转发多中继系统的误码率性能进行比较分析，所述分析方法包括步骤：The present invention adopts the following technical solutions to realize: an asymptotic tight approximation bit error rate performance analysis method, which compares and analyzes the bit error rate performance of an intelligent reflector-assisted communication system and a single-slot amplification-and-forward multi-relay system, and said The analysis method includes the steps:

步骤S1，构建智能反射面辅助通信系统模型，并计算最大比合并器输出的信噪比γ；Step S1, constructing a model of the intelligent reflector auxiliary communication system, and calculating the signal-to-noise ratio γ output by the maximum ratio combiner;

步骤S2，对所述智能反射面辅助通信系统进行误码率分析，并将信噪比γ转化为γ＝γ1+γ2的形式，分别构造信噪比γ1和信噪比γ2的矩量母函数，其中，所述信噪比γ2需构造以满足调和均值形式；所述误码率分析方法包括步骤：Step S2, analyze the bit error rate of the intelligent reflective surface auxiliary communication system, convert the signal-to-noise ratio γ into the form of γ=γ 1 +γ 2 , and construct the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 respectively. Moment generating function, wherein, the signal-to-noise ratio γ 2 needs to be constructed to meet the harmonic mean form; the bit error rate analysis method includes the steps:

步骤S21，定义所述智能反射面辅助通信系统内直接链路和智能反射面转发链路的信噪比分别为γ1和γ2，且有γ＝γ1+γ2；Step S21, defining the signal-to-noise ratios of the direct link and the forwarding link of the intelligent reflecting surface in the intelligent reflecting surface auxiliary communication system as γ 1 and γ 2 respectively, and γ=γ 1 +γ 2 ;

步骤S22，构造所述信噪比γ1和所述信噪比γ2的矩量母函数，分别表示为Mγ1(s)和Mγ2(s)：

Figure BDA0003038057750000021
其中，
Figure BDA0003038057750000022
为从源节点到目的节点的确定性通道hs，d的方差，
Figure BDA0003038057750000023
是从源节点到智能反射面的确定性信道hs,r的方差，
Figure BDA0003038057750000024
是从智能反射面到目的节点的确定性通道hr,d的方差，s是发送的功率归一化信号，m为常数，P为发射功率，
Figure BDA0003038057750000025
是服从均值为0、方差为N0复高斯白噪声；Step S22, constructing moment generating functions of the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 , respectively expressed as M γ1 (s) and M γ2 (s):
Figure BDA0003038057750000021
in,
Figure BDA0003038057750000022
is the variance of the deterministic channel h s, d from the source node to the destination node,
Figure BDA0003038057750000023
is the variance of the deterministic channel h s,r from the source node to the smart reflector,
Figure BDA0003038057750000024
is the variance of the deterministic channel h r,d from the smart reflector to the destination node, s is the transmitted power normalized signal, m is a constant, P is the transmit power,
Figure BDA0003038057750000025
is a complex white Gaussian noise with a mean of 0 and a variance of N 0 ;

步骤S3，根据所述矩量母函数Mγ1(s)和所述矩量母函数

Figure BDA0003038057750000026
得到所述智能反射面辅助通信系统的渐近紧逼近误码率。Step S3, according to the moment generating function M γ1 (s) and the moment generating function
Figure BDA0003038057750000026
The asymptotic close approximation bit error rate of the intelligent reflector-assisted communication system is obtained.

作为上述方案的进一步改进，在步骤S1中，所述智能反射面辅助通信系统模型由源节点、目的节点以及具有N个反射单元的智能反射面构成。As a further improvement of the above solution, in step S1, the smart reflective surface-assisted communication system model is composed of a source node, a destination node, and a smart reflective surface having N reflective units.

作为上述方案的进一步改进，在步骤S1中，最大比合并器输出的所述信噪比γ表示为：

Figure BDA0003038057750000027
其中，N为反射单元数，α∈(0,1]是固定的振幅反射系数，θ为通过智能反射面优化的相移变量，P为发射功率，N0为复高斯白噪声方差。As a further improvement of the above scheme, in step S1, the signal-to-noise ratio γ output by the maximum ratio combiner is expressed as:
Figure BDA0003038057750000027
Among them, N is the number of reflection units, α∈(0,1] is the fixed amplitude reflection coefficient, θ is the phase shift variable optimized by the smart reflector, P is the transmit power, and N 0 is the complex white Gaussian noise variance.

作为上述方案的进一步改进，在步骤S21中，所述信噪比γ1和所述信噪比γ2分别表示为：γ1＝(P|hs,d|2)/N0，

Figure BDA0003038057750000028
其中，X′1与X′2均为调和均值构造过程中的变量。As a further improvement of the above scheme, in step S21, the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 are respectively expressed as: γ 1 =(P|h s,d | 2 )/N 0 ,
Figure BDA0003038057750000028
Among them, X' 1 and X' 2 are variables in the process of harmonic mean construction.

作为上述方案的进一步改进，在步骤S21中，所述X′1表示为：As a further improvement of the above scheme, in step S21, the X' 1 is expressed as:

X′1＝(1+2m)P|hs,r|2/N0，且X′1服从参数为

Figure BDA0003038057750000029
的指数分布，其中，
Figure BDA00030380577500000210
X′ 1 =(1+2m)P|h s,r | 2 /N 0 , and X′ 1 obeys the parameter:
Figure BDA0003038057750000029
The exponential distribution of , where,
Figure BDA00030380577500000210

作为上述方案的进一步改进，在步骤S21中，所述X′2表示为：X'2＝(1+m)N2|hr,d|2/N0，且X′2服从参数为

Figure BDA0003038057750000031
的指数分布。As a further improvement of the above scheme, in step S21, the X' 2 is expressed as: X' 2 =(1+m)N 2 |hr ,d | 2 /N 0 , and X' 2 obeys the parameter of
Figure BDA0003038057750000031
the exponential distribution of .

作为上述方案的进一步改进，在步骤S3中，智能反射面辅助通信系统具有直接链路的渐近紧逼近误码率

Figure BDA0003038057750000032
表示为：As a further improvement of the above scheme, in step S3, the intelligent reflective surface assisted communication system has the asymptotic tight approximation bit error rate of the direct link
Figure BDA0003038057750000032
Expressed as:

Figure BDA0003038057750000033
其中，bPSK＝sin2(π/M)，M代表M-PSK调制的进制数，B为常数。
Figure BDA0003038057750000033
Wherein, b PSK =sin 2 (π/M), M represents the base number of M-PSK modulation, and B is a constant.

作为上述方案的进一步改进，在步骤S3中，智能反射面辅助通信系统中不具有直接链路的渐近紧逼近误码率

Figure BDA0003038057750000034
表示为：As a further improvement of the above scheme, in step S3, the asymptotic tight approximation of the bit error rate without the direct link in the intelligent reflector-assisted communication system
Figure BDA0003038057750000034
Expressed as:

Figure BDA0003038057750000035
Figure BDA0003038057750000035

作为上述方案的进一步改进，所述常数B表示为：As a further improvement of the above scheme, the constant B is expressed as:

Figure BDA0003038057750000036
Figure BDA0003038057750000036

本发明还提供了一种智能反射面辅助通信系统，其通过反射系数和智能反射面链路系数间的合理构建，使得智能反射面转发链路上的信噪比满足调和均值形式，推导出具有简单结构的系统渐近紧逼近公式，并利用控制变量法，对智能反射面辅助通信系统进行性能分析，从而针对智能反射面辅助通信系统和单时隙放大转发多中继系统的误码率性能进行比较分析。The invention also provides an auxiliary communication system of the intelligent reflecting surface, which can make the signal-to-noise ratio on the forwarding link of the intelligent reflecting surface satisfy the harmonic mean form through reasonable construction between the reflection coefficient and the link coefficient of the intelligent reflecting surface, and deduce The system is asymptotically tight approximation formula with simple structure, and the control variable method is used to analyze the performance of the intelligent reflector-assisted communication system, so as to the bit error rate performance of the intelligent reflector-assisted communication system and the single-slot amplify-and-forward multi-relay system Do a comparative analysis.

本发明将系统误码率渐近紧逼近公式的理论数值与实际仿真数值进行拟合分析，并检验了直接链路为系统提供的分集增益作用。随着智能反射单元数的提高，系统误码率性能也随之提升，但达到一定数量时，系统误码率性能无法再得到有效提升，系统误码率渐近紧逼近公式在较低信噪比情况下可精确描述系统误码率性能。The invention fits and analyzes the theoretical value of the asymptotic tight approximation formula of the system bit error rate and the actual simulation value, and tests the diversity gain effect provided by the direct link for the system. With the increase of the number of intelligent reflection units, the system bit error rate performance also improves, but when the number reaches a certain number, the system bit error rate performance can no longer be effectively improved, and the system bit error rate asymptotically closely approximates the formula at lower signal-to-noise ratios. The bit error rate performance of the system can be accurately described in this case.

与放大转发多中继系统相比，智能反射面辅助通信系统只有在低信噪比情况下才具备略好的系统误码率性能，但这不影响其在频谱效率方面的优势。另外，当智能反射面的单元数较少时，即在较低信噪比情况下，智能反射面与源节点之间的距离越近，智能反射面辅助通信系统的误码率性能越好。这就为在实际通信场景中智能反射面的选择及其单元数的确定提供误码率角度的理论依据。Compared with the amplifying and forwarding multi-relay system, the intelligent reflector-assisted communication system has slightly better system bit error rate performance only in the case of low signal-to-noise ratio, but this does not affect its advantage in spectral efficiency. In addition, when the number of units of the smart reflector is small, that is, in the case of a low signal-to-noise ratio, the closer the distance between the smart reflector and the source node, the better the BER performance of the smart reflector-assisted communication system. This provides a theoretical basis for the selection of the intelligent reflective surface and the determination of the number of units in the actual communication scene.

附图说明Description of drawings

图1为本发明实施例1提供的一种渐近紧逼近误码率性能分析方法中分析方法的流程图。FIG. 1 is a flowchart of an analysis method in an asymptotic tight approximation bit error rate performance analysis method provided in Embodiment 1 of the present invention.

图2为本发明实施例2提供一种渐近紧逼近误码率性能分析方法中分析方法中具有直接链路和无直接链路系统的渐近紧逼近误码率理论值与仿真值的关系曲线图。Fig. 2 provides a kind of asymptotic tight approximation bit error rate performance analysis method in Embodiment 2 of the present invention with a direct link and no direct link system in the analysis method The asymptotic tight approximation bit error rate theoretical value and the simulation value Graph.

图3为本发明实施例2提供一种渐近紧逼近误码率性能分析方法中分析方法中不同反射单元数下的系统误码率性能曲线图。FIG. 3 is a system BER performance curve diagram under different numbers of reflection units in the analysis method in an asymptotic tight approximation BER performance analysis method provided in Embodiment 2 of the present invention.

图4为本发明实施例2提供一种渐近紧逼近误码率性能分析方法中分析方法中智能反射面辅助通信系统与放大转发多中继系统的误码率性能比较曲线图。FIG. 4 is a graph showing the comparison of the bit error rate performance of the intelligent reflector-assisted communication system and the amplifying and forwarding multi-relay system in the analysis method of the asymptotic tight approximation bit error rate performance analysis method provided in Embodiment 2 of the present invention.

图5为本发明实施例2提供一种渐近紧逼近误码率性能分析方法中分析方法中不同确定性通道方差的误码率理论值曲线图。FIG. 5 is a curve diagram of theoretical value of bit error rate of different deterministic channel variances in the analysis method in an asymptotic tight approximation bit error rate performance analysis method provided in Embodiment 2 of the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅用以解释本发明，并不用于限定本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

实施例1Example 1

请参阅图1，本实施例介绍了一种渐近紧逼近误码率性能分析方法，其针对智能反射面辅助通信系统和单时隙放大转发多中继系统的误码率性能进行比较分析。所述分析方法包括步骤：Referring to FIG. 1, this embodiment introduces an asymptotic tight approximation bit error rate performance analysis method, which compares and analyzes the bit error rate performance of an intelligent reflector-assisted communication system and a single-slot amplify-and-forward multi-relay system. The analysis method includes the steps:

步骤S1，构建智能反射面辅助通信系统模型，并计算最大比合并器输出的信噪比γ。In step S1, a model of the intelligent reflector-assisted communication system is constructed, and the signal-to-noise ratio γ output by the maximum ratio combiner is calculated.

其中，所述智能反射面辅助通信系统模型由源节点、目的节点以及具有N个反射单元的智能反射面构成。从源节点到目的节点的确定性通道为hs,d，从源节点到智能反射面的确定性信道为hs,r，从智能反射面到目的节点的确定性通道为hr,d，且有[hs,r]n＝[hs,r]n+1＝hs,r，其中hs,r服从均值为0、方差为

Figure BDA0003038057750000051
的瑞利分布，[hr,d]n＝[hr,d]n+1＝hr,d，其中hr,d服从均值为0、方差为
Figure BDA0003038057750000052
的瑞利分布。Wherein, the intelligent reflecting surface auxiliary communication system model is composed of a source node, a destination node and an intelligent reflecting surface having N reflecting units. The deterministic channel from the source node to the destination node is h s,d , the deterministic channel from the source node to the smart reflector is h s,r , the deterministic channel from the smart reflector to the destination node is h r,d , And there is [h s,r ] n =[h s,r ] n+1 =h s,r , where h s,r obeys the mean of 0 and the variance of
Figure BDA0003038057750000051
The Rayleigh distribution of , [h r,d ] n =[h r,d ] n+1 =h r,d , where h r,d obeys the mean of 0 and the variance of
Figure BDA0003038057750000052
the Rayleigh distribution.

从而智能反射面的相位移动矩阵表示为

Figure BDA0003038057750000053
其中，α∈(0,1]是固定的振幅反射系数，而θ1,...,θN是可以通过IRS优化的相移变量θn＝arg(hs,d)-arg([hs,r]n[hr,d]n)。目的节点收到的信号y表示为：
Figure BDA0003038057750000054
其中，P是发射功率，s是发送的功率归一化信号，
Figure BDA0003038057750000055
是服从均值为0、方差为N0复高斯白噪声。Therefore, the phase shift matrix of the smart reflector is expressed as
Figure BDA0003038057750000053
where α∈(0,1] is a fixed amplitude reflection coefficient, and θ 1 ,...,θ N are phase shift variables that can be optimized by IRS θ n =arg(h s,d )-arg([h s,r ] n [h r,d ] n ). The signal y received by the destination node is expressed as:
Figure BDA0003038057750000054
where P is the transmit power, s is the transmitted power normalized signal,
Figure BDA0003038057750000055
It is a complex white Gaussian noise with a mean of 0 and a variance of N 0 .

假设各反射单元的相移变量θ1,...,θN相等，Θ可进一步表示为αdiag(ejθ,...,ej θ)。从而

Figure BDA0003038057750000056
可进一步表示为Nαejθhs,rhr,d，则目的节点收到的信号y可重新转化为：
Figure BDA0003038057750000057
Assuming that the phase shift variables θ 1 , . thereby
Figure BDA0003038057750000056
It can be further expressed as Nαe jθ h s,r h r,d , then the signal y received by the destination node can be re-transformed into:
Figure BDA0003038057750000057

假设目的节点可以完全获取个信道系数，采用最大比合并器对接收到的信号进行处理，则最大比合并器的输出信噪比表示为：Assuming that the destination node can completely obtain the channel coefficients, and the maximum ratio combiner is used to process the received signal, the output signal-to-noise ratio of the maximum ratio combiner is expressed as:

Figure BDA0003038057750000058
Figure BDA0003038057750000058

步骤S2，对所述智能反射面辅助通信系统进行误码率分析，并将信噪比γ转化为γ＝γ1+γ2的形式，分别构造信噪比γ1和信噪比γ2的矩量母函数，其中，所述信噪比γ2需构造以满足调和均值形式。所述误码率分析方法包括步骤：Step S2, analyze the bit error rate of the intelligent reflective surface auxiliary communication system, convert the signal-to-noise ratio γ into the form of γ=γ 1 +γ 2 , and construct the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 respectively. Moment generating function, wherein the signal-to-noise ratio γ 2 needs to be constructed to satisfy the harmonic mean form. The bit error rate analysis method includes the steps:

步骤S21，定义所述智能反射面辅助通信系统内直接链路和智能反射面转发链路的信噪比分别为γ1和γ2，且有γ＝γ1+γ2。Step S21, define the signal-to-noise ratios of the direct link and the forwarding link of the intelligent reflection surface in the intelligent reflecting surface auxiliary communication system as γ 1 and γ 2 respectively, and γ=γ 1 +γ 2 .

根据具有M-PSK调制系统的误码率计算公式以及复数模的性质，将

Figure BDA0003038057750000059
转化为
Figure BDA00030380577500000510
Figure BDA0003038057750000061
为不失一般性，假设|hs,d|和|hs，rhr，d|存在线性关系，即|hs，d|＝mNα|hs,rhr，d|，则γ可进一步表示为
Figure BDA0003038057750000062
Figure BDA0003038057750000063
其中γ1＝(P|hs,d|2)/N0为直接链路对应的信噪比，
Figure BDA0003038057750000064
为智能反射面转发链路对应的等效信噪比。According to the calculation formula of bit error rate with M-PSK modulation system and the properties of complex modulus, the
Figure BDA0003038057750000059
transform into
Figure BDA00030380577500000510
Figure BDA0003038057750000061
Without loss of generality, it is assumed that |h s,d | and |h s,r hr ,d | have a linear relationship, that is, |h s,d |=mNα|h s,r hr ,d |, then γ can be further expressed as
Figure BDA0003038057750000062
Figure BDA0003038057750000063
where γ 1 =(P|h s,d | 2 )/N 0 is the signal-to-noise ratio corresponding to the direct link,
Figure BDA0003038057750000064
Equivalent signal-to-noise ratio corresponding to the forwarding link of the smart reflector.

步骤S22，构造所述信噪比γ1和所述信噪比γ2的矩量母函数，分别表示为Mγ1(s)和Mγ2(s)。Step S22, constructing moment generating functions of the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 , which are respectively expressed as M γ1 (s) and M γ2 (s).

其中，由于γ1＝(P|hs,d|2)/N0服从参数为

Figure BDA0003038057750000065
的指数分布，因此γ1的矩量母函数
Figure BDA0003038057750000066
可以直接表示为：
Figure BDA0003038057750000067
由于γ2不满足调和均值的形式，因此对γ2进行调和均值形式的构造，并进行矩量母函数的表达。Among them, since γ 1 =(P|h s,d | 2 )/N 0 obeys the parameter as
Figure BDA0003038057750000065
the exponential distribution of , so the moment generating function of γ 1
Figure BDA0003038057750000066
It can be directly expressed as:
Figure BDA0003038057750000067
Since γ 2 does not satisfy the form of the harmonic mean, we construct the form of the harmonic mean for γ 2 and express the generating moment function.

智能反射面反射系数α∈(0,1]，假设

Figure BDA0003038057750000068
则γ2可表示为：
Figure BDA0003038057750000069
Figure BDA00030380577500000610
The reflection coefficient of the smart reflector α∈(0,1], assuming
Figure BDA0003038057750000068
Then γ 2 can be expressed as:
Figure BDA0003038057750000069
Figure BDA00030380577500000610

其中，X′1表示为：X′1＝(1+2m)P|hs,r|2/N0，且X′1服从参数为

Figure BDA00030380577500000611
的指数分布，X′2表示为：X'2＝(1+m)N2|hr,d|2/N0，且X′2服从参数为
Figure BDA00030380577500000612
的指数分布。根据调和均值的简单MGF定理，对于信噪比γ2，其相应的矩量母函数
Figure BDA00030380577500000613
表示为：Among them, X' 1 is expressed as: X' 1 =(1+2m)P|h s,r | 2 /N 0 , and X' 1 obeys the parameter:
Figure BDA00030380577500000611
The exponential distribution of , X' 2 is expressed as: X' 2 =(1+m)N 2 |hr ,d | 2 /N 0 , and X' 2 obeys the parameters of
Figure BDA00030380577500000612
the exponential distribution of . According to the simple MGF theorem of harmonic mean, for the signal-to-noise ratio γ 2 , its corresponding moment generating function
Figure BDA00030380577500000613
Expressed as:

Figure BDA00030380577500000614
其中，
Figure BDA00030380577500000615
为从源节点到目的节点的确定性通道hs,d的方差，
Figure BDA00030380577500000616
是从源节点到智能反射面的确定性信道hs,r的方差，
Figure BDA00030380577500000617
是从智能反射面到目的节点的确定性通道hr,d的方差。
Figure BDA00030380577500000614
in,
Figure BDA00030380577500000615
is the variance of the deterministic channel h s,d from the source node to the destination node,
Figure BDA00030380577500000616
is the variance of the deterministic channel h s,r from the source node to the smart reflector,
Figure BDA00030380577500000617
is the variance of the deterministic channel hr ,d from the smart reflector to the destination node.

步骤S3，根据所述矩量母函数

Figure BDA0003038057750000071
和所述矩量母函数
Figure BDA0003038057750000072
得到所述智能反射面辅助通信系统的渐近紧逼近误码率。Step S3, according to the moment generating function
Figure BDA0003038057750000071
and the moment generating function
Figure BDA0003038057750000072
The asymptotic close approximation bit error rate of the intelligent reflector-assisted communication system is obtained.

由于矩量母函数

Figure BDA0003038057750000073
和矩量母函数
Figure BDA0003038057750000074
均已得到，通过给定M-PSK的具体形式，可得到误码率的闭式解。从而当给定M-PSK的具体形式时，智能反射面辅助通信系统中具有直接链路的的渐近紧逼近误码率
Figure BDA0003038057750000075
表示为：
Figure BDA0003038057750000076
没有直接链路的的渐近紧逼近误码率
Figure BDA0003038057750000077
表示为：
Figure BDA0003038057750000078
其中，bPSK＝sin2(π/M)和
Figure BDA0003038057750000079
为常数，
Figure BDA00030380577500000710
Due to the moment generating function
Figure BDA0003038057750000073
and moment generating function
Figure BDA0003038057750000074
Both have been obtained, and the closed-form solution of the bit error rate can be obtained by giving the specific form of M-PSK. Therefore, when the specific form of M-PSK is given, the asymptotic tight approximation of the bit error rate in the intelligent reflector-assisted communication system with direct link
Figure BDA0003038057750000075
Expressed as:
Figure BDA0003038057750000076
Asymptotically tight approximation to bit error rate without direct link
Figure BDA0003038057750000077
Expressed as:
Figure BDA0003038057750000078
where, b PSK = sin 2 (π/M) and
Figure BDA0003038057750000079
is a constant,
Figure BDA00030380577500000710

实施例2Example 2

本实施例介绍了智能反射面辅助通信系统中具有直接链路和无直接链路系统的渐近紧逼近误码率SER理论值与仿真值的关系。请参阅图2，采用蒙特卡罗方法，目的节点处采用最大似然法对最大比合并器输出信号进行检测，系统仿真均采用QPSK调制方式，即M＝4，SNR＝P/N0，并且假设N0＝1，其中，N＝32，

Figure BDA00030380577500000711
This embodiment introduces the relationship between the theoretical value and the simulated value of the asymptotically close approximation bit error rate SER in the intelligent reflector-assisted communication system with and without the direct link. Referring to Figure 2, the Monte Carlo method is used, the maximum likelihood method is used at the destination node to detect the output signal of the maximum ratio combiner, and the system simulation adopts the QPSK modulation method, that is, M=4, SNR=P/N 0 , and Assuming N 0 =1, where N = 32,
Figure BDA00030380577500000711

由图2可知，当信噪比SNR大于10dB时，即在较低误码率条件下，理论值和仿真值之间便具有很好的拟合效果，从而证明了所推导渐近紧逼近误码率SER公式的有效性。随着信噪比的增大，各情况的误码率均呈现减小趋势。与无直接链路情况相比，有直接链路的情况下降趋势更大。这是因为直接链路能够为系统提供重要的分集增益。It can be seen from Figure 2 that when the signal-to-noise ratio SNR is greater than 10dB, that is, under the condition of low bit error rate, there is a good fitting effect between the theoretical value and the simulated value, which proves that the derived asymptotic tight approximation is incorrect. Validity of the code rate SER formula. With the increase of the signal-to-noise ratio, the bit error rate in each case shows a decreasing trend. Compared with the case without direct link, the situation with direct link has a larger downward trend. This is because the direct link can provide significant diversity gain to the system.

请参阅图3，本实施例还针对不同反射单元数下的系统误码率性能进行介绍，智能反射面IRS的反射单元数N∈{4,32,256}，

Figure BDA00030380577500000712
由图3可知，与无直接链路情况相比，有直接链路情况的误码率性能下降趋势更大。当N∈{32,256}时，即在反射单元数达到一定数值时，有直接链路和无直接链路两种情况的仿真值与误码率理论值之间才均具有很好的拟合效果。但反射单元数的继续增加对系统误码率性能不会再有明显的提升效果。Referring to FIG. 3, this embodiment also introduces the system bit error rate performance under different numbers of reflection units. The number of reflection units of the intelligent reflecting surface IRS is N∈{4,32,256},
Figure BDA00030380577500000712
It can be seen from Fig. 3 that compared with the case without the direct link, the bit error rate performance with the direct link has a greater tendency to decrease. When N∈{32,256}, that is, when the number of reflection units reaches a certain value, the simulation value and the theoretical value of the bit error rate in both cases with direct link and no direct link have a good fitting effect. . However, the continuous increase of the number of reflection units will not have a significant improvement effect on the system bit error rate performance.

请参阅图4，本实施例还针对智能反射面辅助通信系统与放大转发多中继系统的误码率性能比较进行介绍，取N＝32，

Figure BDA0003038057750000081
采用放大转发AF多中继系统的误码率作为比较对象。由图4可知，智能反射面辅助通信系统和放大转发多中继系统的误码率均随着信噪比的增大而减小。在信噪比约为9dB时，误码率性能曲线出现相交情况。当信噪比小于9dB时，智能反射面辅助通信系统的误码率性能略好于放大转发多中继系统的误码率性能；当信噪比大于9dB时，放大转发多中继系统的误码率性能明显好于智能反射面辅助通信系统的误码率性能。虽然，在误码率方面智能反射面辅助通信系统没有明显优势，但其对源节点数据的协作转发是在一个时隙内完成的，具有更高的频谱效率。Referring to FIG. 4 , this embodiment also introduces the comparison of the bit error rate performance between the intelligent reflector-assisted communication system and the amplification-and-forward multi-relay system, taking N=32,
Figure BDA0003038057750000081
The bit error rate of the amplify-and-forward AF multi-relay system is used as the comparison object. It can be seen from Figure 4 that the bit error rates of the intelligent reflector-assisted communication system and the amplification and forwarding multi-relay system both decrease with the increase of the signal-to-noise ratio. When the signal-to-noise ratio is about 9dB, the bit error rate performance curves intersect. When the signal-to-noise ratio is less than 9dB, the bit error rate performance of the intelligent reflector-assisted communication system is slightly better than that of the amplification-and-forward multi-relay system; when the signal-to-noise ratio is greater than 9dB, the error rate performance of the amplification-and-forward multi-relay system The bit rate performance is obviously better than that of the intelligent reflector-assisted communication system. Although the intelligent reflector-assisted communication system has no obvious advantage in the bit error rate, the cooperative forwarding of the source node data is completed in one time slot, which has higher spectral efficiency.

当N＝32时，不同

Figure BDA0003038057750000082
的误码率理论值如图5所示，其中，
Figure BDA0003038057750000083
表示无直接链路情况的误码率性能分析。各信道系数的方差和距离成反比关系，即方差越大距离越小，反之亦然。由图5可知，当网络拓扑结构具有对称性时，放大转发多中继系统的误码率性能具备相同性，而智能反射面辅助通信系统的误码率性能不具备相同性。当信噪比小于30.103dB，智能反射面距离源节点更近时系统的误码率性能相对较好；而当信噪比大于30.103dB时，智能反射面距离源节点更远时系统的误码率性能相对较好。当始终保持P＝N2时，智能反射面辅助通信系统的网络拓扑结构具有对称性，其误码率性能才具备相同性。When N=32, different
Figure BDA0003038057750000082
The theoretical value of the bit error rate is shown in Figure 5, where,
Figure BDA0003038057750000083
Indicates the bit error rate performance analysis for the case of no direct link. The variance of each channel coefficient is inversely proportional to the distance, that is, the larger the variance, the smaller the distance, and vice versa. It can be seen from Figure 5 that when the network topology is symmetrical, the bit error rate performance of the amplify-and-forward multi-relay system is identical, but the bit error rate performance of the intelligent reflector-assisted communication system is not identical. When the signal-to-noise ratio is less than 30.103dB, the BER performance of the system is relatively good when the smart reflector is closer to the source node; and when the signal-to-noise ratio is greater than 30.103dB, the system has a bit error rate when the smart reflector is farther from the source node rate performance is relatively good. When P=N 2 is always maintained, the network topology of the intelligent reflective surface-assisted communication system has symmetry, and its bit error rate performance is the same.

以上仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention. Inside.

Claims (6)

1.一种渐近紧逼近误码率性能分析方法，其特征在于，其针对智能反射面辅助通信系统和单时隙放大转发多中继系统的误码率性能进行比较分析，所述分析方法包括步骤：1. a method for asymptotically approaching bit error rate performance analysis, is characterized in that, it carries out comparative analysis for the bit error rate performance of intelligent reflector auxiliary communication system and single time slot amplification and forwarding multi-relay system, and described analysis method Include steps: 步骤S1，构建智能反射面辅助通信系统模型，并计算最大比合并器输出的信噪比γ；Step S1, constructing a model of the intelligent reflector auxiliary communication system, and calculating the signal-to-noise ratio γ output by the maximum ratio combiner; 步骤S2，对所述智能反射面辅助通信系统进行误码率分析，并将信噪比γ转化为γ＝γ1+γ2的形式，分别构造信噪比γ1和信噪比γ2的矩量母函数，其中，所述信噪比γ2需构造以满足调和均值形式；所述误码率分析方法包括步骤：Step S2, analyze the bit error rate of the intelligent reflective surface auxiliary communication system, convert the signal-to-noise ratio γ into the form of γ=γ 1 +γ 2 , and construct the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 respectively. Moment generating function, wherein, the signal-to-noise ratio γ 2 needs to be constructed to meet the harmonic mean form; the bit error rate analysis method includes the steps: 步骤S21，定义所述智能反射面辅助通信系统内直接链路和智能反射面转发链路的信噪比分别为γ1和γ2，且有γ＝γ1+γ2；Step S21, defining the signal-to-noise ratios of the direct link and the forwarding link of the intelligent reflecting surface in the intelligent reflecting surface auxiliary communication system as γ 1 and γ 2 respectively, and γ=γ 1 +γ 2 ; 步骤S22，构造所述信噪比γ1和所述信噪比γ2的矩量母函数，分别表示为
Figure FDA0003472938380000011
和
Figure FDA0003472938380000012
Figure FDA0003472938380000013
其中，
Figure FDA0003472938380000014
为从源节点到目的节点的确定性通道hs,d的方差，
Figure FDA0003472938380000015
是从源节点到智能反射面的确定性信道hs,r的方差，
Figure FDA0003472938380000016
是从智能反射面到目的节点的确定性通道hr,d的方差，s是发送的功率归一化信号，m为常数，P为发射功率，
Figure FDA0003472938380000017
是服从均值为0、方差为N0复高斯白噪声；Step S22, constructing the moment generating functions of the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 , respectively expressed as
Figure FDA0003472938380000011
and
Figure FDA0003472938380000012
Figure FDA0003472938380000013
in,
Figure FDA0003472938380000014
is the variance of the deterministic channel h s,d from the source node to the destination node,
Figure FDA0003472938380000015
is the variance of the deterministic channel h s,r from the source node to the smart reflector,
Figure FDA0003472938380000016
is the variance of the deterministic channel h r,d from the smart reflector to the destination node, s is the transmitted power normalized signal, m is a constant, P is the transmit power,
Figure FDA0003472938380000017
is a complex white Gaussian noise with a mean of 0 and a variance of N 0 ; 步骤S3，根据所述矩量母函数
Figure FDA0003472938380000018
和所述矩量母函数
Figure FDA0003472938380000019
得到所述智能反射面辅助通信系统的渐近紧逼近误码率；Step S3, according to the moment generating function
Figure FDA0003472938380000018
and the moment generating function
Figure FDA0003472938380000019
Obtaining the asymptotic tight approximation bit error rate of the intelligent reflector-assisted communication system; 其中，在步骤S1中，最大比合并器输出的所述信噪比γ表示为：Wherein, in step S1, the signal-to-noise ratio γ output by the maximum ratio combiner is expressed as:
Figure FDA00034729383800000110
其中，N为反射单元数，α∈(0,1]是固定的振幅反射系数，θ为通过智能反射面优化的相移变量，hs,d为从源节点到目的节点的确定性通道，hs,r为从源节点到智能反射面的确定性信道，hr,d为从智能反射面到目的节点的确定性通道；
Figure FDA00034729383800000110
where N is the number of reflection units, α∈(0,1] is the fixed amplitude reflection coefficient, θ is the phase shift variable optimized by the smart reflector, h s,d is the deterministic channel from the source node to the destination node, h s,r is the deterministic channel from the source node to the smart reflector, h r,d is the deterministic channel from the smart reflector to the destination node; 智能反射面辅助通信系统具有直接链路的渐近紧逼近误码率
Figure FDA00034729383800000210
表示为：
Figure FDA0003472938380000022
其中，bPSK＝sin2(π/M)，M代表M-PSK调制的进制数，B为常数；Asymptotically tight approximation of bit error rate for intelligent reflector-assisted communication systems with direct links
Figure FDA00034729383800000210
Expressed as:
Figure FDA0003472938380000022
Wherein, b PSK =sin 2 (π/M), M represents the base number of M-PSK modulation, and B is a constant; 智能反射面辅助通信系统中不具有直接链路的渐近紧逼近误码率
Figure FDA0003472938380000023
表示为：
Figure FDA0003472938380000024
Asymptotic tight approximation of bit error rate without direct link in intelligent reflector assisted communication system
Figure FDA0003472938380000023
Expressed as:
Figure FDA0003472938380000024
 所述常数B表示为：
Figure FDA0003472938380000025
The constant B is expressed as:
Figure FDA0003472938380000025
 2.如权利要求1所述的渐近紧逼近误码率性能分析方法，其特征在于，在步骤S1中，所述智能反射面辅助通信系统模型由源节点、目的节点以及具有N个反射单元的智能反射面构成。2. asymptotic tight approximation bit error rate performance analysis method as claimed in claim 1, is characterized in that, in step S1, described intelligent reflecting surface auxiliary communication system model consists of source node, destination node and has N reflection units of smart reflective surfaces. 3.如权利要求1所述的渐近紧逼近误码率性能分析方法，其特征在于，在步骤S21中，所述信噪比γ1和所述信噪比γ2分别表示为：γ1＝(P|hs,d|2)/N0，
Figure FDA0003472938380000026
其中，X'1与X'2均为调和均值构造过程中的变量。3. The asymptotic tight approximation bit error rate performance analysis method according to claim 1, wherein in step S21, the signal-to-noise ratio γ 1 and the signal-to-noise ratio γ 2 are respectively expressed as: γ 1 =(P|h s,d | 2 )/N 0 ,
Figure FDA0003472938380000026
Among them, X' 1 and X' 2 are variables in the process of harmonic mean construction. 4.如权利要求3所述的渐近紧逼近误码率性能分析方法，其特征在于，在步骤S21中，所述X'1表示为：X'1＝(1+2m)P|hs,r|2/N0，且X'1服从参数为
Figure FDA0003472938380000027
的指数分布，其中，
Figure FDA0003472938380000028
4. The asymptotic tight approximation bit error rate performance analysis method according to claim 3, wherein in step S21, the X' 1 is expressed as: X' 1 =(1+2m)P|h s ,r | 2 /N 0 , and X' 1 obeys the parameters as
Figure FDA0003472938380000027
The exponential distribution of , where,
Figure FDA0003472938380000028
 5.如权利要求3所述的渐近紧逼近误码率性能分析方法，其特征在于，在步骤S21中，所述X'2表示为：X'2＝(1+m)N2|hr,d|2/N0，且X'2服从参数为
Figure FDA0003472938380000029
的指数分布。5. The asymptotic tight approximation bit error rate performance analysis method according to claim 3, wherein in step S21, the X' 2 is expressed as: X' 2 =(1+m)N 2 |h r,d | 2 /N 0 , and X' 2 obeys the parameters as
Figure FDA0003472938380000029
the exponential distribution of . 6.一种智能反射面辅助通信系统，其特征在于，其根据如权利要求1至5任意一项所述的渐近紧逼近误码率性能分析方法对智能反射面辅助通信系统和单时隙放大转发多中继系统的误码率性能进行比较分析。6. an intelligent reflecting surface auxiliary communication system is characterized in that, according to the asymptotic tight approximation bit error rate performance analysis method as described in any one of claims 1 to 5, to intelligent reflecting surface auxiliary communication system and single time slot The bit error rate performance of amplifying and forwarding multi-relay system is compared and analyzed.
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