CN116056106A - RIS-assisted workshop wireless network traversal capacity upper bound calculation method - Google Patents

RIS-assisted workshop wireless network traversal capacity upper bound calculation method Download PDF

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CN116056106A
CN116056106A CN202310204307.2A CN202310204307A CN116056106A CN 116056106 A CN116056106 A CN 116056106A CN 202310204307 A CN202310204307 A CN 202310204307A CN 116056106 A CN116056106 A CN 116056106A
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CN116056106B (en
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颜志
李梦铖
毛建旭
欧阳博
贺文斌
许中伟
梁毅钦
彭紫扬
李卓维
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Hunan University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a RIS-assisted workshop wireless network traversal capacity upper bound calculation method, which comprises the following steps: establishing an RIS-assisted workshop wireless network communication system, wherein a single antenna base station communicates with equipment in a workshop through the RIS; setting a first communication channel and a second communication channel based on the communication relation among the single antenna base station, the RIS and the equipment; establishing a mathematical model of the equipment receiving signal according to the first communication channel and the second communication channel; obtaining a maximum signal-to-noise ratio expression according to a mathematical model of the received signal of the equipment; obtaining a signal-to-noise ratio probability density expression according to the maximum signal-to-noise ratio expression and according to the property of generalized K distribution; obtaining an expected expression of the signal to noise ratio according to the probability density expression of the signal to noise ratio and based on the mathematical relationship between the expected and probability density; and obtaining a traversal capacity upper bound expression of the workshop wireless network communication system based on the expected expression of the signal-to-noise ratio.

Description

RIS-assisted workshop wireless network traversal capacity upper bound calculation method
Technical Field
The invention relates to the technical field of wireless network traversal capacity upper bound calculation, in particular to a RIS-assisted workshop wireless network traversal capacity upper bound calculation method.
Background
The development of the domestic industrial Internet starts to go from the popularization of concepts to the practice of deep ploughing, however, because of the fact that production equipment is numerous, engineering businesses are three-dimensionally crossed and workshop building structures are complex inside an industrial workshop, serious signal shielding is caused, workshop equipment is still connected to a network in a traditional wired mode in each large industrial workshop in China, and the core links of industrial production are still difficult to reach by the wireless communication technologies such as 5G communication, WIFI communication and the like which are mature at present. In order to solve the problem that the stability of a workshop wireless network is difficult to support in an industrial field environment and improve the coverage of the workshop wireless network, RIS is introduced, and the industrial production is intelligently transformed through the RIS.
RIS, full scale Reconfigurable Intelligent Surface, also called reconfigurable intelligent supersurface. A large number of passive reflecting elements are attached to the surface of the RIS, each element can change a certain phase of a signal incident on the element, and the change of the property of a part of a reflected signal can be realized by effectively adjusting the reflecting unit on the RIS, so that a wireless channel is changed.
At present, the performance of RIS auxiliary wireless communication systems at home and abroad has been developed into a deeper study; the prior related research mainly considers the outdoor common scene with a channel model of Rician distribution, but the result of RIS-assisted wireless network performance analysis under the scene is not suitable for a special indoor environment such as an industrial workshop. Therefore, it is necessary to design a method for calculating the performance index of the RIS-assisted wireless network suitable for the workshop environment.
Disclosure of Invention
Based on this, it is necessary to provide an RIS-assisted method for calculating the upper bound of the traversal capacity of the wireless network in the workshop, aiming at the existing problems.
The invention provides a RIS-assisted workshop wireless network traversal capacity upper bound calculation method, which comprises the following steps:
s1: establishing an RIS-assisted workshop wireless network communication system, wherein a single antenna base station communicates with equipment in a workshop through the RIS;
s2: setting a first communication channel and a second communication channel based on the communication relation among the single antenna base station, the RIS and the equipment; establishing a mathematical model of the equipment receiving signal according to the first communication channel and the second communication channel; obtaining a maximum signal-to-noise ratio expression according to the mathematical model of the received signal of the equipment;
s3: obtaining a signal-to-noise ratio probability density expression according to the maximum signal-to-noise ratio expression and according to the property of generalized K distribution;
s4: obtaining an expected expression of the signal to noise ratio according to the probability density expression of the signal to noise ratio and based on the mathematical relationship between the expected and probability density;
s5: obtaining an upper bound expression of the traversal capacity of the workshop wireless network communication system based on the expected expression of the signal-to-noise ratio; and calculating the wireless network traversal capacity upper bound through the traversal capacity upper bound expression.
Preferably, in S2, a channel is set for communication between the single antenna base station and the RIS, denoted as a first communication channel; a channel is set for communication between the RIS and devices within the plant, denoted as a second communication channel.
Preferably, the first communication channel expression is:
Figure SMS_1
；
the second communication channel expression is:
Figure SMS_2
；
wherein ,
Figure SMS_3
representing a first communication channel; />
Figure SMS_4
Representing the amplitude of the first communication channel matrix; />
Figure SMS_5
Representing the phase of the first communication channel matrix; />
Figure SMS_6
Representing a second communication channel; />
Figure SMS_7
Representing the amplitude of the second communication channel matrix;
Figure SMS_8
representing the phase of the second communication channel matrix; i denotes an ith reflecting element via the reflecting surface of the RIS; j represents an imaginary unit.
Preferably, in S2, the first communication channel and the second communication channel are independent from each other and all obey rayleigh distribution, so that a mathematical model of the device received signal is built according to the first communication channel and the second communication channel; the mathematical model expression of the device receiving signal is as follows:
Figure SMS_9
；
wherein ,
Figure SMS_11
indicating that the device receives the signal,/-, is>
Figure SMS_15
Representing the transmit power of a single antenna base station, +.>
Figure SMS_17
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_12
Representing the distance between the RIS and the device; />
Figure SMS_14
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_16
Representing the RIS to device path loss factor; n represents the total number of reflective elements in the reflective surface via the RIS; i denotes an ith reflecting element via the reflecting surface of the RIS; />
Figure SMS_18
Representing a first communication channel; />
Figure SMS_10
Representing the reflection coefficient of the ith reflective element of the RIS; />
Figure SMS_13
Representing a second communication channel; x represents the transmit signal of a single antenna base station and n represents additive white gaussian noise.
Preferably, in S2, the process of obtaining the maximum signal-to-noise ratio expression is:
the expression of the reflection coefficient of the ith reflection element of RIS is:
Figure SMS_19
；
wherein ,
Figure SMS_20
representing the reflection coefficient of the ith reflective element of the RIS; />
Figure SMS_21
Representing the signal amplitude attenuation coefficient caused by the reflection of the ith reflecting element; />
Figure SMS_22
Indicating the phase change caused by the reflection of the ith reflecting element; j represents an imaginary unit;
in combination with the first communication channel expression, the second communication channel expression, and the reflection coefficient expression, the device received signal mathematical model expression may be transformed into:
Figure SMS_23
；
the method is characterized by comprising the following steps of:
Figure SMS_24
；/>
the expression of the signal-to-noise ratio received by the device is:
Figure SMS_25
；
taking out
Figure SMS_26
，/>
Figure SMS_27
The maximum signal-to-noise ratio expression is obtained, which is:
Figure SMS_28
；
Figure SMS_29
；
wherein ,
Figure SMS_33
representing the device received signal, gamma representing the signal-to-noise ratio of the device received,/->
Figure SMS_35
Represents the maximum signal-to-noise ratio,/-, for example>
Figure SMS_39
Representing the transmit power of a single antenna base station, +.>
Figure SMS_32
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_36
Representing the distance between the RIS and the device; />
Figure SMS_40
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_42
Representing the RIS to device path loss factor; n represents the total number of reflective elements in the reflective surface via the RIS; i denotes an ith reflecting element via the reflecting surface of the RIS; x represents a transmitting signal of a single antenna base station, and n represents additive white gaussian noise; />
Figure SMS_30
Representing a first communication channel; n (N) 0 Power representing gaussian white noise; />
Figure SMS_34
Representing the amplitude of the first communication channel matrix; />
Figure SMS_38
Representing the phase of the first communication channel matrix; />
Figure SMS_41
Representing a second communication channel; />
Figure SMS_31
Representing the amplitude of the second communication channel matrix; />
Figure SMS_37
Representing the phase of the second communication channel matrix; i denotes an ith reflecting element via the reflecting surface of the RIS; j represents an imaginary unit.
Preferably, in S3, the process of obtaining the snr probability density expression is:
based on the expression
Figure SMS_43
Let->
Figure SMS_44
The method comprises the steps of carrying out a first treatment on the surface of the Since the first communication channel and the second communication channel are mutually independent Rayleigh fading channels, the first communication channel and the second communication channel are +.>
Figure SMS_45
and />
Figure SMS_46
Is a Rayleigh random variable independent of each other, R i Is expressed as:
Figure SMS_47
；
wherein ,
Figure SMS_48
r represents i Probability density functions of (2); />
Figure SMS_49
A 0 th order Bessel function representing a second type of correction; r represents a variable;
due to the R i Since the probability density function of (2) follows the generalized K distribution, the probability density function of R is obtained based on the property of the generalized K distribution, expressed as:
Figure SMS_50
；
wherein ,
Figure SMS_51
；/>
Figure SMS_52
；
Figure SMS_53
；
Figure SMS_54
；
Figure SMS_55
；
combining the maximum signal-to-noise ratio expression and the probability density function of R to obtain a signal-to-noise ratio probability density expression expressed as:
Figure SMS_56
；
Figure SMS_57
；
wherein ,
Figure SMS_59
representing the probability density of the signal to noise ratio, and gamma represents the signal to noise ratio received by the equipment; />
Figure SMS_63
Is the second moment of the R,
Figure SMS_67
for the fourth moment of R->
Figure SMS_60
For the sixth moment of R->
Figure SMS_64
Representing the transmit power of a single antenna base station, +.>
Figure SMS_68
Representing single antenna base station to RISA distance; />
Figure SMS_71
Representing the distance between the RIS and the device; />
Figure SMS_58
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_62
Representing the RIS to device path loss factor; n (N) 0 Power representing gaussian white noise; />
Figure SMS_66
、/>
Figure SMS_70
Respectively represent k W 、m W Gamma functions of (a); />
Figure SMS_61
Represents the average power of R; />
Figure SMS_65
Representing correction of second kind>
Figure SMS_69
The order bessel function.
Preferably, in S4, the process of obtaining the desired expression of the signal-to-noise ratio is:
based on the SNR probability density expression and the k-m order Bessel function of the second type correction, a SNR probability density conversion formula is obtained and recorded as:
Figure SMS_72
；
wherein ,
Figure SMS_73
representing the probability density of the signal to noise ratio, and gamma represents the signal to noise ratio received by the equipment; />
Figure SMS_74
、/>
Figure SMS_75
Respectively represent k W 、m W Gamma functions of (a); />
Figure SMS_76
Representing the Meijer-G function;
and then deducing a signal to noise ratio probability density conversion formula through the property of the Meijer-G function to obtain a probability density deduction formula, which is recorded as:
Figure SMS_77
；
the mathematical relationship between the expected and probability density is:
Figure SMS_78
；
substituting a probability density deduction formula into a mathematical relation between expected and probability density to obtain an expected expression of signal to noise ratio before deduction, and marking as follows:
Figure SMS_79
；
calculating the expected expression of the signal to noise ratio before deduction through scientific calculation software matetica to obtain the expected expression of the signal to noise ratio, wherein the expected expression is expressed as follows:
Figure SMS_80
；
wherein ,
Figure SMS_81
representing the desired expression->
Figure SMS_82
Representing the transmit power of a single antenna base station, +.>
Figure SMS_83
Represents the average power of R; />
Figure SMS_84
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_85
Representing the distance between the RIS and the device; />
Figure SMS_86
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_87
Representing the RIS to device path loss factor; n (N) 0 Representing the power of gaussian white noise.
Preferably, in S5, the process of obtaining the traversal capacity upper bound expression is:
the expression of the traversal capacity is:
Figure SMS_88
；
the expression of the traversal capacity is converted to an inequality using the Jensen inequality, expressed as:
Figure SMS_89
；
substituting the desired expression of the signal-to-noise ratio into the inequality to obtain a traversal capacity upper bound expression, which is expressed as:
Figure SMS_90
；
wherein C represents the traversal capacity; c (C) up Representing a traversal capacity upper bound; e [. Cndot.]The expression of the desired expression is represented,
Figure SMS_91
representing the transmit power of a single antenna base station, +.>
Figure SMS_92
Represents the average power of R; />
Figure SMS_93
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_94
Representing the distance between the RIS and the device; />
Figure SMS_95
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_96
Representing the RIS to device path loss factor; n (N) 0 Power representing gaussian white noise, +.>
Figure SMS_97
Representing the maximum signal to noise ratio.
Preferably, the average value of the additive Gaussian white noise is 0 and the variance is N 0 ；N 0 Representing the power of gaussian white noise.
Preferably, the apparatus is a mobile cart.
The beneficial effects are that: the fact that a sight distance link exists between a base station and equipment is difficult to ensure for a long time in an industrial workshop is considered in modeling, so that a first communication channel and a second communication channel are arranged in a workshop wireless network communication system, and a calculation result is more in line with the actual situation of the industrial workshop; the signal-to-noise ratio probability density expression and the signal-to-noise ratio expected expression are obtained, and a basis is provided for calculation of the traversal capacity upper bound. The method greatly reduces the complexity of solving, obtains the result similar to the theoretical value, and provides a convenient and effective way for calculating the upper bound of the related traversal capacity of the same type. The method greatly reduces the computational complexity of the solution due to the relatively simple mathematical form of the generalized K distribution.
Drawings
Exemplary embodiments of the present invention may be more fully understood by reference to the following drawings. The accompanying drawings are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the application, and not constitute a limitation of the invention. In the drawings, like reference numerals generally refer to like parts or steps.
Fig. 1 is a flow chart of a method provided according to an exemplary embodiment of the present application.
FIG. 2 is a schematic diagram of a RIS-assisted wireless network communication system for workshops according to an exemplary embodiment of the present application.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It is noted that unless otherwise indicated, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this application belongs.
In addition, the terms "first" and "second" etc. are used to distinguish different objects and are not used to describe a particular order. Furthermore, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those listed steps or elements but may include other steps or elements not listed or inherent to such process, method, article, or apparatus.
The embodiment of the application provides a method for calculating the upper bound of the traversal capacity of a wireless network in a workshop assisted by RIS, which is described below with reference to the accompanying drawings.
The traditional analysis method mostly adopts a mathematical model of component channel fading, and adopts strict mathematical calculation to acquire performance indexes, so that the mathematical calculation is quite complex, and the calculated amount of the RIS reflection element is multiplied along with the increase of the number of the RIS reflection element, which certainly increases the complexity of performance analysis; thus, referring to fig. 1, the present embodiment illustrates a method for calculating a wireless network traversal capacity upper bound of a workshop assisted by RIS, where the method may include the following steps:
s1: establishing an RIS-assisted workshop wireless network communication system, wherein a single antenna base station communicates with equipment in a workshop through the RIS, as shown in fig. 2; in this embodiment, the equipment in the plant is a mobile cart in the plant.
S2: setting a first communication channel and a second communication channel based on the communication relation among the single antenna base station, the RIS and the equipment; establishing a mathematical model of the equipment receiving signal according to the first communication channel and the second communication channel; obtaining a maximum signal-to-noise ratio expression according to the mathematical model of the received signal of the equipment;
specifically, a channel is set for communication between the single antenna base station and the RIS, and is recorded as a first communication channel; a channel is set for communication between the RIS and devices within the plant, denoted as a second communication channel.
The first communication channel expression is:
Figure SMS_98
；
the second communication channel expression is:
Figure SMS_99
；
wherein ,
Figure SMS_100
representing a first communication channel; />
Figure SMS_101
Representing the amplitude of the first communication channel matrix; />
Figure SMS_102
Representing the phase of the first communication channel matrix; />
Figure SMS_103
Representing a second communication channel; />
Figure SMS_104
Representing the amplitude of the second communication channel matrix;
Figure SMS_105
representing the phase of the second communication channel matrix; i denotes an ith reflecting element via the reflecting surface of the RIS; j represents an imaginary unit. />
The first communication channel and the second communication channel are mutually independent and all follow Rayleigh distribution, so that a mathematical model of equipment receiving signals is built according to the first communication channel and the second communication channel; the mathematical model expression of the device receiving signal is as follows:
Figure SMS_106
；
wherein ,
Figure SMS_109
indicating that the device receives the signal,/-, is>
Figure SMS_111
Representing the transmit power of a single antenna base station, +.>
Figure SMS_114
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_108
Representing the distance between the RIS and the device; />
Figure SMS_110
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_113
Representing the RIS to device path loss factor; n represents the total number of reflective elements in the reflective surface via the RIS; i denotes an ith reflecting element via the reflecting surface of the RIS; />
Figure SMS_115
Representing a first communication channel; />
Figure SMS_107
Representing the reflection coefficient of the ith reflective element of the RIS; />
Figure SMS_112
Representing a second communication channel; x represents the transmit signal of a single antenna base station and n represents additive white gaussian noise.
The process of obtaining the maximum signal-to-noise ratio expression is as follows:
the expression of the reflection coefficient of the ith reflection element of RIS is:
Figure SMS_116
；
wherein ,
Figure SMS_117
representing the reflection coefficient of the ith reflective element of the RIS; />
Figure SMS_118
Representing the signal amplitude attenuation coefficient caused by the reflection of the ith reflecting element; />
Figure SMS_119
Indicating the phase change caused by the reflection of the ith reflecting element; j represents an imaginary unit;
in combination with the first communication channel expression, the second communication channel expression, and the reflection coefficient expression, the device received signal mathematical model expression may be transformed into:
Figure SMS_120
；
the method is characterized by comprising the following steps of:
Figure SMS_121
；
the expression of the signal-to-noise ratio received by the device is:
Figure SMS_122
；
taking out
Figure SMS_123
，/>
Figure SMS_124
The maximum signal-to-noise ratio expression is obtained, which is:
Figure SMS_125
；
Figure SMS_126
；
wherein ,
Figure SMS_128
representing the device received signal, gamma representing the signal-to-noise ratio of the device received,/->
Figure SMS_132
Represents the maximum signal-to-noise ratio,/-, for example>
Figure SMS_136
Representing the transmit power of a single antenna base station, +.>
Figure SMS_130
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_134
Representing the distance between the RIS and the device; />
Figure SMS_137
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_139
Representing RIS to device path lossConsumption factor; n represents the total number of reflective elements in the reflective surface via the RIS; i denotes an ith reflecting element via the reflecting surface of the RIS; x represents a transmitting signal of a single antenna base station, and n represents additive white gaussian noise; />
Figure SMS_127
Representing a first communication channel; n (N) 0 Power representing gaussian white noise; />
Figure SMS_131
Representing the amplitude of the first communication channel matrix; />
Figure SMS_135
Representing the phase of the first communication channel matrix; />
Figure SMS_138
Representing a second communication channel; />
Figure SMS_129
Representing the amplitude of the second communication channel matrix; />
Figure SMS_133
Representing the phase of the second communication channel matrix; i denotes an ith reflecting element via the reflecting surface of the RIS; j represents an imaginary unit.
S3: obtaining a signal-to-noise ratio probability density expression according to the maximum signal-to-noise ratio expression and according to the property of generalized K distribution;
specifically, the process of obtaining the signal-to-noise ratio probability density expression is as follows:
based on the expression
Figure SMS_140
Let->
Figure SMS_141
The method comprises the steps of carrying out a first treatment on the surface of the Since the first communication channel and the second communication channel are mutually independent Rayleigh fading channels, the first communication channel and the second communication channel are +.>
Figure SMS_142
and />
Figure SMS_143
Is a Rayleigh random variable independent of each other, R i Is expressed as:
Figure SMS_144
；
wherein ,
Figure SMS_145
r represents i Probability density functions of (2); />
Figure SMS_146
A 0 th order Bessel function representing a second type of correction; r represents a variable;
due to the R i Since the probability density function of (2) follows the generalized K distribution, the probability density function of R is obtained based on the property of the generalized K distribution, expressed as:
Figure SMS_147
；
wherein ,
Figure SMS_148
；
Figure SMS_149
；
Figure SMS_150
；
Figure SMS_151
；
Figure SMS_152
；
combining the maximum signal-to-noise ratio expression and the probability density function of R to obtain a signal-to-noise ratio probability density expression expressed as:
Figure SMS_153
；/>
Figure SMS_154
；
wherein ,
Figure SMS_157
representing the probability density of the signal to noise ratio, and gamma represents the signal to noise ratio received by the equipment; />
Figure SMS_162
Is the second moment of the R,
Figure SMS_166
for the fourth moment of R->
Figure SMS_156
For the sixth moment of R->
Figure SMS_159
Representing the transmit power of a single antenna base station, +.>
Figure SMS_163
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_167
Representing the distance between the RIS and the device; />
Figure SMS_155
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_161
Representing the RIS to device path loss factor; n (N) 0 Power representing gaussian white noise; />
Figure SMS_165
、/>
Figure SMS_168
Respectively represent k W 、m W Gamma functions of (a); />
Figure SMS_158
Represents the average power of R; />
Figure SMS_160
Representing correction of second kind>
Figure SMS_164
The order bessel function.
S4: obtaining an expected expression of the signal to noise ratio according to the probability density expression of the signal to noise ratio and based on the mathematical relationship between the expected and probability density;
specifically, the process of obtaining the desired expression of the signal-to-noise ratio is:
based on the SNR probability density expression and the k-m order Bessel function of the second type correction, a SNR probability density conversion formula is obtained and recorded as:
Figure SMS_169
；
wherein ,
Figure SMS_170
representing the probability density of the signal to noise ratio, and gamma represents the signal to noise ratio received by the equipment; />
Figure SMS_171
、/>
Figure SMS_172
Respectively represent k W 、m W Gamma functions of (a); />
Figure SMS_173
Representing the Meijer-G function;
and then deducing a signal to noise ratio probability density conversion formula through the property of the Meijer-G function to obtain a probability density deduction formula, which is recorded as:
Figure SMS_174
；
the mathematical relationship between the expected and probability density is:
Figure SMS_175
；
substituting a probability density deduction formula into a mathematical relation between expected and probability density to obtain an expected expression of signal to noise ratio before deduction, and marking as follows:
Figure SMS_176
；
calculating the expected expression of the signal to noise ratio before deduction through scientific calculation software matetica to obtain the expected expression of the signal to noise ratio, wherein the expected expression is expressed as follows:
Figure SMS_177
；
wherein ,
Figure SMS_178
representing the desired expression->
Figure SMS_179
Representing the transmit power of a single antenna base station, +.>
Figure SMS_180
Represents the average power of R; />
Figure SMS_181
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_182
Representing the distance between the RIS and the device; />
Figure SMS_183
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_184
Representing the RIS to device path loss factor; n (N) 0 Representing the power of gaussian white noise.
S5: obtaining an upper bound expression of the traversal capacity of the workshop wireless network communication system based on the expected expression of the signal-to-noise ratio; and calculating the wireless network traversal capacity upper bound through the traversal capacity upper bound expression.
Specifically, the process of obtaining the traversal capacity upper bound expression is:
the expression of the traversal capacity is:
Figure SMS_185
；
the expression of the traversal capacity is converted to an inequality using the Jensen inequality, expressed as:
Figure SMS_186
；
substituting the desired expression of the signal-to-noise ratio into the inequality to obtain a traversal capacity upper bound expression, which is expressed as:
Figure SMS_187
；
wherein C represents the traversal capacity; c (C) up Representing a traversal capacity upper bound; e [. Cndot.]The expression of the desired expression is represented,
Figure SMS_188
representing the transmit power of a single antenna base station, +.>
Figure SMS_189
Represents the average power of R; />
Figure SMS_190
Representing the distance between the single antenna base station and the RIS; />
Figure SMS_191
Representing the distance between the RIS and the device; />
Figure SMS_192
Representing the path loss factor from the single antenna base station to the RIS; />
Figure SMS_193
Representing the RIS to device path loss factor; n (N) 0 Power representing gaussian white noise, +.>
Figure SMS_194
Representing the maximum signal to noise ratio.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the embodiments, and are intended to be included within the scope of the claims and description.

Claims (10)

1. The RIS assisted workshop wireless network traversal capacity upper bound calculation method is characterized by comprising the following steps of:
s1: establishing an RIS-assisted workshop wireless network communication system, wherein a single antenna base station communicates with equipment in a workshop through the RIS;
s2: setting a first communication channel and a second communication channel based on the communication relation among the single antenna base station, the RIS and the equipment; establishing a mathematical model of the equipment receiving signal according to the first communication channel and the second communication channel; obtaining a maximum signal-to-noise ratio expression according to the mathematical model of the received signal of the equipment;
s3: obtaining a signal-to-noise ratio probability density expression according to the maximum signal-to-noise ratio expression and according to the property of generalized K distribution;
s4: obtaining an expected expression of the signal to noise ratio according to the probability density expression of the signal to noise ratio and based on the mathematical relationship between the expected and probability density;
s5: obtaining an upper bound expression of the traversal capacity of the workshop wireless network communication system based on the expected expression of the signal-to-noise ratio; and calculating the wireless network traversal capacity upper bound through the traversal capacity upper bound expression.
2. The RIS-assisted wireless network traversal capacity upper bound calculation method according to claim 1, wherein in S2, a channel is set for the communication between the single antenna base station and the RIS, denoted as a first communication channel; a channel is set for communication between the RIS and devices within the plant, denoted as a second communication channel.
3. The RIS assisted wireless network traversal capacity upper bound calculation of claim 2, wherein the first communication channel expression is:
Figure QLYQS_1
；
the second communication channel expression is:
Figure QLYQS_2
；
wherein ,
Figure QLYQS_3
representing a first communication channel; />
Figure QLYQS_4
Representing the amplitude of the first communication channel matrix; />
Figure QLYQS_5
Representing the phase of the first communication channel matrix; />
Figure QLYQS_6
Representing a second communication channel; />
Figure QLYQS_7
Representing the amplitude of the second communication channel matrix;
Figure QLYQS_8
representing the phase of the second communication channel matrix; i denotes an ith reflecting element via the reflecting surface of the RIS; j represents an imaginary unit.
4. A RIS-assisted inter-vehicle wireless network traversal capacity upper bound calculation method according to claim 3, wherein in S2, the first communication channel and the second communication channel are independent of each other and all obey rayleigh distribution, so that a mathematical model of the device received signal is built according to the first communication channel and the second communication channel; the mathematical model expression of the device receiving signal is as follows:
Figure QLYQS_9
；
wherein ,
Figure QLYQS_12
indicating that the device receives the signal,/-, is>
Figure QLYQS_15
Representing the transmit power of a single antenna base station, +.>
Figure QLYQS_17
Representing the distance between the single antenna base station and the RIS; />
Figure QLYQS_11
Representing the distance between the RIS and the device; />
Figure QLYQS_14
Representing the path loss factor from the single antenna base station to the RIS; />
Figure QLYQS_16
Indicating RIS to device path loss causeA seed; n represents the total number of reflective elements in the reflective surface via the RIS; i denotes an ith reflecting element via the reflecting surface of the RIS; />
Figure QLYQS_18
Representing a first communication channel; />
Figure QLYQS_10
Representing the reflection coefficient of the ith reflective element of the RIS; />
Figure QLYQS_13
Representing a second communication channel; x represents the transmit signal of a single antenna base station and n represents additive white gaussian noise. />
5. The RIS-aided workshop wireless network traversal capacity upper bound calculation method of claim 4, wherein in S2, the process of obtaining the maximum signal-to-noise ratio expression is:
the expression of the reflection coefficient of the ith reflection element of RIS is:
Figure QLYQS_19
；
wherein ,
Figure QLYQS_20
representing the reflection coefficient of the ith reflective element of the RIS; />
Figure QLYQS_21
Representing the signal amplitude attenuation coefficient caused by the reflection of the ith reflecting element; />
Figure QLYQS_22
Indicating the phase change caused by the reflection of the ith reflecting element; j represents an imaginary unit;
in combination with the first communication channel expression, the second communication channel expression, and the reflection coefficient expression, the device received signal mathematical model expression may be transformed into:
Figure QLYQS_23
；
the method is characterized by comprising the following steps of:
Figure QLYQS_24
；
the expression of the signal-to-noise ratio received by the device is:
Figure QLYQS_25
；
taking out
Figure QLYQS_26
，/>
Figure QLYQS_27
The maximum signal-to-noise ratio expression is obtained, which is:
Figure QLYQS_28
；
Figure QLYQS_29
；
wherein ,
Figure QLYQS_31
representing the device received signal, gamma representing the signal-to-noise ratio of the device received,/->
Figure QLYQS_34
Represents the maximum signal-to-noise ratio,/-, for example>
Figure QLYQS_38
Representing the transmit power of a single antenna base station, +.>
Figure QLYQS_33
Representing the distance between the single antenna base station and the RIS; />
Figure QLYQS_35
Representing the distance between the RIS and the device; />
Figure QLYQS_39
Representing the path loss factor from the single antenna base station to the RIS; />
Figure QLYQS_41
Representing the RIS to device path loss factor; n represents the total number of reflective elements in the reflective surface via the RIS; i denotes an ith reflecting element via the reflecting surface of the RIS; x represents a transmitting signal of a single antenna base station, and n represents additive white gaussian noise; />
Figure QLYQS_30
Representing a first communication channel; n (N) 0 Power representing gaussian white noise;
Figure QLYQS_37
representing the amplitude of the first communication channel matrix; />
Figure QLYQS_40
Representing the phase of the first communication channel matrix; />
Figure QLYQS_42
Representing a second communication channel; />
Figure QLYQS_32
Representing the amplitude of the second communication channel matrix; />
Figure QLYQS_36
Representing the phase of the second communication channel matrix; i denotes an ith reflecting element via the reflecting surface of the RIS; j represents an imaginary unit.
6. The RIS-aided workshop wireless network traversal capacity upper bound calculation method of claim 5, wherein in S3, the process of obtaining the snr probability density expression is:
based on the expression
Figure QLYQS_43
Let->
Figure QLYQS_44
The method comprises the steps of carrying out a first treatment on the surface of the Since the first communication channel and the second communication channel are mutually independent Rayleigh fading channels, the first communication channel and the second communication channel are +.>
Figure QLYQS_45
and />
Figure QLYQS_46
Is a Rayleigh random variable independent of each other, R i Is expressed as:
Figure QLYQS_47
；
wherein ,
Figure QLYQS_48
r represents i Probability density functions of (2); />
Figure QLYQS_49
A 0 th order Bessel function representing a second type of correction; r represents a variable;
due to the R i Since the probability density function of (2) follows the generalized K distribution, the probability density function of R is obtained based on the property of the generalized K distribution, expressed as:
Figure QLYQS_50
；
wherein ,
Figure QLYQS_51
；
Figure QLYQS_52
；
Figure QLYQS_53
；
Figure QLYQS_54
；
Figure QLYQS_55
；
combining the maximum signal-to-noise ratio expression and the probability density function of R to obtain a signal-to-noise ratio probability density expression expressed as:
Figure QLYQS_56
；
Figure QLYQS_57
；
wherein ,
Figure QLYQS_60
representing the probability density of the signal to noise ratio, and gamma represents the signal to noise ratio received by the equipment; />
Figure QLYQS_64
Is the second moment of the R,
Figure QLYQS_68
for the fourth moment of R->
Figure QLYQS_59
For the sixth moment of R->
Figure QLYQS_65
Representing the transmit power of a single antenna base station, +.>
Figure QLYQS_69
Representing the distance between the single antenna base station and the RIS; />
Figure QLYQS_71
Representing the distance between the RIS and the device; />
Figure QLYQS_58
Representing the path loss factor from the single antenna base station to the RIS; />
Figure QLYQS_63
Representing the RIS to device path loss factor; n (N) 0 Power representing gaussian white noise; />
Figure QLYQS_67
、/>
Figure QLYQS_70
Respectively represent k W 、m W Gamma functions of (a); />
Figure QLYQS_61
Represents the average power of R; />
Figure QLYQS_62
Representing correction of second kind>
Figure QLYQS_66
The order bessel function.
7. The RIS-aided workshop wireless network traversal capacity upper bound calculation method of claim 6, wherein in S4, the process of obtaining the desired expression for the signal-to-noise ratio is:
based on the SNR probability density expression and the k-m order Bessel function of the second type correction, a SNR probability density conversion formula is obtained and recorded as:
Figure QLYQS_72
；
wherein ,
Figure QLYQS_73
representing the probability density of the signal to noise ratio, and gamma represents the signal to noise ratio received by the equipment; />
Figure QLYQS_74
、/>
Figure QLYQS_75
Respectively represent k W 、m W Gamma functions of (a); />
Figure QLYQS_76
Representing the Meijer-G function;
and then deducing a signal to noise ratio probability density conversion formula through the property of the Meijer-G function to obtain a probability density deduction formula, which is recorded as:
Figure QLYQS_77
；
the mathematical relationship between the expected and probability density is:
Figure QLYQS_78
；
substituting a probability density deduction formula into a mathematical relation between expected and probability density to obtain an expected expression of signal to noise ratio before deduction, and marking as follows:
Figure QLYQS_79
；
calculating the expected expression of the signal to noise ratio before deduction through scientific calculation software matetica to obtain the expected expression of the signal to noise ratio, wherein the expected expression is expressed as follows:
Figure QLYQS_80
；
wherein ,
Figure QLYQS_81
representing the desired expression->
Figure QLYQS_82
Representing the transmit power of a single antenna base station, +.>
Figure QLYQS_83
Represents the average power of R;
Figure QLYQS_84
representing the distance between the single antenna base station and the RIS; />
Figure QLYQS_85
Representing the distance between the RIS and the device; />
Figure QLYQS_86
Representing the path loss factor from the single antenna base station to the RIS; />
Figure QLYQS_87
Representing the RIS to device path loss factor; n (N) 0 Representing the power of gaussian white noise.
8. The RIS-aided workshop wireless network traversal capacity upper bound calculation method of claim 7, wherein in S5, the process of obtaining the traversal capacity upper bound expression is:
the expression of the traversal capacity is:
Figure QLYQS_88
；
the expression of the traversal capacity is converted to an inequality using the Jensen inequality, expressed as:
Figure QLYQS_89
；
substituting the desired expression of the signal-to-noise ratio into the inequality to obtain a traversal capacity upper bound expression, which is expressed as:
Figure QLYQS_90
；
wherein C represents the traversal capacity; c (C) up Representing a traversal capacity upper bound; e [. Cndot.]The expression of the desired expression is represented,
Figure QLYQS_91
representing the transmit power of a single antenna base station, +.>
Figure QLYQS_92
Represents the average power of R; />
Figure QLYQS_93
Representing the distance between the single antenna base station and the RIS; />
Figure QLYQS_94
Representing the distance between the RIS and the device; />
Figure QLYQS_95
Representing the path loss factor from the single antenna base station to the RIS; />
Figure QLYQS_96
Representing the RIS to device path loss factor; n (N) 0 Power representing gaussian white noise, +.>
Figure QLYQS_97
Representing the maximum signal to noise ratio.
9. The RIS-assisted vehicle-to-vehicle wireless network traversal capacity upper bound of claim 5, wherein the additive Gaussian white noise has a mean of 0 and a variance of N 0 ；N 0 Representing the power of gaussian white noise.
10. The RIS-aided workshop wireless network traversal capacity upper bound calculation method of claim 1, wherein the device is a mobile cart.
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Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2562952A1 (en) * 2011-08-24 2013-02-27 Research In Motion Limited A method of determining channel state information
US20130051490A1 (en) * 2011-08-24 2013-02-28 Research In Motion Limited Method of determining channel state information
US20150016344A1 (en) * 2012-05-04 2015-01-15 Huawei Technologies Co., Ltd. Signal Transmission Method, Communications Equipment, and System
US20160165466A1 (en) * 2014-12-05 2016-06-09 Lg Electronics Inc. Method and apparatus for feeding partial cqi back by terminal in wireless communication system
WO2021239311A1 (en) * 2020-05-29 2021-12-02 British Telecommunications Public Limited Company Ris-assisted wireless communications
CN114337871A (en) * 2021-12-29 2022-04-12 北京交通大学 RIS auxiliary channel simulation and channel capacity analysis method
CN114826450A (en) * 2022-05-17 2022-07-29 南京航空航天大学 Statistical channel-based traversal rate analysis method and phase optimization method in STAR-RIS auxiliary NOMA system
CN114828151A (en) * 2022-05-17 2022-07-29 南京航空航天大学 Interruption probability and traversal capacity performance analysis method of STAR-RIS auxiliary NOMA system under hardware damage
WO2022164596A1 (en) * 2021-01-28 2022-08-04 Qualcomm Incorporated Reconfigurable intelligent surface (ris)-aided ue passive rf sensing
CN114919627A (en) * 2022-06-17 2022-08-19 重庆交通大学 Train positioning and tracking method based on RIS technology
CN114980154A (en) * 2021-11-26 2022-08-30 北京信息科技大学 Design method of NOMA communication system based on simultaneous transmission and reflection super surface
WO2022186933A1 (en) * 2021-03-05 2022-09-09 Qualcomm Incorporated Ris-aided and non-ris-aided uplink signaling
WO2023283753A1 (en) * 2021-07-12 2023-01-19 Qualcomm Incorporated Techniques for passive communication of a reflective surface with a base station

Patent Citations (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130051490A1 (en) * 2011-08-24 2013-02-28 Research In Motion Limited Method of determining channel state information
EP2562952A1 (en) * 2011-08-24 2013-02-27 Research In Motion Limited A method of determining channel state information
US20150016344A1 (en) * 2012-05-04 2015-01-15 Huawei Technologies Co., Ltd. Signal Transmission Method, Communications Equipment, and System
US20160165466A1 (en) * 2014-12-05 2016-06-09 Lg Electronics Inc. Method and apparatus for feeding partial cqi back by terminal in wireless communication system
WO2021239311A1 (en) * 2020-05-29 2021-12-02 British Telecommunications Public Limited Company Ris-assisted wireless communications
WO2022164596A1 (en) * 2021-01-28 2022-08-04 Qualcomm Incorporated Reconfigurable intelligent surface (ris)-aided ue passive rf sensing
WO2022186933A1 (en) * 2021-03-05 2022-09-09 Qualcomm Incorporated Ris-aided and non-ris-aided uplink signaling
WO2023283753A1 (en) * 2021-07-12 2023-01-19 Qualcomm Incorporated Techniques for passive communication of a reflective surface with a base station
CN114980154A (en) * 2021-11-26 2022-08-30 北京信息科技大学 Design method of NOMA communication system based on simultaneous transmission and reflection super surface
CN114337871A (en) * 2021-12-29 2022-04-12 北京交通大学 RIS auxiliary channel simulation and channel capacity analysis method
CN114826450A (en) * 2022-05-17 2022-07-29 南京航空航天大学 Statistical channel-based traversal rate analysis method and phase optimization method in STAR-RIS auxiliary NOMA system
CN114828151A (en) * 2022-05-17 2022-07-29 南京航空航天大学 Interruption probability and traversal capacity performance analysis method of STAR-RIS auxiliary NOMA system under hardware damage
CN114919627A (en) * 2022-06-17 2022-08-19 重庆交通大学 Train positioning and tracking method based on RIS technology

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
LIQIANG HAN等: "Analysis of RIS-Assisted FSO Systems Over F Turbulence Channel With Pointing Errors and Imperfect CSI", IEEE WIRELESS COMMUNICATIONS LETTERS *
李婷婷;雷宏江;赵辉;潘高峰;: "独立不同分布Nakagami-m信道下选择合并分集信噪比的统计特性及其应用", 中国科学:信息科学, no. 04 *
费红霞;潘炼;: "基于改进的基因表达式编程算法在作业车间调度问题中的应用", 计算机与数字工程, no. 06 *

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