Analysis Method for the Performance of Substation Hybrid Relay Communication Assisted by Intelligent Reflecting Surface

Abstract

The present invention provides a method for analyzing the communication performance of a substation hybrid relay assisted by an intelligent reflecting surface, belonging to the field of communication technology, including: combining the channel coefficient h of the wireless communication assisted by the intelligent reflecting surface (IRS) in the second time slot w , using the framework of the method of moments to statistically characterize the channel coefficient of the overall end-to-end channel; obtaining the signal-to-noise ratio received by the access point according to the signal-to-noise ratio of the wireless link and the properties of the LogN distribution; calculating the outage probability of the wireless communication link assisted by the IRS in the second time slot. The present invention conducts mathematical modeling, theoretical performance derivation and analysis on the power line access and IRS-assisted multi-relay hybrid communication system applied to indoor substations, and comparatively analyzes the influence of factors such as the number and position of IRSs, the impulse noise environment, and inaccurate CSI on the reliable performance of the system, providing necessary theoretical support for the application of the multi-IRS-assisted hybrid communication system in indoor Internet of Things

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to a method for analyzing the communication performance of a substation hybrid relay assisted by an intelligent reflecting surface. Background Art

[0002] The digitalization of substations is an important part of the construction of power systems, and it is necessary to use communication technologies to achieve reliable long-distance transmission of information. In indoor environments such as substations, relay protection rooms, GIS rooms, high-voltage rooms, etc. have the characteristics of many devices and complex layouts, resulting in that wireless communication radio frequency signals are easily affected by obstacles, etc., with large penetration losses and difficulties in public network coverage. Power Line Communication (PLC) technology can utilize existing power lines to complete information transmission and reception while transmitting energy, and it is a key communication technology for the "last mile" of the interconnection of Internet of Things devices. Therefore, for scenarios such as joint indoor and outdoor coverage of substations, comprehensively using technologies such as power line access, multi-media hybrid relay, and intelligent reflecting surface (IRS) assisted communication has important practical value for improving the performance of communication systems.

[0003] The research on hybrid networking combining PLC and RIS assisted communication is still in its infancy. Existing research has derived closed-form expressions for the average bit error rate and outage probability for a single IRS assisted hybrid PLC / Radio Frequency (RF) communication system in an indoor scenario of a smart grid. However, in an indoor local environment, in order to balance the needs of indoor wireless coverage and long-distance communication, it is often necessary to study the application of multiple IRSs. For example, the IRS at the indoor central position can enhance the coverage range, while the IRS near the doors and windows can overcome the influence of wireless signal penetration loss. Most of the existing research on the wireless performance assisted by IRS relies on the Independent Identically Distribution (i.i.d.) fading channel model or the deterministic fading channel. For different reflecting unit assisted channels on the same IRS, it can be reasonably assumed to be i.i.d. because these components usually have sub-wavelength dimensions and are closely mounted on the same panel. However, if multiple IRSs are installed at a relatively long distance, the channels corresponding to the reflecting units on these IRSs cannot be assumed to have the same parameter distribution. Therefore, the above analysis methods for single IRS systems and centralized multi-IRSs are not simply applicable to distributed multi-IRS assisted systems. In addition, existing IRS research often assumes that the system uses an ideal channel state method. For a hybrid relay system with PLC access and IRS assisted communication, it is necessary to study system modeling and performance analysis calculation methods based on non-i.i.d. and non-ideal channel estimation, etc. Summary of the Invention

[0004] The object of the present invention is to provide a method for analyzing the performance of a substation hybrid relay communication assisted by an intelligent reflecting surface, so as to solve at least one of the technical problems existing in the above-mentioned background technology.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for analyzing the performance of a substation hybrid relay communication assisted by an intelligent reflecting surface. Power equipment or sensors in the substation perform power line communication with a data concentrator, which is the first time slot; the data concentrator then performs wireless communication with a mobile terminal through an access point, which is the second time slot; wherein, in the second time slot, the data concentrator executes a decode-and-forward protocol, and sends the decoded signal to the mobile terminal or the intelligent reflecting surface through a wireless access point, and the intelligent reflecting surface adjusts the phase of the received signal and then sends it to the mobile terminal; the method includes:

[0007] Combined with the channel coefficient h of the wireless communication assisted by the intelligent reflecting surface IRS in the second time slot w , the moment method framework is adopted to statistically characterize the channel coefficient of the overall end-to-end channel; the signal-to-noise ratio received by the terminal is obtained according to the properties of the wireless link signal-to-noise ratio and the LogN distribution; the outage probability of the wireless communication link assisted by the IRS in the second time slot is calculated according to the signal-to-noise ratio received by the terminal.

[0008] Optionally, statistically characterizing the channel coefficient of the overall end-to-end channel includes: First, approximate h w as a LogN distribution with a mean μ w and a variance ; then match the first moment and the second moment of h w , and obtain the exact values of μ w and σ w by calculating the k-th moment of h w .

[0009] Optionally, considering that the power line transmission adopts a two-term Bernoulli-Gaussian noise model, its transmission error rate is:

[0010]

[0011] Wherein, and respectively represent the error rates without impulse noise and with impulse noise, and p is the probability of the occurrence of impulse noise;

[0012] The error rate of the wireless link assisted by the IRS in the second time slot is represented by , then the error rate P of the system b is:

[0013]

[0014] Under the LogN distribution condition, the channel bit error rate can be calculated, and integral transformation is performed on the calculation formula of the channel bit error rate; for the log-normal distribution models of the first time slot and the second time slot respectively, the overall system bit error rate is obtained.

[0015] Optionally, non-ideal channel estimation affects the performance of the IRS-assisted wireless channel. The outage probability and bit error rate of the wireless link from the access point to the IRS are estimated by calculating the slowly varying angle of arrival and angle of departure, that is, assuming There is ideal channel state information, h nl follows the Nakagami distribution; represents the complex channel coefficient from the access point to the l-th reflecting element of the n-th IRS, h nl represents the amplitude of.

[0016] Optionally, the equation is used to simulate the influence of non-ideal state information. The complex channel coefficient from the l-th reflecting element of the n-th IRS to the mobile terminal is:

[0017]

[0018] where is the known complex channel estimate at the mobile terminal, ζ nl ∈[0, 2π] is the phase of, g nl represents the amplitude of, assuming follows the Nakagami distribution; ρ is the non-ideal channel estimation influence factor, Δg nl is a complex Gaussian random variable with zero mean and variance d rd is the distance between the IRS and node D, and τ is the path loss factor.

[0019] Optionally, in the case of imperfect channel state information (ICSI), the received signal-to-interference-plus-noise ratio at the mobile terminal is represented using the polar coordinates of the complex channel coefficient. Assume that there are N IRSs between the access point and the terminal, and the n-th IRS is equipped with L n passive reflecting elements. At the same time, assume that the IRS uses continuous phase shifters. Assume that the i-th channel coefficient h i all satisfy h i ~Nakagami(m i , Ω i ) distribution (i ∈ {0,..., LN}), m i is the shape parameter of the distribution, Ω i is the spread parameter of the distribution, calculate the k-th moment of h0, where h0 represents the magnitude of the complex channel coefficient of the direct link from the access point to the mobile terminal.

[0020] Optionally, the received signal-to-interference-plus-noise ratio (SINR) at the mobile terminal is expressed in polar coordinates of the complex channel coefficient as:

[0021]

[0022] where P R is the transmit power of the access point, represents the complex channel coefficient of the direct link from the access point to the terminal, represents the complex channel coefficient of the direct link from the access point to the l-th reflecting element of the n-th IRS; h0 and h nl represent the magnitudes of the complex channel coefficients respectively, both following the Nakagami distribution, φ0 and φ nl represent respectively and phase; a nl ∈(0, 1] and θ nl represent the amplitude reflection coefficient and phase shift of the l-th reflecting element of the n-th IRS respectively; n w is the additive white Gaussian noise with mean 0 and variance N w at node D, i.e., n w ~N(0, N w ).

[0023] Optionally, let A nl = a nl h nl , assuming that each channel coefficient satisfies h i ~Nakagami(m i , Ω i ) distribution (i ∈ {0,..., L N}), and is the k-th moment of h0, derive the expression of the probability density function (PDF) of A nl from the expression of the k-th moment of A nl ; since a nl is a constant and h nl follows the Nakagami distribution, based on the k-th moment of A nl , A nl can be fitted to a Gamma distribution, i.e., (where Gamma(α, β) represents the general form of the Gamma distribution, α is the shape parameter of the distribution, and β is the scale parameter of the distribution); then B n The approximate distribution of can be expressed as By using polynomial expansion, the k-th moment of B n can be obtained In a similar way, the k-th moment μ C (k) of C can be obtained

[0024] Optionally, according to the properties of the LogN distribution, it can be known that and both satisfy the lognormal distribution, where μ J and are the mean and variance of the approximate distribution of J, and μ H and are the mean and variance of the approximate distribution of H; according to the Fenton Wilkinson algorithm, it can be obtained that also satisfies the lognormal distribution, that is By using the mean μ ICSI and the standard deviation σ ICSI of the signal-to-noise ratio distribution under ICSI conditions, the outage probability and bit error rate of the wireless channel in the second time slot under non-ideal channel estimation are obtained

[0025] Advantages of the present invention: Mathematical modeling, theoretical performance derivation and analysis are carried out on the power line access and IRS-assisted multi-relay hybrid communication system applied to indoor substations. The influences of factors such as the number and position of IRSs, the impulse noise environment, and inaccurate CSI on the reliable performance of the system are compared and analyzed, providing necessary theoretical support for the application of the multi-IRS-assisted hybrid communication system in indoor Internet of Things

[0026] The advantages of the additional aspects of the present invention will be more clearly given in the following description part, or can be understood through the practice of the present invention Brief Description of the Drawings

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts

[0028] Figure 1 It is a schematic diagram of the system model of the hybrid communication combining power line communication, wireless access point and reconfigurable intelligent surface in the substation described in the embodiment of the present invention

[0029] Figure 2Schematic diagram for graphical demonstration of the true and approximate distributions of the IRS channel coefficient J in the embodiments of the present invention.

[0030] Figure 3 Schematic diagram showing the influence of the number N of IRSs in the embodiments of the present invention on the system bit error rate.

[0031] Figure 4 Schematic diagram showing the influence of the number N of IRSs in the embodiments of the present invention on the system outage probability.

[0032] Figure 5 Schematic diagram showing the influence of the number L of IRS reflection elements on the system outage probability in the embodiments of the present invention.

[0033] Figure 6 Schematic diagram showing the relationship between the position of the IRS and the outage probability in the embodiments of the present invention.

[0034] Figure 7 Schematic diagram for comparing the system reliability performance at different power noise ratio values K in the embodiments of the present invention.

[0035] Figure 8 Schematic diagram for comparing the system reliability performance at different impulse noise probabilities p in the embodiments of the present invention.

[0036] Figure 9 Schematic diagram showing the influence of the non-ideal channel estimation influence factor ρ on the outage probability in the embodiments of the present invention.

[0037] Figure 10 Schematic diagram showing the relationship between the number L of reflection elements and the outage probability during non-ideal channel estimation in the embodiments of the present invention. Detailed implementation manners

[0038] The following details the implementation manners of the present invention. Examples of the implementation manners are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The implementation manners described through the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation to the present invention.

[0039] Those skilled in the art of the present technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention pertains.

[0040] It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art and will not be interpreted with an idealized or overly formal meaning unless defined as such herein.

[0041] Those skilled in the art can understand that, unless specifically stated otherwise, the singular forms "a", "an", "the" and "said" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present invention means the presence of the described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements and / or their groups.

[0042] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. Moreover, the specific features, structures, materials or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0043] To facilitate the understanding of the present invention, the present invention will be further explained below with specific embodiments in conjunction with the drawings, and the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0044] Those skilled in the art should understand that the drawings are only schematic diagrams of the embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0045] Embodiment

[0046] In this embodiment, the model of PLC (Power Line Communication) and wireless hybrid communication is as Figure 1 shown. The power equipment or sensors in the substation perform PLC with the Data Concentrator (DC); the DC then performs wireless communication with the mobile terminal D through the Access Point (AP).

[0047] In this embodiment, taking the downlink communication as an example, a 2-slot transmission mode can be adopted: in the first slot, the device or sensor transmits the signal to the DC through the power line; in the second slot, the DC executes the DF protocol, and transmits the decoded signal to the wireless terminal D or the IRS module through the wireless AP node, and then the IRS adjusts the phase of the received signal and forwards the signal to the mobile terminal D.

[0048] In this embodiment, the PLC link signal is processed as follows:

[0049] With the support of the AP, the power equipment or sensor sends the information of the first slot to the RF link through the power cable. The signal y received by the AP pl is:

[0050]

[0051] Among them, P S is the transmission power of the power equipment or sensor, and H pl = h pl / (d pl ) η , where h pl is the power line fading coefficient, which follows the LogN distribution, that is d pl represents the communication distance between the power equipment / sensor and the AP, η is the distance attenuation factor of the wireless channel, and its value range is 1.6 - 6, and σ pl has a value range of 2 - 3.5 dB.

[0052] The additive noise n pl of the power line channel adopts a two - term Bernoulli - Gaussian noise model. The additive noise of the power line channel consists of background noise and impulse noise, and its probability density function PDF has the following form:

[0053] (1 - p)·N(0, N G ) + p·N(0, N G + N I )(2)

[0054] Among them, N(,) represents the normal distribution, p is the probability of the occurrence of impulse noise, N G and N I represent the power of background noise and impulse noise respectively, then the average total noise power is N pl = N G + pN I . To simplify the noise model, let K = N I / N G represent the ratio of impulse noise power to background noise power. When K = 0, it means there is no influence of impulse noise, and the signal - to - noise ratio (SNR) of the power line branch can be expressed as:

[0055]

[0056] According to the properties of the LogN distribution, when P s / [N G (1 + K)] is a constant, γ pl still follows LogN. Therefore, the signal - to - noise ratio of the power line branch satisfies the following mixed log - normal distribution:

[0057]

[0058] In this embodiment, the wireless link signal is processed as follows:

[0059] In the second time slot transmission, the access point AP directly sends the signal to the mobile terminal D or sends it to the intelligent reflecting surface IRS, and then the IRS reshapes the received signal and reflects it to D. Assume that there are N IRSs between the AP and D, and the nth IRS is equipped with L n passive reflection elements, and the number of reflection elements included in different IRSs may not be the same.

[0060] Let x R be the signal sent by the AP, and it satisfies P R is the transmission power of the AP; the path loss model is considered as:

[0061]

[0062] where d XY represents the distance between two points X and Y, and X and Y can represent nodes such as power equipment, AP, IRS, or D; d0 = 1m represents the reference distance, f c is the carrier frequency, and α is the path loss exponent.

[0063] Assume that the wireless channels assisted by the same IRS are independent and identically distributed, and the reflection unit channels on different IRSs satisfy different parameter distributions. Let represent the complex channel coefficient of the direct link from the AP to D; represent the complex channel coefficient from the AP to the lth reflection element of the nth IRS; represent the complex channel coefficient from the lth reflection element of the nth IRS to D. Among them, h0, h nl and g nl represent the amplitudes of the complex channel coefficients respectively, and both follow the Nakagami distribution. {φ0, φ nl , ψ nl} ∈ [0, 2π] are respectively and phase. a nl ∈ (0, 1] and θ nl represent the amplitude reflection coefficient and phase shift of the lth reflection element of the nth IRS respectively.

[0064] Then the received signal y w at D is:

[0065]

[0066] where, n w is the additive white Gaussian noise with a mean of 0 and a variance of N w at D, that is, n w ~ N(0, Nw )。

[0067] The received signal-to-noise ratio (SNR) at D can be expressed in polar coordinates using the complex channel coefficients as follows:

[0068]

[0069] where δ nl = θ nl - φ nl - ψ nl + φ0 is the phase error of the l-th reflecting element of the n-th IRS. To achieve the maximum SNR, assuming continuous phase shift resolution and ideal channel state information (CSI), i.e., the n-th IRS can generate an accurate phase shift such that the phase error can be zero, i.e., and φ0 satisfies Continuous phase shift resolution can also satisfy such that a composite received signal with the maximum amplitude can be obtained at D. Therefore, the SNR received at D can be re-expressed as:

[0070]

[0071] In this embodiment, the communication performance of a relay system with multiple IRSs is analyzed, including two types: one is the performance analysis of ideal channel estimation, and the other is the performance analysis of non-ideal channel estimation.

[0072] In the performance analysis of ideal channel estimation, the system outage probability is calculated and analyzed as follows:

[0073] According to the system model, the IRS-assisted power line wireless dual-medium communication transmission is divided into two time slots, and the DF relay protocol is adopted. Then the system outage probability P out can be expressed as:

[0074] P out = P out1 + P out2 - 2P out1 P out2 (9)

[0075] P out1 and P out2 are the outage probabilities of the power line in the first time slot and the IRS-assisted wireless link in the second time slot, respectively.

[0076] In the PLC link, according to the definition of the outage probability, given the equivalent SNR and its distribution, the link outage probability can be obtained as:

[0077] P outi = Pr(γ ≤ γth ) = F γ (γ th ) (10)

[0078] Where \(i\in\{1,2\}\); represents the Cumulative Distribution Function (CDF) of the SNR, \(Q(\cdot)\) represents the tail distribution function of the standard normal distribution; \(\gamma\) th is the SNR threshold for signal outage; the minimum rate threshold \(R\) th = log2(\(\gamma\) th + 1).

[0079] For the first time slot power line signal, according to Equation (4) and Equation (10), the expression for the outage probability can be obtained:

[0080]

[0081] where \(\mu\) L1 = ln(P S / N G ) + 2\(\mu\) pl , \(\mu\) L2 = ln(P S / (N G (1 + K))) + 2\(\mu\) pl , are the mean variances of the SNR without impulse noise and with impulse noise, respectively.

[0082] In the IRS-assisted wireless link, let the channel coefficient of the second time slot IRS-assisted wireless communication Using the moment method framework, the channel coefficients of these end-to-end channels can be statistically characterized. First, approximate \(h\) w as a LogN distribution with mean \(\mu\) w and variance. Then match the first and second moments of \(h\) w , i.e., \(E[h\) w = \(E[Z]\) and where \(Z\) is a LogN distribution variable. The expressions for \(\mu\) w and \(\sigma\) w are:

[0083]

[0084]

[0085] Let \(U\) nl = a nl g nl h nl, and μ T (k) = E[T k represent the k-th moments of h0, U nl and T, respectively. represents the k-th moment of h w and its expression is:

[0086]

[0087] By calculating the exact values of μ w and σ w can be obtained. According to the wireless link SNR formula and the properties of LogN, we have:

[0088]

[0089] Let According to Equation (10), the outage probability of the IRS-assisted wireless communication link in the second time slot can be obtained:

[0090]

[0091] In the performance analysis of ideal channel estimation, the system bit error rate is calculated as follows:

[0092] Considering that the power line transmission adopts a two-term Bernoulli-Gaussian noise model, the transmission bit error rate can be expressed according to Equation (4) as:

[0093]

[0094] is the bit error rate of the power line link in the first time slot, and represent the bit error rates without impulse noise and with impulse noise, respectively, and p is the probability of the occurrence of impulse noise; according to the system model, the bit error rate of the IRS-assisted wireless link in the second time slot is represented by then the system bit error rate can be expressed as:

[0095]

[0096] Under the LogN distribution condition, the calculation formula of the channel bit error rate can be obtained:

[0097]

[0098] where A and b are modulation parameters, and in BPSK modulation, A = 1 and b = 2.

[0099] Let j ∈ {L1, L2, γ w}, perform an integral transform on Equation (19):

[0100]

[0101]

[0102] By further deriving the log-normal distribution models for the first time slot and the second time slot respectively, the bit error rate can be obtained:

[0103]

[0104] where, W m , V m and U m have the following forms:

[0105]

[0106]

[0107]

[0108] In the formula, R 1,m , R 2,m and R 3,m are real constants required to approximate exp(exp(-μ j - tσ j + ln(1 / 2))) as the sum of M Gaussian functions by using curve fitting. μ j and σ j represent the mean and variance when j takes L1, L2, γ w respectively.

[0109] According to the above derivation, the bit error rates of no impulse noise, presence of impulse noise, and wireless link can be obtained, and then the system bit error rate can be obtained by using Equations (17) and (18).

[0110] In this embodiment, the performance analysis of non-ideal channel estimation is as follows:

[0111] Non-ideal channel estimation will affect the performance of the IRS-assisted wireless channel. In practical applications, the positions of the AP and the IRS are usually fixed. Therefore, the AP-IRS link can be accurately estimated by calculating the slowly varying angle of arrival and angle of departure, that is, assuming there is ideal CSI, h nl follows the Nakagami distribution. Use equations to simulate the impact of Imperfect Channel State Information (ICSI). The complex channel coefficient from the l-th reflecting element of the n-th IRS to the mobile terminal is:

[0112]

[0113] where is the channel estimate in complex form known at the mobile terminal, and ζ nl ∈ [0, 2π] is 's phase, and g nl represents 's amplitude. It is assumed that follows a Nakagami distribution; ρ is the non-ideal channel estimation impact factor, and Δg nl is a complex Gaussian random variable with zero mean and variance , and d rd is the distance between the IRS and node D, and τ is the path loss factor.

[0114] According to Equation (6), the signal received at D in the ICSI case can be re-expressed as:

[0115]

[0116] The received signal-to-interference plus noise ratio (SINR) at D, expressed in polar coordinates using the complex channel coefficients, is:

[0117]

[0118] where It is also assumed that the IRS uses continuous phase shifters, i.e., Similar to the channel coefficient h w , the distribution of H can also be approximated as a log-normal distribution with mean μ H and variance . To analyze the impact of non-ideal channel estimation on system performance, the statistical characteristics of J also need to be studied.

[0119] Let A nl = a nl h nl , Assume that each channel coefficient satisfies h i ~ Nakagami(m i , Ω i ) distribution (i ∈ {0,..., L N}), and is the k-th moment of h0 and can be expressed as:

[0120]

[0121] According to the definition of the expression for the k-th moment of A nl :

[0122] First, it is necessary to derive A nl 's PDF expression Since a nl is a constant and h nl follows the Nakagami distribution, therefore

[0123]

[0124] Using can be expressed as:

[0125]

[0126] Based on the k-th moment of A nl , A nl can be fitted to a Gamma distribution, that is (where Gamma(α, β) represents the general form of the Gamma distribution, α is the shape parameter of the distribution, and β is the scale parameter of the distribution); then B n 's approximate distribution can be expressed as Using polynomial expansion, the k-th moment of B n can be obtained In a similar way, the k-th moment μ C (k) of C can be obtained

[0127] Since h0 and C are independent, the k-th moment μ J (k) of J can be obtained by applying the binomial theorem through the moments of its addends, that is, h0 and C. Through the above derivation and equations (12) and (13), the mean μ J and variance of the approximate distribution of J can be obtained, that is

[0128] As Figure 2 shown are the PDF and CDF of the actual distribution of the IRS channel coefficient J and the LogN distribution approximated by the method of moments. Observing the curves in the figure, it can be found that the difference between the true distribution and the approximated distribution is not significant, which proves the accuracy of the approximation result and provides convenience for the derivation of the system outage probability and bit error rate expressions

[0129] Observing the composition of equation (27), where and N w / P R ρ 2 are constants, |H| 2 and |J| 2 are random variables, and they are related to the LogN distribution variables H and J. According to the properties of the LogN distribution, it can be known that and All satisfy the lognormal distribution. According to the Fenton Wilkinson (FW) algorithm, we can obtain also satisfies the lognormal distribution, that is Using the mean μ ICSI and standard deviation σ ICSI of the signal-to-noise ratio distribution under ICSI conditions, we can use equations (16) and (20) to obtain the outage probability and bit error rate performance of the second time slot wireless channel in the case of ICSI.

[0130] In this embodiment, to verify the accuracy of the theoretical formula, a Monte Carlo simulation experiment was carried out using Matlab and compared with the theoretical performance of numerical calculations. Unless otherwise specified, the default values in Table 1 are used for the simulation parameter settings. The power of the power line link is normalized, P s = 1, γ1 represents the input signal-to-noise ratio of the power line link; the communication distance is normalized, and let d pl = 1, the distance attenuation factor is η = 2.5; to ensure that the channel fading does not change the average power of the signal, the channel fading envelope energy is normalized, that is Then N w = P S / γ1, N I = K × N G N G = N w / (1 + p·K); the equivalent noise power at the wireless link D is P R represents the signal transmission power at the AP; the shape parameter of the channel coefficient amplitude distribution on the wireless link satisfies the uniform distribution, that is m n ~ U[2, 3], n ∈ {0, 1,..., N}; according to the path loss model, the extended parameter of the Nakagami distribution can be obtained:

[0131]

[0132] where G X and G Y represent the antenna gains at points X and Y respectively, and X and Y represent nodes such as power equipment, AP, IRS or D; the shape parameter m n and the extended parameter Ω XY of the channel coefficient amplitude distribution assisted by the same IRS are the same, and the shape parameters of the channel coefficient amplitude distributions assisted by different IRSs are different, and the calculated extended parameters are also different.

[0133] Table 1

[0134]

[0135] There are N IRSs in the known system, and each IRS contains 25 reflection units. Assume that the AP, IRS, and D are in a two-dimensional Cartesian coordinate system. The coordinates of the fixed AP are (0, 0), and the coordinates of the receiving end are D(100, 0). The positions and heights of the IRSs are randomly set and satisfy a uniform distribution. The distance parameters required for the channel model and path loss can be obtained based on the positions and heights of the devices and terminals. Let γ1 = 35 dB, K = 40, p = 0.1, Figure 3 and Figure 4 shows the variation of the system bit error rate and outage probability with P R as the number of IRSs increases. It can be seen from the figure that the simulation and theoretical curves are basically in agreement, and as the input power increases, the outage probability and bit error rate performance of the system are better; at the same time, the more IRSs there are, the smaller the input power required to achieve the same outage probability / bit error rate. In addition, when γ1 is set to 35 dB, it can be observed that the system outage probability / bit error rate performance will not increase with P R any more after reaching a certain value. This is because the total outage probability / bit error rate of the system is restricted by the power line link in the first time slot, resulting in a certain upper limit of the system performance. The outage probability and bit error rate performance of the PLC can be improved by increasing γ1, and the upper limit of the system performance can be increased.

[0136] Figure 5 shows the variation of the system outage probability with P R when γ1 = 45 dB, K = 40, p = 0.1, and N = 1, with different numbers of IRS reflection elements for assistance; shows the variation of the system outage probability with P R when there is no IRS assistance and communication is only carried out through the direct link (L = 0) between the AP and D, and the transmission quality of the power line channel is improved, and the upper limit of the system performance is increased; it can be clearly observed from the figure that the introduction of the IRS can significantly improve the system outage probability performance, and the better the system performance with the increase in the number of reflection elements.

[0137] In addition, in this embodiment, the influence of the IRS at different positions on the wireless communication performance in the second time slot is compared; where d represents the lateral distance between the AP and the IRS, the height of the IRS is fixed at 5 m, and γ1 = 45 dB. According to Figure 6 it can be observed that the system performance is the best when d = 100, and the performance curves when d = 40 and d = 70 are similar, which indicates that under the same input power, the closer the IRS is to the AP or D, the better the outage probability performance; the closer it is to the middle position between the AP and D (d = 50), the smaller the performance difference. Therefore, in the actual application scenario, the position of the IRS should be planned and deployed in combination with the system performance requirements and actual situation.

[0138] Let P R = 20 dBm, N = 3, Ln = 25, and other parameters adopt default settings. Figure 7 Figure 1 shows the relationship between the theoretical and simulation performance of the system outage probability and bit error rate and the power noise ratio K. At this time, the system performance is mainly determined by the power line channel condition in the first time slot. As can be seen from the figure, when the pulse noise probability p is fixed, the theoretical performance and simulation results of the system under different K values are consistent, verifying the accuracy of the theoretical analysis; at low signal-to-noise ratios, the system performance corresponding to different K values is not much different because the channel quality is poor at low signal-to-noise ratios, and the system performance mainly depends on the average signal-to-noise ratio of the channel, and the influence of K on the outage probability and bit error rate performance is extremely small; while at high signal-to-noise ratios, as the K value increases, the system performance deteriorates significantly because at this time, compared with the background noise, the pulse noise in the power line branch is the main factor affecting the system performance.

[0139] Let P R = 20 dBm, N = 3, L n = 25, and other parameters adopt default settings. Figure 8 Figure 2 shows the relationship between the theoretical and simulation performance of the system outage probability and bit error rate and the pulse noise probability p. At this time, the system performance is mainly determined by the power line channel condition in the first time slot. As can be seen from the figure, when the K value is fixed, the theoretical performance and simulation results of the system under different p values are consistent, verifying the accuracy of the theoretical analysis; at low signal-to-noise ratios, the bit error rate curves corresponding to different p values basically coincide because the channel quality is poor at low signal-to-noise ratios, resulting in the increase of p having little effect on the channel performance; at high signal-to-noise ratios, as p increases from 0.001 to 0.1, the system performance decreases. This is because when the p value increases, the pulse characteristics in the Bernoulli-Gaussian noise model become more obvious, resulting in the deterioration of the system bit error rate performance.

[0140] Finally, in this embodiment, the influence of non-ideal channel estimation on the outage probability performance of the second time slot IRS-assisted wireless link is analyzed. For the convenience of analysis, the number of IRSs N is taken as 1, the coordinates are (95, 2), τ = 4, and other parameters adopt default settings. Figure 9 Figure 3 shows the variation of the outage probability of the second time slot wireless link with the transmit power P when L = 20 and the non-ideal channel estimation influence factor ρ is different. The theoretical performance and simulation results in the figure are consistent, verifying the accuracy of the theoretical analysis; it can be seen from Figure 3 that the outage probability decreases with the increase of P; under the same P condition, reducing ρ has a greater impact on the system performance; the smaller ρ is, that is, the less accurate the CSI is, the gap in outage probability between the ICSI scheme and the perfect CSI (ρ = 1) scheme increases with the increase of P. R variation. The theoretical performance and simulation results in the figure are consistent, verifying the accuracy of the theoretical analysis; from Figure 9 it can be seen that the outage probability decreases with the increase of P R ; under the same P R condition, reducing ρ has a greater impact on the system performance; the smaller ρ is, that is, the less accurate the CSI is, the gap in outage probability between the ICSI scheme and the perfect CSI (ρ = 1) scheme increases with the increase of P R .

[0141] Figure 10 shows the variation of the wireless link outage probability with the transmit power \(P\) in the case of ICSI when the correlation coefficient \(\rho\) is fixed at \(0.98\) and different values of \(L\). R The variation situation Figure 10 The simulation results show that, under the same \(P\) R condition, the outage probability performance improves with the increase of \(L\). This is because the larger \(L\) is, the larger the end-to-end SINR is.

[0142] Comparison Figure 9 with Figure 10 It can be found that when \(L\) and \(\rho\) are fixed, increasing \(P\) R can reduce the outage probability. However, there is a performance lower bound after \(P\) R reaches a certain value, that is, the outage probability of the ICSI scheme will no longer decrease with the increase of \(P\). R This is because, as can be seen from Equation (27), with the increase of \(P\), the interference caused by ICSI in the numerator accounts for the main part; however, the gap between the CSI and ICSI schemes can be narrowed by increasing \(L\) or \(\rho\). R The power line access and IRS-assisted multi-relay hybrid communication system applied to indoor substations is mathematically modeled, and the theoretical performance is deduced and analyzed. The effects of factors such as the number and location of IRSs, the impulsive noise environment, and inaccurate CSI on the system reliability performance are compared and analyzed, providing necessary theoretical support for the application of multi-IRS-assisted hybrid communication systems in indoor Internet of Things. The research results show that increasing the number of IRSs can significantly improve the system reliability performance, but the system performance is limited by the power line communication in the first time slot. Therefore, the power line link performance is analyzed, and it is proved that better performance can be achieved in the weak impulsive noise scenario. In addition, it is proved that inaccurate CSI in the IRS-assisted wireless communication link will seriously affect the system reliability performance and lead to a performance lower bound at high input power, and the performance upper bound value can be improved by increasing \(L\) or improving the accuracy of the system channel estimation.

[0143]

[0144] ​In summary, the intelligent reflecting surface-assisted transmission substation hybrid relay communication performance analysis method described in the embodiments of the present invention constructs a multi-relay hybrid communication system model based on the DF protocol for the scenarios of power line communication signal access and IRS-assisted wireless signal relay, and gives the signal processing process under the hybrid fading conditions of power line communication and IRS reflection links; based on the wireless Nakagami and power line LogN fading distributions, key performance indicators such as the system outage probability and bit error rate are derived; the accuracy of the theoretical formulas is verified by simulation, and the impacts of the number, location, and impulse noise of IRSs on the system performance are compared and analyzed; considering the impact of non-ideal channel estimation at the IRS on the system performance, expressions such as the bit error rate and outage probability of the system are derived using the cumulative distribution function (CDF) of the signal-to-interference-plus-noise ratio, and the impact of channel estimation accuracy on the system performance is compared and analyzed by simulation.

[0145] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can be implemented in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can be implemented in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0146] These computer program instructions can also be loaded onto a computer or other programmable data processing device to perform a series of operation steps on the computer or other programmable device to generate computer-implemented processing, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one process or multiple processes and / or boxes Figure 1 the steps of the functions specified in one box or multiple boxes.

[0147] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that based on the technical solutions disclosed in the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts should be covered within the protection scope of the present invention.

Claims

1. A method for analyzing the communication performance of a substation hybrid relay assisted by an intelligent reflecting surface, characterized in that Power line communication is performed between power equipment or sensors in a substation and a data concentrator, which is the first time slot; The data concentrator then performs wireless communication with a mobile terminal through an access point, which is the second time slot; wherein, in the second time slot, the data concentrator executes a decode-and-forward protocol, and sends the decoded signal to the mobile terminal or the intelligent reflecting surface through the wireless access point, and the intelligent reflecting surface adjusts the phase of the received signal and then sends it to the mobile terminal; The method includes: Combined with the channel coefficient \(h\) of the second-slot intelligent reflecting surface (IRS)-assisted wireless communication w , using the method of moments framework, statistically characterize the channel coefficient of the overall end-to-end channel; obtain the signal-to-noise ratio (SNR) received by the mobile terminal according to the properties of the wireless link SNR and the LogN distribution; calculate the outage probability of the second-slot IRS-assisted wireless communication link based on the SNR received by the mobile terminal. In the case of non-ideal channel state information, the received channel signal-to-noise-plus-interference ratio (SINR) at the mobile terminal is represented using the polar coordinates of the complex channel coefficients. Assume that there are N IRSs between the access point and the mobile terminal, and the nth IRS is equipped with L n passive reflecting elements. At the same time, assume that the IRS uses continuous phase shifters. Assume that each channel coefficient satisfies h i ~ Nakagami(m i ,Ω i ) distribution, i ∈ {0,..., L N}, m i is the shape parameter of the distribution, and Ω i is the spread parameter of the distribution. Calculate the kth moment of h0, where h0 represents the magnitude of the complex channel coefficient of the direct link from the access point to the mobile terminal; The received channel signal-to-noise-plus-interference ratio at the mobile terminal is represented in polar coordinates using the complex channel coefficient as: where P R is the transmit power of the access point, represents the complex channel coefficient of the direct link from the access point to the mobile terminal, represents the complex channel coefficient from the access point to the l-th reflecting element of the n-th IRS; h0 and h nl represent the magnitudes of the complex channel coefficients respectively, both following the Nakagami distribution, φ0 and φ nl represent respectively and phase; a nl ∈(0,1] and θ nl represent the amplitude reflection coefficient and phase shift of the l-th reflecting element of the n-th IRS respectively; n w is the additive white Gaussian noise with mean 0 and variance N w at the mobile terminal, that is, n w ~N(0,N w ).

2. The method for analyzing the performance of the substation hybrid relay communication assisted by the intelligent reflecting surface according to claim 1, wherein Statistically characterize the channel coefficients of the overall end-to-end channel, including: First, approximate h w as a LogN distribution with mean μ w and variance ; then match the first and second moments of h w , and by calculating the k-th moment of h w , further obtain the exact values of μ w and σ w .

3. The method for analyzing the performance of a substation hybrid relay communication assisted by an intelligent reflecting surface according to claim 1, wherein Considering that the power line transmission adopts a two-term Bernoulli-Gaussian noise model, its transmission bit error rate is as follows: wherein, and respectively represent the bit error rate without impulse noise and with impulse noise, and p is the probability of the occurrence of impulse noise; The bit error rate of the second time-slot IRS-assisted wireless link is denoted by , and the bit error rate of the system is as follows: Under the LogN distribution condition, the channel bit error rate can be calculated, and integral transformation is performed on the calculation formula of the channel bit error rate; for the lognormal distribution models of the first time slot and the second time slot respectively, the overall system bit error rate is obtained.

4. The method for analyzing the performance of the substation hybrid relay communication assisted by the intelligent reflecting surface according to claim 3, wherein Non-ideal channel estimation can affect the performance of IRS-assisted wireless channels. By calculating the slowly varying angles of arrival and departure, the outage probability and bit error rate of the wireless link from the access point to the IRS are estimated, that is, assuming to have ideal channel state information, h nl follows the Nakagami distribution; represents the complex channel coefficient from the access point to the l-th reflecting element of the n-th IRS, h nl represents the magnitude of.

5. The method for analyzing the communication performance of a substation hybrid relay assisted by an intelligent reflecting surface according to claim 4, wherein Simulate the influence of non-ideal state information using equations. The complex channel coefficient from the l-th reflection element of the n-th IRS to the mobile terminal is as follows: where, is the channel estimate in complex form known at the mobile terminal, ζ nl ∈[0,2π] is 's phase, g nl represents 's amplitude. Assume that follows a Nakagami distribution; ρ is the non-ideal channel estimation impact factor, Δg nl is a complex Gaussian random variable with zero mean and variance , d rd is the distance between the IRS and the mobile terminal, and τ is the path loss factor.

6. The method for analyzing the performance of a substation hybrid relay communication assisted by an intelligent reflecting surface according to claim 5, wherein Let A nl = a nl h nl , Assume that the i-th channel coefficient h i satisfies h i ~ Nakagami(m i , Ω i ) distribution, i ∈ {0,..., L N}}, and is the k-th moment of h0. Derive the expression of the probability density function of A nl from the expression of the k-th moment of A nl ; Since a nl is a constant and h nl follows the Nakagami distribution, based on the k-th moment of A nl , A nl can be fitted to a Gamma distribution, that is where Gamma(α, β) represents the general form of the Gamma distribution, α is the shape parameter of the distribution, and β is the scale parameter of the distribution; then the approximate distribution of B n can be expressed as Using polynomial expansion, the k-th moment of B n can be obtained In a similar way, the k-th moment μ C (k) of C can be obtained.

7. The method for analyzing the performance of a substation hybrid relay communication assisted by an intelligent reflecting surface according to claim 6, wherein According to the properties of the LogN distribution, it can be known that and both satisfy the lognormal distribution, where μ J and are the mean and variance of the J approximate distribution, and μ H and are the mean and variance of the H approximate distribution; According to the Fenton Wilkinson algorithm, it can be obtained that also satisfies the lognormal distribution, that is Using the mean μ of the signal-to-noise ratio distribution under ICSI conditions ICSI and the standard deviation σ ICSI , the outage probability and bit error rate of the wireless channel in the second time slot under non-ideal channel estimation are obtained.

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