CN110620628B - Multi-dimensional lognormal approximate wireless and power line relay communication performance calculation method - Google Patents

Abstract

The invention provides a multidimensional lognormal approximate wireless and power line relay communication performance calculation method. The method comprises the following steps: in a one-way relay system comprising a sending terminal S, a relay node R and a destination terminal D, a first branch between the sending terminal S and the relay node R adopts wireless communication, and a second branch between the relay node R and the destination terminal D adopts power line communication; the square of the wireless channel fading coefficient is approximated to multi-dimensional LogN distribution by using a multi-dimensional LogN approximation algorithm, the system performance analysis problem under hybrid fading is converted into a LogN variable and approximate calculation problem under the same distribution of LogN-LogN, and then a Probability Density Function (PDF) parameter of the total signal-to-noise ratio of the system under the conditions of hybrid fading and impulse noise is deduced. The wireless and power line dual-medium relay communication technology can integrate the advantageous communication capacity and resources, improve the overall performance of the system, and has wide development prospect in the smart grid and the Internet of things.

Description

Multi-dimensional lognormal approximate wireless and power line relay communication performance calculation method

Technical Field

The invention relates to the technical field of wireless communication, in particular to a multidimensional lognormal approximate wireless and power line relay communication performance calculation method.

Background

Power Line Communication (PLC) and wireless communication technology are important components of power distribution network communication, and have wide application prospects in the fields of intelligent power utilization, home internet of things and the like. In addition to the basic requirements of speed, reliability and the like in practical application, the development of the power line communication technology needs to consider factors such as construction cost, compatibility, complexity and the like in combination with the current situation. For example, the home internet of things generally needs to pay attention to the problems of mobility, energy consumption, flexibility, cost and the like of communication.

The power line communication can utilize the existing power line network in the building, a new line does not need to be deployed, the construction cost is low, and the signal transmission is not easily influenced by the environment such as the building. However, the power line communication module needs to be fixed on the socket, and mobile access cannot be realized; moreover, the power line channel is susceptible to line impedance, fading, impulse noise, and the like, and the remote communication capability needs to be improved. On the other hand, although the wireless communication mode is flexible in access and simple in networking, wireless high-frequency signals are easily shielded by barriers such as doors, windows and walls, and the signal fading is large. The wireless and PLC have the characteristics, so the advantages can be complemented by utilizing the power line and the wireless dual-medium cooperative communication technology, the construction cost is saved, and the overall performance of the system is improved.

In order to improve the performance of the PLC and realize long-distance reliable communication, domestic and foreign research focuses on the PLC technology based on cooperative relaying, including physical layer cooperation technologies based on decode-and-forward (DF), amplify-and-forward (AF), diversity combining, and the like. Currently, the advantages of cooperative communication in terms of extending coverage and improving performance have been recognized. The PLC technology based on multi-hop relay, dual-media parallel communication and hybrid relay is an important research content. Cheng et al respectively adopts a multipath model and a transmission line theoretical model to research the capacity limit and optimal power distribution problem of a PLC system based on an AF protocol under the condition of limited power bandwidth. The power line model adopts a multipath model based on measured data. The latest research hotspot models power line channel fading as a multidimensional log normal (Lognormal, LogN) model. Anlit et al analyzed the system performance of pure power line communication when AF relay and DF relay were employed, where multiplicative fading coefficients of the PLC were modeled as a LogN model. The above-mentioned paper studies the application of relay technology in PLC, and does not involve cooperation with wireless communication.

For the dual-medium cooperative communication technology, the prior art documents research the hardware architecture of wireless and power line parallel communication and the signal merging problem thereof. In consideration of application scenarios of wireless access and power line relay transmission, Mathur analyzes the average error rate performance of a power line and a wireless hybrid relay communication system when the DF protocol is adopted. Under the Nakagami-LogN mixed attenuation, LogN distribution obeying the signal-to-noise ratio (SNR) of a branch of a power system is approximate to Gamma distribution, so that the problem is converted into a performance analysis problem under the same Gamma-Gamma distribution. Mathur then proposes in the literature a non-approximate algorithm that derives closed expressions of system bit error rate, outage probability, and channel capacity directly using the Cumulative Distribution Function (CDF) of the wireless communication leg (first leg) and the power line leg (second leg) SNR. In the prior art, a direct link is added on the basis of DF hybrid communication, and a Gamma distribution obeying a signal-to-noise ratio of a wireless communication branch (first branch) is approximated to a LogN distribution by solving a Moment Generating Function (MGF) equation set, so as to solve a closed expression of system performance. The above documents are directed to the DF relay forwarding scheme, and do not relate to the analysis of the AF system performance. The AF protocol amplifies both the useful signal and the noise power and is more sensitive to channel parameter variations. Wireless communications employ primarily rayleigh and Nakagami-like distributions to model channel fading. The method has practical significance for researching system performance analysis and communication resource optimal allocation under the condition of power line and wireless mixed channel fading by adopting the general Nakagami wireless communication channel fading. LogN distribution is also often used to model channel fading of shadow fading, free optical communication, power line communication, and indoor wireless communication, because there is no closed analytical expression, it has certain challenges and difficulties to study a system performance analysis algorithm based on LogN fading.

Besides the wireless and power line hybrid communication, the analysis of the performance of the AF relay system using other hybrid media transmission has attracted much attention. In the existing literature, the two-hop amplification forward-transmission relay system under the mixed fading channel condition mainly includes: wireless communication with independently distributed channels, Power line wireless mixed communication (PLC/W), visible light radio frequency mixed communication (VLC/RF), and free space optical radio frequency mixed communication (FSO/RF). A common fading model is shown in table 1:

TABLE 1 fading model for mixed-media AF relay systems

For example, Qahtani et al have studied the performance analysis problem of the wireless AF relay system when the channels satisfy independent distribution, and have given the expressions of outage probability and channel capacity based on the CDF of end-to-end SNR with multiple independent Gamma random variables. Aiming at a cooperation technology of mixed medium communication and a literature of the prior art, a two-hop relay technology of wireless and PLC mixed communication is researched, channel fading adopts a Rayleigh distribution and LogN distribution model, and a closed analytic expression of system channel capacity is obtained by utilizing MGFs of two independent components. Theoretical analysis is performed on the outage probability performance of a visible light radio frequency hybrid communication system in the prior art document, wherein a common Line of sight (LOS) channel model is adopted for VLC communication. The research also utilizes the MGF of the reciprocal of the instantaneous SNR of each branch to obtain the MGF of the total signal-to-noise ratio, thereby deducing a closed expression of the system outage probability. The performance analysis method based on the independent component MGF has high accuracy, but a corresponding MGF expression is difficult to find for a more complex fading model, and the method has great limitation. The prior art document proposes a system structure of hybrid communication of wireless light and radio frequency, wherein an FSO link adopts a Gamma-Gamma distribution model, RF channel fading follows Nakagami-m distribution, and relays all adopt a fixed AF forwarding mode. The study uses an extended binary generalized Meijer-G equation to derive an expression for the average channel capacity of the system. The system performance analysis process researched in the above prior art documents is too complicated, the used theorem and inference are only applicable to a specific fading model, and most relays adopt a fixed AF forwarding mode without considering the performance analysis problem of the variable AF relay. In the above prior art documents, under the LogN and Nakagami hybrid fading conditions, there is no closed expression for the variable AF communication theoretical performance, resulting in a problem that the performance analysis of the key technology is excessively dependent on computer simulation.

Disclosure of Invention

The embodiment of the invention provides a multidimensional lognormal approximate wireless and power line relay communication performance calculation method, which aims to overcome the problems in the prior art.

In order to achieve the purpose, the invention adopts the following technical scheme.

A multidimensional lognormal approximate wireless and power line relay communication performance calculation method comprises the following steps:

in a one-way relay system comprising a sending terminal S, a relay node R and a destination terminal D, a first branch between the sending terminal S and the relay node R adopts wireless communication, and a second branch between the relay node R and the destination terminal D adopts power line communication;

and approximating the square of the channel fading coefficient of the first-hop wireless branch to be multidimensional LogN distribution by using a multidimensional LogN approximation algorithm to obtain a distribution parameter, converting the performance analysis problem under hybrid fading into a LogN variable and approximate calculation problem under the same LogN-LogN distribution, and deriving the PDF parameter of the total signal to noise ratio of the dual-medium AF relay system under the conditions of hybrid fading and impulse noise by using the property of the LogN distribution.

Preferably, the method further comprises: in the 1 st time slot, the terminal S uses the transmission power P_SSending a signal X to a relay node R over a wireless communication channel_S(ii) a In the 2 nd time slot, the relay node R couples the received signal X_SProcessing to obtain a relay signal with power P_RTransmitting a signal X over a power line channel_RFor the destination terminal D, both the wireless communication channel, which satisfies the Nakagami-m distribution, and the power line channel, which involves the LogN distribution fading and the bernoulli-gaussian pulse noise, are affected by multiplicative fading and additive noise.

Preferably, the processing procedure of the 1 st timeslot signal includes:

in the 1 st time slot, the wireless signal received by the relay node R is:

wherein the noise n_WRSatisfy the normal distribution N (0, N)_W)，N_WIs the noise power; h_WRFor the radio fading coefficients, the Nakagami distribution is satisfied:

in the formula m_RIs a Nakagami distribution parameter, m_RNot less than 0.5; Γ (x) is a gamma function; omega_RRepresenting the mean value of the fading amplitude, i.e. omega_R＝E(|H_WR|²) To omega_RNormalization is carried out to make omega_R＝1；

Let Delta be_W＝P_s/N_WAnd representing the average signal-to-noise ratio of the wireless communication channel, obtaining the instantaneous signal-to-noise ratio SNR at the relay node R of the wireless communication branch according to the formula (1) as follows:

γ_WR＝|H_WR|²Δ_W (3)

known as H_WRObeying the Nakagami distribution, then | H_WR|²Satisfying the Gamma distribution G (. alpha.)_R，β_R)，|H_WR|²Has the following form:

in the formula of alpha_R、β_RThe parameter relation with the Nakagami distribution satisfies alpha_R＝m_R，β_R＝Ω_R/m_R；

According to the property of Gamma function, when the average signal-to-noise ratio is delta_WThe instantaneous signal-to-noise ratio of the first branch SR satisfies | H when the constant is fixed_WR|²Δ_W～G(m_R，Δ_WΩ_R/m_R)。

Preferably, the processing procedure of the 2 nd timeslot signal includes:

in the 2 nd time slot, after the relay node R adopts the variable AF protocol to amplify the received signal, the processed signal is processed with power P_RForward to terminal D, order X_RRepresenting the signal forwarded by the relay node R, the power line signal received by the terminal D is:

wherein the noise n_PlDFor impulse noise, a binomial Bernoulli-Gaussian noise model, H_PlDFor power line fading coefficients, the LogN distribution is satisfied:

in the formula of_PlDAnd σ_PlDAre respectively lnH_PlDBy normalizing the channel fading envelope energy, i.e. by the mean and mean square error of

Then there is

The additive noise of the power line channel is composed of two parts of background noise and impulse noise, and the PDF of the additive noise has the following form:

f(n_PlD)＝(1-p)N(0，N_G)+pN(0，N_G+N_I) (7)

wherein N (0, N)_G) And N (0, N)_G+N_I) Respectively represent a normal distribution, p is the probability of occurrence of impulse noise, N_GAnd N_IRepresenting the power of the background noise and the impulse noise respectively, the average total noise power is N_Pl＝N_G+pN_I(ii) a Let K equal to N_I/N_GRepresenting the ratio of impulse noise power to background noise power, by gamma_PlD0And gamma_PlD1Respectively represents the instantaneous signal-to-noise ratio when impulse noise exists in the power line channel, the SNR of the power line branch RD is

In which let Delta_Pl0＝P_R/N_G，Δ_Pl1＝Δ_Pl0V (1+ K), respectively, when only background noise exists and impulse noise exists simultaneouslyAverage signal-to-noise ratio of power line channel, according to the nature of LogN distribution, when Δ_Pl0And Δ_Pl1When each is constant, gamma_PlD0And gamma_PlD1All satisfy the LogN distribution, the instantaneous signal-to-noise ratio of the second branch satisfies:

preferably, the method further comprises:

h will satisfy Gamma distribution using multidimensional LogN approximation algorithm_WR|²The method is approximately multidimensional LogN distribution, and the specific implementation process is as follows:

(1) obtaining the square | H of the wireless fading coefficient_WR|²The moment generating function MGF:

known as H_WRSatisfying the Nakagami distribution, | H, shown in formula (2) for wireless fading coefficients_WR|²Satisfying the Gamma distribution G (. alpha.)_R，β_R)，|H_WR|²PDF of (A) is as shown in formula (4) | H_WR|²The expression of (1) is:

(2) establishing an MGF equation before and after approximation:

will | H_WR|²Approximated as a multidimensional LogN distribution, i.e.

Wherein Z represents the dimension, p_iThe weight that each LogN distribution occupies is represented,

respectively representing the distribution parameters of each LogN variable, and having

Let variable quantity

LN_iThe PDF expression of (1) is:

LN_ithe expression of (1) is:

wherein s is an adjustable variable of a moment generating function, and any real number greater than 0 is taken; omega_tAnd a_tRespectively representing the weight and the zero point of the Gauss-Hermite formula, wherein T is the weight omega_tAnd zero point a_tThe number of (2); MGF equations before and after simultaneous approximation are utilized, and a fsolve function in Matlab is utilized to obtain a variable LN in multi-dimensional log-normal distribution_iParameter (d) of

Obtained by the following equations (10) and (12):

(3) determining optimal s-value combination by joint optimization algorithm

It is obvious from the equation (13) that the value of the adjustable variable s in the MGF equation directly affects the parameter ρ_i、μ_iAnd

the minimum difference degree of the PDF curve is used as a target to carry out mathematical modeling, and the optimal s-value combination in the MGF equation represented by the solution formula (13) is solved through a joint optimization algorithm.

Preferably, the mathematical modeling with the objective of minimizing the difference of the PDF curves, and solving the optimal combination of s values in the MGF equation represented by equation (13) by using a joint optimization algorithm, includes:

taking Z as an example, 2, the two-dimensional LogN after approximation has five variables: rho₁、μ₁、

μ₂、

Five s-values therefore need to be determined: s₁～s₅For the radio fading parameter α_R＝m_R，β_R＝Ω_R/m_RUsing PDF expressions (4) and (11), as s₁～s₅For variables, the following mathematical models were built:

the following constraints are satisfied:

1)

2)H_k＝0.01+0.05*(k-1)；

3)k＝1，2，......，L；

4)s_r＞0，r∈{1，2，3，4，5}；

5)0＜ρ_i< 1 and

in the formula: h_kFor the kth sampling value of the wireless channel fading H, 0.05 represents a sampling interval; l is the total number of sampling points of the probability density function, the wireless channel fading H is sampled at equal intervals from 0.01, the mathematical model takes the goodness of fit of approximate front and back PDF curves as an optimization target, and each fading sampling value H is calculated_kAnd carrying out weighted sum on the squares of the difference values of the two corresponding probability density functions, and solving the mathematical model by adopting a differential evolution optimization algorithm.

PreferablyWhen the power line channel in the second branch is modeled, the fading coefficient of the power line channel satisfies the LogN distribution, the impulse noise in the power line channel adopts a binomial bernoulli-gaussian noise model, wherein the probability of the occurrence of the impulse noise is p, and the power ratio K of the impulse noise to the background noise is N_I/N_G，N_GAnd N_IRepresenting the power of the background noise and the impulse noise respectively, the average total noise power is N_Pl＝N_G+pN_IThe probability of only background noise being present is p₀1-p, the probability of the simultaneous presence of background noise and impulse noise is p₁＝p。

Preferably, the method further comprises:

converting the system performance calculation under the Nakagami-LogN hybrid fading into a LogN variable and calculation approximation problem under the same distribution of the LogN-LogN, further obtaining the distribution parameters of the total signal to noise ratio of the hybrid fading AF relay system, and solving a closed expression of the system interruption probability and the channel capacity through the PDF of the total signal to noise ratio:

the specific treatment process comprises the following steps:

(1) signal-to-noise ratio gamma of target node in two-hop mixed medium relay system based on AF^AFComprises the following steps:

wherein gamma is_WR＝|H_WR|²Δ_WRepresenting the instantaneous signal-to-noise ratio, gamma, of the first branch_PlD＝|H_PlD|²Δ_PlRepresenting the instantaneous signal-to-noise ratio of the second branch;

instantaneous mutual information quantity I of system^AFComprises the following steps:

(2) squaring | H of fading coefficients of wireless communication channel in first branch_WR|²Obeying a two-dimensional LogN distribution:

according to the nature of the LogN distribution, when Δ_WIn the case of a constant value, the value of,

and the reciprocal of the LogN variable also satisfies the LogN distribution, i.e.

(3) Signal-to-noise ratio gamma of the power line channel in the second branch_PlDSatisfy LogN distribution, signal-to-noise ratio gamma_PlDThe reciprocal of (d) is:

in the formula:

and

respectively representing the distribution parameters of the signal-to-noise ratio when only background noise exists in the power line channel,

and

respectively representing the distribution parameters of the signal-to-noise ratio when impulse noise exists in the power line channel;

knowing the sum of LogN variables and the distribution from the LogN, after approximation, adopting the LogN approximation to the harmonic mean value of the double LogN variables, and solving the MGF equation to obtain the total output signal-to-noise ratio gamma of the hybrid fading AF relay system^AFThe two-dimensional LogN distribution parameters are further obtained, and the interruption probability and the channel capacity of the hybrid fading AF relay system are further obtained;

(4) it is known that

Wherein mu_Ri＝μ_i-lnΔ_W，

Let LN_RiRepresents 1/gamma_WRLogN variables of the ith dimension, i.e.

Noise probability p of a fixed power line channel_jWhen j is equal to {0, 1}, let

Integrating MGF of LogN variable by Gauss-Hermite series method to obtain LN_Ri、1/γ_PlDj、C_ijThe expression of (1) is respectively:

wherein

And

respectively representing the probability of noise in the power line channel as p_jUnder the condition of (1)/(gamma)_WRIs z dimension LN_RiAnd 1/gamma_PlDjDistribution parameter of LogN variable sum, i.e. lnC_ijMean and variance of; since the MGF of the two variable sums is equal to the product of the two variable MGFs, according to (17) (18), C_ijMGF of again being equal to

Substituting equation (19) into (20) yields:

two fixed s values(s) are selected₁，s₂) Then get about

And

so as to obtain the distribution parameters of the signal-to-noise ratio of the destination node, that is:

preferably, said further determining the outage probability and the channel capacity of the hybrid fading AF relay system comprises:

when the information rate R of the hybrid fading AF relay system is less than the required minimum rate threshold R_thWhen the time comes, the normal communication of the hybrid fading AF relay system is interrupted, and the threshold is R_thAnd γ ═ exp (2R)_th) -1, the outage probability P of the hybrid fading AF relay system_outComprises the following steps:

P_out＝P_r(I^AF＜R_th)＝P_r(γ^AF＜γ) (23)

will gamma^AFThe Cumulative Distribution Function (CDF) of (1) is substituted for the formula (23) to obtain P_outComprises the following steps:

preferably, said further determining the outage probability and the channel capacity of the hybrid fading AF relay system comprises:

in a two-hop AF relay system adopting a binomial pulse noise model, the calculation formula of the average channel capacity C of the system is as follows:

wherein

And

respectively representing the total signal-to-noise ratio of the system in the presence of only background noise and in the presence of impulse noise,

and

are respectively as

And

known at a fixed power line channel noise probability p_jThen, the system signal-to-noise ratio obeys a two-dimensional LogN distribution, that is:

the PDF formula using lognormal distribution is given as:

adopting an orthogonal method of Hermite-Gauss to carry out direct approximation to obtain a closed analytical formula of channel capacity, and enabling:

it is taken into formula (25) to obtain:

obtained by using Hermite-Gauss product calculation

Wherein

And

and the M points are respectively the Hermite-Gauss integral weight and the zero point, and the weight and the zero point can be obtained by looking up a table, wherein M is a set integer.

According to the technical scheme provided by the embodiment of the invention, the invention provides a general multidimensional lognormal approximate wireless and power line relay communication performance calculation method aiming at the hybrid fading AF relay communication model, and solves the optimal s value by utilizing a joint optimization algorithm, thereby improving the approximation precision. And solving a closed expression of system performances such as system interrupt probability, channel capacity and the like by adopting a multidimensional LogN approximate algorithm. The wireless and power line dual-medium relay communication technology can integrate the advantageous communication capacity and resources, improve the overall performance of the system, and has wide development prospect in the smart grid and the Internet of things.

Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a schematic diagram of a wireless access and power line relay dual-medium communication system model according to an embodiment of the present invention;

fig. 2 is a graph comparing PDF approximation effects obtained by combining different s values according to an embodiment of the present invention;

fig. 3 is a comparison graph of approximate effects of one-dimensional and two-dimensional LogN distributions when optimal s-values are combined according to an embodiment of the present invention;

fig. 4 shows a signal-to-noise ratio γ of a wireless communication branch (first branch) according to an embodiment of the present invention_WRThe comparison graph of the approximate effects of PDF and CDF;

FIG. 5 is a comparison graph of PDF approximation effects of a General Gamma (GG) distribution under different parameter conditions according to an embodiment of the present invention;

FIG. 6(a) is a graph comparing system theory and simulated interrupt probability performance for different channel parameters according to an embodiment of the present invention;

fig. 6(b) is a comparison graph of system theoretical and simulated channel capacity performance under different channel parameters according to the embodiment of the present invention;

FIG. 7 is a diagram illustrating the relationship between the probability performance of an interrupt and the probability p of impulse noise according to an embodiment of the present invention;

FIG. 8 is a block diagram illustrating an exemplary embodiment of the present invention, showing the ratio of the interrupt probability performance to the power K and the threshold R_thSchematic diagram of the relationship of (1).

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.

As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an embodiment of the invention is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.

Aiming at mixed fading and multi-parameter pulse noise models with different independent distributions, such as Nakagami, LogN and the like, how to establish a system performance analysis framework and adopt an approximate algorithm to solve a closed system performance expression is a key scientific problem for performance analysis of a dual-medium cooperative communication system.

Aiming at a dual-medium AF relay cooperation system, the embodiment of the invention takes a Nakagami-LogN hybrid fading model as an example, and provides a general system performance analysis algorithm based on multi-dimensional LogN distribution approximation, namely, the square of a fading coefficient of a wireless communication channel is approximated to multi-dimensional LogN distribution, and the system performance calculation under hybrid fading is converted into the multi-dimensional LogN variable and approximation calculation problem under LogN-logN fading. The method has good universality and can be suitable for multi-medium or mixed fading multi-hop AF relay system models, such as dual-medium communication systems of VLC and PLC, FSO and RF, RF and PLC and the like. In a one-way relay system comprising a transmitting terminal S, a relay node R and a destination terminal D, a first branch between the transmitting terminal S and the relay node R adopts wireless communication, and a second branch between the relay node R and the destination terminal D adopts power line communication. Then, calculating probability density function PDF parameters of signal-to-noise ratios of the first branch and the second branch under the conditions of hybrid fading and impulse noise by using a multi-dimensional LogN approximation algorithm, and deriving distribution parameters of the signal-to-noise ratios of the hybrid fading AF relay system according to the PDF parameters of the signal-to-noise ratios of the first branch and the second branch.

A multi-dimensional lognormal parameter solving algorithm after approximation is provided by utilizing an MGF equation set approximation and joint optimization algorithm, and the similarity and the effectiveness of Probability Density Functions (PDFs) before and after approximation are contrastively verified; the PDF parameters of an end-to-end equivalent Signal-to-Noise Ratio (SNR) under the conditions of hybrid fading and impulse Noise are obtained through the analysis scheme, and further the interruption probability of the system and the theoretical formula of the performance of the channel capacity system are deduced.

The embodiment of the invention analyzes the rule that the impulse noise parameters influence the system performance. And finally, applying the general performance analysis method to other fading models, taking general Gamma distribution as an example, obtaining PDF parameters of the instantaneous signal-to-noise ratio of a wireless communication branch (a first branch), and verifying the effectiveness and reliability of the method by simulation.

Fig. 1 is a schematic diagram of a dual medium communication system model for wireless access and power line relay according to an embodiment of the present invention. As shown in fig. 1, the embodiment of the present invention employs a typical three-node (a sending terminal S, a destination terminal D, and a relay node R), two-slot, one-way relay system model. The mobile access terminal S and the node R carry out wireless communication, the node R and the node D carry out PLC communication, and the relay R is provided with a power line and a wireless dual communication interface.

In the system model shown in fig. 1, the terminal S uses the transmission power P in the 1 st slot_SSending a signal X to a relay node R_S(ii) a In the 2 nd time slot, the relay node R receives the signal X_SProcessing the signal to obtain a relay signal, and then processing the relay signal at a power P_RTransmitting signal X_RTo the destination terminal D. The channels in 2 slots are affected by multiplicative fading and additive noise. Wireless communication channel fading satisfies the Nakagami-m distribution, and power line channels involve LogN distribution fading and bernoulli-gaussian impulse noise.

The terminal S in fig. 1 refers to a smart meter or a sensor on or independent from an electric power device, such as a smart meter in a building or a home, a wireless sensor node in an underground substation, a non-contact infrared temperature camera in a substation, a mobile RFID card reader, and the like. Fig. 1 corresponds to a typical application scenario: in order to solve the difficult problems that the PLC cannot be accessed wirelessly and the high-frequency band radio wave penetration capability is limited, the fading is large and the like, a hybrid cooperation mode of wireless access (S- > R) and PLC relay (R- > D) is adopted between the intelligent instrument or the sensor (S) and the gateway D, and wireless access and remote communication are achieved. The power line relay can overcome the influence of barriers such as walls, doors and windows, make up for the defect of large fading of high-frequency signals of wireless communication, and ensure the coverage effect of indoor communication. Under the background of cooperative fusion and green energy conservation, the method fully excavates the characteristics and potential of different communication media, improves the comprehensive performance of the system including reliability, energy efficiency, complexity and the like, realizes reliable and efficient communication, and has important research value.

The processing procedure of the 1 st time slot signal comprises the following steps:

in the 1 st time slot, the wireless signal received by the relay node R is:

wherein the noise n_WRSatisfy the normal distribution N (0, N)_W)，H_WIs the noise power; h_WRFor the radio fading coefficients, the Nakagami distribution is satisfied:

in the formula m_RIs a Nakagami distribution parameter, m_RNot less than 0.5; Γ (x) is a gamma function; omega_RRepresenting the mean value of the fading amplitude, i.e. omega_R＝E(|H_WR|²) Normalizing to ensure that fading does not change the average power of the received signal, let Ω_R＝1。

Example of the invention let_W＝P_S/N_WRepresenting the average signal-to-noise ratio of the wireless communication channel. Then the instantaneous signal-to-noise ratio at the relay node R of the wireless communication branch (first branch) can be obtained according to equation (1):

γ_WR＝|H_WR|²Δ_W (3)

known as H_WRObeying the Nakagami distribution, then | H_WR|²Satisfying the Gamma distribution G (. alpha.)_R，β_R) The PDF has the following form:

in the formula of alpha_R、β_RThe parameter relation with the Nakagami distribution satisfies alpha_R＝m_R，β_R＝Ω_R/m_R。

According to the property of the Gamma function, when the average signal-to-noise ratio Δ W is a fixed constant, the instantaneous signal-to-noise ratio (SNR) of the wireless communication branch (first branch) SR satisfies | H_WR|²Δ_W～G(m_R，Δ_WΩ_R/m_R)。

The processing procedure of the 2 nd time slot signal comprises the following steps:

in the 2 nd time slot, after the relay node R adopts the variable AF protocol to amplify the received signal, the processed signal is processed with power P_RAnd forwarding to the terminal D. Let X_RRepresenting the signal forwarded by the relay node R, the power line signal received by the terminal D is:

wherein the noise n_PlDFor impulse noise, a binomial bernoulli-gaussian noise model is used. H_PlDFor power line fading coefficients, the LogN distribution is satisfied:

in the formula of_PlDAnd σ_PlDAre respectively lnH_PlDMean and mean square error of. To ensure that the channel fading does not change the average power of the signal, the channel fading envelope energy is normalized, i.e. normalized

Then there is

The additive noise of the power line channel is composed of two parts of background noise and impulse noise, and the PDF of the additive noise has the following form:

f(n_PlD)＝(1-p)N(0，N_G)+pN(0，N_G+N_I) (7)

wherein N (0, N)_G) And N (0, N)_G+N_I) Respectively represent a normal distribution, p is the probability of occurrence of impulse noise, N_GAnd N_IRepresenting the power of the background noise and the impulse noise respectively, the average total noise power is N_Pl＝N_G+pN_I. To simplify the noise model, an embodiment of the present invention makes K ═ N_I/N_GRepresenting pulsesThe ratio of the noise power to the background noise power. If gamma is used_PlD0And gamma_PlD1Respectively represents the instantaneous signal-to-noise ratio when impulse noise exists in the power line channel, the SNR of the power line branch RD is

In which let Delta_Pl0＝P_R/N_G，Δ_Pl1＝Δ_Pl0And (1+ K) respectively representing the average signal-to-noise ratio of the power line channel when only background noise exists and impulse noise exists simultaneously. According to the nature of the LogN distribution, when Δ_Pl0And Δ_Pl1When each is constant, gamma_PlD0And gamma_PlD1All satisfy the LogN distribution, so the instantaneous signal-to-noise ratio of the power line branch satisfies

In the dual-medium cooperative system based on the variable AF, the amplification factor at the relay node is

Given an impulse noise parameter p, the instantaneous SNR of the destination node D is:

high signal-to-noise ratio (P)_S/N_W，P_R/N_Pl> 1), equation (10) can be approximated as:

thereby obtaining a relay system in double-hop AFIn the system, the signal-to-noise ratio gamma of the destination node^AFComprises the following steps:

i.e. the total signal-to-noise ratio of the system is closely related to the signal-to-noise ratio of each branch.

Instantaneous mutual information quantity I of system^AFComprises the following steps:

universal approximation algorithm based on hybrid LogN

The performance evaluation indexes of the system are directly related to the signal-to-noise ratio of the target terminal D, so that the probability density distribution function of the signal-to-noise ratio needs to be analyzed firstly, and the log normal distribution parameters of the signal-to-noise ratio of each branch are obtained by utilizing a multi-dimensional LogN approximation algorithm. The PDF distribution characteristics of the signal-to-noise ratio of the first-hop wireless communication branch (first branch) are analyzed in detail, and the fact that the square of a wireless channel fading coefficient which obeys Gamma distribution is approximated to multidimensional LogN distribution is firstly proposed. The algorithm utilizes MGF equality before and after approximation, obtains multidimensional lognormal distribution parameters by solving an MGF equation, determines key parameters of the MGF equation by adopting a joint optimization algorithm, and finally verifies the correctness of theoretical analysis. In order to further verify the universality of the algorithm, the embodiment of the invention also applies the multidimensional LogN approximation algorithm to other fading models, and obtains a comparison graph of PDFs before and after approximation.

Multi-dimensional LogN distribution approximation based on Gamma wireless link SNR

The square of the channel fading coefficient of the wireless communication branch (first branch) satisfies the Gamma distribution, and the Gamma distribution has higher similarity with the specific LogN distribution. According to the formula (12), the end-to-end signal-to-noise ratio of the system is closely related to the reciprocal of the SNR of each branch, according to the property of the LogN distribution, the reciprocal of the LogN variable also meets the LogN distribution, the distribution parameters are easy to obtain, and the MGF of the LogN variable and the reciprocal thereof can pass through Gauss-HermiCalculating the te series; on the other hand, the signal-to-noise ratio of the power line branch satisfies the LogN distribution, and if the sum of the LogN variables is known to still obey the LogN distribution, the harmonic mean value of the double LogN variables after the approximation can still be approximated by the LogN. Therefore, the embodiment of the invention uses the MGF approximate algorithm to divide the square | H of the channel fading coefficient of the wireless communication branch (first branch)_WR|²And the multi-dimensional LogN distribution is approximated, so that the system performance analysis problem under the hybrid fading is converted into a LogN variable and approximate calculation problem under the same distribution of LogN-LogN.

In addition, in the process of approximation from Gamma to multidimensional LogN, LogN variables and approximation, the embodiment of the invention considers that the selection of the adjustable variable s directly influences the determination and approximation precision of the approximated PDF parameters, so that a combined parameter optimization algorithm based on the MGF equation is provided. And the optimal s combination is solved by taking the goodness of fit of the PDF or MGF curve as an optimization target, so that the approximation precision of the algorithm is further improved.

Known as | H_WR|²The Gamma distribution is satisfied, and the expression of MGF is as follows:

first, the embodiment of the present invention will couple | H_WR|²Approximated as a multidimensional LogN distribution, i.e.

Wherein Z represents the dimension, p_iRepresents the weight occupied by each LogN distribution and has

For convenience of the following description, the embodiments of the present invention order variables

The PDF is:

MGF of LogN variable is subjected to integral processing through Gauss-Hermite series method, and LN can be obtained_iMGF expression (MGF):

wherein s is an adjustable variable of a moment generating function, and any real number larger than 0 can be taken; omega_tAnd a_tRespectively representing the weight and the zero point of the Gauss-Hermite formula, wherein T is the weight omega_tAnd zero point a_tThe number of (2). MGF equations before and after simultaneous approximation are used, and a fsolve function in Matlab is used to obtain a variable LN in multi-dimensional logarithmic distribution_iParameter (d) of

The following equations (14) and (16) can be obtained:

obviously, the value of the adjustable variable s in the MGF equation directly affects the parameter rho_i、μ_iAnd

and the approximation accuracy of the probability density function. Theoretically, the Z value of the approximation dimension also affects the approximation accuracy, and the larger the Z value, the higher the approximation accuracy, but when the Z value increases, the number of s values that need to be determined also increases, and for example, when Z is 2, the number of fixed s values is 5, and when Z is 3, the number of fixed s values is 8. In comprehensive consideration, in the embodiment of the present invention, Z is taken as an example, numerical calculation and analysis are performed by using Matlab, and five variables are distributed in the approximated two-dimensional LogN: rho₁、μ₁、

μ₂、

Thus five s-values need to be determined. The embodiment of the invention takes the minimum PDF curve difference as a target to carry out mathematical modeling and solve the optimal s₁～s₅And (4) combining. For radio fading parameter alpha_R＝m_R，β_R＝Ω_R/m_RUsing PDF expressions (4) and (15), as s₁～s₅For variables, the following mathematical models were built:

the following constraints are satisfied:

1)

2)H_k＝0.01+0.05*(k-1)；

3)k＝1，2，......，L；

4)s_r＞0,r∈{1，2，3，4，5}；

5)0＜ρ_i< 1 and

in the formula: h_kFor the kth sampling value of the wireless communication channel fading H, 0.05 represents a sampling interval; l is the total number of sampling points of the probability density function (in the embodiment of the present invention, L is 100), and the wireless communication channel fading H is sampled at equal intervals from 0.01.

The objective function calculates each fading sample value H_kAnd (3) the difference value of the two corresponding probability density functions, namely the probability density function value of the corresponding Gamma distribution and the two-dimensional LogN distribution is subtracted at each sampling point, the square of the difference value is calculated, and finally the weighted sum is carried out. The mathematical model established by the invention takes the goodness of fit of the approximate front and back PDF curves as an optimization target, and aims to find the optimal s combination so as to obtain the LogN distribution parameter which is most consistent with the PDF of Gamma distribution. The mathematical model can be solved by adopting an optimization algorithm such as differential evolution and the like,by adopting the algorithm, an optimal s-value combination table approximated by the MGF equation can be obtained for practical application reference, as shown in Table 2.

TABLE 2 optimal s-value combination under different parameter conditions

Fixed radio fading parameters, take m_RFig. 2 compares the effect of s-value selection on PDF approximation accuracy at 1.5. The dotted line represents the randomly selected s-value, the dotted line represents the combination of s-values obtained by the joint optimization algorithm, and it can be seen from fig. 2 that the optimized PDF curve of the two-dimensional LogN is substantially consistent with the Gamma distribution, so that it can be seen that the approximation accuracy when the optimal s-value is adopted is much higher than that when the random s-value is adopted, which indicates that the joint optimization of s-value is very necessary and the accuracy of the proposed optimization algorithm is verified.

Under different parameter conditions, the embodiment of the invention respectively obtains one-dimensional and two-dimensional approximate optimal s combinations by using a differential evolution optimization algorithm, calculates corresponding performance values, further obtains two-dimensional LogN and one-dimensional LogN probability density distribution parameters, and the approximate effect pair is shown in FIG. 3. As can be seen from fig. 3: when different fading parameters are adopted, the one-dimensional LogN distribution deviates from the original Gamma distribution curve, and the two-dimensional LogN distribution is distributed in m_RWhen different values are taken, the values are basically consistent with the PDF of Gamma distribution. Therefore, the multi-dimensional LogN distribution approximation algorithm provided by the embodiment of the invention has higher approximation precision, and the approximation algorithm is suitable for any channel fading condition. According to the nature of the LogN distribution, when Δ_WIn the case of a constant value, the value of,

therefore, the embodiment of the invention can obtain the PDF parameter of the instantaneous signal-to-noise ratio of the wireless communication branch (first branch). In order to further verify the validity of the two-dimensional LogN distribution approximation, monte carlo simulation is performed in the embodiment of the present invention. Let Delta denote the channel average signal-to-noise ratio, then there is N _W1/delta, the transmission power of terminal S is P _S1. Let Δ ═16dB，m_RFig. 4 shows the signal-to-noise ratio γ of the wireless communication branch (first branch) as 1.5_WRThe PDF Distribution graph of the simulation data and a Cumulative Distribution Function (CDF) Distribution graph are compared with theoretical PDF and CDF curves determined by a two-dimensional lognormal approximation algorithm. As can be seen from the figure: the two-dimensional LogN distribution calculated theoretically is highly consistent with PDF and CDF curves of actual simulation data, and the multi-dimensional LogN approximation algorithm provided by the embodiment of the invention has higher approximation precision. The theoretical simulation results fully show that the square | H of the channel fading coefficient of the wireless communication branch (first branch)_WR|²Satisfying two-dimensional LogN distribution, consistent with the above analysis results.

Hybrid LogN approximation based on other fading models

To further demonstrate the versatility of the multidimensional LogN approximation algorithm, embodiments of the present invention apply the algorithm to other fading models. It is known that the General Gamma (GG) distribution is the generalization of the two-parameter Gamma distribution, while the common Nakagami-m, Gamma, Rayleigh and Weibull distributions are all special cases of GG, and the squares of GG variables still follow the GG distribution. Therefore, in the embodiment of the present invention, the GG distribution is taken as an example, and assuming that the fading coefficient of the wireless communication channel follows the GG distribution, the instantaneous signal-to-noise ratio γ of the wireless communication branch (first branch) is_WRStill obey the GG distribution, whose PDF is:

wherein m is_R(0.5≤m_RInfinity) and ξ_R(0≤ξ_RInfinity) as a fading parameter, normalized beta_R＝Γ(m_R+1/ξ_R)/Γ(m_R)，

For average signal-to-noise ratio, Γ (x) is the gamma function.

The GG distribution is approximated to two-dimensional LogN distribution by using a multi-dimensional LogN approximation algorithm, and a PDF curve before and after approximation under different parameter conditions is compared in a graph 5 (the graph 5)a)m_R＝2，ξ_R＝0.5，

(FIG. 5b) m_R＝2，ξ_R＝1，

As can be seen from fig. 5: when different fading parameters are adopted, the two-dimensional LogN distribution is basically consistent with the PDF curve of GG distribution, and the approximation precision is high. The GG distribution is a general form of other distributions, and follows different fading models under different parameters, and the simulation result fully shows that the multidimensional LogN distribution can fit different fading models, namely the multidimensional LogN approximation algorithm has universality.

From the above analysis, it can be known that the multidimensional LogN distribution can fit Gamma distribution under different parameters, and has better fitting effect with other fading models. Therefore, the system performance analysis method is not only suitable for the Nakagami-LogN communication system model, but also can be used for analyzing the performance of any hybrid fading system based on AF forwarding. In a mixed medium communication system, the channel fading coefficients at both ends of the relay are subject to Rice, Weibull distribution or other more complex fading models, and the algorithm can approximate the fading coefficient of each channel to be multidimensional LogN distribution. Specifically, if the PDF and MGF expressions for the distribution are available, embodiments of the present invention may approximate it as a multidimensional LogN distribution using the steps described above. On the contrary, for some unknown fading, the embodiments of the present invention may obtain SNR data of a link by using simulation or big data, and then obtain a distribution parameter of the multidimensional LogN by using an EM estimation algorithm. And converting the system performance calculation under the hybrid fading into a LogN variable and approximate calculation problem under the same distribution of the LogN-LogN, and further obtaining a closed expression of the system performance.

Performance analysis: in this section, embodiments of the present invention analyze the outage probability P for a mixed-media relay communication system_outAnd channel capacity C. From the above analysis, the signal-to-noise ratio of the wireless communication branch (first branch) obeys two-dimensional LogN distribution, and the reciprocal of the known LogN variable still satisfies LogN is distributed, therefore

On the other hand, gamma is known from analysis_PlDSatisfying the LogN distribution, the reciprocal of the signal-to-noise ratio of the power line branch (second branch) is:

in the formula:

and

respectively representing the distribution parameters of the signal-to-noise ratio when only background noise exists in the power line channel,

and

respectively representing the distribution parameters of the signal-to-noise ratio when impulse noise exists in the power line channel.

According to an approximation algorithm such as Fenton Wilkinson (FW), the sum of LogN variables also satisfies the LogN distribution, i.e.

The reciprocal of C is also known from the properties of the LogN variable

In this section, the embodiment of the present invention still uses a high-precision performance analysis algorithm based on 1-time MGF parameter approximation to obtain MGFs of two log n distributed bivariate harmonic averages, thereby calculating the instantaneous signal-to-noise ratio γ of the terminal D^AFThe PDF parameter of (1).

It is known that

Wherein mu_Ri＝μ_i-lnΔ_W，

Is easy to expound, makes LN_RiRepresents 1/gamma_WRLogN variables of the ith dimension, i.e.

Noise probability p of a fixed power line channel_jWhen j is equal to {0, 1}, the embodiment of the invention leads

MGF of LogN variable is subjected to integral processing through Gauss-Hermite series method, and LN can be obtained_Ri、1/γ_PlDj、C_ijThe expression of (1) is respectively:

wherein

And

respectively representing the probability of noise in the power line channel as p_jUnder the condition of (1)/(gamma)_WRIs z dimension LN_RiAnd 1/gamma_PlDjDistribution parameters of LogN variables and sums. Since the MGF of the two variable sums is equal to the product of the two variable MGFs, according to (19) (20), C_iMGF of again being equal to

Substituting equation (21) into equation (22) yields:

two fixed s values(s) are selected₁，s₂) Then can get about

And

thereby obtaining the distribution parameter of the signal-to-noise ratio of the destination node. And s₁And s₂Is directly related to the parameter

And

determination of (d) and probability density approximation accuracy. In the process of approximating the Gamma distribution to the multidimensional LogN distribution, the embodiment of the invention obtains the optimal s value combination by the method of the minimum difference degree of PDF curves before and after approximation, while the equation set (23) approximates the two LogN variable sums to the LogN distribution, while the PDFs of the two LogN variable sums are difficult to obtain, so that the minimum difference degree of the MGF curves is used as the target to carry out mathematical modeling in this part, and the optimal s is solved₁And s₂And (4) combining. MGF expressions (19), (20) and (21) are utilized by equation (23) as s₁And s₂For variables, fixing the noise probability of the power line communication branch (second branch) and the signal-to-noise ratio dimension of the wireless communication branch (first branch), the following mathematical model can be established:

in the formula: s_kIs a variable of MGF equation, L isAnd the function model takes MGF goodness of fit before and after approximation as an optimization target, calculates the square of the difference value of the two MGFs corresponding to each s value and then weights the square. Aiming at finding the best s₁，s₂And further, the LogN distribution parameter which is most consistent with the MGF of the sum of the two LogN variables is obtained.

Additive noise of the power line channel (second branch) is known as a binomial bernoulli-gaussian noise model, i.e. p₀When 1-p only background noise is present, p₁The background noise and the impulse noise exist simultaneously when p. The embodiment of the invention fixes the noise probability p of the power line_jUnder the condition, respectively obtain 1/gamma_WREach dimension LN_RiAnd 1/gamma_PlDjPDF parameter of LogN variable sum

And further obtaining the distribution of the total signal-to-noise ratio of the system when the noise probability is fixed:

therefore, the distribution of the end-to-end signal-to-noise ratio in the hybrid fading AF relay system is:

interrupt probability analysis

When the system information rate R is less than the required minimum rate threshold R_thThe normal communication of the system is interrupted. Let the threshold be R_thAnd γ ═ exp (2R)_th) 1, the outage probability P of the system_outComprises the following steps:

P_out＝P_r(I^AF＜R_th)＝P_r(γ^AF＜γ) (25)

will gamma^AFThe Cumulative Distribution Function (CDF) of (1) is substituted for the equation (25), and P can be obtained_outIs composed of

Channel capacity analysis

Finally, the embodiment of the invention deduces the channel capacity expression of the system, and in a two-hop AF relay system adopting a binomial noise model, the average channel capacity is as follows:

wherein

And

respectively representing the total signal-to-noise ratio of the system in the presence of only background noise and in the presence of impulse noise,

and

are respectively as

And

the PDF of (a). Knowing the noise probability p of a fixed power line channel_jIn time, the signal-to-noise ratio of the system obeys two-dimensional LogN distribution, and can be obtained by utilizing a PDF formula of lognormal distribution

Obviously, a closed expression of integration is difficult to obtain in the formula (27), and the embodiment of the invention adopts an orthogonal method of Hermite-Gauss to carry out direct approximation, so as to obtain a closed analytic formula of channel capacity. First order

Bringing it into (27) to obtain

Obtained by using Hermite-Gauss product calculation

Wherein

And

and respectively obtaining the weight and the zero point of the Hermite-Gauss integral of the M point by looking up a table. In addition, when M is large enough, a more precise approximation can be achieved, and in the embodiment of the present invention, M is 20.

Numerical simulation result

In order to verify the accuracy of a theoretical formula, the method adopts Matlab to carry out Monte Carlo simulation experiment, and carries out comparative analysis with the theoretical performance of numerical calculation. Without loss of generality, in the simulation and theoretical calculation processes, if no special description exists, the following default settings are adopted for parameters in the system model:

(1) after power normalization, the total power of the system is 2, P_S＝1，P_R＝1；

(2) Assuming that the average signal-to-noise ratio of the power line and the wireless communication channel is equal, denoted by Δ, the average noise power is N ₀1/Δ, thus N_W＝N₀，N_G＝N₀/(1+p×K)，N_I＝K×N_G；

(3) Let P be 0.1 and K be 20 in a binomial bernoulli-gaussian noise model;

(4) system interrupt threshold R_th＝0.1。

With default parameter settings, fig. 6 is a schematic diagram illustrating comparison of theoretical simulation performance of a system under different channel parameters according to an embodiment of the present invention. Fig. 6(a) and (b) respectively compare the system outage probability (exit) and the channel Capacity (Capacity) performance when different channel fading parameters are taken. Wherein Simu represents the simulation result and Theo represents the theoretical result. As can be seen from fig. 6, under the same set of channel fading parameters, as the average signal-to-noise ratio Δ increases, the system performance calculated according to the derived theoretical formula is substantially consistent with the simulation result, further proving the correctness and reliability of the theoretical derivation; the channel fading parameters are fixed, the interruption probability of the system is reduced along with the increase of delta, and the average channel capacity is increased along with the increase of delta, which shows that the reliability of the system can be obviously improved by increasing the average signal-to-noise ratio of the system;

let m_R＝2，σ_PlDFig. 7 shows a schematic diagram of the relationship between the interruption probability theory and the simulation performance and the impulse noise probability p, where 2.5 and 20 are used, and the default settings are used in others. As can be seen from FIG. 7, the theoretical performance of the system under different pulse noise probabilities is consistent with the simulation result, and the correctness of theoretical analysis is verified; when the signal-to-noise ratio is low, interruption probability curves corresponding to different p values are basically overlapped, because the quality of a channel is poor when the signal-to-noise ratio is low, the system performance mainly depends on the average signal-to-noise ratio of the channel, and the influence of the pulse noise probability on the system performance is extremely small; at high snr, it is clear that the probability of impulse noise increases from p 0.001 to p 0.1, and the probability of system outage increases gradually. The reason is that when the p value is increased, the impulse noise component is also increased, namely, the impulse characteristics in the bernoulli-gaussian noise model are more obvious, and the performance of the system is deteriorated.

In order to further analyze the influence of impulse noise parameters on system performance, fig. 8 shows the system interrupt probability theory, the simulation performance, the noise power ratio K, and the threshold R_thIs onIs a schematic drawing in which m_R＝3，σ_PlDP is 3.5 and 0.1. Different values of K and R_thThe system theoretical performance under the combination of the values is consistent with the simulation result, and the reliability of the theoretical formula is indicated. From fig. 8, it is known that: when the threshold value R is_thWhen the system is fixed, at a low signal-to-noise ratio, the interruption probability difference corresponding to different K values is smaller, and at a high signal-to-noise ratio, the interruption performance of the system is obviously deteriorated along with the increase of the power ratio of the impulse noise to the background noise, because when the K value is increased, the impulse noise component in the power line channel is increased, and the communication quality of the system is deteriorated; when the power ratio K is fixed, R_thThe interrupt probability curves corresponding to 0.06 are all at R_thBelow the 0.1 curve, i.e. the probability of interruption decreases with decreasing threshold value, because of the information rate threshold R_thAs it becomes smaller, the information rate requirements on the system become lower and the outage probability decreases under the same channel conditions.

In summary, the invention provides a general performance analysis method for the AF relay communication model of hybrid fading, and solves the optimal s value by using a joint optimization algorithm, thereby improving the approximation accuracy. And solving a closed expression of system performances such as system interrupt probability, channel capacity and the like by adopting a multidimensional LogN approximate algorithm. The wireless and power line dual-medium relay communication technology provided by the embodiment of the invention can integrate the superior communication capacity and resources, improve the overall performance of the system and have a wide development prospect in the smart grid and the Internet of things.

The embodiment of the invention applies the algorithm to other fading models, takes general Gamma distribution as an example, and obtains the approximated multidimensional LogN distribution parameters. Research shows that aiming at a mixed channel fading model, the square Gamma distribution of the wireless communication branch fading coefficient is approximate to the multidimensional LogN distribution, and the reliability is higher; in addition, impulse noise parameters are key factors influencing the system performance, and relevant conclusions can provide necessary theoretical support for application of indoor and outdoor dual-medium cooperative communication technology.

Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.

The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. A multidimensional lognormal approximate wireless and power line relay communication performance calculation method is characterized by comprising the following steps:

in a one-way relay system comprising a sending terminal S, a relay node R and a destination terminal D, a first branch between the sending terminal S and the relay node R adopts wireless communication, and a second branch between the relay node R and the destination terminal D adopts power line communication;

approximating the square of a first-hop wireless branch channel fading coefficient to multi-dimensional LogN distribution by using a multi-dimensional LogN approximation algorithm to obtain a distribution parameter, converting a performance analysis problem under hybrid fading into a LogN variable and approximate calculation problem under the same distribution of LogN-LogN, and using the property of LogN distribution;

calculating probability density function PDF parameters of signal-to-noise ratios of the first branch and the second branch under the conditions of hybrid fading and impulse noise by using a multi-dimensional LogN approximation algorithm, and deriving PDF distribution parameters of the signal-to-noise ratio of the hybrid fading AF relay system according to the PDF parameters of the signal-to-noise ratios of the first branch and the second branch;

in the 1 st time slot, the terminal S uses the transmission power P_SSending a signal X to a relay node R over a wireless communication channel_S(ii) a In the 2 nd time slot, the relay node R couples the received signal X_SProcessing to obtain a relay signal with power P_RTransmitting a signal X over a power line channel_RFor the destination terminal D, the wireless communication channel and the power line channel are both affected by multiplicative fading and additive noise, the wireless communication channel fading satisfies Nakagami-m distribution, and the power line channel relates to LogN distribution fading and Bernoulli-Gaussian pulse noise;

the processing procedure of the 1 st time slot signal comprises the following steps:

in the 1 st time slot, the wireless signal received by the relay node R is:

wherein the noise n_WRSatisfy the normal distribution N (0, N)_W)，N_WIs the noise power; h_WRFor the radio fading coefficients, the Nakagami distribution is satisfied:

in the formula m_RIs a Nakagami distribution parameter, m_RNot less than 0.5; Γ (x) is a gamma function; omega_RRepresenting the mean value of the fading amplitude, i.e. omega_R＝E(|H_WR|²) To omega_RNormalization is carried out to make omega_R＝1；

Let Delta be_W＝P_S/N_W，Δ_WAnd representing the average signal-to-noise ratio of the wireless communication channel, obtaining the instantaneous signal-to-noise ratio SNR at the relay node R of the wireless communication branch according to the formula (1) as follows:

γ_WR＝|H_WR|²Δ_W (3)

known as H_WRObeying the Nakagami distribution, then | H_WR|²Satisfying the Gamma distribution G (. alpha.)_R，β_R)，|H_WR|²Has the following form:

in the formula of alpha_R、β_RThe parameter relation with the Nakagami distribution satisfies alpha_R＝m_R，β_R＝Ω_R/m_R；

According to the property of Gamma function, when the average signal-to-noise ratio is delta_WThe instantaneous signal-to-noise ratio of the first branch SR satisfies | H when the constant is fixed_WR|²Δ_W～G(m_R，Δ_WΩ_R/m_R)；

The processing procedure of the 2 nd time slot signal comprises the following steps:

in the 2 nd time slot, after the relay node R adopts the variable AF protocol to amplify the received signal, the processed signal is processed with power P_RForward to terminal D, order X_RRepresenting the signal forwarded by the relay node R, the power line signal received by the terminal D is:

wherein the noise n_PlDFor impulse noise, a binomial Bernoulli-Gaussian noise model, H_PlDFor power line fading coefficients, the LogN distribution is satisfied:

in the formula of_PlDAnd σ_PlDAre respectively lnH_PlDBy normalizing the channel fading envelope energy, i.e. by the mean and mean square error of

Then there is

The additive noise of the power line channel is composed of two parts of background noise and impulse noise, and the PDF of the additive noise has the following form:

f(n_PlD)＝(1-p)N(0，N_G)+pN(0，N_G+N_I) (7)

wherein N (0, N)_G) And N (0, N)_G+N_I) Respectively represent a normal distribution, p is the probability of occurrence of impulse noise, N_GAnd N_IRepresenting the power of the background noise and the impulse noise respectively, the average total noise power is N_Pl＝N_G+pN_I(ii) a Let K equal to N_I/N_GRepresenting the ratio of impulse noise power to background noise power, by gamma_PlD0And gamma_PlD1Respectively represents the instantaneous signal-to-noise ratio when impulse noise exists in the power line channel, the SNR of the power line branch RD is

In which let Delta_Pl0＝P_R/N_G，Δ_Pl1＝Δ_Pl0(1+ K) respectively representing the average signal-to-noise ratio of the power line channel when only background noise exists and impulse noise exists simultaneously, and when the delta is in accordance with the property of LogN distribution_Pl0And Δ_Pl1When each is constant, gamma_PlD0And gamma_PlD1All satisfy the LogN distribution, the instantaneous signal-to-noise ratio of the second branch satisfies:

the implementation process of approximating the square of the channel fading coefficient of the first-hop wireless branch to the multidimensional LogN distribution by using the multidimensional LogN approximation algorithm is as follows:

(1) obtaining the square | H of the wireless fading coefficient_WR|²The moment generating function MGF:

known as H_WRSatisfying the Nakagami distribution, | H, shown in formula (2) for wireless fading coefficients_WR|²Satisfying the Gamma distribution G (. alpha.)_R，β_R)，|H_WR|²PDF of (A) is as shown in formula (4) | H_WR|²The expression of (1) is:

(2) establishing an MGF equation before and after approximation:

will | H_WR|²Approximated as a multidimensional LogN distribution, i.e.

Wherein Z represents the dimension, p_iThe weight that each LogN distribution occupies is represented,

respectively representing the distribution parameters of each LogN variable, and having

Let variable quantity

LN_iThe PDF expression of (1) is:

LN_ithe expression of (1) is:

wherein s is an adjustable variable of a moment generating function, and any real number greater than 0 is taken; omega_tAnd a_tRespectively representing the weight and the zero point of the Gauss-Hermite formula, wherein T is the weight omega_tAnd zero point a_tThe number of (2); MGF equations before and after simultaneous approximation are utilized, and a fsolve function in Matlab is utilized to obtain a variable LN in multi-dimensional log-normal distribution_iParameter (d) of

Obtained by the following equations (10) and (12):

(3) determining optimal s-value combination by joint optimization algorithm

It is obvious from the equation (13) that the value of the adjustable variable s in the MGF equation directly affects the parameter ρ_i、μ_iAnd

the minimum difference degree of a PDF curve is taken as a target to carry out mathematical modeling, and the optimal s value combination in the MGF equation represented by the solution formula (13) is solved through a joint optimization algorithm;

converting the system performance calculation under the Nakagami-LogN hybrid fading into a LogN variable and calculation approximation problem under the same distribution of the LogN-LogN, further obtaining the distribution parameters of the total signal to noise ratio of the hybrid fading AF relay system, and solving a closed expression of the system interruption probability and the channel capacity through the PDF of the total signal to noise ratio:

the specific treatment process comprises the following steps:

(1) in two-hop mixed media based on AFIn a relay system, the signal-to-noise ratio gamma of a destination node^AFComprises the following steps:

wherein gamma is_WR＝|H_WR|²Δ_WRepresenting the instantaneous signal-to-noise ratio, gamma, of the first branch_PlD＝|H_PlD|²Δ_PlRepresenting the instantaneous signal-to-noise ratio of the second branch;

instantaneous mutual information quantity I of system^AFComprises the following steps:

(2) squaring | H of fading coefficients of wireless communication channel in first branch_WR|²Obeying a two-dimensional LogN distribution:

according to the nature of the LogN distribution, when Δ_WIn the case of a constant value, the value of,

and the reciprocal of the LogN variable also satisfies the LogN distribution, i.e.

(3) Signal-to-noise ratio gamma of the power line channel in the second branch_PlDSatisfy LogN distribution, signal-to-noise ratio gamma_PlDThe reciprocal of (d) is:

in the formula:

and

respectively representing the distribution parameters of the signal-to-noise ratio when only background noise exists in the power line channel,

and

respectively representing the distribution parameters of the signal-to-noise ratio when impulse noise exists in the power line channel;

knowing the sum of LogN variables and the distribution from the LogN, after approximation, adopting the LogN approximation to the harmonic mean value of the double LogN variables, and solving the MGF equation to obtain the total output signal-to-noise ratio gamma of the hybrid fading AF relay system^AFThe two-dimensional LogN distribution parameters are further obtained, and the interruption probability and the channel capacity of the hybrid fading AF relay system are further obtained;

(4) it is known that

Wherein mu_Ri＝μ_i-lnΔ_W，

Let LN_RiRepresents 1/gamma_WRLogN variables of the ith dimension, i.e.

Noise probability p of a fixed power line channel_jWhen j is equal to {0, 1}, let

Integrating MGF of LogN variable by Gauss-Hermite series method to obtain LN_Ri、1/γ_PlDj、C_ijThe expression of (1) is respectively:

wherein

And

respectively representing the probability of noise in the power line channel as p_jUnder the condition of (1)/(gamma)_WRIs z dimension LN_RiAnd 1/gamma_PlDjDistribution parameter of LogN variable sum, i.e. lnC_ijMean and variance of; since the MGF of the two variable sums is equal to the product of the two variable MGFs, according to (17) (18), C_ijMGF of again being equal to

Substituting equation (19) into (20) yields:

two fixed s values(s) are selected₁，s₂) Then get about

And

thereby obtaining the objectiveThe distribution parameters of the node signal-to-noise ratio are as follows:

the specific processing process of converting the system performance calculation under the Nakagami-LogN hybrid fading into the LogN variable and calculation approximation problem under the same LogN-LogN distribution so as to obtain the distribution parameters of the total signal-to-noise ratio of the hybrid fading AF relay system and solving the closed expression of the system interruption probability and the channel capacity through the PDF of the total signal-to-noise ratio comprises the following steps:

(1) signal-to-noise ratio gamma of target node in two-hop mixed medium relay system based on AF^AFComprises the following steps:

wherein gamma is_WR＝|H_WR|²Δ_WRepresenting the instantaneous signal-to-noise ratio, gamma, of the first branch_PlD＝|H_PlD|²Δ_PlRepresenting the instantaneous signal-to-noise ratio of the second branch;

instantaneous mutual information quantity I of system^AFComprises the following steps:

(2) squaring | H of fading coefficients of wireless communication channel in first branch_WR|²Obeying a two-dimensional LogN distribution:

according to the nature of the LogN distribution, when Δ_WIn the case of a constant value, the value of,

and the reciprocal of the LogN variable also satisfies the LogN distribution, i.e.

(3) Signal-to-noise ratio gamma of the power line channel in the second branch_PlDSatisfy LogN distribution, signal-to-noise ratio gamma_PlDThe reciprocal of (d) is:

in the formula:

and

respectively representing the distribution parameters of the signal-to-noise ratio when only background noise exists in the power line channel,

and

respectively representing the distribution parameters of the signal-to-noise ratio when impulse noise exists in the power line channel;

knowing the sum of LogN variables and the distribution from the LogN, after approximation, adopting the LogN approximation to the harmonic mean value of the double LogN variables, and solving the MGF equation to obtain the total output signal-to-noise ratio gamma of the hybrid fading AF relay system^AFThe two-dimensional LogN distribution parameters are further obtained, and the interruption probability and the channel capacity of the hybrid fading AF relay system are further obtained;

(4) it is known that

Wherein mu_Ri＝μ_i-lnΔ_W，

Let LN_RiRepresents 1/gamma_WRLogN variables of the ith dimension, i.e.

Noise probability p of a fixed power line channel_jWhen j is equal to {0, 1}, let

Integrating MGF of LogN variable by Gauss-Hermite series method to obtain LN_Ri、1/γ_PlDj、C_ijThe expression of (1) is respectively:

wherein

And

respectively representing the probability of noise in the power line channel as p_jUnder the condition of (1)/(gamma)_WRIs z dimension LN_RiAnd 1/gamma_PlDjDistribution parameter of LogN variable sum, i.e. lnC_ijMean and variance of; since the MGF of the two variable sums is equal to the product of the two variable MGFs, according to (17) (18), C_ijMGF of again being equal to

Substituting equation (19) into (20) yields:

two fixed s values(s) are selected₁，s₂) Then get about

And

so as to obtain the distribution parameters of the signal-to-noise ratio of the destination node, that is:

2. the method as claimed in claim 1, wherein the mathematical modeling with the objective of minimizing the difference of the PDF curves, and solving the optimal combination of s values in the MGF equation expressed by equation (13) by a joint optimization algorithm, comprises:

let Z be 2, then the approximated two-dimensional LogN has five variables distributed: rho₁、μ₁、

μ₂、

Five s-values therefore need to be determined: s₁～s₅For the radio fading parameter α_R＝m_R，β_R＝Ω_R/m_RUsing PDF expressions (4) and (11), as s₁～s₅For variables, the following mathematical models were built:

the following constraints are satisfied:

1)

2)H_k＝0.01+0.05*(k-1)；

3)k＝1，2，……，L；

4)s_r＞0，r∈{1，2，3，4，5}；

5)0＜ρ_i< 1 and

in the formula: h_kFor the kth sampling value of the wireless channel fading H, 0.05 represents a sampling interval; l is the total number of sampling points of the probability density function, the wireless channel fading H is sampled at equal intervals from 0.01, the mathematical model takes the goodness of fit of approximate front and back PDF curves as an optimization target, and each fading sampling value H is calculated_kAnd carrying out weighted sum on the squares of the difference values of the two corresponding probability density functions, and solving the mathematical model by adopting a differential evolution optimization algorithm.

3. The method according to claim 1, wherein, when modeling the power line channel in the second branch, the power line channel fading coefficient satisfies a LogN distribution, and impulse noise in the power line channel adopts a binomial Bernoulli-Gaussian noise model, wherein the probability of occurrence of the impulse noise is p, and the power ratio K ═ N of the impulse noise and background noise_I/N_G，N_GAnd N_IRepresenting the power of the background noise and the impulse noise respectively, the average total noise power is N_Pl＝N_G+pN_IThe probability of only background noise being present is p₀1-p, the probability of the simultaneous presence of background noise and impulse noise is p₁＝p。

4. The method of claim 1, wherein said further determining the outage probability and the channel capacity of the hybrid-fading AF relay system comprises:

when the information rate R of the hybrid fading AF relay system is less than the required minimum rate threshold R_thWhen the time comes, the normal communication of the hybrid fading AF relay system is interrupted, and the threshold is R_thAnd γ ═ exp (2R)_th) -1, the outage probability P of the hybrid fading AF relay system_outComprises the following steps:

P_out＝P_r(I^AF＜R^th)＝P_r(γ^AF＜γ) (23)

will gamma^AFThe Cumulative Distribution Function (CDF) of (1) is substituted for the formula (23) to obtain P_outComprises the following steps:

5. the method of claim 1, wherein said further determining the outage probability and the channel capacity of the hybrid-fading AF relay system comprises:

in a two-hop AF relay system adopting a binomial pulse noise model, the calculation formula of the average channel capacity C of the system is as follows:

wherein

And

respectively representing the total signal-to-noise ratio of the system in the presence of only background noise and in the presence of impulse noise,

and

are respectively as

And

known at a fixed power line channel noise probability p_jThen, the system signal-to-noise ratio obeys a two-dimensional LogN distribution, that is:

the PDF formula using lognormal distribution is given as:

adopting an orthogonal method of Hermite-Gauss to carry out direct approximation to obtain a closed analytical formula of channel capacity, and enabling:

it is taken into formula (25) to obtain:

obtained by using Hermite-Gauss product calculation

Wherein

And

and the M points are respectively the Hermite-Gauss integral weight and the zero point, and the weight and the zero point can be obtained by looking up a table, wherein M is a set integer.

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