CN108900269B - Error rate performance analysis method of wireless and power line dual-medium cooperative communication system - Google Patents
Error rate performance analysis method of wireless and power line dual-medium cooperative communication system Download PDFInfo
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Abstract
The invention provides a method for analyzing the error rate performance of a wireless and power line dual-medium cooperative communication system, belonging to the technical field of dual-medium cooperative communication. The dual-medium cooperative communication system comprises a signal source S, a relay node R and a destination node D, wherein a wireless communication link SR is arranged between the signal source S and the relay node R, a wireless communication link SD is arranged between the signal source S and the destination node D, and a power line communication link RD is arranged between the relay node R and the destination node D. Firstly, the method calculates the error rate P of SR1 BERThen, calculating a distribution parameter after the signal-to-noise ratio of the SD is approximately in logarithmic normal distribution based on a probability density function approximation algorithm of a moment generating function equation; then calculating the cumulative distribution function of the instantaneous output signal-to-noise ratio after the SD and the RD are selectively combined and the error rate P of the second jump2 BER(ii) a Finally combined with P1 BERAnd P2 BERAnd obtaining the total error rate, and performing performance analysis according to the total error rate. The invention reduces the calculation complexity, can obtain the optimal distribution parameter of the instantaneous signal-to-noise ratio, and accurately calculates the error rate of the system.
Description
Technical Field
The invention relates to the technical field of a dual-medium cooperative communication system, in particular to a method for analyzing the error rate performance of a wireless and power line dual-medium cooperative communication system.
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. The PLC may rely on existing power line infrastructure to transmit information; the wireless communication has the characteristics of flexible wireless access mode, simple networking and the like. The wireless communication and the PLC have the characteristics respectively, and the power line and the wireless dual-medium cooperative communication technology are combined, so that the resource optimization and complementation can be integrated, the construction cost is saved, and the overall performance of the system is improved.
Recent research models power line channel fading as a Log normal distribution (LogN) model. Wireless communications are primarily distributed using rayleigh and Nakagami. The Nakagami model can simulate deep fading and shallow fading, is easy to process mathematically and is widely applied; the rayleigh distribution nature belongs to the special case of Nakagami.
In a power line and wireless cooperative relay system, the system performance analysis aiming at the Nakagami-LogN mixed fading condition has the following main problems: the communication theoretical performance does not have a closed expression, the complexity of performance calculation is too high, the performance analysis of the key technology excessively depends on computer simulation and the like.
Considering that under the Nakagami fading condition, the instantaneous fading energy and the signal-to-noise ratio of the channel both meet Gamma distribution, and the Gamma distribution and the LogN distribution have certain similarity, the patent provides a method for calculating the LogN distribution parameters approximate to the Gamma and LogN distribution functions, which can be applied to the system theoretical performance calculation under the Nakagami-LogN mixed fading condition and has wider application prospect and practical value.
Disclosure of Invention
The invention aims to provide a bit error rate performance analysis method of a wireless and power line dual-medium cooperative communication system, which can simplify the complexity of system performance calculation, obtain the optimal distribution parameter of the instantaneous signal-to-noise ratio and accurately calculate the bit error rate and the interruption rate of the system, so as to solve the technical problems in the background art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a method for analyzing the error rate performance of a wireless and power line dual-medium cooperative communication system, wherein the dual-medium cooperative communication system comprises a signal source S, a relay node R and a destination node D, the signal source S is in wireless communication with the relay node R and the destination node D respectively, and the relay node R is in power line communication with the destination node D, and the method comprises the following steps:
step S110: calculating the bit error rate P of the wireless link SR of the signal source S and the relay node R1 BER；
Step S120: establishing a performance function model based on a PDF (Portable document Format) approximation algorithm of a moment generating function MGF equation, and solving parameters approximate to LogN distribution according to the performance function model;
step S130: a wireless link SD to the destination node D for the signal source S and its signal-to-noise ratio γWDAnd the power line link RD from the relay node R to the destination node D and the signal-to-noise ratio gamma thereofPLDTo obtain the instantaneous output signal-to-noise ratio gamma after SC combinationDFCumulative distribution function FDF(λ)；
Step S140: according to said FDF(lambda), converting the error rate performance analysis under the mixed fading condition into the performance analysis under the same LogN distribution condition to obtain the error rate P of the second hop after SC combination2 BER；
Step S140: incorporating said bit error rate P1 BERAnd said bit error rate P2 BERObtaining the total error rate of the system
Further, the step S110 includes:
combining the wireless channel fading coefficient and the average signal-to-noise ratio, and obtaining the bit error rate P by using the moment generating function MGF and the Gaussian hypergeometric function1 BERThe closed expression of (c) is:
wherein omegaRRepresents the variance of the fading amplitude, m, of the radio link SRRRepresenting a fading parameter, Δ, of the radio link SRWRepresenting the average signal-to-noise ratio of the wireless communication link,2F1(..; -;) represents a gaussian hypergeometric function, and Γ (·) represents a gamma function.
Further, the step S120 includes:
step S121: respectively establishing MGF equations of Gamma distribution and LogN distribution variables:
known as HWDRepresents the fading coefficient of the wireless link SD, then
Satisfies G (. alpha.)D,βD) In which α isD＝mD,βD＝ΩD/mD(ii) a Wherein omegaDRepresents the variance of the fading amplitude, m, of the radio link SDDThe shape parameter representing the fading of the wireless link SD, and omega is made to satisfy the channel fading normalizationD＝1；
G (alpha)D,βD) Distributed by
Is approximated as
Let MPl(si)＝MD(si) The approximated MGF equation can be found:
wherein, wnAnd anRespectively representing the weight and the zero of the Gauss-Hermite formula.
Step S122: based on the approximated MGF equation established in step S121, a performance function model is established, and a parameter of LogN distribution after approximation is obtained:
with G (alpha)D,βD) Are distributed and
and establishing a performance function model for the target with the minimum distribution difference:
the following conditions are satisfied:
1)：
2)：
3)：Hj＝0.01+0.05*(j-1)；
4)：j＝1,2,…N；
5)：s1>0；
6)：s2>0；
wherein HjThe sampling value of the wireless channel fading H is represented, and N represents the total sampling point number of the probability density function;
the PDF distribution parameter s can be obtained according to the performance function model1、s2And
parameter μ approximated as LogN distributionD、σD；
Step S123: according to
Binding parameter muD、σDDetermining gammaWDIs approximated as
The latter parameter muwDAnd
wherein,
μwD＝ln(ΔW)+μD。
further, the step S130 includes:
known as HPLDRepresenting the fading coefficient, H, of the power line link RDPLDSatisfy the requirement of
Let gamma bePLDRepresenting the instantaneous signal-to-noise ratio at the receiving end of the power line link RD, based on the average signal-to-noise ratio DeltaPLAnd the nature of the lognormal variable, determining
Will also satisfy the lognormal distribution
And is
Output signal-to-noise ratio gamma in combination with power line link RDPLDAnd the output signal-to-noise ratio gamma of the wireless link SDWDTo obtain the instantaneous output signal-to-noise ratio gamma after SC combinationDFCumulative distribution function FDF(λ)：
FDF(λ)＝Pr(γDF＜λ)＝Pr(γWD＜λ)；
The complementary cumulative distribution function of the standard normal distribution, also called Q function, is used for calculating to obtain:
wherein, λ represents the interrupt threshold signal-to-noise ratio after SC combination.
Further, the step S140 includes:
for the cumulative distribution function FDF(lambda) integration, converting the error rate performance analysis under the mixed fading condition into the performance analysis under the same LogN distribution condition, and then obtaining the error rate P2 BERComprises the following steps:
wherein,
representing the Poisson distribution with the mean value A obeyed by the pulse number k of the power line link RD; PN represents the maximum number of impulse noise, and the PN is more than 20;
converting the error rate performance analysis under the mixed fading condition into the performance analysis under the same LogN distribution condition, the error rate P2 BERComprises the following steps:
wherein, according to the fading distribution parameter of the power line link RD
And
approximate distribution parameter of
Solving for the constant Wt.k、Vt.k、Ut.k。
Further, said combining said bit error rate P1 BERAnd said bit error rate P2 BERObtaining the total error rate of the system
Comprises the following steps:
the invention has the beneficial effects that: the complexity of system performance calculation can be simplified, the optimal distribution parameter of the instantaneous signal-to-noise ratio can be obtained, and the error rate and the interruption rate of the system can be accurately calculated.
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.
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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 an architecture diagram of a wireless and power line dual-medium cooperative communication system according to an embodiment of the present invention.
FIG. 2 is a graph of delta according to an embodiment of the present inventionWThe PDF curve at 1 is compared with the diagram.
FIG. 3 is a graph of delta according to an embodiment of the present inventionWThe PDF curve at 2 is compared with the diagram.
Fig. 4 is a schematic diagram illustrating comparison between simulation performance and theoretical performance of an interruption probability monte carlo according to an embodiment of the present invention.
Fig. 5 is a schematic diagram illustrating comparison between simulation performance and theoretical performance of the bit error rate monte carlo according to the embodiment of the present invention.
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 or similar reference numerals refer to the same or similar elements or modules having the same or similar functionality 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 modules, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, modules, and/or groups thereof.
It should be noted that, unless otherwise explicitly stated or limited, the terms "connected" and "fixed" and the like in the embodiments of the present invention are to be understood in a broad sense and may be fixedly connected, detachably connected, or integrated, mechanically connected, electrically connected, directly connected, indirectly connected through an intermediate medium, connected between two elements, or in an interaction relationship between two elements, unless explicitly stated or limited. Specific meanings of the above terms in the embodiments of the present invention can be understood by those skilled in the art according to specific situations.
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 of the embodiments of the present invention, the following description will be further explained by taking specific embodiments as examples with reference to the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
It will be understood by those of ordinary skill in the art that the figures are merely schematic representations of one embodiment and that the elements or devices in the figures are not necessarily required to practice the present invention.
Example one
As shown in fig. 1, an embodiment of the present invention provides a wireless and power line dual-medium cooperative communication system, which employs a dual-medium hybrid cooperative three-node (terminal S, D and relay R) two-hop relay model. Wireless communication (WIC) is performed between the mobile terminal S and the node R, D. Power Line (PLC) communication is performed between nodes R and D. Wherein the radio channel fading satisfies the Nakagami distribution.
In the above system, the first time slot is S and the transmitting power P is adoptedSSending a signal X to a relay node R and a destination node DS(ii) a The received signal is processed (hard decision decoded) for R in the second time slot to obtain a relay signal, and then the relay signal is processed with power PRSending a signal to the destination node D.
The channels in both time slots are affected by multiplicative fading and additive noise. Since the implementation complexity of the selective SC combining is low, and is suitable for the dual-medium hybrid communication system, the terminal D finally combines the received signals by using the SC combining algorithm.
In fig. 1, S refers to a smart meter or a sensor on or independent from an electrical device, such as a smart meter in a building or 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 in a mobile way, the penetration capacity of high-frequency-band radio waves is limited, the fading is large and the like, a hybrid cooperation mode of wireless access (S- > R) and PLC-wireless parallel relay (R- > D) is adopted between an intelligent instrument or a sensor (S) and a gateway D, and the mobile access and the remote communication are realized.
The wireless signals received by the first slot nodes R and D are:
wherein the noise nWRAnd nWDSatisfy the normal distribution N (0, N)W)；HWRAnd HWDFor the radio fading coefficients, the Nakagami distribution is satisfied:
where I is in { D, R }, mINakagami parameter is not less than 0.5; r (x) is a gamma function;
is the variance of fading amplitude, and is normalized to omega to ensure that fading does not change the average power of the received signalIIs 1.
Let Delta beW＝PS/NWRepresenting the channel average signal-to-noise ratio. Then according to the forwarding formulas (1) and (2), the instantaneous snr at the receiving end of the wireless channel is:
it is known that
Satisfying the Gamma distribution G (. alpha.)I,βI) Having the form:
wherein G (. alpha.) isI,βI) The parameter relation of the Nakagami distribution and the Nakagami distribution satisfies alphaI＝mI；βI＝ΩI/mI. According to the property of Gamma distribution, under the condition of the same average signal-to-noise ratio, when delta isWAt a fixed constant, there is γWI～G(mI,ΔWΩI/mI)。
The second time slot relay node R adopts the decoding and forwarding DF protocol to make hard decision on the received signal and uses power PRAnd forwarded to the destination node D. Let XRThe signal indicating relay forwarding, the signal received by the receiving end is:
wherein HPLDSatisfy the power line fading coefficient
Wherein muPLDAnd σPLDRespectively represent lnHPMean and mean square error of. The channel fading envelope energy is normalized to ensure that the channel fading does not change the average power of the signal, making,
N in the formula (7)PLDFor the pulse noise of the power line, Mid-A pulse noise is adoptedAnd (4) an acoustic model. The model is composed of Gaussian background noise NGAnd impulse noise NIThe probability density function of the impulse noise amplitude Z is:
wherein N isk＝N0(k/a + T)/(1+ T), representing the instantaneous total noise power of the power line, T ═ NG/NIRepresenting the ratio of the background noise power and the impulse noise power. N is a radical of0＝NG+NIIs the average total noise power. At a specific sampling moment, the impulse noise of the Mid-A model is formed by overlapping k Gaussian noises, and each noise model meets N (0, N)IA). The number of pulses k obeys a Poisson distribution with mean A (e)-A·Ak) K! PN represents the maximum number of impulse noises, and PN is greater than 20.
Let Delta bePL＝PR/NkThe instantaneous snr at the receiving end of the power line can be expressed as:
then after node D adopts SC, the total output signal-to-noise ratio of the system is:
γDF＝max(γPLD,γWD) (11)
the instantaneous mutual information quantity of the system is as follows:
example two
The second embodiment of the present invention provides a method for analyzing the interrupt probability performance of the dual-media cooperative system as shown in fig. 1. To obtain the outage probability of the system, the information rate of each branch needs to be analyzed. When the system information rate R is less than the required minimum rate threshold, normal communication by the system will be interrupted. According to the shannon formula, the information rate of each branch is directly related to the signal-to-noise ratio, so the PDF of the signal-to-noise ratio of each branch is firstly analyzed.
Signal to noise ratio gamma of wireless channelWRAnd gammaWDAnd the Gamma distribution is satisfied. When the signal-to-noise ratio of the receiving end is smaller than the signal-to-noise ratio gamma corresponding to the interruption thresholdthThe communication link is broken. According to the equations (4) and (6), the Gamma distribution function is integrated, and then the interruption probability of the SR branch is:
wherein v (a, b) represents an incomplete Gamma function and the mathematical expression is
F (x) is the gamma function.
Similarly, the interruption probability of the wireless direct SD branch is:
known power line channel fading coefficient HPLDThe LogN is satisfied. According to the LogN property, the average signal-to-noise ratio deltaPLWhen it is constant, then γPLDWill also satisfy the lognormal distribution
And is
For gammaPLDSatisfying the LogN distribution, the interrupt probability of the PLC link can be represented by a Q function:
the interruption probability of each branch in the joint formulas (13), (14) and (15) can be calculated to obtain the total interruption probability of the dual-medium cooperative relay system under the mixed fading and impulse noise conditions:
EXAMPLE III
The third embodiment of the present invention provides a method for analyzing the bit error rate performance of the system shown in fig. 1.
In order to solve the bit error rate of the DF cooperative relay system, the communication system is divided into two hops: the SR link is the 1 st hop, and the RD and SD parallel communication links are the 2 nd hops. Let P1 BERBit error rate for SR link (1 st hop); p2 BERError rate after SC combining for the 2 nd hop parallel communication link.
The fading coefficient H of the SR branch of the 1 st hop is knownWRSatisfying the Nakagami distribution when the average signal-to-noise ratio of the link is deltaWWhen to HWDAnd (3) calculating integral, and obtaining an error rate closed expression of the wireless SR branch by utilizing MGF and Gaussian super-geometric function:
wherein,2F1(..; -. The.) is a Gaussian hypergeometric function.
To obtain the 2 nd hop error rate, the computing system needs to adopt the instantaneous output signal-to-noise ratio gamma after SC combinationDFThe cumulative distribution function of (a). Since the wireless branch and the power line branch signals in the 2 nd hop are independent of each other, the cumulative distribution function F is obtainedDF(λ) is:
FDF(λ)＝Pr(γDF＜λ)＝Pr(γWD＜λ)Pr(γPLD＜λ) (18)
it is obvious that formula (18) relates to the product of formulae (14) and (15), for formula (18) FDFThe (lambda) integration can obtain the bit error rate P2 BER：
Under the mixed attenuation, functions like ν (a, b) and Γ (x) in the formula (18) are integrated, and the algorithm complexity is large, so the embodiment adopts a PDF approximation method to process the formula (19) to expect to obtain a closed expression.
Since the LogN distribution has certain similarity with the Gamma distribution, G (alpha) can be convertedD,βD) Distributed by
Is approximated as
Signal to noise ratio γ according to the nature of the LogN distributionWDAnd if the distribution is also obeyed to the LogN distribution, the error rate performance analysis can be converted into the performance analysis problem under the same LogN distribution.
In the PDF approximation process, the PDF parameters after approximation are solved in a way that PDF statistics are equal. Let G (alpha)D,βD) And LogN (mu)D,σ2 D) Are equal, then:
after equation transformation, the key parameters of LogN can be obtained:
the method aims at the problem of poor approximation precision when the mean value and the variance are equal to perform PDF approximation. In the third embodiment, a PDF approximation algorithm based on a Moment Generating Function (MGF) equation is provided, which has higher precision and can be used to calculate the instantaneous signal-to-noise ratio γWDThe PDF parameter of (1).
It is known that
Satisfying the Gamma distribution G (. alpha.)D,βD) In which α isD＝mD，βD＝ΩD/mD，ΩD＝1；
Wherein HWDWhen i is (1,2), G (α) is approximated by MGF approximationD,βD) Distributed by
Is approximated as
Make MPl(si)＝MD(si) Obtaining:
wherein, wnAnd anRespectively representing the weight and the zero of the Gauss-Hermite formula, GN representing the number of the weight and the zero of the Gauss-Hermite formula, and generally 5, 8 or 12 can be taken, and the higher the value of GN is, the higher the precision of Gauss-Hermite approximate calculation is.
As shown in FIG. 2, is when ΔWH2 under different approximation method for 1WDCompare the PDF curves of (a). Under the normalized condition of channel fading (omega)D1) for different parameters m and s1、s2Combined to give H2WDComparing the PDF curves of the two approximation methods. As can be seen from fig. 2, compared with the PDF statistical value approximation method, the MGF equation approximation method lacks an analytical expression, but can pass through s1And s2The optimization selection is carried out, and the precision of the algorithm is high; fading parameter mDThe smaller the channel fading, the more serious the channel fading, so the MGF equation approximation method is suitable for the case of low channel fading degree, when m isD>1.5, the probability density approximation effect of the channel is good; when m isD>At 1.5, s can be1Set to 3; s2With mDThe value increases when m increasesDWhen 2, s2Taking 7; when m isDWhen increasing to 2.5, s210 can be taken; when m isDWhen equal to 3, s2Preferably 15 is used.
Example four
The fourth embodiment of the invention provides a method for reducing the parameter mu in the third embodimentDAnd
and a method for calculating complexity, wherein a performance function model is established based on the minimum PDF curve difference as a target.
To reduce complexity, s is used in this embodiment1Is set to 3. In practical application, the mathematical modeling can be carried out on the target with the minimum difference degree of the probability density curve, and the optimal s can be solved1And s2Combining, for radio fading parameters alphaD＝mD；βD＝ΩD/mDAll right (1)Using PDF expressions (6) and (8), with s1And s2For variables, the following mathematical models were established:
the following conditions are satisfied:
1)：
2)：
3)：Hj＝0.01+0.05*(j-1)；
4)：j＝1,2,…N；
5)：s1>0；
6)：s2>0；
wherein HjThe sampling value of the wireless channel fading H is represented, and N represents the total number of sampling points of the probability density function (N is taken as 100). The mathematical model takes the goodness of fit of a PDF curve as an optimization target, and calculates each fading sampling value HiThe square of the difference of the corresponding two probability density function values is then weighted. The mathematical model can be solved by adopting an intelligent optimization algorithm such as a genetic algorithm. Using the above method, the approximate optimal s-value of the MGF equation can be established, as shown in Table 1.
TABLE 1
EXAMPLE five
The fifth embodiment of the invention provides a method for approximating PDF of fading normalization and combining signal-to-noise ratio deltaWCalculating gammaWDThe method for equivalent parameters comprises the following specific steps:
1) in that
I.e. omegaDUnder the condition of 1, for
Different fading parameters mDIs approximated by using MGF equation, s1And s2Method for optimizing selection, calculating G (alpha)D,βD) Parameter μ approximated as LogN distributionDAnd σD；
2) Because of the fact that
Step 2 requires according toWDetermining a variable gammaWDIs approximated as
The latter key parameters:
σWD 2＝σD 2 (24)
μWD＝ln(ΔW)+μD (25)
according to the above calculation procedure, as shown in FIG. 3, when Δ isWGamma at 2, under different approximation methodsWDCompare the PDF curves of (a). In fig. 3, compared with the mean variance approximation method, the MGF method adopted in the present embodiment has a better approximation effect. Obviously, the proposed MGF approximation method can obtain a better PDF approximation effect without repeated computer numerical experiments.
In the fourth embodiment, after the PDF approximation processing, the error rate performance analysis under the hybrid fading condition is converted into the performance analysis problem under the same LogN distribution condition, and then the error rate performance of the 2 nd hop is:
wherein Wt.k、Vt.k、Ut.kConstant and power line channel fading distribution parameter
And
approximate distribution parameter of
In relation, the following relationship is satisfied:
Yt,k＝σL+T2+4(μL+R2k-ln0.5)σL/R3k 2；
T1＝0.769；T2＝1.527；T3＝1.393；
R1k、R2kand R3kThe values of (a) are shown in table 2:
TABLE 2
Then the error code of the two-hop link under BPSK modulation can be calculated according to the equations (17) and (26)Rate P1 BERAnd P2 BERAnd finally the total error rate of the hybrid cooperative system
Comprises the following steps:
simulation contrast experiment
In order to verify the accuracy of the theoretical formula, a monte carlo simulation experiment was performed using Matlab software. The Monte Carlo simulation method is also called statistical experiment method, is a random simulation and calculation method based on probability and statistical theory, and adopts statistical sampling theory to approximately solve mathematic and engineering problems, and has been widely applied to experimental verification in the field of information communication. Firstly, the simulation performance and the theoretical performance of numerical calculation are compared and analyzed, so that the reliability of the performance mechanism of the system is ensured by analyzing the factors such as hybrid fading, power and the like subsequently.
Referring to the existing references, in order to avoid loss of generality, parameters in the simulation and calculation process are set by the following defaults if no special description exists: defining power by variance of noise PDF distribution, and setting total system power as 2, PS＝1，P R1 is ═ 1; to highlight the impact of channel fading and noise distribution on performance, the average signal-to-noise ratio of the system channel is assumed to be SNR, NW＝N k1/SNR, i.e. DeltaPL＝ΔWΔ; parameters of impulse noise: and A is 0.2, T is 0.01, and the maximum value of k in the theoretical formula is PN 100.
By adopting the parameter setting, MGF represents the approximation of the moment generating function, and Mean-Var represents the approximation of the Mean variance. Fig. 4 and 5 compare the outage probability and the error rate performance of the DF relaying system with different channel attenuation parameters. In consideration of the fact that the channel condition of the direct link SD is not as good as that of the short-range wireless link SR in practical application, m is set in the simulationDIs 1, mRThe value is greater than 1. The analysis can conclude that:
1) in fig. 4, since the derived outage probability formula does not involve probability density approximation, as the SNR increases, the theoretical performance (theo) and the simulated (simul) performance curves for calculating the outage probability according to the theoretical formula are compared and matched, and the reliability of the outage probability theoretical formula is verified. In fig. 4, when the fading index is constant, the larger the average SNR is, the smaller the outage probability of the system is.
2) Fig. 5 compares the simulated (simul) and theoretical (theo) results of the system bit error rate. Although the probability density of the Gamma distribution and the LogN distribution is approximate on the direct link SD, the theoretical performance and the simulation performance are basically consistent under the condition of high signal-to-noise ratio (when the SNR is more than 14 dB).
In summary, the power line and wireless dual-medium cooperative communication technology provided by the embodiment of the invention can integrate advantageous resources, save construction cost and improve the overall performance of the system. Aiming at a dual-medium hybrid cooperative system, a system performance analysis framework is established by adopting a hybrid channel fading and multi-dimensional pulse noise model based on Nakagami and LogN, and a closed system performance expression is solved by adopting algorithms such as MGF equation approximation and the like. Aiming at indoor and outdoor universal wireless Nakagami fading, the signal-to-noise ratio of a wireless branch adopts Gamma distribution-LogN distribution approximate transformation, so that better reliability is achieved, and relevant conclusions can provide necessary theoretical support for application of an indoor and outdoor double-medium cooperative communication technology.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
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 (4)
1. A method for analyzing error rate performance of a wireless and power line dual-medium cooperative communication system, wherein the dual-medium cooperative communication system comprises a signal source S, a relay node R and a destination node D, the signal source S is in wireless communication with the relay node R and the destination node D respectively, and the relay node R is in power line communication with the destination node D, the method comprises the following steps:
step S110: calculating the bit error rate P of the wireless link SR of the signal source S and the relay node R1 BER(ii) a The step S110 includes:
combining the wireless channel fading coefficient and the average signal-to-noise ratio, and obtaining the bit error rate P by using the moment generating function MGF and the Gaussian hypergeometric function1 BERThe closed expression of (c) is:
wherein omegaRRepresents the variance of the fading amplitude, m, of the radio link SRRRepresenting a fading parameter, Δ, of the radio link SRWRepresenting the average signal-to-noise ratio of the wireless communication link,2F1(..; -) represents a Gaussian hypergeometric function, and Γ () represents a gamma function;
step S120: establishing a performance function model based on a PDF (Portable document Format) approximation algorithm of a moment generating function MGF equation, and solving parameters approximate to LogN distribution according to the performance function model;
the step S120 includes:
step S121: respectively establishing MGF equations of Gamma distribution and LogN distribution variables:
known as HWDRepresents the fading coefficient of the wireless link SD, then
Satisfying gamma distribution, using G (alpha)D,βD) Is represented by, whereinD＝mD,βD＝ΩD/mD(ii) a Wherein omegaDRepresents the variance of the fading amplitude, m, of the radio link SDDThe shape parameter representing the fading of the wireless link SD, and omega is made to satisfy the channel fading normalizationD＝1；
G (alpha)D,βD) Distributed by
Is approximated as
Let MPl(si)＝MD(si) The approximated MGF equation can be found:
wherein, wnAnd anRespectively representing the weight and zero point of the Gauss-Hermite formula, GN representing the weight and zero point of the Gauss-Hermite formulaThe number of zeros;
step S122: based on the approximated MGF equation established in step S121, a performance function model is established, and a parameter of LogN distribution after approximation is obtained:
with G (alpha)D,βD) Are distributed and
and establishing a performance function model for the target with the minimum distribution difference:
the following conditions are satisfied:
1)：
2)：
3)：Hj＝0.01+0.05*(j-1)；
4)：j＝1,2,…N；
5)：s1>0；
6)：s2>0；
wherein HjThe sampling value of the wireless channel fading H is represented, and N represents the total sampling point number of the probability density function;
the PDF distribution parameter s can be obtained according to the performance function model1、s2And
parameter μ approximated as LogN distributionD、σD；
Step S123: according to
Binding parameter muD、σDDetermining gammaWDIs approximated as
The latter parameter muwDAnd
wherein,
μwD＝ln(ΔW)+μD；
step S130: outputting a signal-to-noise ratio gamma according to the power line link RDPLDAnd the output signal-to-noise ratio gamma of the wireless link SDWDTo obtain the instantaneous output signal-to-noise ratio gamma after SC combinationDFCumulative distribution function FDF(λ); lambda represents the interrupt threshold signal-to-noise ratio after SC merging;
step S140: according to said FDF(lambda), converting the error rate performance analysis under the mixed fading condition into the performance analysis under the same LogN distribution condition to obtain the error rate P of the second hop after SC combination2 BER；
Step S150: incorporating said bit error rate P1 BERAnd said bit error rate P2 BERObtaining the total error rate of the system
2. The method for analyzing bit error rate performance of a wireless and power line dual medium cooperative communication system according to claim 1, wherein the step S130 comprises:
known as HPLDRepresenting the fading coefficient, H, of the power line link RDPLDSatisfy the requirement of
Let gamma bePLDRepresenting the instantaneous signal-to-noise ratio at the receiving end of the power line link RD, based on the average signal-to-noise ratio DeltaPLAnd the nature of the lognormal variable, determining
Will also satisfy the lognormal distribution
And is
Output signal-to-noise ratio gamma in combination with power line link RDPLDAnd the output signal-to-noise ratio gamma of the wireless link SDWDTo obtain the instantaneous output signal-to-noise ratio gamma after SC combinationDFCumulative distribution function FDF(λ)：
FDF(λ)＝Pr(γDF＜λ)＝Pr(γWD＜λ)；
Calculating by using a Q function to obtain:
wherein, λ represents the interrupt threshold signal-to-noise ratio after SC combination.
3. The method for analyzing bit error rate performance of a wireless and power line dual medium cooperative communication system according to claim 2, wherein the step S140 comprises:
for the cumulative distribution function FDF(lambda) integration, converting the error rate performance analysis under the mixed fading condition into the performance analysis under the same LogN distribution condition, and then obtaining the error rate P2 BERComprises the following steps:
wherein,
representing the number of pulses k obeying of the power line link RDPoisson distribution with mean a; PN represents the maximum number of impulse noise, and the PN is more than 20;
converting the error rate performance analysis under the mixed fading condition into the performance analysis under the same LogN distribution condition, the error rate P2 BERComprises the following steps:
wherein, according to the fading distribution parameter of the power line link RD
And
approximate distribution parameter of
Solving for the constant Wt.k、Vt.k、Ut.k。
4. The method of claim 3, wherein the method comprises the following steps: said combined bit error rate P1 BERAnd the error rate
Obtaining the total error rate of the system
Comprises the following steps:
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