CN113141222B - Asymptotic approach error rate performance analysis method - Google Patents
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Abstract
The invention discloses a method for analyzing the performance of asymptotic close approximation error rate, which comprises the following steps: step S1, constructing an intelligent reflector auxiliary communication system model, and calculating the signal-to-noise ratio gamma output by the maximum ratio combiner; step S2, performing bit error rate analysis on the intelligent reflector assisted communication system, and converting γ into γ ═ γ1+γ2Form of (1) each constituting γ1And gamma2A moment mother function of; step S3, according to gamma1And gamma2Moment mother function of
And
and obtaining the asymptotic approach error rate. The invention reasonably constructs the reflection coefficient and the intelligent reflecting surface link coefficient, so that the signal-to-noise ratio on the intelligent reflecting surface forwarding link satisfies the harmonic mean value form, deduces a system asymptotic close approximation formula with a simple structure, and performs performance analysis on the intelligent reflecting surface auxiliary communication system by using a control variable method, thereby performing performance analysis on the error rate performance of the intelligent reflecting surface auxiliary communication system and the single-time-slot amplify-and-forward multi-relay systemAnd (6) performing line comparison analysis.
Description
Technical Field
The invention relates to the field of intelligent reflector auxiliary communication, in particular to a method for analyzing asymptotic approach error rate performance of an intelligent reflector auxiliary communication system.
Background
In future wireless communication systems, the intelligent reflecting surface technology provides a potential approach for solving the problems of needing larger bandwidth, higher spectral efficiency, more intelligent transmission technology and the like. The intelligent reflecting surface technology is a plane composed of a large number of low-cost passive reflecting elements, and the amplitude and the phase of an incident signal can be adjusted by controlling each element through software. The intelligent reflector technology has the advantages of strong expandability, low implementation cost, wide working frequency band, capability of realizing wireless propagation environment configuration and the like.
The intelligent reflector auxiliary communication system is considered to be a single-time-slot amplifying and forwarding multi-relay system without forwarding power, but the error rate performance comparison of the two systems has no quantitative analysis and theoretical basis.
Disclosure of Invention
The invention provides a method for analyzing asymptotic approach error rate performance of an intelligent reflector auxiliary communication system, which aims to solve the technical problem of comparative analysis of error rate performance of the intelligent reflector auxiliary communication system and a single-time-slot amplification forwarding multi-relay system.
The invention is realized by adopting the following technical scheme: a method for analyzing the performance of asymptotic approach error rate is used for carrying out comparative analysis on the performance of error rate of an intelligent reflector auxiliary communication system and a single-time-slot amplification forwarding multi-relay system, and comprises the following steps:
step S1, constructing an intelligent reflector auxiliary communication system model, and calculating the signal-to-noise ratio gamma output by the maximum ratio combiner;
step S2, performing bit error rate analysis on the intelligent reflector assisted communication system, and converting the signal-to-noise ratio γ into γ ═ γ1+γ2Respectively constructing the signal-to-noise ratio gamma1And signal-to-noise ratio gamma2The moment mother function of (2), wherein the signal-to-noise ratio γ2Need to be constructed to satisfy a harmonic mean form; the bit error rate analysis method comprises the following steps:
step S21, defining the signal-to-noise ratio of direct link and intelligent reflecting surface forwarding link in the intelligent reflecting surface auxiliary communication system as gamma respectively1And gamma2And has γ ═ γ1+γ2；
Step S22, constructing the signal-to-noise ratio gamma1And said signal-to-noise ratio γ2Are expressed as Mγ1(s) and Mγ2(s)：
Wherein,
for a deterministic channel h from a source node to a destination nodes，dThe variance of (a) is determined,
is a deterministic channel h from the source node to the intelligent reflecting surfaces,rThe variance of (a) is determined,
is a deterministic channel h from the intelligent reflecting surface to the destination noder,dS is the transmitted power normalized signal, m is a constant, P is the transmitted power,
obeying a mean value of 0 and a variance of N0Complex white gaussian noise;
step S3, according to the moment mother function Mγ1(s) and the moment mother function
And obtaining the asymptotic approach error rate of the intelligent reflector auxiliary communication system.
As a further improvement of the above solution, in step S1, the intelligent reflective surface auxiliary communication system model is composed of a source node, a destination node, and an intelligent reflective surface having N reflective units.
As a further improvement of the above scheme, in step S1, the signal-to-noise ratio γ output by the maximal ratio combiner is represented as:
wherein N is the number of reflecting units, and alpha is belonged to (0, 1)]Is a fixed amplitude reflection coefficient, theta is a phase shift variable optimized by the intelligent reflecting surface, P is the transmitting power, N0Is the complex gaussian white noise variance.
As a further improvement of the above, in step S21, the signal-to-noise ratio γ1And said signal-to-noise ratio γ2Respectively expressed as: gamma ray1＝(P|hs,d|2)/N0，
Wherein, X'1And X'2Are all variables in the harmonic mean construction process.
As a further improvement of the above scheme, in step S21, the X'1Expressed as:
X′1＝(1+2m)P|hs,r|2/N0and X'1Compliance parameter of
In which the index of the distribution of (a),
as a further improvement of the above scheme, in step S21, the X'2Expressed as: x'2＝(1+m)N2|hr,d|2/N0And X'2Compliance parameter of
Is referred to asNumber distribution.
As a further improvement of the above solution, in step S3, the intelligent reflector assisted communication system has an asymptotic close-proximity error rate of the direct link
Expressed as:
As a further improvement of the above solution, in step S3, the bit error rate of asymptotic close approximation without a direct link in the intelligent reflector assisted communication system
Expressed as:
as a further improvement of the above solution, the constant B is expressed as:
the invention also provides an intelligent reflector auxiliary communication system, which enables the signal-to-noise ratio on the intelligent reflector forwarding link to meet the harmonic mean value form through reasonable construction between the reflection coefficient and the intelligent reflector link coefficient, deduces a system asymptotic close approximation formula with a simple structure, and performs performance analysis on the intelligent reflector auxiliary communication system by using a control variable method, thereby performing comparative analysis on the error rate performance of the intelligent reflector auxiliary communication system and the single-time-slot amplify-and-forward multi-relay system.
The invention carries out fitting analysis on the theoretical numerical value and the actual simulation numerical value of the system bit error rate asymptotic approach formula and tests the diversity gain function provided by the direct link for the system. With the increase of the number of the intelligent reflection units, the system bit error rate performance is also improved, but when the number of the intelligent reflection units reaches a certain number, the system bit error rate performance cannot be effectively improved, and the system bit error rate performance can be accurately described by a system bit error rate asymptotic approach formula under the condition of a lower signal-to-noise ratio.
Compared with an amplifying and forwarding multi-relay system, the intelligent reflector auxiliary communication system has slightly better system error rate performance only under the condition of low signal-to-noise ratio, but the advantage of the intelligent reflector auxiliary communication system in the aspect of frequency spectrum efficiency is not influenced. In addition, when the number of units of the intelligent reflecting surface is small, namely under the condition of low signal to noise ratio, the closer the distance between the intelligent reflecting surface and the source node is, the better the error rate performance of the intelligent reflecting surface auxiliary communication system is. Therefore, theoretical basis of error rate angle is provided for selection of the intelligent reflecting surface and determination of unit number in actual communication scene.
Drawings
Fig. 1 is a flowchart of an analysis method in an asymptotic close-proximity error rate performance analysis method according to embodiment 1 of the present invention.
Fig. 2 is a graph showing a relationship between a theoretical value and a simulated value of an asymptotic approach error rate in an analysis method of an asymptotic approach error rate performance analysis method for a system with a direct link and a system without a direct link according to embodiment 2 of the present invention.
Fig. 3 is a system error rate performance curve diagram under different numbers of reflection units in an analysis method in an asymptotic approach error rate performance analysis method provided in embodiment 2 of the present invention.
Fig. 4 is a graph comparing error rate performance of the intelligent reflector assisted communication system and the amplify-and-forward multi-relay system in the analysis method in the asymptotic approach error rate performance analysis method provided in embodiment 2 of the present invention.
Fig. 5 is a graph of theoretical error rate values of different deterministic channel variances in an analysis method in an asymptotic approach error rate performance analysis method according to embodiment 2 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
Referring to fig. 1, the present embodiment introduces a method for analyzing error rate performance of asymptotic tight approach, which performs comparative analysis on error rate performance of an intelligent reflector assisted communication system and a single timeslot amplify-and-forward multi-relay system. The analysis method comprises the following steps:
and step S1, constructing an intelligent reflector auxiliary communication system model, and calculating the signal-to-noise ratio gamma output by the maximum ratio combiner.
The intelligent reflecting surface auxiliary communication system model is composed of a source node, a destination node and an intelligent reflecting surface with N reflecting units. The deterministic path from the source node to the destination node is hs,dThe deterministic channel from the source node to the intelligent reflecting surface is hs,rThe deterministic channel from the intelligent reflecting surface to the destination node is hr,dAnd has [ h ]s,r]n＝[hs,r]n+1＝hs,rWherein h iss,rObedience mean of 0 and variance of
Rayleigh distribution of [ h ]r,d]n＝[hr,d]n+1＝hr,dWherein h isr,dObedience mean of 0 and variance of
The rayleigh distribution of (a).
So that the phase shift matrix of the intelligent reflecting surface is expressed as
Wherein, alpha is (0, 1)]Is a fixed amplitude reflection coefficient, and θ1,...,θNIs a phase shift variable θ that can be optimized by IRSn＝arg(hs,d)-arg([hs,r]n[hr,d]n). The signal y received by the destination node is represented as:
where P is the transmit power, s is the transmitted power normalization signal,
obeying a mean value of 0 and a variance of N0Complex white gaussian noise.
Suppose the phase shift variable theta of each reflection unit1,...,θNEqual, Θ can be further expressed as α diag (e)jθ,...,ej θ). Thereby to obtain
Can be further expressed as N alpha ejθhs,rhr,dThen the signal y received by the destination node can be converted into:
assuming that the destination node can completely acquire a channel coefficient, and the received signal is processed by using the maximal ratio combiner, the output signal-to-noise ratio of the maximal ratio combiner is expressed as:
step S2, performing bit error rate analysis on the intelligent reflector assisted communication system, and converting the signal-to-noise ratio γ into γ ═ γ1+γ2Respectively constructing the signal-to-noise ratio gamma1And signal-to-noise ratio gamma2The moment mother function of (2), wherein the signal-to-noise ratio γ2It needs to be constructed to satisfy the harmonic mean form. The bit error rate analysis method comprises the following steps:
step S21, defining the signal-to-noise ratio of direct link and intelligent reflecting surface forwarding link in the intelligent reflecting surface auxiliary communication system as gamma respectively1And gamma2And has γ ═ γ1+γ2。
According to the error rate calculation formula and the complex modulus property of the M-PSK modulation system
Is converted into
To avoid loss of generality, | h is assumeds,dI and | hs，rhr，dThe linear relation is | h |s，d|＝mNα|hs,rhr，dIf y can be further expressed as
Wherein gamma is1＝(P|hs,d|2)/N0For the signal-to-noise ratio corresponding to the direct link,
and forwarding the equivalent signal-to-noise ratio corresponding to the link for the intelligent reflecting surface.
Step S22, constructing the signal-to-noise ratio gamma1And said signal-to-noise ratio γ2Are expressed as Mγ1(s) and Mγ2(s)。
Wherein, due to gamma1＝(P|hs,d|2)/N0Compliance parameter of
Is distributed exponentially, thus gamma1Moment mother function of
Can be directly expressed as:
due to gamma2Forms that do not satisfy the harmonic mean, hence, for γ2And constructing a harmonic mean value form, and expressing a moment mother function.
Intelligent reflecting surface reflection coefficient alpha epsilon (0, 1)]Suppose that
Then gamma is2Can be expressed as:
wherein, X'1Expressed as: x'1＝(1+2m)P|hs,r|2/N0And X'1Compliance parameter of
Index distribution of (2), X'2Expressed as: x'2＝(1+m)N2|hr,d|2/N0And X'2Compliance parameter of
Is used as the index distribution of (1). For the signal-to-noise ratio γ, according to the simple MGF theorem of harmonic means2Their corresponding moment mother functions
Expressed as:
Step S3, according to the moment mother function
And the moment mother function
And obtaining the asymptotic approach error rate of the intelligent reflector auxiliary communication system.
Due to the moment mother function
And the mother function of the moment
It has been found that by giving a particular form of M-PSK, a closed-form solution to the bit error rate can be obtained. So that the asymptotic close approximation of the bit error rate with a direct link in a smart reflector assisted communication system given a particular form of M-PSK
Expressed as:
asymptotic close approximation of bit error rate without direct link
Expressed as:
wherein, bPSK＝sin2(π/M) and
is a constant number of times, and is,
example 2
The embodiment describes the relationship between the theoretical value of the asymptotic close-proximity error rate SER and the simulation value of the system with the direct link and the system without the direct link in the intelligent reflector assisted communication system. Referring to fig. 2, a monte carlo method is adopted, a maximum likelihood method is adopted at a destination node to detect an output signal of a maximal ratio combiner, and QPSK modulation is adopted in system simulation, that is, M is 4, SNR is P/N0And assume N01, wherein N is 32,
as can be seen from FIG. 2, when the SNR is greater than 10dB, i.e. under the condition of low bit error rate, the theoretical value and the simulated value have good fitting effect, thereby proving the effectiveness of the derived formula of the asymptotic approximation bit error rate SER. As the signal-to-noise ratio increases, the error rate of each case tends to decrease. The direct link situation is more down-graded than the direct link-free situation. This is because the direct link can provide significant diversity gain to the system.
Referring to fig. 3, the present embodiment also introduces the system bit error rate performance under different numbers of reflection units, where the number N of reflection units of the intelligent reflection surface IRS belongs to {4,32,256},
as can be seen from fig. 3, the error rate performance of the case with the direct link is more reduced than that of the case without the direct link. When N belongs to {32,256}, namely when the number of reflection units reaches a certain value, a good fitting effect is achieved between the simulated value and the error rate theoretical value in the two cases of direct link and no direct link. But the continuous increase of the number of the reflecting units does not have obvious improvement effect on the error rate performance of the system.
Referring to fig. 4, the present embodiment is further introduced to compare the bit error rate performance of the intelligent reflector assisted communication system and the amplify-and-forward multi-relay system, where N is 32,
and adopting the error rate of the amplifying and forwarding AF multi-relay system as a comparison object. As can be seen from fig. 4, the bit error rates of the intelligent reflector assisted communication system and the amplify-and-forward multi-relay system both decrease with the increase of the signal-to-noise ratio. The bit error rate performance curves intersect at a signal-to-noise ratio of about 9 dB. When the signal-to-noise ratio is less than 9dB, the error rate performance of the intelligent reflector auxiliary communication system is slightly better than that of the amplification forwarding multi-relay system; when the signal-to-noise ratio is larger than 9dB, the error rate performance of the amplifying and forwarding multi-relay system is obviously better than that of the intelligent reflector auxiliary communication system. Although the intelligent reflector-assisted communication system has no obvious advantage in the aspect of bit error rate, the cooperative forwarding of the source node data is completed in one time slot, and the frequency spectrum efficiency is higher.
When N is 32, it is different
The theoretical value of the bit error rate is shown in fig. 5, wherein,
representing the bit error rate performance analysis for the case without a direct link. The variance of each channel coefficient is inversely related to the distance, i.e., the larger the variance, the smaller the distance, and vice versa. As can be seen from fig. 5, when the network topology has symmetry, the bit error rate performance of the amplify-and-forward multi-relay system is identical, but the bit error rate performance of the intelligent reflector assisted communication system is not identical. When the signal-to-noise ratio is less than 30.103dB, the error rate performance of the system is relatively good when the intelligent reflecting surface is closer to the source node; and when the signal-to-noise ratio is larger than 30.103dB, the error rate performance of the system is relatively better when the intelligent reflecting surface is farther away from the source node. When always keeping P ═ N2Network of time-lapse, intelligent reflector assisted communication systemThe topological structure has symmetry, and the error rate performance of the topological structure has the same property.
The present invention is not limited to the above preferred embodiments, and any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A method for analyzing performance of asymptotic approach error rate is characterized in that the method carries out comparative analysis on the error rate performance of an intelligent reflector auxiliary communication system and a single-time-slot amplification forwarding multi-relay system, and the analysis method comprises the following steps:
step S1, constructing an intelligent reflector auxiliary communication system model, and calculating the signal-to-noise ratio gamma output by the maximum ratio combiner;
step S2, performing bit error rate analysis on the intelligent reflector assisted communication system, and converting the signal-to-noise ratio γ into γ ═ γ1+γ2Respectively constructing the signal-to-noise ratio gamma1And signal-to-noise ratio gamma2The moment mother function of (2), wherein the signal-to-noise ratio γ2Need to be constructed to satisfy a harmonic mean form; the bit error rate analysis method comprises the following steps:
step S21, defining the signal-to-noise ratio of direct link and intelligent reflecting surface forwarding link in the intelligent reflecting surface auxiliary communication system as gamma respectively1And gamma2And has γ ═ γ1+γ2；
Step S22, constructing the signal-to-noise ratio gamma1And said signal-to-noise ratio γ2Are expressed as the moment mother functions of
And
wherein,
for a deterministic channel h from a source node to a destination nodes,dThe variance of (a) is determined,
is a deterministic channel h from the source node to the intelligent reflecting surfaces,rThe variance of (a) is determined,
is a deterministic channel h from the intelligent reflecting surface to the destination noder,dS is the transmitted power normalized signal, m is a constant, P is the transmitted power,
obeying a mean value of 0 and a variance of N0Complex white gaussian noise;
step S3, according to the moment mother function
And the moment mother function
Obtaining an asymptotic approach error rate of the intelligent reflector auxiliary communication system;
wherein, in step S1, the snr γ outputted by the maximal ratio combiner is represented as:
intelligent reflector assistanceCommunication system with asymptotic close-proximity error rate of direct link
Expressed as:
wherein, bPSK＝sin2(pi/M), wherein M represents a binary number modulated by M-PSK, and B is a constant;
asymptotic close-proximity error rate without direct link in intelligent reflector auxiliary communication system
Expressed as:
the constant B is expressed as:
2. the method for analyzing error rate performance of asymptotic close approximation as claimed in claim 1, wherein in step S1, said intelligent reflector assisted communication system model is composed of a source node, a destination node and an intelligent reflector having N reflection units.
3. The method for analyzing error rate performance of asymptotic close approximation as claimed in claim 1, wherein in step S21, said snr γ1And said signal-to-noise ratio γ2Respectively expressed as: gamma ray1＝(P|hs,d|2)/N0，
Wherein, X'1And X'2Are all variables in the harmonic mean construction process.
4. The method of analyzing performance of asymptotic close approximation error rate according to claim 3, wherein in step S21, X'1Expressed as: x'1＝(1+2m)P|hs,r|2/N0And X'1Compliance parameter of
In which the index of the distribution of (a),
5. the method of analyzing performance of asymptotic close approximation error rate according to claim 3, wherein in step S21, X'2Expressed as: x'2＝(1+m)N2|hr,d|2/N0And X'2Compliance parameter of
Is used as the index distribution of (1).
6. An intelligent reflector auxiliary communication system, characterized in that, the method for analyzing the error rate performance of asymptotic approach according to any one of claims 1 to 5 is used for comparing and analyzing the error rate performance of the intelligent reflector auxiliary communication system and the single-slot amplification forwarding multi-relay system.
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