CN115118369A - Wireless energy-carrying bidirectional relay system performance analysis method based on interference influence - Google Patents

Abstract

The invention provides a wireless energy-carrying bidirectional relay system performance analysis method based on interference influence, which comprises the following steps: s1: constructing an extended bidirectional relay model under the influence of interference; s2: assuming that three time slots are consumed for information transmission of the relay model, constructing a transmission frame structure model of three-time slot information energy simultaneous transmission; s3: analyzing the transmission capability of the system by taking the interruption performance as an analysis index, deducing closed solutions of a cumulative distribution function of the end-to-end signal-to-interference-and-noise ratio, and then solving the interruption probability of the whole system according to the closed solutions, S4: the system interruption probability is used as an analysis index, and a closed expression of the system interruption probability is deduced; the invention analyzes the information energy simultaneous transmission performance and the transmission optimization mode of the extended bidirectional DF relay network under the influence of interference, deduces the closed expression of the interrupt probability under the transmission model, and analyzes the influence of the number of the interferences, the interference power and the power division ratio in the system on the interrupt performance.

Description

A performance analysis method of wireless energy-carrying two-way relay system under the influence of interference

technical field

The invention belongs to the technical field of safety auxiliary systems, and relates to a performance analysis method of a wireless energy-carrying two-way relay system under the influence of interference.

Background technique

The increase makes the energy problem an urgent problem to be solved by the wireless communication technology. Traditional energy-saving methods such as resource allocation, power control and other technologies often reduce the energy expenditure of the system by reducing the "throttling" method of energy utilization. In recent years, with the development of low-power device technology and wireless energy transmission technology, the use of radio frequency energy in wireless environment for energy collection and information transmission plays an increasingly important role in wireless communication transmission. This technology that can perform energy collection and information transmission at the same time is called wireless energy-carrying communication technology, and has been studied in a large number of low-power wireless communication systems.

The relay system is an important application scenario of wireless energy-carrying communication technology. The combination of wireless energy-carrying technology and relay technology can effectively attract energy-constrained nodes in the network to act as relays to assist in information transmission. Therefore, it has received a lot of research. people's attention. The earliest research literature is based on the relay transmission of wireless energy harvesting, and combined with amplification and forwarding, two energy-carrying communication schemes, power split relay and time switching relay, are proposed. The bit error rate of the energy-carrying relay system is based on , and the closed-form expression of the probability density function of the signal-to-noise ratio under high signal-to-noise ratio is derived. Taking the two-hop decoding and forwarding energy-carrying communication system as the research object, the direct transmission The system outage performance in the link case is deduced, and the optimal power split ratio is deduced to minimize the outage probability. Subsequently, wireless energy-carrying technology has been gradually introduced into the research of multi-user/multi-relay communication systems, bidirectional relay systems, and non-orthogonal multiple-access relay communication systems. There are also literatures that study the outage probability and average throughput of cooperative non-orthogonal multiple access relay system under different cooperative relay schemes, and deduce the asymptotic analytical formula under high signal-to-noise ratio. Even so, none of the above-mentioned documents consider the influence of co-channel interference in the network.

Due to the broadcast characteristics of wireless signal transmission and the reusability of spectrum resources, in actual transmission, the received signal received by the receiving end often entrains signals from other interference sources. From the perspective of signal transmission, interference will reduce the signal-to-noise ratio of signal transmission and affect the transmission performance of the system. Therefore, it is often necessary to reduce the impact of interference on information transmission through interference management and interference alignment. However, from the perspective of energy transmission, Disturbance can be thought of as a source of energy that facilitates energy harvesting. Therefore, it is of great significance to study the simultaneous interpretation of information energy under the influence of interference. At present, many relevant literatures have carried out research on the energy harvesting relay network under the influence of interference. For example, the literature studies the simultaneous transmission of information energy when the energy harvesting relay is affected by multiple interference sources, and analyzes the system traversal capacity and interruption probability when the relay adopts the DF transmission method. Following the relative lack of research on transmission performance and optimization, there is no research to analyze the interruption performance of a two-way energy-carrying DF relay system under the influence of interference.

Considering that the dual influence characteristics of interference on the energy-carrying communication system will make the original performance analysis no longer applicable to the bidirectional DF relay system under the influence of interference, this paper takes the extended bidirectional relay transmission network as the research object, combined with the PS energy harvesting method. and DF information forwarding method, studied the information energy simultaneous transmission scheme when the relay and the receiver were affected by multiple interference sources respectively, deduced the closed-form expression of the system outage probability, and analyzed the number of interference sources, interference power and The influence of power division ratio parameters, etc. on the system interruption performance.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference, so as to solve the problems raised in the above background art.

The object of the present invention can be realized by the following technical solutions: a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference, comprising the following steps:

S1: Build an extended two-way relay model under the influence of interference, as follows:

Consider an extended bidirectional relay network consisting of two sets of transmission pairs (S ₁ -D ₁ , S ₂ -D ₂ ) and an energy harvesting relay R, where the relay R does not provide its own energy for information exchange, the information clearing house Energy consumption depends on energy collection. _In wireless communication networks, spectrum reuse technology is often used to improve spectrum utilization. Multiplexing will lead to co _- channel interference. The influence of co-channel interference of M ₃ , M ₁ , and M ₂ independent and identically distributed interference sources, and due to the influence of obstacles, etc., S ₁ and S ₂ cannot transmit their own information to their corresponding receivers through the direct link The terminals D ₁ and D ₂ need to share the relay for information transmission. At the same time, it is assumed that D ₁ (D ₂ ) is within the transmission range of S ₂ (S ₁ ), each node is equipped with a single antenna, and the system works in half-duplex model;

S2: Assuming that the information transmission of the relay model needs to consume three time slots, construct a transmission frame structure model for simultaneous transmission of information energy in three time slots, including:

In the _first time slot, the relay receives the transmission information from the source S1, and divides the received information into two parts, one part is used for energy collection, and the other part is used for information decoding. At the same time, due to the broadcast characteristics of wireless transmission , D ₂ also receives the information from the source end S ₁ ; in the second time slot, the relay receives the information from the source end S ₂ , and then repeats the operation of the first time slot for the received information, and at the same time, D ₁ also receives the source end S 2. In the third time slot, the relay decodes the information received in the first _two time slots separately and performs digital network coding on the correctly decoded user information, and then uses the collected energy to pass the network The encoded information packets after encoding processing are forwarded to the destination nodes D ₁ and D ₂ . In the entire transmission process, it is assumed that all channels in the system are independently distributed flat block fading channels, that is, within the time T when a two-way information transmission is completed, the channel coefficients remain unchanged;

In time slot 1, source S ₁ sends information x ₁ , and the information that relay R and node D ₂ will receive are:

是源端S₁到中继R的信道参数，

是源端S₁到节点D₂的信道参数，M₃为中继R处遭受的干扰源个数，M₂为节点D₂处遭受的干扰源个数，x_f，k和P_f，k分别是中继R处第k个干扰源的传输信息和发送功率，x_l，k和P_l，k分别是节点D₂处第k个干扰源的传输信息和发送功率，f_k～CN(0，Ω_f)和l_k～CN(0，Ω_l)分别为中继R和节点D₂处干扰链路的信道参数，

和

分别为中继R和节点D₂在第一时隙遭受的高斯白噪声；Among them, x ₁ and P ₁ are the transmission information and transmission power of the source S ₁ , respectively,

is the channel parameter from source _S1 to relay R,

is the channel parameter from source S ₁ to node D ₂ , M ₃ is the number of interference sources at the relay R, M ₂ is the number of interference sources at node D ₂ , x _{f, k} and P _{f, k} are the transmission information and transmit power of the k-th interferer at relay R, respectively, x _{l, k} and P _{l, k} are the transmission information and transmit power of the k-th interferer at node D ₂ , respectively, f _k ~ CN ( 0, Ω _f ) and l _k ~ CN(0, Ω _l ) are the channel parameters of the interfering link at relay R and node D ₂ , respectively,

and

are the Gaussian white noise suffered by relay R and node D ₂ in the first time slot, respectively;

In time slot 2, the source S ₂ transmits the information x ₂ to the relay R and the node D ₁ , and the information received by the two receiving nodes are:

是源端S₂到中继R的信道参数，

是源端S₂到节点D₁的信道参数，由于系统中的信道为平坦衰落信道，在时隙2内中继受到的干扰源影响与在时隙1受到的影响相同，即中继仍受到M₃个干扰源影响，M₁为节点D₁遭受的干扰源影响个数，x_g，k和P_g，k是节点D₁处第k个干扰源的传输信息和发送功率，g_k～CN(0，Ω_g)是节点D₁处第k个干扰源到节点D₁的信道参数，

和

分别为中继R和节点D₁在时隙2受到的高斯白噪声影响；Among them, x ₂ and P ₂ are the transmission information and transmission power of the source end S ₂ , respectively,

is the channel parameter from source _S2 to relay R,

is the channel parameter from source S ₂ to node D _1. Since the channel in the system is a flat fading channel, the influence of the interference source on the relay in time slot 2 is the same as that in time slot 1, that is, the relay is still affected by M ₃ interference sources, M ₁ is the number of interference sources suffered by node D ₁ , x _{g, k} and P _{g, k} is the transmission information and transmission power of the k-th interference source at node D ₁ , g _k ~ CN(0, Ω _g ) is the channel parameter from the k-th interferer at node D ₁ to node D ₁ ,

and

are the influence of white Gaussian noise on relay R and node D ₁ in time slot 2, respectively;

In the system model, it is considered that the relay does not provide its own energy for information transmission, but relies on energy harvesting to obtain energy to assist in information transmission. Considering that the relay adopts the energy harvesting method of power division, the information to be received is divided into two parts by the power divider. part, one part is used for energy collection, and the other part is used for information processing. Assuming that the power division ratios of time slot 1 and time slot 2 for energy harvesting are ρ ₁ and ρ ₂ respectively, the relay is in the time slot 1 and time slot 2 stages. The collected energy is:

And R is used to process the information from the source S1 and _S2 , respectively _:

Among them, η is the energy conversion efficiency at the relay, which is mainly determined by the hardware conditions of the relay's energy receiver. It is assumed that the power division only divides the signal power part without affecting the noise power part, thus formula (7), (8) The lower bound formula of an energy harvesting relay transmission process is given, which is based on the assumption that the RF signal reception occurs before the frequency band signal is converted into a baseband signal, and a large amount of white Gaussian noise is generated in this process;

According to formulas (7) and (8), the signal-to-interference-to-noise ratios of the information x _{1 of the source S 1 and} the information x ₂ of the source S ₂ by the relay R decoding can be written as:

Similarly, according to formulas (2) and (4), the signal-to-interference-to-noise ratio of node D ₁ decoding the information x _{2 of the source end S 2 and} node D ₂ decoding the information x ₁ of the source end S ₁ can be written as follows:

解码方式可采用如最大似然估计等方法，编码方式可采用数字网络编码，再采用时隙1和时隙2内收集到的能量将编码信息包x_R转发给D₁和D₂，整个过程中收集到的能量总量为：E＝E₁+E₂，因此，在时隙3内中继的发送功率为：In time slot 3, R uses the received information y _R,1 , y _R,2 to decode the information x ₁ of the source end S ₁ and the information x ₂ of the source end S ₂ respectively, and then use network coding to decode the decoded Two pieces of information are encoded to form an encoded packet

The decoding method can use methods such as maximum likelihood estimation, and the encoding method can use digital network coding, and then use the energy collected in time slot 1 and time slot 2 to forward the encoded information packet x _R to D ₁ and D ₂ , the whole process The total amount of energy collected is: E=E ₁ +E ₂ , therefore, the transmit power of the relay in time slot 3 is:

At this time, the information received by nodes D ₁ and D ₂ are:

是中继R到节点D₁的信道参数，

是中继R到节点D₂的信道参数，由于系统中的信道均为平坦块衰落信道，节点D₁和节点D₂在第三时隙受到的干扰源与前两时隙受到的干扰源相同，即在此时隙内，D₁仍然遭受来自M₁个干扰源的影响，D₂仍然遭受来自M₂个干扰源的影响，

和

分别为节点D₁和节点D₂在时隙3受到的高斯白噪声影响；in,

is the channel parameter of relay R to node D ₁ ,

is the channel parameter from relay R to node D _2. Since the channels in the system are all flat block fading channels, the interference source received by node D ₁ and node D ₂ in the third time slot is the same as the interference source received by the first two time slots. , that is, in this time slot, D ₁ still suffers from M ₁ interference sources, D ₂ still suffers from M ₂ interference sources,

and

are the influence of white Gaussian noise on node D ₁ and node D ₂ in time slot 3, respectively;

If D ₁ and D ₂ can successfully decode x _R , they can use the information x ₂ and x ₁ received in the first and second time slots to perform interference cancellation to remove the influence of unwanted information. In this way, D ₁ and D ₂ can obtain the required user information respectively, for example: D ₁ decodes the required user information x ₁ by using the information x _R received in time slot 3 and the information x ₂ received in time slot 2.

According to formulas (14) and (15), the signal-to-interference and noise ratios of D ₁ and D ₂ decoding x _R can be calculated as:

S3: Taking the interruption performance as the analysis index, the system transmission capability is analyzed, and the closed-form solution of the cumulative distribution function of the end-to-end signal-to-interference-noise ratio is derived. as follows:

Assuming that all channels follow an independent Rayleigh distribution, for each received signal, its received signal-to-noise ratio follows an exponential distribution and the probability density function is:

为各个有用信息的信噪比，

为它们对应的方差，为简化后续分析，不失一般性地假设各节点处的噪声功率值相同，则可得到

分别为Among them, γ _q refers to the signal-to-noise ratio of any received signal, and λ _q is the variance corresponding to γ _q . According to formulas (9), (10), (11), (12), (16), (17), It can be concluded that γ _q ∈ V,

is the signal-to-noise ratio of each useful information,

are their corresponding variances, in order to simplify the subsequent analysis, without loss of generality, assuming that the noise power values at each node are the same, we can get

respectively

And γ _f,k,i , γ _l,k , γ _g,k is the signal-to-noise ratio of each interference signal, μ _f,k,i , μ _l,k , μ _g,k are their corresponding variances, respectively :

in,

推导干扰影响下的携能传输链路信噪比的累积概率分布密度函数以及矩母函数概念可求得中继R、节点D₁、节点D₂处的干扰的PDF分别为：In order to obtain the closed-form solution of the terminal probability of the system, it is assumed that the transmission power of the interference sources near the same node is the same, that is, P _f,k =P _I,f , P _l,k =P _I,l , P _g,k = P _I,g , then at this time, the interference signal received by each node is the superposition of multiple independent and identically distributed interference signals, that is, the interference at the relay R, the node D ₁ , and the node D ₂ are M ₃ and M ₁ , respectively. , M the statistical value of ₂ independent and identically distributed variables, and

By deriving the cumulative probability distribution density function of the signal-to-noise ratio of the energy-carrying transmission link under the influence of interference and the concept of the moment generating function, the PDFs of the interference at the relay R, node D ₁ , and node D ₂ can be obtained as follows:

in,

According to the probability density function given above, the corresponding end-to-end signal-to-interference-noise ratios given by formulas (9), (10), (11), (12), (16), and (17) can be calculated. The cumulative distribution functions are as follows:

是MeijerG函数，

B₃(k)＝B₀(B₂(k)-B₁(k))；Among them, K _v (x) is the improved Bessel function of the second kind,

is the MeijerG function,

B ₃ (k)=B ₀ (B ₂ (k)-B ₁ (k));

S4: The interruption probability is an important indicator to measure the transmission performance of the system. If the instantaneous reachable transmission rate R of the link is lower than the transmission rate threshold R _th of the system, the link is interrupted, that is, P _out = Pr{R≤ R _th }, taking the system outage probability as the analysis index, the closed-form expression of the system outage probability is deduced, including:

The transmission performance is limited by multiple transmission links. The successful decoding of the information x ₁ at the receiving end D ₁ not only requires that the relay link S ₁ -RD ₁ is not interrupted, but also requires that the transmission of S ₂ -D ₁ is not interrupted; , the successful decoding of the information x ₂ at the receiving end D ₂ requires that the relay link S ₂ -RD ₂ and the link S ₁ -D ₂ are not interrupted at the same time. Define the transmission rate thresholds of S ₁ and S ₂ as R _th1 and R _th2 , respectively, then the interruption probability of the system is:

Through mathematical analysis and algebraic calculations, formula (29) is transformed into

为源端S_i到中继R的传输速率，

为源端S_i到节点D_j的传输速率，

为中继R到节点D_j的传输速率；in,

is the transmission rate from source S _i to relay R,

is the transmission rate from source S _i to node D _j ,

is the transmission rate of relay R to node D _j ;

According to the definition of cumulative distribution function, formula (30) can be easily obtained after mathematical deformation:

代入上式得出F₁和F₂，进一步，再将求得的F₁和F₂代入公式(30)，便求出系统的中断概率；requested

Substitute into the above formula to obtain F ₁ and F ₂ , and further, substitute the obtained F ₁ and F ₂ into formula (30) to obtain the outage probability of the system;

S5: The interrupt performance of the system is simulated, analyzed and verified.

Compared with the prior art, the advantages of the method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference of the present invention are as follows: the information energy simultaneous transmission performance and transmission performance of the extended two-way DF relay network under the influence of interference are analyzed. According to the transmission optimization method, the closed-form expression of the outage probability under the transmission model is deduced, and the influence of the number of interferences, the interference power and the power division ratio on the outage performance in the system is analyzed. The simulation results show that the deduced closed-form The outage probability obtained by the expression is completely consistent with the outage probability curve obtained by Monte Carlo simulation; the interference has an impact on the transmission performance and optimal design of the system, and it is proved that by optimizing the power division ratio, the relay is used for decoding information and The information energy used for energy harvesting can obtain the best compromise, thereby improving the transmission performance of the whole system.

Description of drawings

FIG. 1 is a schematic diagram of a two-way relay model of a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference according to the present invention.

FIG. 2 is a schematic diagram of a transmission frame structure of a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference according to the present invention.

FIG. 3 is a schematic diagram of the influence of the number of interferences on the interruption performance of a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference according to the present invention.

FIG. 4 is a schematic diagram of the influence of interference power on interruption performance based on a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference according to the present invention.

FIG. 5 is a schematic diagram of the influence of power division ratio on outage probability based on a method for analyzing the performance of a wireless energy-carrying two-way relay system under the influence of interference according to the present invention.

Detailed ways

The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solutions of the present invention, but the present invention is not limited to these embodiments.

A performance analysis method for a wireless energy-carrying two-way relay system under the influence of interference, comprising the following steps:

S1: Build an extended two-way relay model under the influence of interference, as follows:

Consider an extended bidirectional relay network (shown in Figure 1) with two sets of transmission pairs (S ₁ -D ₁ , S ₂ -D ₂ ) and an energy harvesting relay R, where the relay R does not exchange information Provide its own energy, and the energy consumption required for information exchange depends on energy collection. In order to improve spectrum utilization in wireless communication networks, spectrum multiplexing technology is often used, and multiplexing will lead to co-channel interference. Assume that the relay R and the receiver D ₁ and D ₂ are respectively affected by co-channel interference from M ₃ , M ₁ , and M ₂ independent and identically distributed interference sources, and due to being blocked by obstacles, etc., S ₁ and S ₂ cannot connect themselves through the direct transmission link. Information is transmitted to its corresponding receivers D ₁ and D ₂ , and a shared relay is required for information transmission. At the same time, it is assumed that D ₁ (D ₂ ) are within the transmission range of S ₂ (S ₁ ), and each node is equipped with a single antenna , the system works in half-duplex mode;

S2: Assuming that the information transmission of the relay model needs to consume three time slots, construct a transmission frame structure model for simultaneous transmission of information energy in three time slots (as shown in Figure 2), including:

In the _first time slot, the relay receives the transmission information from the source S1, and divides the received information into two parts, one part is used for energy collection, and the other part is used for information decoding. At the same time, due to the broadcast characteristics of wireless transmission , D ₂ also receives the information from the source end S ₁ ; in the second time slot, the relay receives the information from the source end S ₂ , and then repeats the operation of the first time slot for the received information, and at the same time, D ₁ also receives the source end S 2. In the third time slot, the relay decodes the information received in the first _two time slots separately and performs digital network coding on the correctly decoded user information, and then uses the collected energy to pass the network The encoded information packets after encoding processing are forwarded to the destination nodes D ₁ and D ₂ . In the entire transmission process, it is assumed that all channels in the system are independently distributed flat block fading channels, that is, within the time T when a two-way information transmission is completed, the channel coefficients remain unchanged;

In time slot 1, source S ₁ sends information x ₁ , and the information that relay R and node D ₂ will receive are:

是源端S₁到中继R的信道参数，

是源端S₁到节点D₂的信道参数，M₃为中继R处遭受的干扰源个数，M₂为节点D₂处遭受的干扰源个数，x_f，k和P_f，k分别是中继R处第k个干扰源的传输信息和发送功率，x_l，k和P_l，k分别是节点D₂处第k个干扰源的传输信息和发送功率，f_k～CN(0，Ω_f)和l_k～CN(0，Ω_l)分别为中继R和节点D₂处干扰链路的信道参数，

和

分别为中继R和节点D₂在第一时隙遭受的高斯白噪声；Among them, x ₁ and P ₁ are the transmission information and transmission power of the source S ₁ , respectively,

is the channel parameter from source _S1 to relay R,

is the channel parameter from source S ₁ to node D ₂ , M ₃ is the number of interference sources at the relay R, M ₂ is the number of interference sources at node D ₂ , x _{f, k} and P _{f, k} are the transmission information and transmit power of the k-th interferer at relay R, respectively, x _{l, k} and P _{l, k} are the transmission information and transmit power of the k-th interferer at node D ₂ , respectively, f _k ~ CN ( 0, Ω _f ) and l _k ~ CN(0, Ω _l ) are the channel parameters of the interfering link at relay R and node D ₂ , respectively,

and

are the Gaussian white noise suffered by relay R and node D ₂ in the first time slot, respectively;

In time slot 2, the source S ₂ transmits the information x ₂ to the relay R and the node D ₁ , and the information received by the two receiving nodes are:

是源端S₂到中继R的信道参数，

是源端S₂到节点D₁的信道参数，由于系统中的信道为平坦衰落信道，在时隙2内中继受到的干扰源影响与在时隙1受到的影响相同，即中继仍受到M₃个干扰源影响，M₁为节点D₁遭受的干扰源影响个数，x_g，k和P_g，k是节点D₁处第k个干扰源的传输信息和发送功率，g_k～CN(0，Ω_g)是节点D₁处第k个干扰源到节点D₁的信道参数，

和

分别为中继R和节点D₁在时隙2受到的高斯白噪声影响；Among them, x ₂ and P ₂ are the transmission information and transmission power of the source end S ₂ , respectively,

is the channel parameter from source _S2 to relay R,

is the channel parameter from source S ₂ to node D _1. Since the channel in the system is a flat fading channel, the influence of the interference source on the relay in time slot 2 is the same as that in time slot 1, that is, the relay is still affected by M ₃ interference sources, M ₁ is the number of interference sources suffered by node D ₁ , x _{g, k} and P _{g, k} is the transmission information and transmission power of the k-th interference source at node D ₁ , g _k ~ CN(0, Ω _g ) is the channel parameter from the k-th interferer at node D ₁ to node D ₁ ,

and

are the influence of white Gaussian noise on relay R and node D ₁ in time slot 2, respectively;

In the system model, it is considered that the relay does not provide its own energy for information transmission, but relies on energy harvesting to obtain energy to assist in information transmission. Considering that the relay adopts the energy harvesting method of power division, the information to be received is divided into two parts by the power divider. part, one part is used for energy collection, and the other part is used for information processing. Assuming that the power division ratios of time slot 1 and time slot 2 for energy harvesting are ρ ₁ and ρ ₂ respectively, the relay is in the time slot 1 and time slot 2 stages. The collected energy is:

And R is used to process the information from the source S1 and _S2 , respectively _:

Among them, η is the energy conversion efficiency at the relay, which is mainly determined by the hardware conditions of the relay's energy receiver. It is assumed that the power division only divides the signal power part without affecting the noise power part, thus formula (7), (8) The lower bound formula of an energy harvesting relay transmission process is given, which is based on the assumption that the RF signal reception occurs before the frequency band signal is converted into a baseband signal, and a large amount of white Gaussian noise is generated in this process;

According to formulas (7) and (8), the signal-to-interference-to-noise ratios of the information x _{1 of the source S 1 and} the information x ₂ of the source S ₂ by the relay R decoding can be written as:

Similarly, according to formulas (2) and (4), the signal-to-interference-to-noise ratio of node D ₁ decoding the information x _{2 of the source end S 2 and} node D ₂ decoding the information x ₁ of the source end S ₁ can be written as follows:

解码方式可采用如最大似然估计等方法，编码方式可采用数字网络编码，再采用时隙1和时隙2内收集到的能量将编码信息包x_R转发给D₁和D₂，整个过程中收集到的能量总量为：E＝E₁+E₂，因此，在时隙3内中继的发送功率为：In time slot 3, R uses the received information y _R,1 , y _R,2 to decode the information x ₁ of the source end S ₁ and the information x ₂ of the source end S ₂ respectively, and then uses network coding to decode the decoded Two pieces of information are encoded to form an encoded packet

The decoding method can use methods such as maximum likelihood estimation, and the encoding method can use digital network coding, and then use the energy collected in time slot 1 and time slot 2 to forward the encoded information packet x _R to D ₁ and D ₂ , the whole process The total amount of energy collected is: E=E ₁ +E ₂ , therefore, the transmit power of the relay in time slot 3 is:

At this time, the information received by nodes D ₁ and D ₂ are:

是中继R到节点D₁的信道参数，

是中继R到节点D₂的信道参数，由于系统中的信道均为平坦块衰落信道，节点D₁和节点D₂在第三时隙受到的干扰源与前两时隙受到的干扰源相同，即在此时隙内，D₁仍然遭受来自M₁个干扰源的影响，D₂仍然遭受来自M₂个干扰源的影响，

和

分别为节点D₁和节点D₂在时隙3受到的高斯白噪声影响；in,

is the channel parameter of relay R to node D ₁ ,

is the channel parameter from relay R to node D _2. Since the channels in the system are all flat block fading channels, the interference source received by node D ₁ and node D ₂ in the third time slot is the same as the interference source received by the first two time slots. , that is, in this time slot, D ₁ still suffers from M ₁ interference sources, D ₂ still suffers from M ₂ interference sources,

and

are the influence of white Gaussian noise on node D ₁ and node D ₂ in time slot 3, respectively;

If D ₁ and D ₂ can successfully decode x _R , they can use the information x ₂ and x ₁ received in the first and second time slots to perform interference cancellation to remove the influence of unwanted information. In this way, D ₁ and D ₂ can obtain the required user information respectively, for example: D ₁ decodes the required user information x ₁ by using the information x _R received in time slot 3 and the information x ₂ received in time slot 2.

According to formulas (14) and (15), the signal-to-interference and noise ratios of D ₁ and D ₂ decoding x _R can be calculated as:

S3: Taking the interruption performance as the analysis index, the system transmission capability is analyzed, and the closed-form solution of the cumulative distribution function of the end-to-end signal-to-interference-noise ratio is derived. as follows:

Assuming that all channels follow an independent Rayleigh distribution, for each received signal, its received signal-to-noise ratio follows an exponential distribution and the probability density function is:

为各个有用信息的信噪比，

为它们对应的方差，为简化后续分析，不失一般性地假设各节点处的噪声功率值相同，则可得到

分别为Among them, γ _q refers to the signal-to-noise ratio of any received signal, and λ _q is the variance corresponding to γ _q . According to formulas (9), (10), (11), (12), (16), (17), It can be concluded that γ _q ∈ V,

is the signal-to-noise ratio of each useful information,

are their corresponding variances, in order to simplify the subsequent analysis, without loss of generality, assuming that the noise power values at each node are the same, we can get

respectively

And γ _f,k,i , γ _l,k , γ _g,k is the signal-to-noise ratio of each interference signal, μ _f,k,i , μ _l,k , μ _g,k are their corresponding variances, respectively :

in,

推导干扰影响下的携能传输链路信噪比的累积概率分布密度函数以及矩母函数概念可求得中继R、节点D₁、节点D₂处的干扰的PDF分别为：In order to obtain the closed-form solution of the terminal probability of the system, it is assumed that the transmission power of the interference sources near the same node is the same, that is, P _f,k =P _I,f , P _l,k =P _I,l , P _g,k = P _I,g , then at this time, the interference signal received by each node is the superposition of multiple independent and identically distributed interference signals, that is, the interference at the relay R, the node D ₁ , and the node D ₂ are M ₃ and M ₁ , respectively. , M the statistical value of ₂ independent and identically distributed variables, and

By deriving the cumulative probability distribution density function of the signal-to-noise ratio of the energy-carrying transmission link under the influence of interference and the concept of the moment generating function, the PDFs of the interference at the relay R, node D ₁ , and node D ₂ can be obtained as follows:

in,

According to the probability density function given above, the corresponding end-to-end signal-to-interference-noise ratios given by formulas (9), (10), (11), (12), (16), and (17) can be calculated. The cumulative distribution functions are as follows:

是MeijerG函数，

B₃(k)＝B₀(B₂(k)-B₁(k))；Among them, K _v (x) is the improved Bessel function of the second kind,

is the MeijerG function,

B ₃ (k)=B ₀ (B ₂ (k)-B ₁ (k));

S4: The interruption probability is an important indicator to measure the transmission performance of the system. If the instantaneous reachable transmission rate R of the link is lower than the transmission rate threshold R _th of the system, the link is interrupted, that is, P _out = Pr{R≤ R _th }, taking the system outage probability as the analysis index, the closed-form expression of the system outage probability is deduced, including:

The transmission performance is limited by multiple transmission links. The successful decoding of the information x ₁ at the receiving end D ₁ not only requires that the relay link S ₁ -RD ₁ is not interrupted, but also requires that the transmission of S ₂ -D ₁ is not interrupted; , the successful decoding of the information x ₂ at the receiving end D ₂ requires that the relay link S ₂ -RD ₂ and the link S ₁ -D ₂ are not interrupted at the same time. Define the transmission rate thresholds of S ₁ and S ₂ as R _th1 and R _th2 , respectively, then the interruption probability of the system is:

Through mathematical analysis and algebraic calculations, formula (29) is transformed into

为源端S_i到中继R的传输速率，

为源端S_i到节点D_j的传输速率，

为中继R到节点D_j的传输速率；in,

is the transmission rate from source S _i to relay R,

is the transmission rate from source S _i to node D _j ,

is the transmission rate of relay R to node D _j ;

According to the definition of cumulative distribution function, formula (30) can be easily obtained after mathematical deformation:

代入上式得出F₁和F₂，进一步，再将求得的F₁和F₂代入公式(30)，便求出系统的中断概率；requested

Substitute into the above formula to obtain F ₁ and F ₂ , and further, substitute the obtained F ₁ and F ₂ into formula (30) to obtain the outage probability of the system;

其中，Ω为小尺度的瑞利衰落方差，

为源端S_i与中继R间的距离，

为中继R与节点D_j间的距离，m为路径损耗；S5: Simulation analysis and verification of the interruption performance of the system are carried out; the details are as follows: The main parameters used in the simulation are: μ=0.8, σ ² =10 ^-6 W, P ₁ =P ₂ =P _t , P _f = P _l =P _g =P _I , the channel gain

where Ω is the small-scale Rayleigh fading variance,

is the distance between the source S _i and the relay R,

is the distance between the relay R and the node D _j , m is the path loss;

As shown in Figure 3, taking the transmission power of the source node as the x-axis, the influence of the number of interferences on the system outage probability is analyzed. The performance simulation is carried out, wherein the MC simulation is obtained through 10 ^-6 channel realizations, and the simulation parameters used are set as: (M ₁ , M ₂ , M ₃ )=((1, 1, 1), (3, 3, 3), (5, 5, 5)), P _t = [0, 30]dBm, the outage probability curve obtained by the closed-form expression is completely consistent with the outage probability curve obtained by the Monte Carlo simulation, which proves that the closed-form The correctness of the derivation of the expression, at the same time, with the increase of the transmission power, the probability of system interruption decreases, because increasing the transmission power can improve the signal-to-interference noise ratio of the system, thereby improving the interruption performance of the system. The increase of the number of the system increases the interruption probability of the system. This is because the increase of the number of interference increases the impact of the interference on the system and increases the signal-to-interference-noise ratio of the system, which leads to the increase of the system interruption time and the deterioration of the interruption performance;

As shown in Figure 4, taking the transmission power of the source node as the x-axis, the influence of the interference power ratio on the system performance is analyzed. The simulation also adopts the derived closed-form expression of outage probability and Monte Carlo (MC) simulation. The performance simulation is carried out using the method, wherein, the MC simulation is obtained through 10 ^-6 channel realizations, and the simulation parameters used are set as: P _t = 20dBm, P _I = {2, 5, 10}dBm, obtained through closed-form expressions The outage probability curve is completely consistent with the outage probability curve obtained by the Monte Carlo simulation, which proves the correctness of the closed-form expression. The influence of interference on the system increases the signal-to-interference-noise ratio of the system, resulting in increased system interruption time and worse interruption performance;

As shown in Figure 5, the influence of the power division ratio on the system outage probability is analyzed. Taking the energy division ratio in the system as the x-axis, considering ρ ₁ =ρ ₂ =ρ, the simulation also adopts the derived closed-form expression of the outage probability. Formula and Monte Carlo (MC) simulation method for performance simulation, wherein, MC simulation is obtained through 10 ^-6 channel realizations, and the simulation parameters used are set as: P _t =[0,30]dBm, (M ₁ , M ₂ , M ₃ )=((1, 1, 1), (3, 3, 3), (5, 5, 5)), the outage probability curve obtained by the closed-form expression and the Monte Carlo simulation The obtained outage probability curve is completely consistent, which proves the correctness of the closed-form expression derivation. With the increase of ρ, the outage probability of the system is in the form of a concave function curve, and the minimum outage probability can be obtained at a specific value of ρ, and at the same time , as the number of disturbances increases, the optimal value of ρ that satisfies the minimum interruption probability increases.

Contents not described in detail in this specification belong to the prior art known to those skilled in the art. The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention pertains can make various modifications or additions to the described specific embodiments or substitute in similar manners, but will not deviate from the spirit of the present invention or go beyond the definitions of the appended claims range.

Claims (1)

1. A wireless energy-carrying bidirectional relay system performance analysis method based on interference influence is characterized by comprising the following steps:

s1: constructing an extended bidirectional relay model under the influence of interference, which comprises the following specific steps:

consider a transmission system comprising two sets of transmission pairs (S) ₁ -D ₁ ，S ₂ -D ₂ ) And an extended bidirectional relay network of an energy-collecting relay R, wherein the relay R does not provide self energy for information exchange, energy consumption required by the information exchange depends on energy collection, a frequency spectrum multiplexing technology is often adopted in the wireless communication network for improving the frequency spectrum utilization rate, and the multiplexing can cause the appearance of co-channel interference, and the relay R and a receiving end D are assumed to be ₁ 、D ₂ Are respectively subjected to the signals from M ₃ 、M ₁ 、M ₂ Influence of co-channel interference of independent and co-distributed interference sources, S, due to obstruction by obstacles and the like ₁ And S ₂ The information of the receiver can not be transmitted to the corresponding receiving end D of the receiver through the direct transmission link ₁ And D ₂ Common relay is required for information transmission, and at the same time, D is assumed ₁ (D ₂ ) Respectively at S ₂ (S ₁ ) Within the transmission range of (2), each node is provided with a single antenna, and the system works in a half-duplex mode;

s2: assuming that three time slots are consumed for information transmission of the relay model, constructing a transmission frame structure model of three-time slot information energy simultaneous transmission, specifically comprising:

in the first time slot, the relay receives the data from the source terminal S ₁ And dividing the received information into two parts, one part is used for energy collection, and the other part is used for energy collectionPart for information decoding, while, due to the broadcast nature of the wireless transmission, D ₂ Also receives the source S ₁ The information of (a); in the second time slot, the relay receives the data from the source terminal S ₂ Then repeating the operation of the first slot for the received information, and, at the same time, D ₁ Also receives the source end S ₂ The information of (a); in the third time slot, the relay respectively decodes the information received by the first two time slots and carries out digital network coding processing on the correctly decoded user information, and then the coded information packet after the network coding processing is transmitted to a destination node D by adopting the collected energy ₁ And D ₂ In the whole transmission process, all channels in the system are assumed to be independently distributed flat block fading channels, namely, the channel coefficient is kept unchanged within the time T of completing one-time bidirectional information transmission;

in time slot 1, the source end S ₁ Sending information x ₁ Relay R and node D ₂ The information to be received is:

wherein x is ₁ 、P ₁ Respectively being a source end S ₁ The transmission information and the transmission power of the mobile station,

is the source end S ₁ The channel parameters to the relay R are such that,

is the source end S ₁ To node D ₂ Of the channel parameter, M ₃ For the number of sources of interference suffered at the relay R, M ₂ Is node D ₂ Number of sources of interference, x _f，k And P _f，k Respectively, the k-th at the relay RTransmission information and transmission power, x, of the interference source _l，k And P _l，k Are respectively node D ₂ Transmission information and transmission power of the k-th interference source, f _k ～CN(0，Ω _f ) And l _k ～CN(0，Ω _l ) Respectively relay R and node D ₂ The channel parameters of the interfering link(s),

and

respectively relay R and node D ₂ White gaussian noise suffered at the first slot;

in time slot 2, the source end S ₂ Transmitting information x ₂ For relay R and node D ₁ The information received by the two receiving nodes is respectively as follows:

wherein x is ₂ And P ₂ Respectively being a source end S ₂ The transmission information and the transmission power of the mobile station,

is the source end S ₂ The channel parameters to the relay R are such that,

is the source end S ₂ To node D ₁ Because the channel in the system is a flat fading channel, the influence of the interference source on the relay in the time slot 2 is the same as that on the time slot 1, i.e. the relay is still influenced by M ₃ Influence of an interference source, M ₁ Is node D ₁ The number of the experienced interference sources is affected,x _g，k and P _g，k Is node D ₁ (ii) transmission information and transmission power of the k-th interference source, g _k ～CN(0，Ω _g ) Is node D ₁ To node D from the k < th > interference source ₁ The channel parameters of (a) are determined,

and

respectively relay R and node D ₁ The white gaussian noise received in slot 2;

because the relay is considered to not provide self energy for information transmission in the system model, but obtain energy by energy collection to assist information transmission, the relay is considered to adopt an energy collection mode of power division, namely the received information is divided into two parts by a power divider, one part is used for energy collection, the other part is used for information processing, and the power division ratios of the time slot 1 and the time slot 2 for energy collection are respectively rho ₁ 、ρ ₂ Then, the energy collected by the relay in the slot 1 and slot 2 stages is:

and R is used to process the data from the source S ₁ And S ₂ The information of (a) is:

where η is the energy conversion efficiency at the relay, which is mainly determined by the energy receiver hardware conditions of the relay, assuming that the power division only divides the signal power part without affecting the noise power part, thus equations (7), (8) give a lower bound equation for the energy harvesting relay transmission process, which is assumed to occur before the RF signal reception occurs before the band signal is converted to the baseband signal, and a large amount of white gaussian noise is generated in the process;

according to the formulas (7) and (8), the relay R decoding source end S can be written ₁ Information x of ₁ And source end S ₂ Information x of ₂ The signal to interference plus noise ratios are respectively as follows:

similarly, according to the formulas (2) and (4), the node D can be written ₁ Decoding source terminal S ₂ Information x of ₂ And node D ₂ Decoding source terminal S ₁ Information x of ₁ The signal to interference plus noise ratio (SINR) is as follows:

in time slot 3, R utilizes the received information y _R，1 、y _R，2 Respectively decode the source end S ₁ Information x of ₁ And source end S ₂ Information x of ₂ Then, the two decoded messages are coded by adopting network coding to form a coded packet

The decoding method can adopt methods such as maximum likelihood estimation, the coding method can adopt digital network coding, and the energy collected in the time slot 1 and the time slot 2 is adopted to code the information packet x _R Forward to D ₁ And D ₂ The total amount of energy collected in the whole process is as follows: e ═ E ₁ +E ₂ Therefore, the transmission power relayed in slot 3 is:

at this time, node D ₁ And D ₂ The received information is respectively:

wherein,

is relaying R to node D ₁ The channel parameters of (a) are determined,

is relaying R to node D ₂ Because the channels in the system are all flat block fading channels, node D ₁ And node D ₂ The interference source in the third time slot is the same as that in the first two time slots, i.e. in this time slot, D ₁ Still suffering from the stress from M ₁ Influence of a disturbance source, D ₂ Still suffering from the stress from M ₂ The influence of the individual sources of interference,

and

are respectively node D ₁ And node D ₂ White gaussian noise in slot 3;

if D is ₁ And D ₂ Can successfully decode x _R They can utilize the information x received in the first and second time slots ₂ And x ₁ Interference cancellation is performed to remove the effect of unwanted information, so that D ₁ And D ₂ The required user information can be obtained separately, for example: d ₁ Information x received using time slot 3 _R And information x received in slot 2 ₂ Decoding the required user information x ₁ Can adopt

D can be calculated by the formulas (14) and (15) ₁ And D ₂ Decoding x _R The signal to interference plus noise ratios are respectively as follows:

s3: the interruption performance is taken as an analysis index, the transmission capability of the system is analyzed, closed solutions of the cumulative distribution function of the end-to-end signal-to-interference-and-noise ratio are deduced, and then the interruption probability of the whole system is solved according to the closed solutions, wherein the interruption probability is as follows:

assuming that all channels are subject to independent rayleigh distributions, for each received signal its received signal-to-noise ratio is subject to an exponential distribution and the probability density function is:

wherein, γ _q Denotes the signal-to-noise ratio, λ, of any received signal _q Is gamma _q The corresponding variance, according to equations (9), (10), (11), (12), (16), (17), can be derived as γ _q ∈V，

For the signal-to-noise ratio of the respective useful information,

for their corresponding variances, to simplify subsequent analysis, assuming the noise power values at each node are the same without loss of generality, one can obtain

Are respectively as

And gamma is _f，k，i 、γ _l，k 、γ _g，k For the signal-to-noise ratio, mu, of the respective interference signal _f，k，i 、μ _l，k 、μ _g，k The corresponding variances are labeled as follows:

wherein,

to obtain a closed-form solution of the probability of the system terminals, it is assumed that the transmission powers of the interference sources in the vicinity of the same node are the same, i.e. P _f，k ＝P _I，f 、P _l，k ＝P _I，l 、P _g，k ＝P _I，g Then, at this time, the interference signal received by each node is the superposition of a plurality of independent and equally distributed interference signals, i.e. relay R and node D ₁ Node D ₂ Where the interference is M ₃ 、M ₁ 、M ₂ Statistics of individual independent identically distributed variables, and

the relay R and the node D can be obtained by deducing the cumulative probability distribution density function and the moment mother function concept of the energy-carrying transmission link signal-to-noise ratio under the influence of interference ₁ Node D ₂ The PDF of the interference at (a) is:

wherein,

from the probability density function given above, the cumulative distribution function corresponding to the end-to-end signal-to-interference-and-noise ratio given by the equations (9), (10), (11), (12), (16) and (17) can be found as follows:

wherein, K _v (x) For the second class of improved bezier functions,

is a function of MeijerG and is,

B ₃ (k)＝B ₀ (B ₂ (k)-B ₁ (k))；

s4: the interruption probability is an important index for measuring the transmission performance of the system, and if the instantaneous reachable transmission rate R of the link is lower than the transmission rate threshold value R of the system _th Then the link is broken, i.e. P _out ＝Pr{R≤R _th And deducing a closed expression of the system interruption probability by taking the system interruption probability as an analysis index, wherein the closed expression specifically comprises the following steps:

the transmission performance is limited by a plurality of transmission links, information x ₁ At the receiving end D ₁ Not only does successful decoding require the relay link S ₁ -R-D ₁ Without interruption, while also requiring S ₂ -D ₁ The transmission is uninterrupted; similarly, information x ₂ At the receiving end D ₂ Successful decoding of (2) requires a relay link S ₂ -R-D ₂ And a link S ₁ -D ₂ While not interrupting. Definition of S ₁ And S ₂ Respectively of transmission rate of R _th1 And R _th2 Then the outage probability of the system is:

through mathematical analysis and algebraic calculation, equation (29) is transformed into

Wherein,

as a source end S _i The rate of transmission to the relay R is,

as a source end S _i To node D _j The rate of transmission of (a) is,

for relaying R to node D _j The transmission rate of (c);

the mathematical transformation of equation (30) is readily derived from the definition of the cumulative distribution function:

obtained by

Substituting the above formula to obtain F ₁ And F ₂ Further, the obtained F ₁ And F ₂ Substituting the formula (30) to obtain the interruption probability of the system;

s5: the interrupt performance of the system is subjected to simulation analysis and verification.

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