CN115118369A - Wireless energy-carrying bidirectional relay system performance analysis method based on interference influence - Google Patents
Wireless energy-carrying bidirectional relay system performance analysis method based on interference influence Download PDFInfo
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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
Technical Field
The invention belongs to the technical field of safety auxiliary systems, and relates to a wireless energy-carrying bidirectional relay system performance analysis method based on interference influence.
Background
Increasing the power problem, making the wireless communication technology a critical issue to solve. Traditional energy-saving techniques such as resource allocation, power control, etc. tend to reduce the energy expenditure of the system by "throttling" the energy usage. In recent years, with the development of low power consumption device technology and wireless energy transmission technology, energy collection and information transmission by using radio frequency energy in a wireless environment have gained importance in wireless communication transmission. Such a technology capable of simultaneously performing energy collection and information transmission is called a wireless energy-carrying communication technology, and research is currently performed in a large number of low-power wireless communication systems.
The relay system is an important application scenario of the wireless energy-carrying communication technology, and combines the wireless energy-carrying technology with the relay technology, so that energy-limited nodes in a network can be effectively attracted to act as relays to assist information transmission, and therefore, the relay system is concerned by a large number of researchers. The earliest research literature provides two energy-carrying communication schemes of power division relay and time switching relay based on relay transmission of wireless energy collection and combined with amplification forwarding, and also researches the error rate of an energy-carrying relay system adopting differential decoding forwarding under the Nakagami-m channel condition, deduces a closed expression of a signal-to-noise ratio probability density function under high signal-to-noise ratio, takes a two-hop decoding forwarding energy-carrying communication system as a research object, researches the system interruption performance under the condition of a direct transmission link, and deduces the optimal power division ratio under the condition of minimizing interruption probability. Subsequently, wireless energy-carrying technology is gradually introduced into research of multi-user/multi-relay communication systems, two-way relay systems, and non-orthogonal multiple access relay communication systems. In the literature, the interruption probability and the average throughput of the cooperative non-orthogonal multiple access relay system under different cooperative relay schemes are researched, and a progressive analytic expression under a high signal-to-noise ratio is deduced. Nevertheless, none of the above documents considers the problem of co-channel interference effects in the network.
Due to the broadcast characteristic of wireless signal transmission and the reusability of spectrum resources, in actual transmission, a receiving signal received by a receiving end often carries signals from other interference sources. From the perspective of signal transmission, interference may reduce the transmission signal-to-noise ratio of a signal and affect the transmission performance of a system, so that the influence of interference on information transmission often needs to be reduced through interference management, interference alignment and other ways; but from an energy transfer perspective, interference can be considered as a source of energy, facilitating energy harvesting. Therefore, it is of great significance to research the information energy simultaneous transmission under the influence of interference. At present, a plurality of related documents research energy collection relay networks under the influence of interference. For example, the literature researches an information energy co-transmission mode under the influence of a plurality of interference sources on an energy collection relay, and analyzes the system traversal capacity and the interruption probability under the condition that the relay adopts a DF transmission mode, however, the researches on the bidirectional relay transmission performance and optimization under the influence of the interference are relatively deficient, and the research on the interruption performance under the influence of the interference on the bidirectional energy-carrying DF relay system is not developed for a while.
Considering the characteristics of dual influence of interference on an energy-carrying communication system, the original performance analysis is not suitable for a bidirectional DF relay system under the influence of the interference, an expanded bidirectional relay transmission network is taken as a research object, a PS energy collection mode and a DF information forwarding mode are combined, an information energy co-transmission scheme under the influence of a plurality of interference sources on a relay and a receiving end is researched, a closed expression of system interruption probability is deduced, and the influence of the number of the interference sources, the interference power, power division ratio parameters and the like on the system interruption performance is analyzed.
Disclosure of Invention
The present invention provides a method for analyzing the performance of a wireless energy-carrying bidirectional relay system based on the influence of interference, so as to solve the problems in the background art.
The purpose of the invention can be realized by the following technical scheme: a wireless energy-carrying bidirectional relay system performance analysis method based on interference influence comprises the following steps:
s1: constructing an extended bidirectional relay model under the influence of interference, which comprises the following specific steps:
consider a transmission comprising two groupsInput pair (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 the obstruction of 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 for energy collection and the other part for information decoding, while, due to the broadcast nature of wireless transmission, D 2 Also receives the source end 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, that is, 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 Transmission information and transmission power, x, of the kth interferer at relay R, respectively 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 Number of interference sources affected, x g，k And P g，k Is node D 1 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 set,
and
respectively relay R and node D 1 The white gaussian noise received in slot 2;
because the relay is considered in the system model not to provide self energy for information transmission, but to acquire energy by energy collection to assist information transmission, the relay is considered to adopt a power-dividing energy collection mode, 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,suppose that the power division ratios for the time slot 1 and the time slot 2 for energy harvesting are ρ respectively 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 and does not affect 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 coding 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 use 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 obey independent rayleigh distribution, for each received signal its received signal-to-noise ratio obeys 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 can be expressed as γ according to the equations (9), (10), (11), (12), (16) and (17) 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 For their corresponding variances, respectively:
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 The interference of (A) 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 signal-to-noise ratio of the energy-carrying transmission link 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,
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.
Compared with the prior art, the method for analyzing the performance of the wireless energy-carrying bidirectional relay system based on the interference influence has the advantages that: analyzing the information energy simultaneous transmission performance and the transmission optimization mode of the extended bidirectional DF relay network under the influence of interference, deducing a closed expression of the interrupt probability under the transmission model, analyzing the influence of the interference number, the interference power and the power division ratio value on the interrupt performance in the system, wherein simulation results show that the interrupt probability calculated through the deduced closed expression is completely consistent with an interrupt probability curve obtained through Monte Carlo simulation; interference affects both the transmission performance and the optimization design of the system, and it is proved that the best compromise can be obtained by optimizing the power division ratio, so that the transmission performance of the whole system can be improved.
Drawings
Fig. 1 is a schematic diagram of a bidirectional relay model of a wireless energy-carrying bidirectional relay system performance analysis method based on interference influence.
Fig. 2 is a schematic diagram of a transmission frame structure of a method for analyzing the performance of a wireless energy-carrying bidirectional relay system under the influence of interference according to the present invention.
Fig. 3 is a schematic diagram illustrating the influence of the number of interferences on the interrupt performance in the method for analyzing the performance of the wireless energy-carrying bidirectional relay system based on the influence of the interferences.
Fig. 4 is a schematic diagram illustrating an impact of interference power on an interrupt performance in a method for analyzing a performance of a wireless energy-carrying bidirectional relay system under the influence of interference according to the present invention.
Fig. 5 is a schematic diagram illustrating an influence of power division ratio on an interruption probability in a method for analyzing a performance of a wireless energy-carrying bidirectional relay system based on an interference influence according to the present invention.
Detailed Description
The following are specific embodiments of the present invention and are further described with reference to the drawings, but the present invention is not limited to these embodiments.
A wireless energy-carrying bidirectional relay system performance analysis method based on interference influence comprises the following steps:
s1: constructing an extended bidirectional relay model under the influence of interference, which comprises the following specific steps:
consider a transmission pair comprising two sets (S) 1 -D 1 ，S 2 -D 2 ) And an extended bidirectional relay network (as shown in fig. 1) of an energy-collecting relay R, wherein the relay R does not provide its own energy for information exchange, energy consumption for information exchange depends on energy collection, a spectrum multiplexing technique is often adopted in a wireless communication network to improve spectrum utilization, and multiplexing can cause co-channel interference, assuming that the relay R and a receiving end D occur 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, a transmission frame structure model (as shown in fig. 2) of three-time slot information energy simultaneous transmission is constructed, which specifically includes:
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 for energy collection and the other part for information decoding, while, due to the broadcast nature of wireless transmission, D 2 Also receives the source end 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, that is, 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 a sourceTerminal 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 Transmission information and transmission power, x, of the kth interferer at relay R, respectively 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 are measured,
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 Number of interference sources affected, x g，k And P g，k Is node D 1 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 and does not affect 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 Received in the third time slotThe interference source is the same as the interference source received by 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 interference 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 use 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 capacity 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 obey independent rayleigh distribution, for each received signal its received signal-to-noise ratio obeys 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 For their corresponding variances, respectively:
wherein,
to obtain a closed-form solution for the probability of a terminal in the system, 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,
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 requires the relay link S 2 -R-D 2 And link S 1 -D 2 While not interrupting. Definition of S 1 And S 2 Respectively, are 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; the method comprises the following specific steps: the main parameters used in the simulation are: mu is 0.8, sigma 2 ＝10 -6 W，P 1 ＝P 2 ＝P t ，P f ＝P l ＝P g ＝P I Channel gain
Wherein omega is the Rayleigh fading variance of small scale,
as a source end S i The distance to the relay R is such that,
for relaying R and node D j M is the path loss;
as shown in fig. 3, the influence of the interference number on the system outage probability is analyzed by taking the transmission power of the source node as the x-axis, and performance simulation is performed by using a derived outage probability closed expression and a Monte Carlo (MC) simulation method, wherein the MC simulation is performed by 10 -6 And obtaining the secondary channel, wherein the used simulation parameters are set as follows: (M) 1 ，M 2 ，M 3 )＝((1，1，1)，(3，3，3)，(5，5，5))、P t ＝[0，30]dBm, the interrupt probability curve obtained by the closed expression is completely consistent with the interrupt probability curve obtained by adopting Monte Carlo simulation, the deduction correctness of the closed expression is proved, and meanwhile, the system interrupt probability is reduced along with the increase of the transmission power because the increase of the transmission power can improveThe signal-to-interference-and-noise ratio of the system improves the interruption performance of the system, and meanwhile, the interruption probability of the system increases along with the increase of the number of the interferences, so that the influence of the interferences on the system is improved due to the increase of the number of the interferences, the signal-to-interference-and-noise ratio of the system is increased, the interruption time of the system is increased, and the interruption performance is poor;
as shown in fig. 4, the influence of the interference power ratio on the system performance is analyzed by using the transmission power of the source node as the x-axis, and the simulation also adopts the derived interrupt probability closed expression and Monte Carlo (MC) simulation method to perform the performance simulation, wherein the MC simulation is performed by 10 -6 And obtaining the secondary channel, wherein the used simulation parameters are set as follows: p is t ＝20dBm，P I The interruption probability curve obtained through the closed expression is completely consistent with the interruption probability curve obtained through Monte Carlo simulation, the deduction correctness of the closed expression is proved, the interruption probability of the system is increased along with the increase of the interference power, the influence of the interference on the system is also improved due to the increase of the interference power, the signal-to-interference-and-noise ratio of the system is increased, the interruption time of the system is increased, and the interruption performance is poor;
as shown in FIG. 5, the influence of the power split ratio on the system outage probability is analyzed, taking the energy split ratio in the system as the x-axis and taking ρ into account 1 ＝ρ 2 The simulation also uses a derived break probability closed form expression and a Monte Carlo (MC) simulation method to perform performance simulation, wherein the MC simulation is performed by 10 -6 And obtaining the secondary channel, wherein the used simulation parameters are set as follows: p t ＝[0，30]dBm、(M 1 ，M 2 ，M 3 ) The interruption probability curve obtained by closed expression is completely matched with the interruption probability curve obtained by Monte Carlo simulation, the derivation correctness of the closed expression is proved, the interruption probability of the system is in the form of a concave function curve along with the increase of rho, the minimum interruption probability can be obtained at a specific rho value, and meanwhile, the optimal rho value meeting the minimum interruption probability is increased along with the increase of the number of interferences.
Those not described in detail in this specification are within the skill of the art. The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
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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