CN110740502B - Control method for node transmitting power of full-duplex bidirectional relay system - Google Patents
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Abstract
The invention discloses a control method of node transmitting power of a full-duplex bidirectional relay system, which is suitable for a decoding forwarding full-duplex bidirectional relay system adopting superposition coding, and aims to minimize the sum of the node transmitting power by taking system QoS (quality of service) requirements and superposition coding power distribution factor value limitation as constraint conditions; and dynamically adjusting the transmitting power of the transmitter of the source node and the relay node and the superposition coding power distribution factor at the relay node by utilizing the channel knowledge and according to the requirement of the source node on the data rate, and minimizing the sum of the transmitting power of the nodes under the condition of meeting the requirement of the system QoS.
Description
Technical Field
The invention relates to the technical field of wireless communication, in particular to a method for controlling node transmitting power of a full-duplex bidirectional relay system by adopting superposition coding, which is suitable for the full-duplex bidirectional relay system based on a decoding and forwarding mechanism.
Background
Cooperative diversity, a new technology, has been highly regarded by academia and industry as a technology capable of improving the coverage area of a wireless network and resisting the adverse effect of channel fading on wireless signal transmission through cooperation between users. A conventional three-node cooperative diversity system includes two source nodes and a relay node, wherein the two source nodes must communicate with each other via the relay node due to the influence of communication distance or channel fading, so called two-way relay system. In a conventional three-node cooperative diversity system, a relay node can work in two modes, namely half-duplex (half-duplex) and full-duplex (full-duplex). In half-duplex mode, the relay nodes receive and forward signals in different time slots or frequency bands. In the full-duplex mode, the relay node can receive and forward signals in the same time and the same frequency band. Thus, theoretically, the spectrum utilization of a full-duplex relay doubles that of a half-duplex relay. However, huge signal Self-Interference (Self-Interference) is generated due to simultaneous co-frequency signal reception and retransmission. While additional hardware and software and computational resources may be relied upon to remove these self-interferences, they are not all eliminated. On the other hand, although this self-interference can be eliminated to the maximum extent, the high complexity of software, hardware and computation consumes enormous energy resources. Therefore, from a practical point of view, it is necessary to consider the full-duplex relay technology in the presence of residual self-interference and pay attention to the consideration of energy resource consumption.
Currently, outage probability and spectral efficiency studies for full-duplex cooperative diversity systems have been fully developed. The method is characterized in that the problems of interruption probability and spectral efficiency of a full-duplex cooperative diversity system are respectively researched, and the system performance is optimized through technologies such as power distribution, relay selection and the like. However, research on the energy efficiency performance of the cooperative diversity system is mainly focused on the half-duplex mode. Aiming at a two-stage bidirectional relay system adopting half-duplex amplification forwarding relay, the aim of minimizing the energy consumption of the system through a power distribution and relay selection technology is researched. The energy efficiency and frequency efficiency relation of the amplification forwarding, decoding forwarding and compression forwarding half-duplex cooperative diversity system is researched, and the energy efficiency performance of the half-duplex cooperative diversity system adopting different relay strategies is compared. For example, information interchange between two source nodes is completed by using a decoding forwarding half-duplex relay, information interchange transmission between the source nodes is divided into 5 modes, and the time length of each mode is optimized, so that the problem of system energy consumption optimization is solved. In addition, on the basis, the optimal energy consumption difference of the system when the relay node adopts different coding modes (digital network coding, physical layer network coding and superposition coding) is compared. It should be noted that: for the energy efficiency problem, the half-duplex system is considered in the industry, and the research on the energy consumption of the full-duplex cooperative diversity system is less.
Disclosure of Invention
The invention aims to provide a node transmitting power control method of a full-duplex bidirectional relay system, which is based on the full-duplex bidirectional relay system adopting superposition coding and achieves the minimization of node transmitting power sum on the condition of meeting the requirement of system interrupt probability performance.
In order to realize the purpose, the invention adopts the following technical scheme:
full duplexA control method for node transmitting power of bidirectional relay system features that three nodes in the system, two source nodes and one relay node, all work in full-duplex mode, and the assumed channel is frequency non-selective Rayleigh fading channel S1And S2Is a source node, R is a decoding forwarding relay node positioned between the source nodes, and the source node S in the system1、S2And three nodes of a relay node R can obtain accurate channel state information through channel estimation, and the method is characterized in that the transmitting power of a source node and a relay node transmitter and the superposition coding power distribution factor of the relay node are dynamically adjusted by utilizing channel knowledge and according to the requirement of the source node on the data rate, and the source node S is realized under the condition of meeting the requirement of the system interrupt probability performance1、S2And the minimization of the sum of the transmission power of the three nodes of the relay node R; firstly, checking whether the channel condition can meet the requirement of the system communication service, if so, calculating the transmitting power of each node in the system by a power control algorithm for minimizing the sum of the transmitting power of the nodes, and calculating a power threshold; if the source node S1、S2And the sum of the transmitting power of the three nodes of the relay node R is less than or equal to the power threshold, and then the source node S1、S2The information is sent simultaneously with the relay node R to complete the source node S1And S2The information intercommunication between the two devices; if the channel condition can not satisfy the system communication service requirement or the channel condition can satisfy the system communication service requirement, the source node S1、S2And the sum of the transmitting power of the three nodes of the relay node R is greater than the power threshold, and the source node S1、S2And the relay node R is in a silent state, the system generates an interrupt, and under the condition of meeting the performance requirement of the system interrupt, the sum of the transmitting power of the nodes is smaller.
The node power control algorithm process for minimizing the sum of the node transmitting power is as follows: at the kth time slot, k ∈ {1, 2, 3 … }, the source node S1Code modulating information to be transmitted into transmission signal x1[k]Let x be1[k]Having unit power and transmitting to the relay node R; at the same time, the source node S2Code modulating information to be transmitted into transmission signal x2[k]Suppose x2[k]Has unit power and transmits to the relay R; the relay node R receives the source node S1And S2While sending the signal, adopting superposition coding technique to receive the source node S1And S2The combined signal is decoded into the source node sending information, and then the source node sending information is coded and modulated into the sending signalAt the same time xR[k]Forward to the source node S1And S2Wherein rho is a superposition coding power distribution factor, and rho is more than or equal to 0 and less than or equal to 1; source node S1And S2Received signal xR[k]Then, removing the signal item sent by itself, demodulating and decoding to obtain the information sent by the source node of the other party, and implementing the source node S1And S2Interaction of the information;
at the k-th time slot, the source node S1、S2And the signals received by the relay node R are respectively
Since the channel characteristics are quasi-static and have reciprocity, h1And h2Not only to represent the source nodes S separately1And S2Channel gain to the relay node R, and also to the source node S on behalf of the relay node R1And S2The channel gain of (a); p1、P2And PRRespectively representing source nodes S1、S2And the transmission power of the relay node R; g11、g22And gRRAre respectively source nodes S1、S2And residual self-interference factor after relay node R is eliminated by self-interference, and g is assumed11=g22=gRRG is equal to g and 0 is equal to or less than g and equal to 1; n is1、n2And nRRespectively representing source nodes S1、S2And Gaussian white noise received by the relay node R, wherein the variance of the Gaussian white noise received by each node in the system is 1, and noise signals at different nodes are statistically independent;
at this time, the relay node R goes to the source node S1Has an achievable rate of
Relay node R to source node S2Has an achievable rate of
Source node S1The achievable rate to relay R is
Source node S2The achievable rate to relay R is
In the formulae (4), (5), (6) and (7), | h1|2、|h2|2Respectively representing the channel gain h1And h2Square of the mold;
under the condition of meeting the requirement of system interrupt performance, minimizing the node transmission power sum, and establishing a formula (8) of an optimization problem, wherein the formula is as follows:
the formula (8a), the formula (8b), the formula (8c) and the formula (8d) constitute the formula (8), in the formula (8b), PoutRepresenting the probability of system outage, sQRepresenting the maximum outage probability that the system can accept; in the formula (8a), P1 *、P2 *、And ρ*Respectively, the optimal solution of equation (8), i.e. for the variable P1、P2、PRAnd rho;
the optimal solution P given by the formula (8)1 *、P2 *、And ρ*As the transmission power of the source nodes S1 and S2 and the relay node R and the superposition coding power distribution factor at the relay node R, respectively, the interruption probability S between the source nodes S1 and S2 by the relay node R can be setQThe interaction of the messages is performed and the sum of the transmission powers of the source nodes S1, S2 and the relay node R is minimized.
The optimal solution of the formula (8) consisting of the solving formula (8a), the solving formula (8b), the solving formula (8c) and the solving formula (8d) can adopt a progressive optimization solving method:
first, neglecting the constraint (8b), assume the source node S1、S2Can successfully decode with both the relay node R, i.e. IR1≥λ2、IR2≥λ1、I1R≥λ1、I2R≥λ2And the formula (9) are established at the same time;
λ1and λ2Are respectively source nodes S1And S2And has a1≤λ2,IR1、IR2、I1RAnd I2RAre given by formula (4), formula (5), formula (6) and formula (7), respectively; lambda1And λ2Is the normalized rate of the frequency band, and the dimension is bit/s/Hz;
at the source node S1、S2And under the condition that the relay node R and the relay node R can be successfully decoded, establishing a problem of minimizing the sum of the transmission power of the nodes, namely a formula (10), and obtaining:
the formula (10) is composed of the formula (10) represented by the formula (10a), the formula (10b), the formula (10c), the formula (10d), the formula (10e), the formula (10f), the formula (10g) and the formula (10h), and g represents a node S1、S2And a residual self-interference factor at R,andrespectively, the optimal solution of equation (10), i.e. for the variable P1、P2、PRAnd rho;
if the system adopts the solution of the formula (10) to send the information, the system interruption probability is zero at the moment;
in full duplex mode, the same time and frequency transmission and reception may cause self-interference, and equation (10) may not have a feasible solution, i.e., at the source node S1And S2Respectively at a transmission rate of1And λ2And under the condition that the residual self-interference factors of the three nodes are g, the three nodes can not be foundAndsuch that the source node S1、S2And the relay node R can both successfully decode;
if a feasible solution exists for equation (10),to the source node S1、S2And the transmission power and the set threshold of three nodes of the relay node RAt this time, if the solution given by equation (10) is givenAndis less than or equal toNamely, it isSource node S in a system1、S2And the relay node R will adoptAndsending information; if it isThen the source node S1、S2The relay node R keeps a silent state, does not send any information and generates interruption by the system;
the system outage probability at this time is defined as: a feasible solution exists for equation (10) andthe sum of the probability of no feasible solution of the formula (10) and the system outage probability is
Pr (-) represents the probability, E represents the event of formula (10) with no feasible solution,the inverse event of E is expressed, namely that a feasible solution exists in the formula (10);
the formula (10) is a convex optimization problem, and feasible solutions thereof can be obtained by using a Karush-Kuhn-Tucker condition, a lagrange multiplier method is used, and a KKT condition is used to obtain an optimal solution of the formula (10), which is divided into the following 2 conditions:
case 1: when the inequality (13) is established, the optimal solution of the equation (10) is
Case 2: when inequality (15) or inequality (16) holds, the optimal solution of equation (10) is
Therefore, when inequalities (13), (15), or (16) are satisfied, equation (10) has an optimal solution; when inequalities (13), (15), and (16) are not all true, equation (10) has no optimal solution;
at this time, the system outage probability given by equation (11) is
To facilitate the solution of the outage probability given by equation (18), the upper bound on the sum of the node transmit powers in equations (12) and (14) is given below, i.e.,the upper bound of (c);
according to the node transmitting power given by the formula (12), the node transmitting power can be obtainedThe upper bound of (A) is:
according to the node transmission power given by equation (14), the node transmission power can be obtainedThe upper bound of (A) is:
given by formulae (19) and (20)As an upper bound ofAndand substituting equation (18) to obtain one of the system outage probabilitiesThe approximate solution is:
in the formula (21), σ1And σ2Are respectively | h1|2And | h2|2The mean value of (a);
the observation of the formula (21) revealed that,is thatA decreasing function of, i.e. largeWill result in smallOn the contrary, largeWill correspond to small
Because, the system requiresMust be ensured, and therefore, from the energy efficiency point of view
Given by equation (22)Namely the threshold of the sum of the transmitting power of the source nodes S1, S2 and the relay node R; when the optimal solution given by equation (10)Andis less than or equal toThen, the source nodes S1 and S2 interact with each other through the relay node R, and the optimal solution given by the formula (10)Andis equal to or greater thanWhen the system is in use, the source nodes S1 and S2 and the relay node R keep silent state, and do not send any information, so that the system is interrupted.
The specific steps are summarized as follows:
step 3, source node S1、S2And the relay node R calculates a power threshold according to equation (22);
step 4, if the source node S1、S2And the sum of the transmission power of the relay R is less than or equal to the power threshold, and the source S1、S2The relay node R sends information and then goes to step 6; if the source node S1、S2And the sum of the transmission power of the relay node R is greater than the power threshold, then the next step 5 is carried out;
step 5, source node S1、S2The relay node R keeps a silent state, does not transmit any information and generates one interruption;
and 6, ending the method.
The invention has the advantages and beneficial effects that: under the condition of a frequency non-selective Rayleigh fading channel, the invention takes the QoS requirement of system interrupt probability performance and the limitation of the value of a superposition coding power distribution factor as constraint conditions, and aims to minimize the sum of node transmitting power; by utilizing channel knowledge and according to the requirement of a source node on the data rate, the transmitting power of a transmitter of the source node and the relay node and the superposition coding power distribution factor at the relay node are dynamically adjusted, the transmitting power of the node is minimized under the condition of meeting the requirement of system QoS, smaller total transmitting power of the system is provided, the energy efficiency performance advantage is achieved, and the effectiveness of the algorithm is verified through simulation experiments. Simulation experiments show that the power control algorithm has remarkable advantages in the sum of the transmitting power.
Drawings
FIG. 1 is a schematic view of the process of the present invention;
FIG. 2 shows the total transmission power of the system and λ2A simulation graph of the relationship between the two;
FIG. 3 shows the probability of system outage and λ2The relationship between the two is simulated.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention adopts the superposition weavingA node transmitting power control method of a full-duplex bidirectional relay system of codes is provided, wherein the relay system is provided with three nodes, namely two source nodes and one relay node which work in a full-duplex mode under the environment of a frequency non-selective Rayleigh fading channel. Wherein S is1And S2And R is a decoding forwarding relay node positioned between the source nodes, and each node in the system can obtain accurate channel state information through channel estimation. The method comprises the steps that channel knowledge is utilized, the transmitting power of a source node and a relay node transmitter and the superposition coding power distribution factor at a relay node are dynamically adjusted according to the requirement of the source node on the data rate, and the sum of the transmitting power of three nodes is minimized under the condition that the requirement of the system interrupt probability performance is met; firstly, checking whether the channel condition can meet the requirement of the system communication service, if so, calculating the transmitting power of each node in the system by a node power control algorithm for minimizing the sum of the transmitting power of the nodes, and calculating the total transmitting power limit; if the sum of the transmitting power of the three nodes is less than or equal to the total transmitting power limit, the three nodes transmit information to complete one-time information interaction; if the sum of the transmitting powers of the three nodes is greater than the total transmitting power limit when the channel condition can not meet the system communication service requirement or the channel condition can meet the system communication service requirement, each node is in a silent state, the system generates one-time interruption, and a smaller sum of the transmitting powers of the nodes is provided under the condition of meeting the system interruption performance requirement. Firstly, checking whether the channel condition can meet the requirement of the system communication service, if so, calculating the sending power and the total sending power limit of the node, and if not, sending the information to complete the information interaction, otherwise, keeping the node in a silent state and generating an interruption by the system; and the minimum sum of the sending power of the nodes is realized under the condition of meeting the performance requirement of the system interrupt probability.
In the experiment, assume σ1=σ2=10,sQ=0.01,λ 11 bit/s/Hz; the sum of the transmit powers of the three nodes in the system, i.e. the total transmit power, is given by the sum of the transmit powers of the three nodes in equation (12) or equation (14)Average values of multiple simulation experiments.
FIG. 2 shows the total transmit power of the system and λ2Curve of relationship between, wherein1Fixing the value; in the figure, "2 time slot amplifying and forwarding half duplex" means: the two source nodes and the relay node work in a half-duplex mode, 2 time slots are needed for information interaction between the two source nodes, the 1 st time slot is used for sending information to the relay, the relay node processes a combined signal sent by the source nodes by adopting an amplification forwarding protocol and broadcasts the combined signal to the two source nodes at the 2 nd time slot, and the source nodes perform self-interference signal elimination on the received broadcast signal and then perform demodulation and decoding to obtain a signal sent by the other side.
"3-slot network coding half duplex" means: the two source nodes and the relay node work in a half-duplex mode, information interaction between the two source nodes needs 3 time slots and 1 st time slot, the first source node sends a message to the relay node, the relay node demodulates and decodes a received signal to obtain a message sent by the source node, the second source node sends a message to the relay node, the relay node demodulates and decodes the received signal to obtain a message sent by the source node, the 3 rd time slot and the relay node perform network coding operation, namely, the messages obtained by the 1 st time slot and the 2 nd time slot are subjected to bit exclusive OR and then coded and modulated into a sending signal, the sending signal is broadcasted to the two source nodes at the 3 rd time slot, and the source node demodulates and decodes the received signal and performs network coding reverse operation to obtain a message sent to the user.
"3 slot superposition coding half duplex" means: the two source nodes and the relay node work in a half-duplex mode, information interaction between the two source nodes needs 3 time slots and 1 st time slot, the first source node sends a message to the relay, the relay demodulates and decodes a received signal to obtain a message sent by the source node, the second source node sends a message to the relay, the relay demodulates and decodes the received signal to obtain a message sent by the source node, the 3 rd time slot carries out superposition coding on the messages obtained by the 1 st time slot and the 2 nd time slot, then the messages are modulated into a sending signal, the sending signal is broadcasted to the two source nodes at the 3 rd time slot, and the source node demodulates and decodes the received signal to obtain a message sent by the other party.
As can be seen from FIG. 2, regardless of λ2Taking any value, the algorithm provided by the invention has the minimum total transmission power, and the small residual self-interference factor g has smaller total transmission power; even if the algorithm provided by the invention adopts a larger residual self-interference factor g, such as-20 dB, the algorithm can always provide a smaller total transmitting power sum and has the energy efficiency performance advantage.
FIG. 3 shows the probability of system outage and λ2The relationship between them, where all comparison objects and parameter settings are the same as in fig. 2. As can be seen from FIG. 3, the algorithm provided by the present invention can meet the requirement of the system on the interrupt probability, i.e. the interrupt probability of the system is less than or equal to sQ。
It should be understood by those skilled in the art that the above embodiments are only for illustrating the present invention and are not to be used as a limitation of the present invention, and that changes and modifications to the above embodiments may fall within the scope of the appended claims within the spirit of the present invention.
Claims (1)
1. A control method for node transmitting power of full duplex bidirectional relay system, three nodes in the system, two source nodes and one relay node, all work in full duplex mode, supposing that the channel is frequency nonselective Rayleigh fading channel, S1And S2Is a source node, R is a decoding forwarding relay node positioned between the source nodes, and the source node S in the system1、S2And three nodes of a relay node R can obtain accurate channel state information through channel estimation, and the method is characterized in that the transmitting power of a source node and a relay node transmitter and the superposition coding power distribution factor of the relay node are dynamically adjusted by utilizing channel knowledge and according to the requirement of the source node on the data rate, and the source node S is realized under the condition of meeting the requirement of the system interrupt probability performance1、S2And the transmission power of three nodes of the relay node RMinimization of sum; firstly, checking whether the channel condition can meet the requirement of the system communication service, if so, calculating the transmitting power of each node in the system by a power control algorithm for minimizing the sum of the transmitting power of the nodes, and calculating a power threshold; if the source node S1、S2And the sum of the transmitting power of the three nodes of the relay node R is less than or equal to the power threshold, and then the source node S1、S2The information is sent simultaneously with the relay node R to complete the source node S1And S2The information intercommunication between them; if the channel condition can not satisfy the system communication service requirement or the channel condition can satisfy the system communication service requirement, the source node S1、S2And the sum of the transmitting power of the three nodes of the relay node R is greater than the power threshold, and the source node S1、S2When the relay node R is in a silent state, the system generates interruption, and under the condition of meeting the performance requirement of system interruption, the sum of the transmitting power of the nodes is smaller;
the node power control algorithm process for minimizing the sum of the node transmitting power is as follows: at the kth time slot, k ∈ {1, 2, 3 … }, the source node S1Code modulating information to be transmitted into transmission signal x1[k]Let x be1[k]Having unit power and transmitting to the relay node R; at the same time, the source node S2Code modulating information to be transmitted into transmission signal x2[k]Suppose x2[k]Has unit power and transmits to the relay R; the relay node R receives the source node S1And S2While sending the signal, the superposition coding technique is adopted to receive the source node S1And S2The combined signal is decoded into the source node sending information, and then the source node sending information is coded and modulated into the sending signalAt the same time xR[k]Forward to the source node S1And S2Wherein rho is a superposition coding power distribution factor, and rho is more than or equal to 0 and less than or equal to 1; source node S1And S2Received signal xR[k]Then remove the self-transmissionThe signal item is demodulated and decoded to obtain the information sent by the source node of the other side, so as to realize the source node S1And S2Interaction of information among the users;
at the k-th time slot, the source node S1、S2And the signals received by the relay node R are respectively
Since the channel characteristics are quasi-static and have reciprocity, h1And h2Not only to represent the source nodes S separately1And S2Channel gain to the relay node R, and also to the source node S on behalf of the relay node R1And S2The channel gain of (a); p1、P2And PRRespectively representing source nodes S1、S2And the transmission power of the relay node R; g11、g22And gRRAre respectively source nodes S1、S2And residual self-interference factor after relay node R is eliminated by self-interference, and g is assumed11=g22=gRRG is equal to g and 0 is equal to or less than g and equal to 1; n is1、n2And nRRespectively representing source nodes S1、S2And Gaussian white noise received by the relay node R, wherein the variance of the Gaussian white noise received by each node in the system is 1, and noise signals at different nodes are statistically independent;
at this time, the relay node R goes to the source node S1Has an achievable rate of
Relay node R to source node S2Has an achievable rate of
Source node S1The achievable rate to relay R is
Source node S2The achievable rate to relay R is
In the formulae (4), (5), (6) and (7), | h1|2、|h2|2Respectively representing the channel gain h1And h2The square of the mold;
under the condition of meeting the requirement of system interrupt performance, minimizing the node transmission power sum, and establishing a formula (8) of an optimization problem, wherein the formula is as follows:
the formula (8a), the formula (8b), the formula (8c) and the formula (8d) constitute the formula (8), in the formula (8b), PoutRepresenting the probability of system outage, sQRepresenting the maximum outage probability that the system can accept; in the formula (8a), P1 *、And ρ*Respectively, the optimal solution of equation (8), i.e. for the variable P1、P2、PRAnd rho;
the optimal solution P given by the formula (8)1 *、And ρ*As the transmission power of the source nodes S1, S2 and the relay node R and the superposition coding power distribution factor at the relay node R, respectively, the interruption probability S between the source nodes S1 and S2 by the relay node R can be setQPerforming message interaction and minimizing the sum of the transmission power of the source nodes S1 and S2 and the relay node R;
the optimal solution of the formula (8) consisting of the solving formula (8a), the formula (8b), the formula (8c) and the formula (8d) is solved by adopting a progressive optimization solving method:
first, neglecting the constraint (8b), assume the source node S1、S2Can successfully decode with both the relay node R, i.e. IR1≥λ2、IR2≥λ1、I1R≥λ1、I2R≥λ2And the formula (9) are established at the same time;
λ1and λ2Are respectively source nodes S1And S2And has a1≤λ2,IR1、IR2、I1RAnd I2RAre given by formula (4), formula (5), formula (6) and formula (7), respectively; lambda [ alpha ]1And λ2Is the normalized rate of the frequency band, and the dimension is bit/s/Hz;
at the source node S1、S2And under the condition that the relay node R and the relay node R can be successfully decoded, establishing a problem of minimizing the sum of the transmission power of the nodes, namely a formula (10), and obtaining:
formula (10a), formula (10b), formula (10)c) The formula (10) is composed of the formula (10) of the formula (10d), the formula (10e), the formula (10f), the formula (10g) and the formula (10h), and g represents a node S1、S2And a residual self-interference factor at R,andrespectively, the optimal solution of equation (10), i.e. for the variable P1、P2、PRAnd rho;
if the system adopts the solution of the formula (10) to send the information, the system interruption probability is zero at the moment;
in full duplex mode, the same time and frequency transmission and reception may cause self-interference, and equation (10) may not have a feasible solution, i.e., at the source node S1And S2Respectively at a transmission rate of1And λ2And under the condition that the residual self-interference factors of the three nodes are g, the three nodes can not be foundAndso that the source node S1、S2And the relay node R can both successfully decode;
if feasible solution exists in the formula (10), the source node S is processed1、S2And the transmission power and the set threshold of three nodes of the relay node RAt this time, if the solution given by equation (10) is givenAndis less than or equal toNamely, it isSource node S in a system1、S2And the relay node R will adoptAndsending information; if it isThen the source node S1、S2The relay node R keeps a silent state, does not send any information and generates interruption by the system;
the system outage probability at this time is defined as: a feasible solution exists for equation (10) andthe sum of the probability of no feasible solution of the formula (10) and the system outage probability is
Pr (-) represents the probability, E represents the event that there is no feasible solution for equation (10),the inverse event of E is expressed, namely that a feasible solution exists in the formula (10);
the formula (10) is a convex optimization problem, and feasible solutions thereof can be obtained by using a Karush-Kuhn-Tucker condition, a lagrange multiplier method is used, and a KKT condition is used to obtain an optimal solution of the formula (10), which is divided into the following 2 conditions:
case 1: when the inequality (13) holds, the optimal solution of the equation (10) is
Case 2: when inequality (15) or inequality (16) holds, the optimal solution of equation (10) is
Therefore, when inequalities (13), (15), or (16) are satisfied, equation (10) has an optimal solution; when inequalities (13), (15), and (16) are not all true, equation (10) has no optimal solution;
at this time, the system outage probability given by equation (11) is
To facilitate the solution of the outage probability given by equation (18), the upper bound on the sum of the node transmit powers in equations (12) and (14) is given below, i.e.,the upper bound of (c);
according to the node transmitting power given by the formula (12), the node transmitting power can be obtainedThe upper bound of (A) is:
according to the node transmission power given by equation (14), it is possible to obtainThe upper bound of (A) is:
given by formulae (19) and (20)As an upper bound ofAndand substituting equation (18) to obtain an approximate solution to the probability of system outage:
in the formula (21), σ1And σ2Are respectively | h1|2And | h2|2The mean value of (a);
the observation of the formula (21) revealed that,is thatA decreasing function of, i.e. largeWill result in smallOn the contrary, largeWill correspond to small
Because, the system requiresMust be guaranteed and therefore must be taken from an energy efficiency point of view
Given by equation (22)Namely the threshold of the sum of the transmitting power of the source nodes S1, S2 and the relay node R; when the optimal solution given by equation (10)Andis less than or equal toThen, the source nodes S1 and S2 interact with each other through the relay node R, and the optimal solution given by the formula (10)Andis equal to or greater thanWhen the system is in use, the source nodes S1 and S2 and the relay node R keep a silent state, no information is sent, and the system is interrupted;
the method comprises the following specific steps:
step 1, source node S1、S2And the relay node R verifies whether inequalities (13), (15) and (16) are true or not respectively;
step 2, if the inequality (13) is established, the source node S1、S2And the relay node R calculates the respective transmission powers according to the equation (12), and the relay node R calculates the superposition coding power distribution factor according to the equation (12), and if the inequality (15) or the inequality (16) is established, the source node S1、S2And the relay node R calculates respective transmission powers according to equation (14), and the relay node R calculates a superposition coding power allocation factor according to equation (14); if inequalities (13), (15) and (16) are not true, go to step 5;
step 3, source node S1、S2And the relay node R calculates the power threshold according to equation (22);
step 4, if the source node S1、S2And the sum of the transmission power of the relay R is less than or equal to the power threshold, and the source S1、S2The relay node R sends information and then goes to step 6; if the source node S1、S2And the sum of the transmission power of the relay node R is greater than the power threshold, then the next step 5 is carried out;
step 5, source node S1、S2The relay node R keeps a silent state, does not transmit any information and generates one interruption;
and 6, ending the method.
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