A fair resource allocation method for D2D networks based on energy harvesting

Abstract

The present invention relates to a D2D network joint resource fair allocation method based on energy collection, comprising: constructing an energy collection model for the D2D network underlying cellular communication system for energy collection; considering the communication quality of cellular communication and D2D communication, constructing an optimization problem to maximize the minimum amount of data in the system, and converting the optimization problem into a time and power allocation sub-problem and a spectrum resource allocation sub-problem; using variable substitution and Taylor expansion theory to design an iterative algorithm to solve the time and power allocation sub-problem; using the Hungarian algorithm and binary search method to design an algorithm to solve the spectrum resource allocation sub-problem, and obtaining the optimal allocation of spectrum resources. The present invention proposes a multi-objective optimization problem to maximize the minimum amount of transmitted data in the system, coordinates the communication quality of all D2D devices to ensure fair allocation of system resources, and simultaneously considers the communication quality of cellular users and D2D devices in the system, so that the resource allocation design can be better applied in practice.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to a D2D network joint resource fair allocation method based on energy collection. Background Art

[0002] With the advent of the 5G era of the Internet of Everything, wireless networks are facing significant challenges, including network congestion, energy consumption, and spectrum scarcity caused by the massive number of devices accessing them. Years ago, D2D communication was proposed as a technology that allows direct communication between devices, mitigating network pressure caused by mobile devices to the devices themselves rather than base stations. Currently, the rapid development of D2D demonstrates its enormous potential, and it is already being explored as a key 5G technology for practical implementation.

[0003] Since communication between devices can cause unnecessary energy loss for content providers, researchers have considered communication strategies from aspects such as distance, social factors, and power control to improve the energy efficiency of D2D communication. However, this has not effectively solved the problem of limited battery capacity and charging methods for devices. Therefore, researchers have turned their attention to the combination of energy harvesting technology and D2D communication technology. The devices can self-replenish energy, extending the life of the network and devices and promoting green communication. Energy harvesting refers to the ability of devices to collect renewable energy such as solar energy, wind energy, and radio frequency energy from the environment for their own operation. Radio frequency signals have the advantage of transmitting information and energy at the same time, and can utilize idle interference signals and are therefore being studied more.

[0004] When spectrum resources are limited, D2D and cellular communications can work together to achieve higher spectrum efficiency. Many resource allocation algorithms have been designed in the existing technology to control the interference caused by reused spectrum resources to achieve better system performance. However, since energy harvesting changes the available power of the device, the resource allocation method of the traditional D2D network is no longer applicable to the D2D network based on RF energy harvesting. In addition, there is a lack of research on D2D communication based on energy harvesting in the existing technology, and there is a lack of consideration for the communication quality of DUE (D2D device), resulting in a lack of fairness in resource allocation.

[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a D2D network joint resource fair allocation method based on energy harvesting, which solves the shortcomings of the prior art problems.

[0007] The object of the present invention is achieved through the following technical solution: a method for fair allocation of D2D network joint resources based on energy harvesting, the method comprising:

[0008] S1. Construct a D2D network underlying cellular communication system based on a linear RF energy harvesting model for energy harvesting. The system includes a collection of multiple D2D devices DUE. and a set M = {1, ..., m, ..., M} of cellular communication devices CUE, where D2D communication is used between DUE pairs and cellular communication is performed between CUE devices and base stations;

[0009] S2. Considering the communication quality of cellular communication and D2D communication simultaneously, an optimization problem is constructed to maximize the minimum amount of data in the system, and the optimization problem is converted into a time and power allocation sub-problem and a spectrum resource allocation sub-problem;

[0010] S3. Design an iterative algorithm to solve the time and power allocation subproblems using variable substitution and Taylor expansion theory;

[0011] S4. Design an algorithm using the Hungarian algorithm and binary search method to solve the spectrum resource allocation sub-problem and obtain the optimal fair allocation of spectrum resources.

[0012] The DUE device pair includes a D2D transmitter DUE_T device and a D2D receiver DUE_R device. The DUE_T device collects supplementary energy using a time division protocol. Within a period of time T, the nth DUE_T device collects energy in the energy collection time slot. Energy is harvested in the time slot, and then information is transmitted The collected energy is used for data transmission. The energy collected by DUE_Tn is Where η is the conversion efficiency of the energy harvesting circuit, P B is the base station transmission power, g B,n is the channel gain between DUE_T and the base station;

[0013] DUE_Tn transmission power The duration of the first phase and harvesting energy The collected energy can be used to obtain the transmission power of DUE_Tn:

[0014] In the communication phase, the DUE device reuses the uplink spectrum resources of the CUE device. When the nth DUE device reuses the channel of the mth CUE device, the cellular communication channel and the D2D communication channel are modeled as follows: and Where C is the path loss constant, ξ m,BFor logarithmic shadow fading with a standard deviation of 8 dB, the signal interference noise ratios at the DUE_Rn receiving point and the base station receiving point are:

[0015]

[0016]

[0017] in, is the transmit power of CUEm, is the transmission power of DUE_Tn, ρ m,n It is a binary variable, representing the spectrum reuse indicator factor of whether the DUE device reuses the CUEm spectrum;

[0018] Then the information transmission rates of the DUE device and the CUE device are expressed as and

[0019] The optimization problem is expressed as: The constraints are as follows:

[0020] st

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] ρ m,n ∈{0,1},

[0027] ρ m,n ∈{0,1},

[0028] in, and They are the minimum transmission rate thresholds for CUE and DUE devices respectively. is the energy harvesting time slot, is the information transmission time slot, and the sum of the two time slots does not exceed the period T; To collect the minimum threshold of energy, that is, the minimum energy required for normal communication needs, It is the highest threshold of energy collection, i.e. the maximum capacity of DUE; and are the maximum transmit powers of the DUE and CUE devices respectively; the spectrum reuse indicator factor ρ m,n The spectrum of a CUE device is restricted to be reused by at most one D2D link, and each D2D link can find the spectrum of a CUE device for reuse.

[0029] The time and power allocation sub-problem is expressed as: in, a1=bh m,n +Ah n , b1=σ 2 +ah m,n -Bh n , c1=bh m,n , d1=σ 2 +ah m,n ,

[0030] After Taylor's first-order expansion, it becomes where t k is a constant, yes The gradient vector of .

[0031] The iterative algorithm designed by using variable substitution and Taylor expansion theory to solve the time and power allocation subproblems includes the following:

[0032] A1. Initialization time t k , k = 0, the number of iterations is 0;

[0033] A2. If f(t (k) )-f(t (k-1) )>ε, then continue with the following steps; otherwise, jump directly to step A7, where ε is the solution accuracy;

[0034] A3. Solving convex optimization problems Get the current t k The best time

[0035] A4. Let k = k + 1;

[0036] A5. Update t k ,

[0037] A6. Return to step A2.

[0038] A7. Calculate the optimal energy harvesting time CUE transmit power DUE transmit power

[0039] The algorithm designed by using the Hungarian algorithm and the binary search method to solve the spectrum resource allocation sub-problem includes the following contents:

[0040] B1. Obtain the information rate of each CUE-DUE multiplexing pair using optimal time and power allocation Minimum information transmission rate threshold with DUE device Compare

[0041] B2. Calculate the amount of data transmitted by M×N CUE-DUE multiplexing pairs

[0042] B3. Initialize the left boundary of the binary search i = 1, the right boundary j = M × N, and the initialization matrix K = 0 M×N ;

[0043] B4, all D m,n * Sort from small to large and store in vector Φ;

[0044] B5. The middle index of the binary search is mid = (i + j) / 2, and the middle value is Φ mid

[0045] B6. If ji>1, continue with the following steps; otherwise, skip directly to step B10.

[0046] B7, traverse all D m,n * , if D m,n * <Φ mid , K m,n =1, otherwise K m,n =0;

[0047] B8. Apply the Hungarian algorithm to find the minimum cost of the matrix K, denoted as x;

[0048] B9. If x>0, let j=mid, otherwise i=mid;

[0049] B10, return to step B6;

[0050] B11, Φ mid The minimum amount of data to be transmitted is the maximum;

[0051] B12, traverse all D m,n * , if D m,n * <Φ mid , then D m,n * =inf; otherwise D m,n *=-D m,n * ;

[0052] B13, to D m,n * The Hungarian algorithm is applied to the matrix to obtain the optimal spectrum resource matching matrix ρ.

[0053] Establish a feasibility check problem, and the optimization goal is to maximize the information rate of CUE The optimization variables are time and power, and the constraints are all the constraints of the time and power allocation subproblem (except the constraint ); then solve the feasibility check problem to get the optimal value And verify whether the constraints are satisfied It can be clearly seen that is the maximum information transmission rate in the feasible domain, if the constraint is satisfied This indicates that there is a feasible solution to the time and power allocation subproblem. Otherwise, if there is no feasible solution, it is excluded. A feasibility check is performed on each CUE-DUE spectrum reuse candidate pair, and candidate pairs without feasible solutions can be excluded.

[0054] The algorithm is simulated with data under different requirements of minimum energy thresholds, energy collection efficiency and different cellular user rate thresholds, and the designed algorithm is compared with other basic algorithms to verify the theoretical analysis and reflect the performance advantage of the proposed algorithm in terms of the number of transmissions.

[0055] The present invention has the following advantages:

[0056] 1. D2D devices can collect energy from surrounding devices for information transmission. Energy self-sustainability extends the life of devices and networks.

[0057] 2. A multi-objective optimization problem is proposed to maximize the minimum amount of transmitted data within the system, coordinate the communication quality of all D2D devices to ensure fair distribution of system resources, and consider the communication quality of cellular users and D2D devices in the system at the same time, so that the resource allocation design can be better applied in practice.

[0058] 3. An iterative approximation algorithm and a fair matching algorithm based on the Hungarian algorithm and binary search method are designed to obtain the approximate optimal solution to the problem.

[0059] 4. Perform feasibility checks on all candidate pairs of CUE-DUE spectrum resource reuse and eliminate candidate pairs that do not meet the requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic diagram of the process of the present invention;

[0061] Figure 2It is a system model diagram of the present invention;

[0062] Figure 3 The feasible region of the feasibility problem established for feasibility checking;

[0063] Figure 4 A flowchart of solving the time and power allocation sub-problems of the present invention;

[0064] Figure 5 A flowchart of solving the spectrum resource allocation sub-problem of the present invention;

[0065] Figure 6 The simulation diagram shows the comparison between the proposed algorithm and the genetic algorithm under different cellular communication transmission rate thresholds;

[0066] Figure 7 The simulation diagram shows the comparison between the proposed algorithm and the genetic algorithm under different minimum energy collection thresholds and base station transmission powers.

[0067] Figure 8 The simulation diagram compares the transmission data volume of the designed maximum and minimum algorithm with other algorithms under different energy conversion efficiencies. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application provided below in conjunction with the drawings is not intended to limit the scope of protection of the present application for which protection is claimed, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present application. The present invention is further described below in conjunction with the drawings.

[0069] like Figure 1 and Figure 2 As shown, the present invention is applicable to a system with a base station and multiple normally distributed mobile devices. A random selection of mobile devices from all users adopts D2D communication. At a certain moment, the mobile devices are divided into D2D communication devices (DUE) and cellular communication devices (CUE). The CUE communicates with the base station, while the DUE communicates directly after pairing. In this physical scenario, the resource fair allocation problem of the D2D network can be mathematically modeled as follows:

[0070] Optimization problem:

[0071] Constraints: st

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] ρ m,n ∈{0,1},

[0078] ρ m,n ∈{0,1},

[0079] like Figure 3 As shown, in the time and power allocation algorithm of the present invention, the feasibility check is performed to confirm whether there is a feasible solution to the time and power allocation sub-problem, and the feasible domain of the feasibility problem is proposed. The feasibility check problem is described as:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] in Arranged Optimization variables With monotonicity, the optimal for And about and Two constraints can be used and They are equivalently expressed as and So the feasible domain of the above problem is Figure 3 As shown. Due to the feasibility issue and are all monotonic, so the optimal solution to the feasibility problem can be obtained at the boundary, that is, Compare the optimal value of the above problem with the rate threshold of CUE, that is, verify whether the constraint is satisfied If the conditions are met, then there is a feasible solution to the time and power allocation sub-problems and the CUE-DUE pair can be used as a spectrum reuse candidate pair. If the conditions are not met, then the pair is excluded.

[0086] like Figure 4 As shown, subproblem 1, namely the time and power optimization subproblem, can be described as:

[0087]

[0088] st

[0089]

[0090]

[0091]

[0092]

[0093] First, the optimal solution satisfies and It can be expressed as Where A=TηP B g B,n ,B=ηP B g B,n . The above question is still about The optimal for in Finally, the objective function is equivalently expressed by mathematical transformation as follows: in a1=bh m,n +Ah n , b1=σ 2 +ah m,n -Bh n , c1=bh m,n , d1=σ 2 +ah m,n .

[0094] By Taylor's first-order expansion where t k is a constant, yes Therefore, the time and power optimization algorithm can specifically include the following steps:

[0095] A1. Initialization time tk , k=0; the number of iterations is 0.

[0096] A2. If f(t (k) )-f(t (k-1) )>ε (where ε is the solution accuracy), continue with the following steps; otherwise, skip directly to step A7;

[0097] A3. Solving convex optimization problems Get the current t k The best time

[0098] A4, k=k+1;

[0099] A5. Update t k ,

[0100] A6. Return to step A2.

[0101] A7. Calculate the optimal energy harvesting time CUE transmit power DUE transmit power

[0102] like Figure 5 As shown, the spectrum resource allocation sub-problem can be expressed as:

[0103]

[0104] st ρ m,n ∈{0,1},

[0105] ρ m,n ∈{0,1},

[0106] Furthermore, the spectrum resource allocation algorithm specifically includes the following steps:

[0107] B1. Obtain the information rate of each CUE-DUE multiplexing pair using optimal time and power allocation Minimum information transmission rate threshold with DUE Compare

[0108] B2. Calculate the amount of data transmitted by M×N CUE-DUE multiplexing pairs

[0109] B3. Initialize the left boundary of the binary search i = 1, the right boundary j = M × N, and the matrix K = 0 M×N ;

[0110] B4, all D m,n * Sort from small to large and store in vector Φ;

[0111] B5. The middle index of the binary search is mid = (i + j) / 2, and the middle value is Φ mid ;

[0112] B6. If ji>1, continue with the following steps; otherwise, skip directly to step B10.

[0113] B7, traverse all D m,n * , if D m,n * <Φ mid , K m,n = 1. Otherwise K m,n =0;

[0114] B8. Apply the Hungarian algorithm to find the minimum cost of the matrix K, denoted as x;

[0115] B9. If x>0, let j=mid; otherwise, let i=mid;

[0116] B10, return to step B6;

[0117] B11, Φ mid The minimum amount of data to be transmitted is the maximum;

[0118] B12, traverse all D m,n * , if D m,n * <Φ mid , then D m,n * =∞; otherwise D m,n * =-D m,n * ;

[0119] B13, to D m,n * The Hungarian algorithm is applied to the matrix to obtain the optimal spectrum resource matching matrix ρ.

[0120] like Figure 6 As shown, the information transmission rate threshold R of different CUEs t c hBelow is a simulation diagram showing the performance of the proposed algorithm 1 and the genetic algorithm in terms of transmitted data volume. The proposed algorithm and the genetic algorithm were used to solve time and power allocation, respectively, and their performance on the minimum data volume was compared. It can be seen that the proposed algorithm has a higher data volume than the genetic algorithm. When the solving algorithms are the same, a higher base station transmit power results in a larger data volume because the DUE collects more energy in the same time. A higher threshold means that the CUE must increase its transmit power, which also causes greater interference to the D2D link. Therefore, as shown in the figure, the minimum D2D data volume decreases as the rate threshold increases.

[0121] like Figure 7 The following simulations show the data volume performance of the proposed algorithm and the genetic algorithm under different minimum energy harvesting thresholds. Similarly, the figure shows that the time and power allocation algorithm proposed by the present invention outperforms the genetic algorithm in data volume transmission. The higher the energy threshold, the more energy the DUE requires to complete a transmission. The DUE transmitter must spend more time harvesting energy within a cycle, and the information transmission time is correspondingly reduced. Therefore, the minimum data volume in the figure decreases as the energy threshold increases.

[0122] like Figure 8 As shown, it is a simulation diagram of the data volume performance of the spectrum resource allocation algorithm proposed in the present invention and other benchmark algorithms under different energy conversion efficiencies. Other benchmark algorithms include the Hungarian algorithm and the maximum-minimum comparison algorithm. The Hungarian algorithm allocates spectrum resources with the goal of maximizing the total data volume of the system, and the maximum-minimum comparison algorithm is to find the maximum and minimum data volume. From the figure, we can see that the minimum data volume of the spectrum resource allocation algorithm proposed in the present invention is the same as that of the maximum-minimum algorithm, which is higher than the Hungarian algorithm. As for the performance of the total data volume transmitted by the system, the Hungarian algorithm is the best, the algorithm proposed in the present invention is second, and the maximum-minimum comparison algorithm is the worst. Therefore, the spectrum resource allocation algorithm proposed in the present invention can achieve a better total data volume while the minimum data volume is the best. It can be seen from the figure that the higher the energy conversion efficiency, the greater the amount of data transmitted. Obviously, higher conversion efficiency allows the device to obtain sufficient energy for data transmission in a shorter time, and the time is also longer, so the data volume is on an upward trend.

[0123] The foregoing description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the disclosed form and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments, and can be modified within the scope of the present invention through the above teachings or techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. A D2D network joint resource fair allocation method based on energy harvesting, characterized by: The method comprises: S1. Construct a D2D network underlying cellular communication system based on a linear RF energy harvesting model for energy harvesting. The system includes a collection of multiple D2D devices DUE. and a set M = {1, ..., m, ..., M} of cellular communication devices CUE, where D2D communication is used between DUE pairs and cellular communication is performed between CUE devices and base stations; S2. Considering the communication quality of cellular communication and D2D communication simultaneously, an optimization problem is constructed to maximize the minimum amount of data in the system, and the optimization problem is converted into a time and power allocation sub-problem and a spectrum resource allocation sub-problem; S3. Design an iterative algorithm to solve the time and power allocation subproblems using variable substitution and Taylor expansion theory; S4. Design an algorithm using the Hungarian algorithm and binary search method to solve the spectrum resource allocation sub-problem and obtain the optimal fair allocation of spectrum resources.

2. The method for fair allocation of D2D network joint resources based on energy harvesting according to claim 1, characterized in that: The DUE device pair includes a D2D transmitter DUE_T device and a D2D receiver DUE_R device. The DUE_T device collects supplementary energy using a time division protocol. Within a period of time T, the nth DUE_T device collects energy in the energy collection time slot. Energy is harvested in the time slot, and then information is transmitted The collected energy is used for data transmission, and the energy collected by DUE_T n is Where η is the conversion efficiency of the energy harvesting circuit, P B is the base station transmission power, g B,n is the channel gain between DUE_T and the base station; DUE_T n transmission power The duration of the first phase and harvesting energy The collected energy can be used to obtain the transmission power of DUE_Tn:

3. The method for fair allocation of D2D network joint resources based on energy harvesting according to claim 2, characterized in that: In the communication phase, the DUE device reuses the uplink spectrum resources of the CUE device. When the nth DUE device reuses the channel of the mth CUE device, the cellular communication channel and the D2D communication channel are modeled as follows: and Where C is the path loss constant, ξ m,B For logarithmic shadow fading with a standard deviation of 8 dB, the signal-to-interference-noise ratios at the DUE_R n receiving point and the base station receiving point are: in, is the transmit power of CUE m, is the transmission power of DUE_T n, ρ m,n is a binary variable, representing the spectrum reuse indicator factor of whether DUE device n reuses the spectrum of CUE m; Then the information transmission rates of the DUE device and the CUE device are expressed as and 4. The method for fair resource allocation in a D2D network based on energy harvesting according to claim 1, characterized in that: The optimization problem is expressed as: The constraints are as follows: in, and They are the minimum transmission rate thresholds for CUE and DUE devices respectively. is the energy harvesting time slot, is the information transmission time slot, and the sum of the two time slots does not exceed the period T; To collect the minimum threshold of energy, that is, the minimum energy required for normal communication needs, It is the highest threshold of energy collection, i.e. the maximum capacity of DUE; and are the maximum transmit powers of the DUE and CUE devices respectively; the spectrum reuse indicator factor ρ m,n The spectrum of a CUE device is restricted to be reused by at most one D2D link, and each D2D link can find the spectrum of a CUE device for reuse.

5. The method for fair allocation of D2D network joint resources based on energy harvesting according to claim 1, characterized in that: The time and power allocation sub-problem is expressed as: in, a1=bh m,n +Ah n , b1=σ 2 +ah m,n -Bh n , c1=bh m,n , d1=σ 2 +ah m,n , After Taylor's first-order expansion, it becomes where t k is a constant, yes The gradient vector of .

6. The method for fair allocation of D2D network joint resources based on energy harvesting according to claim 5, characterized in that: The iterative algorithm designed by using variable substitution and Taylor expansion theory to solve the time and power allocation subproblems includes the following: A1. Initialization time t k , k = 0, the number of iterations is 0; A2. If f(t (k) )-f(t (k-1) )>ε, then continue with the following steps; otherwise, jump directly to step A7, where ε is the solution accuracy; A3. Solving convex optimization problems Get the current t k The best time A4. Let k = k + 1; A5. Update t k , A6. Return to step A2. A7. Calculate the optimal energy harvesting time CUE transmit power DUE transmit power 7. The method for fair allocation of D2D network joint resources based on energy harvesting according to claim 1, characterized in that: The algorithm designed by using the Hungarian algorithm and the binary search method to solve the spectrum resource allocation sub-problem includes the following contents: B1. Obtain the information rate of each CUE-DUE multiplexing pair using optimal time and power allocation Minimum information transmission rate threshold with DUE device Compare B2. Calculate the amount of data transmitted by M×N CUE-DUE multiplexing pairs B3. Initialize the left boundary of the binary search i = 1, the right boundary j = M × N, and the initialization matrix K = 0 M×N ; B4, all D m,n * Sort from small to large and store in vector Φ; B5. The middle index of the binary search is mid = (i + j) / 2, and the middle value is Φ mid B6. If ji>1, continue with the following steps; otherwise, skip directly to step B10. B7, traverse all D m,n * , if D m,n * <Φ mid , K m,n =1, otherwise K m,n =0; B8. Apply the Hungarian algorithm to find the minimum cost of the matrix K, denoted as x; B9. If x>0, let j=mid, otherwise i=mid; B10, return to step B6; B11, Φ mid The minimum amount of data to be transmitted is the maximum; B12, traverse all D m,n * , if D m,n * <Φ mid , then D m,n * =inf; otherwise D m,n * =-D m,n * ; B13, to D m,n * The Hungarian algorithm is applied to the matrix to obtain the optimal spectrum resource matching matrix ρ.

8. A D2D network joint resource fair allocation method based on energy harvesting according to any one of claims 1 to 7, characterized in that: Before solving the time and power allocation sub-problems, a feasibility check operation needs to be performed on the problem; the feasibility check operation includes: establishing a feasibility check problem, and the optimization goal is to maximize the information rate of CUE The optimization variables are time and power, and the constraints are all the constraints of the time and power allocation sub-problem; then the feasibility check problem is solved to obtain the optimal value And verify whether the constraints are satisfied It can be clearly seen that is the maximum information transmission rate in the feasible domain, if the constraint is satisfied This indicates that there is a feasible solution to the time and power allocation subproblem. Otherwise, if there is no feasible solution, it is excluded. A feasibility check is performed on each CUE-DUE spectrum reuse candidate pair, and candidate pairs without feasible solutions can be excluded.

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