A self-energy recovery-based cr-noma system security and energy efficiency analysis method

Abstract

The present application relates to a kind of CR-NOMA system security energy efficiency analysis method based on self energy recovery, belong to wireless communication technical field.The present application is based on self energy recovery's full duplex multi-relay CR-NOMA system, under the premise of guaranteeing user communication service quality and minimum energy capture threshold, the system security energy efficiency maximization problem is studied.Multiple target optimization problem is decomposed into relay power distribution coefficient optimization, relay node power segmentation factor optimization Two sub-problems, respectively using improved golden section algorithm, mathematical function analysis method is optimized, further proposes multi-objective joint iteration algorithm, to obtain the optimal solution of original problem.The present application effectively improves system security energy efficiency, improves spectrum utilization efficiency.

Description

Technical Field

[0001] This invention relates to a method for analyzing the safety and energy efficiency of a CR-NOMA system based on self-energy recovery, belonging to the field of wireless communication technology. Background Technology

[0002] With the advent of the 5G era, a large number of mobile smart terminal devices and applications have emerged. Therefore, to meet the demands of mobile communication services, wireless communication networks need to have more efficient system transmission rates, making more effective use of available spectrum, providing higher data rates, and enhancing user experience. Non-orthogonal multiple access (NOMA) is considered a very promising communication technology because it can significantly improve spectrum efficiency, enable massive connectivity, reduce communication latency, and has good scalability and adaptability, making it widely applicable in different scenarios. It has great potential in improving spectrum efficiency and expanding the number of users. Cognitive radio (CR) is a new type of wireless communication technology designed to improve the efficiency of radio spectrum utilization, making the spectrum used more intelligently and efficiently. Applying NOMA technology to CR networks can not only improve spectrum efficiency but also significantly increase network capacity and coverage, while improving network reliability and providing more efficient wireless communication services. It is one of the important technologies for effectively improving system performance in the 5G era. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a safety and energy efficiency analysis method for CR-NOMA system based on self-energy recovery, thereby solving the above-mentioned technical problem and improving the safety and energy efficiency of the system.

[0004] The technical solution of this invention is: a safety and energy efficiency analysis method for CR-NOMA systems based on self-energy recovery. Addressing the safety and energy efficiency problem of full-duplex CR-NOMA systems based on self-energy recovery, this invention employs SWIPT technology to recover energy from loop self-interference signals generated by full-duplex relay nodes. Furthermore, it proposes an optimal relay selection strategy for multiple relay nodes to reduce the probability of system security interruption and improve system security performance. Under the premise of ensuring user communication service quality and energy capture threshold, the method aims to maximize safety and energy efficiency by jointly optimizing the relay power allocation coefficient and relay node power segmentation factor. By analyzing the impact of various factors on system performance, the safety and energy efficiency of the secondary user transmission system is evaluated, achieving a balance between secure communication and energy harvesting.

[0005] The specific steps are as follows:

[0006] Step 1: Construct a full-duplex multi-relay CR-NOMA system model based on self-energy recovery, and calculate the received signal used by the relay node for information decoding, the received energy signal, and the received signal of the relay node after self-interference cancellation.

[0007] The specific steps of Step 1 are as follows:

[0008] Step 1.1: Construct a full-duplex multi-relay CR-NOMA system model based on self-energy recovery, using an underlay spectrum sharing mode; the system consists of a primary network (PN) and a secondary network (SN); the primary network consists of one primary user PU; the secondary network consists of one cognitive base station BS, N secondary relay nodes Rn (n = 1, 2, ..., N), secondary users Sui (i = 1, 2), and one eavesdropping user E;

[0009] Step 1.2: The received signal used by the relay node for information decoding, the received energy signal, and the received signal of the relay node after self-interference cancellation are as follows:

[0010]

[0011]

[0012]

[0013] According to the NOMA criterion, a2 < a1, then

[0014] In the formula, Represents relay node R n The generated loop self-interference signal and Let be the self-interference channel coefficient, and represent the β (0≤β≤1) power division factor. R represents n Additive white Gaussian noise, n c This represents the processing noise from the conversion of radio frequency signals to baseband signals, and follows an n-order property. c ~CN(0,σ c 2 );

[0015] Step 2: Obtain the decoding rate of the relay node, the decoding rate of the secondary user, and the eavesdropping rate of the illegal eavesdropping user according to the NOMA protocol transmission mechanism, and calculate the total energy value captured by the relay node.

[0016] The specific steps of Step 2 are as follows:

[0017] Step 2.1: The SINR received by the relay end is represented as follows:

[0018]

[0019]

[0020] The relay decoding rates are as follows:

[0021]

[0022]

[0023] Step 2.2: According to the NOMA decoding rules, the received SINR of SU1 and SU2 are as follows:

[0024]

[0025]

[0026] The decoding rates for secondary users SU1 and SU2 are as follows:

[0027]

[0028]

[0029] The sum rate of the signals received by the secondary user is:

[0030] R tot =R1+R2

[0031] Step 2.3: Assumptions Then the rates at which unauthorized user E eavesdrops on users SU1 and SU2 are respectively:

[0032]

[0033]

[0034] The sum rate of eavesdropping users is:

[0035]

[0036] Step 2.4: Relay Node R n The energy of the source signal is captured, and the loop self-interference signal of the full-duplex relay node is self-energy recovered. The total energy captured is:

[0037] Step 3: For the multi-relay selection problem, the optimal relay selection strategy is proposed by jointly considering the channel state information of secondary users and the channel state information of users illegally eavesdropping.

[0038] The specific steps of Step 3 are as follows:

[0039] Step 3.1: The achievable security rate is defined as the difference between the secondary user's achievable rate and the eavesdropping user's transmission rate. Therefore, the secondary user's achievable security rate is expressed as follows:

[0040]

[0041]

[0042] Step 3.2: For SU1 and SU2, the interrupt event can be represented as follows:

[0043]

[0044]

[0045] R i Let i = 1, 2, be the target safe speeds of SU1 and SU2, and the system safety interruption probability be:

[0046]

[0047] Step 3.3: Given Therefore, the optimal relay node n * Represented as

[0048] Step 4: Construct the secondary user safety energy efficiency objective function, and determine the secondary user safety energy efficiency index based on the ratio of system safety rate to actual energy consumption;

[0049] The specific steps of Step 4 are as follows:

[0050] Step 4.1: Determine the safe speed R of the SU s =R tot -R E Actual energy consumption

[0051] Step 4.2: Determine the objective function The constraints are satisfied:

[0052]

[0053]

[0054] E tot ≥e

[0055] b1 + b2 = 1, 0 < b2 < 0.5

[0056] 0≤β≤1

[0057] Constraint 1 indicates that User 2 can successfully decode User 1's signal, R th Indicates the minimum transmission rate for user decoding;

[0058] Constraint 2 indicates that the minimum decoding rate must be met during the relay decoding process;

[0059] Constraint 3 indicates that the energy collected by the relay node meets the minimum energy capture threshold;

[0060] Constraint 4 represents the range of values ​​for the relay power allocation coefficient;

[0061] Constraint 5 represents the range of values ​​for the relay node power division factor.

[0062] Step 5: Treat safety and energy efficiency as the original problem and find the optimal solution by optimizing the relay power allocation coefficient and the relay node power partitioning factor to obtain a local optimal solution;

[0063] The specific steps in Step 5 are as follows:

[0064] Step 5.1: Decompose it into two sub-problems: relay power allocation coefficient and relay node power division factor, and optimize them separately;

[0065] Step 5.2: b2 is only related to the safety rate, so the optimization problem is transformed into a single-variable optimization problem P1 with respect to b2, that is:

[0066]

[0067] According to the constraint transformation, we get 0 ≤ b2 ≤ min(ω1 / ω2, 0.5), where The optimal power allocation coefficient is solved using an improved golden section algorithm;

[0068] Step 5.3: With the relay power allocation coefficient fixed, optimize the relay power division factor β and the optimization function P2, i.e. Through safety and energy efficiency η SEE Differentiating with respect to β, we get in And because of R s Since η > 0, we can obtain η. SEE (β) is a monotonically decreasing function of β. According to the constraint terms, the range of β is max(χ1,χ2)≤β≤χ3.

[0069] in:

[0070] For a given b2 * This allows us to obtain the closed-form optimal solution β for the optimal power division coefficient. *For β * =max(χ1,χ2).

[0071] Step 6: Use a multi-objective joint optimal safety and energy efficiency iterative algorithm to obtain the global optimal solution, thereby maximizing the safety and energy efficiency of the system;

[0072] The specific steps of Step 6 are as follows:

[0073] Step 6.1: Propose a multi-objective joint iterative algorithm based on safety and energy efficiency to jointly optimize the optimal values ​​of the two sub-problems;

[0074] Step 6.2: Initialize variables and constants η, P s , R th R0, e, b2(0), β(0), maximum number of iterations S, convergence accuracy τ>0, η SEE (0)=-τ,η SEE (-1)=η SEE (0)-τ;

[0075] Step 6.3: When |η SEE (i)-η SEE (i-1)|≥τ;

[0076] Step 6.4: i = i + 1;

[0077] Step 6.5: Calculate b2(i);

[0078] Step 6.6: Calculate β(i);

[0079] Step 6.7: Calculate η SEE (i);

[0080] Step 6.8: If i < S, return to Step 6.2;

[0081] Step 6.9: Otherwise, output the optimal solution.

[0082] The beneficial effects of this invention are: a full-duplex multi-relay CR-NOMA network based on self-energy recovery. An optimal relay selection strategy is proposed for multi-relay selection, employing Wireless Power-Carrying Communication (SWIPT) technology to capture the signal energy of source nodes and to recover energy from loop self-interference signals generated by full-duplex relay nodes. Under the premise of ensuring user communication service quality and a minimum energy capture threshold, the problem of maximizing system safety and energy efficiency is studied. The multi-objective optimization problem is decomposed into two sub-problems: relay power allocation coefficient optimization and relay node power partitioning factor optimization. These are optimized using an improved golden section algorithm and a mathematical function analysis method, respectively. Furthermore, a multi-objective joint iterative algorithm is proposed to obtain the optimal solution to the original problem. The proposed scheme can effectively improve system safety and energy efficiency and increase spectrum utilization efficiency. Attached Figure Description

[0083] Figure 1 This is a system model diagram of the present invention;

[0084] Figure 2 This is a diagram of the full-duplex relay node architecture of the present invention;

[0085] Figure 3 This is a schematic diagram of the transmission time slots of the system of the present invention. Detailed Implementation

[0086] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0087] Example 1: As Figure 1 The system model diagram shown in this invention considers a SWIPT-CR-NOMA system using an underlay spectrum sharing mode. This system consists of a primary network (PN) and secondary networks (SN). The primary network consists of one primary user (PU); the secondary network consists of one cognitive base station (BS) and N secondary relay nodes (R). n (n = 1, 2, ..., N), Sub-user SU i The relay consists of (i = 1, 2) and a listening user E. Assume all relay nodes operate in full-duplex mode and are equipped with dual antennas; the receiving antenna is used to receive information and capture energy, and the transmitting antenna is used to forward information. Other nodes operate in half-duplex mode and are equipped with a single antenna.

[0088] like Figure 2 The diagram shows the full-duplex relay node architecture of this invention, which utilizes PS-SWIPT technology. The cognitive base station sends source signals to the relay node, R... nIt has energy harvesting capabilities and can harvest energy from the RF signals of cognitive base stations. Because it operates in full-duplex mode, it can also eliminate loop self-interference, perform self-energy recovery on self-interference signals, and process the received signals according to different power division ratios for signal decoding and energy harvesting. The harvested energy is transferred to the battery for temporary storage and used to drive the transmission circuit. Finally, the signal is forwarded to the destination node using the DF protocol.

[0089] like Figure 3 As shown in the schematic diagram of the transmission time slots of the present invention, the unit time T is divided into two identical time slots. In the first time slot, the cognitive base station BS uses downlink NOMA to transmit data to the optimal relay node R. n The superimposed signal of legitimate users is sent, and the optimal relay node collects the RF signal energy while simultaneously achieving self-energy recovery; the optimal relay node R in the second time slot... n The received signal is decoded and forwarded to the destination nodes SU1 and SU2 using DF mode. At the same time, the illegal eavesdropping user E attempts to steal legitimate user information.

[0090] Therefore, the optimization problem is constructed as follows:

[0091] Construct the objective function Satisfy constraints E tot ≥e, b1+b2=1, 0<b2<0.5, 0≤β≤1.

[0092] Constraint 1 indicates that User 2 can successfully decode User 1's signal, R th Constraint 1 indicates the minimum transmission rate for user decoding; Constraint 2 indicates the minimum decoding rate to be met during relay decoding; Constraint 3 indicates the minimum energy capture threshold to be met by the energy collected by the relay node; Constraint 4 indicates the range of values ​​for the relay power allocation coefficient; and Constraint 5 indicates the range of values ​​for the relay node power division factor.

[0093] This problem is a multivariate optimization problem, constrained by variables b2 and β, and exhibits non-convexity. Traditional optimization methods are too complex to solve directly. To effectively address this problem, this paper decomposes it into two subproblems: relay power allocation coefficient and relay node power partitioning factor. The optimal solutions to these subproblems are then optimized using a multi-objective joint iterative algorithm.

[0094] The specific implementation is as follows:

[0095] Step 1: Construct a full-duplex multi-relay CR-NOMA system model based on self-energy recovery, and calculate the received signal used by the relay node for information decoding, the received energy signal, and the received signal of the relay node after self-interference cancellation.

[0096] The specific steps of Step 1 are as follows:

[0097] Step 1.1: Construct a full-duplex multi-relay CR-NOMA system model based on self-energy recovery, using an underlay spectrum sharing mode; the system consists of a primary network (PN) and a secondary network (SN); the primary network consists of one primary user PU; the secondary network consists of one cognitive base station BS, N secondary relay nodes Rn (n = 1, 2, ..., N), secondary users Sui (i = 1, 2), and one eavesdropping user E;

[0098] Step 1.2: The received signal used by the relay node for information decoding, the received energy signal, and the received signal of the relay node after self-interference cancellation are as follows:

[0099]

[0100]

[0101]

[0102] According to the NOMA criterion, a2 < a1, then

[0103] In the formula, Represents relay node R n The generated loop self-interference signal and Let be the self-interference channel coefficient, and represent the β (0≤β≤1) power division factor. R represents n Additive white Gaussian noise, n c This represents the processing noise from the conversion of radio frequency signals to baseband signals, and follows an n-order property. c ~CN(0,σ c 2 );

[0104] Step 2: Obtain the decoding rate of the relay node, the decoding rate of the secondary user, and the eavesdropping rate of the illegal eavesdropping user according to the NOMA protocol transmission mechanism, and calculate the total energy value captured by the relay node.

[0105] The specific steps of Step 2 are as follows:

[0106] Step 2.1: The SINR received by the relay end is represented as follows:

[0107]

[0108]

[0109] The relay decoding rates are as follows:

[0110]

[0111]

[0112] Step 2.2: According to the NOMA decoding rules, the received SINR of SU1 and SU2 are as follows:

[0113]

[0114]

[0115] The decoding rates for secondary users SU1 and SU2 are as follows:

[0116]

[0117]

[0118] The sum rate of the signals received by the secondary user is:

[0119] R tot =R1+R2

[0120] Step 2.3: Assumptions Then the rates at which unauthorized user E eavesdrops on users SU1 and SU2 are respectively:

[0121]

[0122]

[0123] The sum rate of eavesdropping users is:

[0124]

[0125] Step 2.4: Relay Node R n The energy of the source signal is captured, and the loop self-interference signal of the full-duplex relay node is self-energy recovered. The total energy captured is:

[0126] Step 3: For the multi-relay selection problem, the optimal relay selection strategy is proposed by jointly considering the channel state information of secondary users and the channel state information of users illegally eavesdropping.

[0127] The specific steps of Step 3 are as follows:

[0128] Step 3.1: The achievable security rate is defined as the difference between the secondary user's achievable rate and the eavesdropping user's transmission rate. Therefore, the secondary user's achievable security rate is expressed as follows:

[0129]

[0130]

[0131] Step 3.2: For SU1 and SU2, the interrupt event can be represented as follows:

[0132]

[0133]

[0134] R i Let i = 1, 2, be the target safe speeds of SU1 and SU2, and the system safety interruption probability be:

[0135]

[0136] Step 3.3: Given Therefore, the optimal relay node n * Represented as

[0137] Step 4: Construct the secondary user safety energy efficiency objective function, and determine the secondary user safety energy efficiency index based on the ratio of system safety rate to actual energy consumption;

[0138] The specific steps of Step 4 are as follows:

[0139] Step 4.1: Determine the safe speed R of the SU s =R tot -R E Actual energy consumption

[0140] Step 4.2: Determine the objective function The constraints are satisfied:

[0141]

[0142]

[0143] E tot ≥e

[0144] b1 + b2 = 1, 0 < b2 < 0.5

[0145] 0≤β≤1

[0146] Constraint 1 indicates that User 2 can successfully decode User 1's signal, R th Indicates the minimum transmission rate for user decoding;

[0147] Constraint 2 indicates that the minimum decoding rate must be met during the relay decoding process;

[0148] Constraint 3 indicates that the energy collected by the relay node meets the minimum energy capture threshold;

[0149] Constraint 4 represents the range of values ​​for the relay power allocation coefficient;

[0150] Constraint 5 represents the range of values ​​for the relay node power division factor.

[0151] Step 5: Treat safety and energy efficiency as the original problem and find the optimal solution by optimizing the relay power allocation coefficient and the relay node power partitioning factor to obtain a local optimal solution;

[0152] The specific steps in Step 5 are as follows:

[0153] Step 5.1: Decompose it into two sub-problems: relay power allocation coefficient and relay node power division factor, and optimize them separately;

[0154] Step 5.2: b2 is only related to the safety rate, so the optimization problem is transformed into a single-variable optimization problem P1 with respect to b2, that is:

[0155]

[0156] According to the constraint transformation, we get 0 ≤ b2 ≤ min(ω1 / ω2, 0.5), where The optimal power allocation coefficient is solved using an improved golden section algorithm;

[0157] Step 5.3: With the relay power allocation coefficient fixed, optimize the relay power division factor β and the optimization function P2, i.e. Through safety and energy efficiency η SEE Differentiating with respect to β, we get in And because of R s Since η > 0, we can obtain η. SEE (β) is a monotonically decreasing function of β. According to the constraint terms, the range of β is max(χ1,χ2)≤β≤χ3.

[0158] in:

[0159] For a given b2 * This allows us to obtain the closed-form optimal solution β for the optimal power division coefficient. * For β * =max(χ1,χ2).

[0160] Step 6: Use a multi-objective joint optimal safety and energy efficiency iterative algorithm to obtain the global optimal solution, thereby maximizing the safety and energy efficiency of the system;

[0161] The specific steps of Step 6 are as follows:

[0162] Step 6.1: Propose a multi-objective joint iterative algorithm based on safety and energy efficiency to jointly optimize the optimal values ​​of the two sub-problems;

[0163] Step 6.2: Initialize variables and constants η, P s , R th R0, e, b2(0), β(0), maximum number of iterations S, convergence accuracy τ>0, η SEE (0)=-τ,η SEE (-1)=η SEE (0)-τ;

[0164] Step 6.3: When |η SEE (i)-η SEE (i-1)|≥τ;

[0165] Step 6.4: i = i + 1;

[0166] Step 6.5: Calculate b2(i);

[0167] Step 6.6: Calculate β(i);

[0168] Step 6.7: Calculate η SEE (i);

[0169] Step 6.8: If i < S, return to Step 6.2;

[0170] Step 6.9: Otherwise, output the optimal solution.

[0171] The multi-objective joint optimization iterative algorithm proposed in this invention can reasonably improve the safety and energy efficiency of the system.

[0172] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for safety and energy efficiency analysis of a CR-NOMA system based on self-energy recovery, characterized in that: Step 1: Construct a full-duplex multi-relay CR-NOMA system model based on self-energy recovery, and calculate the received signal used by the relay node for information decoding, the received energy signal, and the received signal of the relay node after self-interference cancellation. Step 2: Obtain the decoding rate of the relay node, the decoding rate of the secondary user, and the eavesdropping rate of the illegal eavesdropping user according to the NOMA protocol transmission mechanism, and calculate the total energy value captured by the relay node; Step 3: For the multi-relay selection problem, the optimal relay selection strategy is proposed by jointly considering the channel state information of secondary users and the channel state information of users illegally eavesdropping. Step 4: Construct the secondary user safety energy efficiency objective function, and determine the secondary user safety energy efficiency index based on the ratio of system safety rate to actual energy consumption; Step 5: Treat safety and energy efficiency as the original problem and find the optimal solution by optimizing the relay power allocation coefficient and the relay node power partitioning factor to obtain a local optimal solution; Step 6: Initialize the system parameters, optimization variables and iteration conditions. Calculate the safety energy efficiency corresponding to each iteration by alternately optimizing the power allocation coefficient and power division factor. When the difference in safety energy efficiency between two adjacent iterations meets the convergence condition or reaches the maximum number of iterations, the algorithm stops iterating and outputs the maximum safety energy efficiency of the system and its corresponding optimal parameters. The specific steps of Step 4 are as follows: Step 4.1: Confirm SU Safe rate Actual energy consumption ; Step 4.2: Determine the objective function P0 The constraints are satisfied: ； ； ； ； ； Constraint 1 indicates that User 2 can successfully decode User 1's signal. Indicates the minimum transmission rate for user decoding; Constraint 2 indicates that the minimum decoding rate must be met during the relay decoding process; Constraint 3 indicates that the energy collected by the relay node meets the minimum energy capture threshold; Constraint 4 represents the range of values ​​for the relay power allocation coefficient; Constraint 5 represents the range of values ​​for the relay node power division factor.

2. The method for safety and energy efficiency analysis of a CR-NOMA system based on self-energy recovery as described in claim 1, characterized in that, The specific steps of Step 1 are as follows: Step 1.1: Construct a full-duplex multi-relay CR-NOMA system model based on self-energy recovery, using an underlay spectrum sharing mode; the system consists of a main network and a secondary network; the main network consists of one primary user PU; the secondary network consists of one cognitive base station BS, N secondary relay nodes Rn, n=1,2,…,N, secondary users Sui, i=1,2, and one eavesdropping user E; Step 1.2: The received signal used by the relay node for information decoding, the received energy signal, and the received signal of the relay node after self-interference cancellation are as follows: ； ； ； According to the NOMA criterion, there is ,but ; In the formula, Represents relay node The generated loop self-interference signal and , The self-interference channel coefficient represents... Power division factor, express Additive white Gaussian noise, This represents the processing noise from the conversion of radio frequency signals to baseband signals, and obeys... .

3. The method for safety and energy efficiency analysis of a CR-NOMA system based on self-energy recovery as described in claim 1, characterized in that, The specific steps of Step 2 are as follows: Step 2.1: The SINR received by the relay end is represented as follows: ； ； The relay decoding rates are as follows: ； ； Step 2.2: According to the NOMA decoding rules, SU 1 and SU The received SINR values ​​for 2 are as follows: ； ； Then the secondary user SU 1 and SU The decoding rates for 2 are as follows: ； ； The sum rate of the signals received by the secondary user is: ； Step 2.3: Assumptions Then, unauthorized user E eavesdrops on user... SU 1 and SU The rates of 2 are respectively: ； ； The sum rate of eavesdropping users is: ； Step 2.4: Relay Node R n The energy of the source signal is captured, and the loop self-interference signal of the full-duplex relay node is self-energy recovered. The total energy captured is: .

4. The method for safety and energy efficiency analysis of a CR-NOMA system based on self-energy recovery as described in claim 1, characterized in that, The specific steps of Step 3 are as follows: Step 3.1: The achievable security rate is defined as the difference between the secondary user's achievable rate and the eavesdropping user's transmission rate. Therefore, the secondary user's achievable security rate is expressed as follows: ； ； Step 3.2: For SU 1 and SU 2. Interruption events can be represented as follows: ； ； R i i=1,2, is SU 1 and SU With a target security rate of 2, the probability of system security interruption is: ； Step 3.3: Given Therefore, the optimal relay node n * Represented as .

5. The method for safety and energy efficiency analysis of a CR-NOMA system based on self-energy recovery according to claim 1, characterized in that, The specific steps in Step 5 are as follows: Step 5.1: Decompose it into two sub-problems: relay power allocation coefficient and relay node power division factor, and optimize them separately; Step 5.2: b2 is only related to the safety rate, so the optimization problem is transformed into a single-variable optimization problem P1 with respect to b2, that is: ； According to the constraint transformation, ,in , The optimal power allocation coefficient is solved using an improved golden section algorithm. Step 5.3: With the relay power allocation coefficient fixed, optimize the relay power division factor β and the optimization function P2, i.e. Through safety and energy efficiency η SEE Differentiating with respect to β, we get ,in And because Therefore, we can obtain η. SEE (β) is a monotonically decreasing function of β. Solving for the constraints, the range of values ​​for β is: ; in: ; For a given b2 * This allows us to obtain the closed-form optimal solution β for the optimal power division coefficient. * for .

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