IRS-assisted wireless energy supply communication system physical layer security robust transmission scheme

Abstract

The invention relates to an IRS-assisted wireless energy supply communication system physical layer security robust transmission scheme, and belongs to the technical field of wireless communication. Comprising the following steps: step 1, establishing a WPCN secure communication robust optimization system architecture based on IRS assistance; 2, optimizing energy and information transmission between the HAP and the user, wherein the energy and information transmission between the HAP and the user comprises the following steps: energy and information transmission between the HAP and the user; and optimizing the method. According to the WPCN safety communication system provided by the invention, the IRS is utilized to assist the communication system, and robustness design is carried out, so that the secrecy rate of the system is improved; in the information transmission mode, the beamforming technology in physical layer security is utilized, the information transmission rate difference between a legal user and an eavesdropping user is increased, and the security of user information transmission is further ensured.

Description

Technical Field

[0001] The invention relates to a safe transmission method of an IRS-assisted wireless energy supply communication system, and belongs to the technical field of wireless communications. Background Art

[0002] In recent years, the rapid development of information technology has pushed the Internet of Things to the forefront of global technological innovation and industrial transformation. Its application scope covers a wide range of fields, including smart cities, smart homes, industrial Internet, medical health, intelligent transportation systems, and intelligent management of agricultural Internet of Things. According to the latest data authoritatively released by the Ministry of Industry and Information Technology, the scale of IoT terminal connections has historically exceeded about 10 billion, accounting for more than one-third of the total number of global IoT connections. At the same time, the number of mobile user groups has reached millions and continues to rise at an average annual growth rate of about 25%. It is expected that by 2030, the number of IoT terminal connections will grow to 80 billion. The publication number is CN113794493A, and the name of the invention is a beamforming method, device, computer equipment and storage medium. The technical solution discloses a performance optimization solution under a cognitive radio (CR) system with a technical background, which solves the problem of user service quality in the case of conflicts between master and slave users. Its robustness optimization is reflected in considering that the channel conditions are imperfect and adopting a channel model with CSI estimation errors.

[0003] Maintaining the normal operation of large-scale energy-constrained devices and ensuring the security of information transmission are key challenges in IoT (Internet of Things) design. Faced with the problem of energy constraints, traditional wireless networks often use the method of charging device batteries to meet their continuous energy needs; or regularly replace new batteries for these devices. However, such operations will consume a lot of manpower and material resources, and there may be communication interruptions. For the issue of information transmission security, it mainly focuses on application layer encryption technology, using private keys to implement data encryption processing, and the receiving end performs decryption operations based on the corresponding keys. However, faced with the demand for large-scale connections in IoT scenarios, distributing keys and managing them will become extremely complex and time-consuming.

[0004] The existing methods for maintaining the normal operation of energy-constrained devices and ensuring secure information transmission in IoT scenarios have the following main defects:

[0005] 1) Existing solutions require frequent replacement of batteries of wireless devices, which results in waste of resources and communication interruption;

[0006] 2) Existing methods to ensure secure information transmission mostly use encryption technology, but the process of managing and distributing it in large-scale connection scenarios will be very complicated.

[0007] Therefore, it is urgent to propose a physical layer secure and robust transmission scheme for IRS-assisted wireless power supply communication system to solve the above technical problems. Summary of the invention

[0008] To solve the above problems, a physical layer secure robust transmission scheme for an IRS-assisted wireless power supply communication system is provided. A brief overview of the present invention is given below to provide a basic understanding of certain aspects of the present invention. It should be understood that this overview is not an exhaustive overview of the present invention. It is not intended to determine the key or important parts of the present invention, nor is it intended to limit the scope of the present invention.

[0009] The technical solution of the present invention:

[0010] The IRS-assisted physical layer secure robust transmission scheme for wireless power supply communication system includes the following steps:

[0011] Step 1: Establishment of robust optimization system architecture for WPCN secure communication based on IRS assistance;

[0012] Step 2: Optimizing the transmission of energy and information between HAP and users, including the following steps:

[0013] Step 2.1: Energy and information transmission between HAP and users;

[0014] Step 2.2: Optimize the method.

[0015] Preferably: in step 1, the IRS-assisted wireless power supply communication system includes a HAP, a wireless device, an eavesdropper, and an IRS;

[0016] HAP (hybrid access point): responsible for energy transmission and information transmission; communicates with wireless devices through wireless connection;

[0017] Wireless device (legal wireless device user with limited single antenna energy): communicates with HAP through wireless connection and receives energy from HAP to maintain communication;

[0018] Eavesdropper (single-antenna eavesdropper eve): a single-antenna device used to eavesdrop on communications between HAPs and wireless devices;

[0019] IRS (Intelligent Reflective Surface): IRS is equipped with reflective units to enhance signal transmission between HAP and wireless devices;

[0020] During the energy transmission process, a channel is established between HAP and IRS, and then the energy is transmitted to the wireless device through the IRS reflection unit. In the information transmission stage, the channel from the wireless device to HAP is used for uplink information transmission, while the channel from IRS to HAP is used for downlink energy transmission.

[0021] Preferably: in step 1, the IRS-assisted wireless power supply communication system is composed of a HAP with N antennas, a wireless device, an eavesdropper and an IRS equipped with M reflection units, and the reflection factors of the IRS reflection units are different in the uplink and downlink stages; N and M are natural numbers, and T is transposed;

[0022] The reflection coefficients of the uplink and downlink stages can be expressed as and The reflection matrix can be expressed as The channel between HAP and IRS during energy transmission is established as The channel between HAP and wireless device is established as The channel between IRS and wireless device is established as During the information transmission phase, the channel from the wireless device to the HAP is established as follows: The channel from IRS to HAP is established as The channel from the legitimate wireless device to the IRS is established as The channel between the legitimate wireless device and the eavesdropping end is established as The channel between IRS and the eavesdropper is established as

[0023] Preferably: In step 2.1, the entire process of transmission between the HAP and the user (wireless device) is as follows: Figure 2 Shown include:

[0024] Energy transfer phase;

[0025] Information transmission stage;

[0026] Confidentiality rate;

[0027] Optimization goals.

[0028] Preferably: in step 2.1, during the energy transmission phase, the received signal of the legal wireless device is:

[0029]

[0030] in, and are the Gaussian transmission distortion noise at the transmitting and receiving ends respectively;

[0031] The energy collected from the legitimate user can be expressed as:

[0032]

[0033] Where η∈[0,1] represents the energy conversion efficiency;

[0034] Information transmission phase: After the energy transmission phase, the legitimate wireless device transmits confidential information to the HAP in the information transmission phase. The received information is:

[0035]

[0036] Among them, s I is a confidential signal generated at the wireless device, and They are the Gaussian transmission distortion noise at the sending and receiving ends during the information transmission phase;

[0037] Confidentiality rate: The information eavesdropped by the eavesdropper is:

[0038]

[0039] The confidentiality rate of the entire system is:

[0040] R = τ1[R U -R E ] +

[0041] Among them, R U =log2(1+γ U ), R E =log2(1+γ E );

[0042]

[0043] Optimization objective: Combine the HAP energy beamforming vector w, IRS energy reflection coefficient ξ and information reflection coefficient ψ. The optimization problem is as follows:

[0044] P1:

[0045] st||w|| 2 ≤P max

[0046]

[0047] τ0+τ1=1

[0048] 0≤τ k ≤1,k∈{0,1}

[0049] Preferably: in step 2.2, by introducing auxiliary variables, the original problem is transformed into a series of convex optimization sub-problems, and the original variables are restored using the Gaussian randomization method, and finally convergence is achieved.

[0050] Preferably: in step 2.2, introduce auxiliary variable p = [p1, p2, p3, p4] T Relax the objective function so that it satisfies R U ≥p1-p2 and R E ≤p3-p4, problem P1 can be transformed into the following problem:

[0051] P2:

[0052] st||w|| 2 ≤P max

[0053]

[0054] τ0+τ1=1

[0055] 0≤τ k ≤1,k∈{0,1}

[0056] τ1log2(Γ U (w,ξ,ψ)+τ0(1+μ Et )(ξ H G A w)(ξ H G A w) H (ψ H G U )(ψ H G U ) H ≥p1

[0057] τ1log2(Γ U (w,ξ,ψ))≤p2

[0058] τ1log2(Γ E (w,ξ,ψ)+τ0(1+μ Et )(ξ H G A w)(ξ H G A w) H (ψ H G E )(ψ H G E ) H )≤p3

[0059] τ1log2(Γ E (w,ξ,ψ))≥p4

[0060] The steps to solve this problem are as follows: input the convergence parameter ε and iteration variable n, iteratively update w, ξ and ψ, the process is as follows:

[0061] 1) Initialization: In the first iteration, n = 0, and w is randomly generated (0) , (0) and ψ (0) ;

[0062] 2) Optimize w given ξ and ψ: This subproblem is a convex problem and can be solved directly;

[0063] 3) Optimize ξ given w and ψ: This subproblem is a convex problem and can be solved directly, using Gaussian randomization to recover ξ;

[0064] 4) Optimize ψ given w and ξ: This subproblem is a convex problem and can be solved directly, using Gaussian randomization to recover ψ;

[0065] Repeat the above steps until convergence.

[0066] The present invention has the following beneficial effects:

[0067] The WPCN secure communication system provided by the present invention utilizes the IRS auxiliary communication system and performs robustness design, thereby improving the confidentiality rate of the system;

[0068] In the information transmission mode of the present invention, the beamforming technology in physical layer security is used to increase the information transmission rate difference between the legitimate user and the eavesdropping user, and further ensure the security of the user's transmitted information. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a schematic diagram of the IRS-assisted WPCN safety communication robust optimization system.

[0070] Figure 2 It is the proposed energy and information transmission flow chart.

[0071] Figure 3 It is the change of confidentiality rate and hardware loss coefficient.

[0072] Figure 4 It is the relationship between the confidentiality rate and the HAP transmission power. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is described below by the specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0074] Specific implementation method 1: Combination Figure 1-4This embodiment is described. The physical layer secure robust transmission scheme of the IRS-assisted wireless energy supply communication system of this embodiment includes the following steps:

[0075] Step 1: Establishment of robust optimization system architecture for WPCN secure communication based on IRS assistance;

[0076] like Figure 1 As shown, it is assumed that in a WPCN network (wireless power supply communication network), an IRS-assisted hybrid base station and a wireless device are placed for communication; the IRS-assisted wireless power supply communication system includes a HAP, a wireless device, an eavesdropper, and an IRS;

[0077] HAP (hybrid access point): responsible for energy transmission and information transmission; communicates with wireless devices through wireless connection;

[0078] Wireless device (legal wireless device user with limited single antenna energy): communicates with HAP through wireless connection and receives energy from HAP to maintain communication;

[0079] Eavesdropper (single-antenna eavesdropper eve): a single-antenna device used to eavesdrop on communications between HAPs and wireless devices;

[0080] IRS (Intelligent Reflective Surface): IRS is equipped with reflective units to enhance signal transmission between HAP and wireless devices. Considering that there may be obstacles between HAP and wireless devices, reflective units are placed near HAP and wireless devices to overcome the obstruction of obstacles.

[0081] During the energy transmission process, a channel is established between HAP and IRS, and then the energy is transmitted to the wireless device through the IRS reflection unit to optimize the transmission efficiency of energy and information. In the information transmission stage, the channel from the wireless device to HAP is used for uplink information transmission, while the channel from IRS to HAP is used for downlink energy transmission. Considering the channel characteristics between the wireless device and the eavesdropper, corresponding measures are taken to reduce the amount of useful information received by the eavesdropper and prevent the eavesdropper from receiving information.

[0082] In step 1, the IRS-assisted wireless power supply communication system consists of a HAP with N antennas, a wireless device, an eavesdropper, and an IRS equipped with M reflection units. The reflection factors of the IRS reflection units are different in the uplink and downlink stages; N and M are natural numbers, T is the transpose, refers to the complex field, M×M means the variable is an M×M-dimensional matrix;

[0083] The reflection coefficients of the uplink and downlink stages can be expressed as and The reflection matrix can be expressed as The channel between HAP and IRS during energy transmission is established as The channel between HAP and wireless device is established as The channel between IRS and wireless device is established as During the information transmission phase, the channel from the wireless device to the HAP is established as follows: The channel from IRS to HAP is established as The channel from the legitimate wireless device to the IRS is established as The channel between the legitimate wireless device and the eavesdropping end is established as The channel between IRS and the eavesdropper is established as Where w is the transmit beamforming vector of the HAP, s E Refers to the unit power energy signal symbol, refers to the noise variance Additive white Gaussian noise AWGN at the eavesdropping user.

[0084] Step 2: Optimize the energy and information transmission process between HAP and users, including the following steps:

[0085] Step 2.1: Energy and information transmission process between HAP and users;

[0086] In step 2.1, the entire process of transmission between HAP and user (wireless device) is as follows: Figure 2 Shown include:

[0087] Energy transmission stage: HAP (hybrid wireless access point) sends radio frequency signals to legal wireless devices to provide energy. This energy is mainly used to maintain circuit operation and data transmission. In the energy transmission stage, the receiving signal of the legal wireless device is:

[0088]

[0089] in, and are the Gaussian transmission distortion noise at the transmitting and receiving ends respectively;

[0090] The energy collected from the legitimate user can be expressed as:

[0091]

[0092] Among them, η∈[0,1] represents the energy conversion efficiency, τ0 refers to the duration of the energy transfer phase, and μ Et Refers to the hardware damage coefficient of the transmitter, E refers to the calculation |y E | 2 expectations;

[0093] Information transmission phase: After the energy transmission phase, the legitimate wireless device transmits confidential information to the HAP in the information transmission phase. The received information is:

[0094]

[0095] Among them, s I is a confidential signal generated at the wireless device, and are the Gaussian transmission distortion noise at the transmitter and receiver during the information transmission phase, τ1 refers to the duration of the energy transmission phase, Ω refers to the energy phase shift matrix of IRS, Refers to the additive Gaussian white noise at the legitimate user end during the WIT phase;

[0096] Confidentiality rate: Since the eavesdropper’s hardware is of high quality, the information eavesdropped on by the eavesdropper is:

[0097]

[0098] The confidentiality rate of the entire system is:

[0099] R = τ1[R U -R E ] +

[0100] Among them, R U =log2(1+γ U ), R E =log2(1+γ E );

[0101]

[0102] Among them, γ U Refers to the signal-to-noise ratio of the legitimate user end, γ E Refers to the signal-to-noise ratio of the eavesdropping end, R U Refers to the information transmission rate of legitimate users, R E Refers to the eavesdropper's information transmission rate, μ It Refers to the hardware damage coefficient of the sender in the WIT phase, μ Ir Refers to the hardware damage coefficient of the receiving end, Refers to the noise variance of the legitimate user end in the WIT phase, Refers to the noise variance of the eavesdropping end during the WIT phase;

[0103] Optimization goal: Jointly optimize the HAP energy beamforming vector, IRS energy reflection coefficient and information reflection coefficient to maximize the confidentiality rate of the system; meet the base station transmission power and IRS reflection constraints; the optimization goal is to jointly optimize the HAP energy beamforming vector w, IRS energy reflection coefficient ξ and information reflection coefficient ψ. The optimization problem is as follows:

[0104] P1:

[0105] st||w|| 2 ≤P max

[0106]

[0107] τ0+τ1=1

[0108] 0≤τ k ≤1,k∈{0,1}

[0109] Among them, P max refers to the maximum transmit power of the HAP, ξ m refers to the mth element in the IRS energy reflection coefficient vector, ψ m refers to the mth element in the IRS information reflection coefficient vector, τ k Refers to the time allocation factor of the energy transmission stage and the information transmission stage. If k is 0, it is pure energy transmission, and if k is 1, it is pure information transmission;

[0110] Step 2.2: Optimization method:

[0111] By introducing auxiliary variables, the original problem is transformed into a series of convex optimization sub-problems, and the original variables are restored using the Gaussian randomization method, ultimately reaching convergence; it can effectively handle complex optimization problems, and through the combination of convex optimization and Gaussian randomization, it ensures the stability and efficiency of the solution process;

[0112] In step 2.2, introduce auxiliary variables p = [p1, p2, p3, p4] T Relax the objective function so that it satisfies R U ≥p1-p2 and R E ≤p3-p4, problem P1 can be transformed into the following problem:

[0113] P2:

[0114] st||w|| 2 ≤P max

[0115]

[0116] τ0+τ1=1

[0117] 0≤τ k ≤1,k∈{0,1}

[0118] τ1log2(Γ U (w,ξ,ψ)+τ0(1+μ Et )(ξ H G A w)(ξ H G A w) H (ψ H G U )(ψ H G U ) H ≥p1

[0119] τ1log2(Γ U (w,ξ,ψ))≤p2

[0120] τ1log2(Γ E (w,ξ,ψ)+τ0(1+μ Et )(ξ H G A w)(ξ H G A w) H (ψ H G E )(ψ H G E ) H )≤p3

[0121] τ1log2(Γ E (w,ξ,ψ))≥p4

[0122] The steps to solve this problem are as follows: input the convergence parameter ε and the iteration variable n, then iteratively update w, ξ and ψ, the process is as follows:

[0123] 1) Initialization: In the first iteration, n = 0, and the initial variable w is randomly generated (0) , (0) and ψ (0) ;

[0124] 2) Optimize w given ξ and ψ: This subproblem is a convex problem and can be solved directly;

[0125] 3) Optimize ξ given w and ψ: This subproblem is a convex problem and can be solved directly, and then ξ can be recovered using Gaussian randomization;

[0126] 4) Optimize ψ given w and ξ: This subproblem is a convex problem and can be solved directly, and then ψ can be recovered using Gaussian randomization;

[0127] Repeat the above steps until convergence;

[0128] The present invention can utilize wireless signals for energy collection by using WPCN, which has high reliability and controllability. It also considers information security transmission from the perspective of wireless channels; compared with traditional solutions, it can reduce the loss of manpower and material resources, and can effectively ensure the security of information; it further considers the hardware damage of the transmitting and receiving ends due to the actual RF components, and optimizes the robustness design of the system.

[0129] Step 3: Simulation and Results

[0130] Assume that HAP, IRS, legitimate wireless devices and eavesdropping devices are located at (0m, 0m), (5m, 0m), (10m, 2m) and (5m, 7m) respectively; the number of HAP antennas N = 16, the number of IRS reflection units M = 32; the energy collection coefficient is set to η = 1; the energy transmission and information transmission time are set to τ0 = 0.1 and τ1 = 0.9 respectively; the direct channel is modeled using Rayleigh channel, the path loss exponent is set to 3.5, and the path loss exponent of the cascade channel related to IRS is set to 2.2; the Rician factor of the channel related to IRS is set to β = 10, and the Rician factor of the direct channel is set to β = 0; the large-scale fading coefficient PL0 = -30dB at the reference distance D0 = 1m; the maximum antenna transmission power is set to P max =30dBm, the noise power is set to The convergence tolerance is set to ε = 10 -4 ; The following benchmark algorithms were selected: 1) RIS-Robust Design, 2) RIS-Non-Robust Design, 3) NonRIS-Robust Design, 4) NonRIS-Non-Robust Design;

[0131] Depend on Figure 3 It can be seen that according to our algorithm, the confidentiality rate is higher than that of the other three schemes, which confirms the effectiveness of the proposed algorithm; this is because deploying IRS can increase the spatial freedom of the system; Figure 4 It can be seen that robust design can significantly improve the confidentiality rate. This is because robust design can well compensate for the loss caused by hardware, and the effect is more obvious when the loss is large. Therefore, it can be foreseen that the algorithm proposed in the present invention is more applicable in actual communication systems.

[0132] The present invention is mainly applied in the context of the Internet of Things (IoT), and considers the performance optimization scheme of the WPCN system; in terms of the system model, the present invention considers the problem of secure communication in the presence of eavesdroppers, and performs joint optimization from the two stages of energy transmission and information security transmission; in terms of optimization problems, the robustness optimization of the present invention is reflected in considering the situation where the transceiver of the actual system has inevitable hardware damage.

[0133] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be arranged and combined, and those skilled in the art can exhaust all possibilities based on the mathematical knowledge of arrangement and combination. Therefore, the present invention will no longer describe the technical solutions after arrangement and combination one by one, but it should be understood that the technical solutions after arrangement and combination have been disclosed by the present invention.

[0134] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A physical layer secure and robust transmission scheme for an IRS-assisted wireless energy supply communication system, characterized by: The following steps are involved: Step 1: Establishment of robust optimization system architecture for WPCN secure communication based on IRS assistance; Step 2: Optimizing the transmission of energy and information between HAP and users, including the following steps: Step 2.1: Energy and information transmission between HAP and users; Step 2.2: Optimize the method.

2. The physical layer secure robust transmission scheme of the IRS-assisted wireless power supply communication system according to claim 1 is characterized by: In step 1, the IRS-assisted wireless power supply communication system includes HAP, wireless device, eavesdropper and IRS; HAP: responsible for energy transmission and information transmission; communicates with wireless devices through wireless connection; Wireless device: communicates with HAP via wireless connection and receives energy from HAP to maintain communication; Eavesdropper: A single-antenna device used to eavesdrop on communications between HAPs and wireless devices; IRS: IRS is equipped with a reflector unit to enhance signal transmission between HAP and wireless devices; During the energy transmission process, a channel is established between HAP and IRS, and then the energy is transmitted to the wireless device through the IRS reflection unit. In the information transmission stage, the channel from the wireless device to HAP is used for uplink information transmission, while the channel from IRS to HAP is used for downlink energy transmission.

3. The physical layer secure robust transmission scheme of the IRS-assisted wireless energy supply communication system according to claim 2 is characterized in that: In step 1, the IRS-assisted wireless power supply communication system consists of a HAP with N antennas, a wireless device, an eavesdropper, and an IRS equipped with M reflection units. The reflection factors of the IRS reflection units are different in the uplink and downlink stages; The reflection coefficients of the two stages can be expressed as and The reflection matrix can be expressed as The channel between HAP and IRS during energy transmission is established as The channel between HAP and wireless device is established as The channel between IRS and wireless device is established as During the information transmission phase, the channel from the wireless device to the HAP is established as follows: The channel from IRS to HAP is established as The channel from the wireless device to the IRS is established as The channel between the wireless device and the eavesdropping end is established as The channel between IRS and the eavesdropper is established as 4. The physical layer secure robust transmission scheme of the IRS-assisted wireless energy supply communication system according to claim 3 is characterized by: Step 2.1 includes: Energy transfer phase; Information transmission stage; Confidentiality rate; Optimization goals.

5. The physical layer secure robust transmission scheme of the IRS-assisted wireless energy supply communication system according to claim 4 is characterized in that: In step 2.1, during the energy transmission phase, the received signal of the wireless device is: in, and are the Gaussian transmission distortion noise at the transmitting and receiving ends respectively; The energy collected at the user can be expressed as: Where η∈[0,1] represents the energy conversion efficiency; Information transmission phase: After the energy transmission phase, the wireless device transmits confidential information to the HAP in the information transmission phase. The received information is: Among them, s I is a confidential signal generated at the wireless device, and They are the Gaussian transmission distortion noise at the sending and receiving ends during the information transmission phase; Confidentiality rate: The information eavesdropped by the eavesdropper is: The confidentiality rate of the entire system is: R=τ1[R U -R E ] + Among them, R U =log2(1+γ U ),R E =log2(1+γ E ); Optimization objective: Combine the HAP energy beamforming vector w, IRS energy reflection coefficient ξ and information reflection coefficient ψ. The optimization problem is as follows: s.t.||w|| 2 ≤P max τ0+τ1=1 0≤τ k ≤1,k∈{0,1} 6. The physical layer secure robust transmission scheme of the IRS-assisted wireless energy supply communication system according to claim 5 is characterized by: In step 2.2, by introducing auxiliary variables, the original problem is transformed into a series of convex optimization sub-problems, and the original variables are restored using the Gaussian randomization method, ultimately reaching convergence.

7. The physical layer secure robust transmission scheme of the IRS-assisted wireless power supply communication system according to claim 6 is characterized by: In step 2.2, introduce auxiliary variables p = [p1, p2, p3, p4] T Relax the objective function so that it satisfies R U ≥p1-p2 and R E ≤p3-p4, problem P1 can be transformed into the following problem: s.t.||w|| 2 ≤P max τ0+τ1=1 0≤τ k ≤1,k∈{0,1} τ1log2(Γ U (w,ξ,ψ)+τ0(1+μ Et )(ξ H G A w)(ξ H G A w) H (ψ H G U )(ψ H G U ) H ≥p1 τ1log2(Γ U (w,ξ,ψ))≤p2 τ1log2(Γ E (w,ξ,ψ)+τ0(1+μ Et )(ξ H G A w)(ξ H G A w) H (ψ H G E )(ψ H G E ) H )≤p3 τ1log2(Γ E (w,ξ,ψ))≥p4 The steps to solve this problem are as follows: input the convergence parameter ε and iteration variable n, iteratively update w, ξ and ψ, the process is as follows: 1) Initialization: In the first iteration, n = 0, and w is randomly generated (0) , (0) and ψ (0) ; 2) Optimize w given ξ and ψ: This subproblem is a convex problem and can be solved directly; 3) Optimize ξ given w and ψ: This subproblem is a convex problem and can be solved directly, using Gaussian randomization to recover ξ; 4) Optimize ψ given w and ξ: This subproblem is a convex problem and can be solved directly, using Gaussian randomization to recover ψ; Repeat the above steps until convergence.

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