Method for joint time and power allocation in energy harvesting cognitive wireless network based on double-layer game

Abstract

The application provides a kind of energy harvesting cognitive wireless network joint time and power distribution method based on double-layer game, first, energy harvesting (energy harvesting, EH) is introduced into CR network, constructs EH-CR network, and applies the energy harvesting architecture of "harvesting-use" to collect and use energy.Then, the interaction between PU and SU is modeled as Stackelberg game, and the interaction between SUs is modeled as hypergame. In order to improve the fairness between SUs, the method introduces a fairness evaluation coefficient. Then, by solving the NE solution of hypergame, the balanced spectrum sensing time coefficient and the balanced power distribution scheme can be obtained.

Description

Technical Field

[0001] This invention belongs to the field of network communication technology, specifically relating to a method for joint time and power allocation of energy harvesting cognitive wireless networks based on two-layer game theory. Background Technology

[0002] With the research and development of 6G network standards, efforts are being made to combine several new technologies to provide uninterrupted and satisfactory services for wireless equipment applications. CR networks, as a type of network that can effectively improve spectrum resource utilization, have received widespread attention. To more effectively improve spectrum resource utilization, CR networks typically employ three typical spectrum sharing technologies: Overlay, Underlay, and Interweave. Considering the Underlay spectrum sharing method, while ensuring the communication quality of PUs (Power Users), this method allows SUs to continuously transmit data, thereby improving the utilization of licensed frequency bands.

[0003] In CR networks, traditional optimization theories typically neglect the interdependence between users (PUs) and suppliers (SUs), while game theory considers this dependency and attempts to find a non-negative (NE) solution that can realize the CR network. Under the NE solution, neither PUs nor SUs gain more benefits; therefore, this solution is a non-improvable equilibrium. In recent years, some literature has applied game theory to explore the power allocation problem in CR networks. For example, existing technologies have proposed the application of NOMA technology in OFDM systems, using game theory methods for power allocation to improve system throughput. Existing technologies have also designed two objective functions to maximize network energy efficiency and minimize interference, thereby optimizing the transmission power and transmission channels of the CR network. Existing technologies have proposed a resource allocation method based on spectrum-aware interference pricing to solve the resource allocation problem in multi-user CR networks. The transmission of SUs is controlled by pricing the interference power of SUs by the primary base station (PBS), and the interaction between PBS and SUs is modeled as a Stackelberg game, aiming to optimize resource allocation to maximize the payoff of PBS while also maximizing the payoff of SUs. However, these studies do not consider using a supermodel game model. Summary of the Invention

[0004] This invention addresses the problem of improving the throughput of EH-CR networks by proposing a joint time and power allocation method based on a two-layer game theory approach. Specifically, energy harvesting (EH) is first introduced into the CR network to construct the EH-CR network, and a "harvest-use" energy harvesting architecture is applied to collect and utilize energy. Then, the interaction between the PU (Power Intake Unit) and SUs (Supply Utility Units) is modeled as a Stackelberg game, and the interaction between SUs is modeled as a supermodel game. To improve fairness among SUs, a fairness evaluation coefficient is introduced. Next, by solving the NE solution of the supermodel game, an equilibrium spectrum-aware time coefficient and an equilibrium power allocation scheme can be obtained. Compared to existing solutions, this invention uses a supermodel game model, and the proposed spectrum-aware time coefficient and power allocation scheme are deterministic strategies, rather than probabilistic ones. Currently, no similar research has considered using a two-layer game theory approach to solve the joint time and power allocation problem of EH-CR networks in the Underlay mode.

[0005] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0006] A method for joint time and power allocation of energy harvesting cognitive wireless networks based on two-layer game theory is characterized by: introducing energy harvesting (EH) into the CR network to construct an EH-CR network, and applying an "harvest-use" energy harvesting architecture to harvest and use energy; modeling the interaction between PU and SUs as a Stackelberg game, and the interaction between SUs as a supermodel game; introducing a fairness evaluation coefficient, and obtaining an equilibrium spectrum sensing time coefficient and an equilibrium power allocation scheme by solving the NE solution of the supermodel game.

[0007] Furthermore, the EH-CR network system model consists of a primary user network and a secondary user network. The primary user network includes a pair of primary transmitters (PTs) and primary receivers (PRs). The secondary user network comprises n sub-users (SUs). The SUs communicate with each other via SBS. It is assumed that the EH-CR network can use N licensed frequency bands shared by the PTs, and all SUs access these licensed frequency bands for communication. When the PT sends data to the PR, the SUs collect the RF signal energy emitted by the PT and use the collected energy for spectrum sensing and data transmission. It is assumed that the PT and SUs... i The gain between them is β i η, 0≤η≤1 represents the energy harvesting efficiency, P T This indicates the transmit power of PT, SBS, and SU. i The gain between them is h i The gain between PT and SBS is g0, and W represents the bandwidth of the licensed frequency band;

[0008] The time frame T is divided into two time slots: the spectrum sensing time slot τT and the data transmission time slot (1-τ)T, where τ represents the spectrum sensing time coefficient; it is assumed that SUs can collect RF energy from the PU signal throughout the entire time frame T, and the energy collected by each SU is exhausted throughout the entire time frame T;

[0009] During the energy harvesting phase, PT uses power P T Data is sent to PR, while SUs collect wireless RF energy from the PU signal; assuming each SU is equipped with a separate antenna for EH, the energy collected by the i-th SU is represented as follows:

[0010] E i =ηP T β i T (i=1,2,...,n) (3-1)

[0011] SUs use cooperative spectrum sensing to detect whether PU is operating on the licensed frequency band. SUs use energy detection to perform spectrum sensing and then report the average energy level of the received signal to SBS. That is, in a given frequency band, there are two cases: H0 indicates that the licensed frequency band is not occupied, and H1 indicates that the licensed frequency band is occupied.

[0012]

[0013] Where r(t) is the received signal, s(t) is the PU signal, g(t) is the channel gain, and n(t) is Gaussian noise; H0 and H1 represent the idle and busy states of the licensed frequency band, respectively; the decision statistic r(t) for local detection of each SU is calculated as follows:

[0014]

[0015] Where M represents the number of perceived samples, given by M = τTf s Given, f s This is the sampling frequency; the average energy level of SUs is expressed as:

[0016]

[0017] Next, SBS will E(r t The detection probability p is compared with a preset threshold I to determine whether the PU exists in the licensed frequency band; two metrics are used to evaluate the performance of the spectrum sensing process: detection probability p d And the false alarm probability p f ;p d To correctly determine the probability of PU's existence, and p f The probability of incorrectly determining the existence of PU; since PU predefines a target p dTherefore, the preset threshold I and false alarm probability p f They are represented as follows:

[0018] I = (2erfc) -1 (2p d )+γ+1)σ 2 (3-5)

[0019]

[0020] Where σ 2 It is the noise power, γ is the signal-to-noise ratio of the PU, erfc(·) and erfc -1 (·) represent the complementary error function and the inverse complementary error function, respectively;

[0021] During the data transmission phase, SUs access licensed frequency bands in Underlay mode; SUs employ a two-layer power allocation strategy, namely: in the absence of a PU, SUs use high-power P... 0,i Transmitting data; in the presence of PU, SUs transmit data at low power P. 1,i Transmit data;

[0022] Assume P H0 and P H1 Let represent the probabilities of the licensed frequency bands being unused and used, respectively, and let SUs satisfy the minimum target detection probability. The goal is to find a NE solution that maximizes the utility of the primary and secondary user networks while satisfying all constraints in the EH-CR network.

[0023] Furthermore, the interaction between PU and SUs is modeled as a Stackelberg game, and the interaction between SUs is modeled as a supermodel game. In the Stackelberg game, leaders and followers are used to describe the hierarchical structure of behavior. The PU is the leader, which guarantees its own communication quality by pricing the interference from SUs. The PU sets a set of prices for each unit of interference power of each SU to maximize its revenue. The SUs are the followers, who pay for the interference caused to the PU. In the supermodel game, the SUs choose an equilibrium spectrum-aware time coefficient and an equilibrium power allocation scheme to maximize the utility of the secondary user network.

[0024] Furthermore, in the EH-CR network, the energy used for spectrum sensing and data transmission cannot exceed the collected energy; the energy constraint is given by the following equation:

[0025]

[0026] Where P ses τTP represents the power of cooperative spectrum sensing. ses and These represent the energy consumed by spectrum sensing and data transmission, respectively.

[0027] When the licensed frequency band is idle and the SU can correctly detect the absence of the PU, the SU can access the licensed frequency band and use high-power P. 0,i Data is transmitted; in this case, the effective data rate of SUs is:

[0028]

[0029] When the licensed frequency band is busy and the SUs cannot correctly detect the presence of the PU, the SUs can access the licensed frequency band and use a low-power P. 1,i Data is transmitted; in this case, the effective data rate of SUs is:

[0030]

[0031] The throughput of SUs is expressed as:

[0032] R(τ,P 0,i ,P 1,i )=(1-τ)TW(R 0,i +R 1,i (3-10)

[0033] SU i The throughput limit is expressed as follows:

[0034]

[0035] in SU i The throughput threshold;

[0036] A fairness evaluation coefficient is introduced to assess the fairness among SUs, given by the following formula:

[0037]

[0038] in and These are the SU values ​​in the k-th and (k-1)-th iterations, respectively. i The fairness evaluation coefficient; d is the fairness evaluation standard. This indicates the case where all SUs achieve the same throughput. Indicates the sum of SU in each iteration i The change; c represents the speed control coefficient, controlling F. i (k) The rate of change; if in the last iteration, SU j If Δ2 increases, then SUi Will increase or To avoid F i (k) The reduction;

[0039] In a primary user network, the PU acts as the leader, and the PU's utility function is given by the following equation:

[0040]

[0041] in a i SU i The utility cost of interfering with PU units;

[0042] Given that PU can tolerate the interference from SUs, SUs chooses the equilibrium interference price to maximize PU's revenue; the revenue problem of PU is defined as optimization problem P1; under the constraint of SUs' interference, maximizing PU's revenue is the objective of optimization problem P1, as follows:

[0043]

[0044] st p tot ≤P I

[0045] Where P I This indicates the maximum interference power that the PU can tolerate;

[0046] In the secondary user network, SU i The utility function includes the revenue function and the payoff function, i.e.

[0047]

[0048] In the above formula, the first and second terms represent the gains obtained from the throughput of SUs, ω i Let SUs represent the utility gain per unit rate; the third term in the above equation represents the payoff function; to simplify the calculation, equation (3-15) is rewritten as:

[0049]

[0050] in

[0051] We construct an optimization problem P2 to maximize the profit of SUs, as follows:

[0052]

[0053] Furthermore, based on the Stackelberg game model and the supermodel game model, a convex optimization method is proposed to solve problems (3-14) and (3-17), with the goal of finding the equilibrium point between PU and SUs;

[0054] make It is the NE solution to the optimization problem P1. It is a NE solution to the optimization problem P2; therefore, The equilibrium solution of the Stackelberg game is given by the following equation:

[0055]

[0056] In a Stackelberg game, PU, ​​as the sole leader, can obtain the equilibrium disturbance price of SUs by solving the optimization problem P1, defined as... As followers, SUs obtains the balanced spectrum sensing time coefficient and the balanced power allocation scheme by solving the optimization problem P2, defined as follows:

[0057] In the spectrum sensing phase, P is first... 0,i and P 1,i If the value is fixed to any positive value satisfying equation (3-17), then the optimization problem of the spectrum sensing time coefficient τ is expressed as:

[0058]

[0059]

[0060] in φ3=a i F i (k) p tot ;

[0061] when At that time, U s1,i (τ) is a quasi-concave function;

[0062] Due to U s1,i (τ) is quasi-concave, therefore Therefore, the equalization spectrum sensing time coefficient τ * By maximizing Therefore, Newton's iteration algorithm is used to solve this problem, as shown in the following equation:

[0063]

[0064] Where k represents the number of iterations, the equalized spectrum sensing time coefficient τ is obtained. * As shown in the following formula:

[0065]

[0066] In secondary user networks, SUs maximize their utility by adjusting their transmission power; this is due to the fairness factor F. i (k) Then the relationships between SUs become complex; in order to solve the optimization problem in (3-17), in the secondary user network, the interactions between SUs are modeled as G={S,{P 0,i ,P 1,i},{U s,i The supermodel game of}}, where S represents the set of SUs, {P 0,i ,P 1,i} represents the policy space of SUs, {U s,i} represents the utility function of SUs;

[0067] G = {S, {P} 0,i ,P 1,i},{U s,i}} is a typical supermodal game, and a typical supermodal game has only one NE solution;

[0068] Since equation (3-17) satisfies the Slater condition, the optimal response in equation (3-17) is... and The optimal response is obtained by constructing the Lagrange function. for:

[0069]

[0070] Best Response for:

[0071]

[0072] Achieving balanced interference power pricing a i , means as follows:

[0073]

[0074] NE solution to Stackelberg game The equations are given by equations (3-25), (3-36), (3-41), and (3-48), respectively.

[0075] Compared to existing technologies, this invention and its preferred embodiment propose a joint time and power allocation method based on a two-layer game theory for an Underlay EH-CR network. Specifically, firstly, EH is introduced into the CR network to construct an EH-CR network, and a "harvest-use" energy harvesting architecture is applied to collect and use energy. Then, the interaction between PUs and SUs is modeled as a Stackelberg game, and the interaction between SUs is modeled as a supermodel game. To improve fairness among SUs, a fairness evaluation coefficient is introduced. Next, utility functions based on the respective payoffs of the primary user network and secondary user networks are defined. Then, by solving the NE solution of the supermodel game, an equilibrium spectrum-aware time coefficient and an equilibrium power allocation scheme can be obtained. Next, this NE solution is substituted into the payoff function of the primary user network to maximize the payoff of the primary user network; thus, an NE solution of the Stackelberg game can be obtained. Furthermore, by introducing EH technology and a two-layer game theory scheme, the payoff of PUs and the total throughput of SUs can be improved, while simultaneously enhancing fairness among SUs. Finally, experimental simulations were used to verify the feasibility and effectiveness of introducing EH technology to improve PU revenue, and the feasibility and effectiveness of introducing a fairness evaluation coefficient to improve the total throughput of SUs. Simulation results show that, compared with traditional methods, the proposed method improves the total throughput of SUs while ensuring fairness. Furthermore, while maintaining PU communication quality, compared with existing methods, the proposed method improves PU performance in... The profit increased by approximately 18.2% at that time. The throughput of SUs increased by approximately 13.3% compared to existing technologies; the total throughput of SUs increased by approximately 18.13% compared to existing technologies; when At that time, the total throughput of SUs increased by approximately 13.5% compared to existing technologies, such as Figures 3-7 As shown. Attached Figure Description

[0076] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0077] Figure 1 This is a schematic diagram of the EH-CR network system model according to an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram of the time slot model of the EH-CR network according to an embodiment of the present invention;

[0079] Figure 3 This is a comparison graph showing the relationship between the benefits of PU and the number of iterations in an embodiment of the present invention;

[0080] Figure 4 This is a comparison graph showing the relationship between the total throughput of SUs and the number of SUs in an embodiment of the present invention;

[0081] Figure 5 This is a comparison curve of the relationship between the throughput threshold of SUs and the total throughput of SUs in an embodiment of the present invention;

[0082] Figure 6 This is a comparison curve of the relationship between the throughput threshold of SUs and the revenue of PU in an embodiment of the present invention;

[0083] Figure 7 This is a comparison curve of the relationship between the embodiment of the present invention and the total throughput of SUs. Detailed Implementation

[0084] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below for detailed explanation:

[0085] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0086] System Model

[0087] The EH-CR network system model proposed in this invention is as follows: Figure 1 As shown, this model is a complex network system composed of a primary user network and a secondary user network. The primary user network includes a primary transmitter (PT) and a primary receiver (PR); the secondary user network consists of n sub-users (SUs). The SUs communicate with each other via SBS. It is assumed that the EH-CR network can use N licensed frequency bands shared by the PU, and all SUs access these licensed bands for communication. When the PT transmits data to the PR, the SUs collect the RF signal energy emitted by the PT and use the collected energy for spectrum sensing and data transmission. Assume that the PT and SUs... i The gain between them is β i η (0≤η≤1) represents the energy harvesting efficiency, P T This indicates the transmit power of PT, SBS, and SU. i The gain between them is h i The gain between PT and SBS is g0, and W represents the bandwidth of the licensed frequency band.

[0088] exist Figure 2 In this model, time frame T is divided into two time slots: the spectrum sensing time slot τT and the data transmission time slot (1-τ)T, where τ represents the spectrum sensing time coefficient. It is assumed that SUs can collect RF energy from the PU signal throughout time frame T, and that the energy collected by each SU is exhausted within the entire time frame T.

[0089] During the energy harvesting phase, PT uses power P T Data is sent to the PR, while the SUs collect radio RF energy from the PU signal. Assuming each SU is equipped with a separate antenna for EH, the energy collected by the i-th SU can be represented as follows:

[0090] E i =ηP T β i T (i=1,2,...,n) (3-1)

[0091] Then, the SUs employ cooperative spectrum sensing to detect whether the PU is operating on the licensed frequency band. The SUs use energy detection for spectrum sensing and then report the average energy level of the received signal to the SBS. The spectrum sensing problem can be described by a binary assumption problem: given a frequency band, there are two possibilities, where H0 indicates the licensed frequency band is unoccupied, and H1 indicates the licensed frequency band is occupied.

[0092]

[0093] Where r(t) is the received signal, s(t) is the PU signal, g(t) is the channel gain, and n(t) is Gaussian noise; H0 and H1 represent the idle and busy states of the licensed frequency band, respectively. The decision statistic r(t) for local detection of each SU can be calculated as:

[0094]

[0095] Where M represents the number of perceived samples, which can be expressed by M = τTf s Given, f s This is the sampling frequency. Therefore, the average energy level of SUs can be expressed as:

[0096]

[0097] Next, SBS will E(r t The value is compared with a preset threshold I to determine whether the state of the PU exists in the licensed frequency band. Two metrics are used to evaluate the performance of the spectrum sensing process: detection probability p. d And the false alarm probability p f p d To correctly determine the probability of PU's existence, and p f The probability of incorrectly determining the existence of PU. Since PU has a predefined target p. d Therefore, the preset threshold I and false alarm probability p f They can be represented as follows:

[0098] I = (2erfc) -1(2p d )+γ+1)σ 2 (3-5)

[0099]

[0100] Where σ 2 It is the noise power, γ is the signal-to-noise ratio (SNR) of the PU, erfc(·) and erfc -1 (·) represent the complementary error function and the inverse complementary error function, respectively.

[0101] Finally, during the data transmission phase, SUs access the licensed frequency band in Underlay mode. SUs employ a two-layer power allocation strategy: in the absence of a PU, SUs use high-power P... 0,i Transmitting data; in the presence of PU, SUs transmit data at low power P. 1,i Transmitting data.

[0102] Assumption and Let represent the probabilities of the licensed frequency bands being unused and used, respectively, and let SUs satisfy the minimum target detection probability. The objective of this invention is to find a NE solution that maximizes the utility of the primary user network and the secondary user network while satisfying all constraints in the EH-CR network.

[0103] Problem Description

[0104] This invention proposes a joint time and power allocation method for Underlay EH-CR networks based on a two-layer game theory approach. This method models the interaction between PUs and SUs as a Stackelberg game and the interaction between SUs as a super-modal game model. In the Stackelberg game, a hierarchical structure of behavior is described using two types of players: leaders and followers. The PU is the leader, which guarantees its own communication quality by pricing interference from SUs. The PU sets a set of prices for each unit of interference power from each SU to maximize its revenue. The SUs are the followers, who pay for the interference they cause to the PU. Therefore, in the super-modal game, the SUs choose an equilibrium spectrum-aware time coefficient and an equilibrium power allocation scheme to maximize the utility of the sub-user network. Consequently, some definitions are first given, which are considered in the formulation of the optimization problem.

[0105] Energy Limitation

[0106] In the EH-CR network, because the energy harvesting architecture selected in this invention is a "harvest-use" architecture, the energy harvester does not have a capacitor to store the harvested energy. Therefore, the energy used for spectrum sensing and data transmission cannot exceed the harvested energy. Thus, the energy constraint is given by the following equation:

[0107]

[0108] Where P ses τTP represents the power of cooperative spectrum sensing. ses and These represent the energy consumed by spectrum sensing and data transmission, respectively.

[0109] SUs throughput

[0110] In an Underlay EH-CR network, the licensed frequency band of the PU can be shared with the SUs under certain interference limitations. When the licensed frequency band is idle and the SUs can correctly detect the absence of the PU, the SU can access the licensed frequency band and transmit at high power. 0,i Data is transmitted. In this case, the effective data rate of SUs is:

[0111]

[0112] When the licensed frequency band is busy and the SUs cannot correctly detect the presence of the PU, the SUs can access the licensed frequency band and use a low-power P. 1,i Data is transmitted. In this case, the effective data rate of SUs is:

[0113]

[0114] Therefore, the throughput of SUs can be expressed as:

[0115] R(τ,P 0,i ,P 1,i )=(1-τ)TW(R 0,i +R 1,i (3-10)

[0116] SU i Throughput Limitation

[0117] In the data transmission time slot, SU i The throughput threshold should be met; otherwise, SU i The profits will not be enough to cover the costs of interfering with the PU. Therefore, SU i The throughput limit can be expressed as follows:

[0118]

[0119] in SU i The throughput threshold.

[0120] Fairness evaluation coefficient

[0121] In an EH-CR network, selfish SUs may use as much energy as possible to transmit data for higher throughput, thereby maximizing their own utility. This undermines fairness among SUs. Therefore, a fairness evaluation coefficient is used to assess fairness among SUs, given by the following equation:

[0122]

[0123] in and These are the SU values ​​in the k-th and (k-1)-th iterations, respectively. i The fairness evaluation coefficient; d is the fairness evaluation standard. This indicates the case where all SUs achieve the same throughput. Indicates the sum of SU in each iteration i The change; c represents the speed control coefficient, controlling F. i (k) The rate of change. If in the last iteration, SU j If Δ2 increases, then SU i Will increase or To avoid F i (k) The reduction.

[0124] Utility function

[0125] In a primary user network, the PU acts as the leader, and the PU's utility function is given by the following equation:

[0126]

[0127] in a i SU i The utility cost of interfering with PU units.

[0128] Given that PU can tolerate the interference from SUs, SUs chooses the equilibrium interference price to maximize PU's revenue. The revenue problem for PU is defined as optimization problem P1. Under the constraint of SUs' interference, maximizing PU's revenue is the objective of optimization problem P1, as follows:

[0129]

[0130] st ptot ≤P I

[0131] Where P I This indicates the maximum interference power that the PU can tolerate.

[0132] In the secondary user network, SU i The utility function includes the revenue function and the payoff function, i.e.

[0133]

[0134] In the above formula, the first and second terms represent the gains obtained from the throughput of SUs, ω i Let SUs represent the utility gain per unit rate; the third term in the above equation represents the payoff function. To simplify the calculation, equation (3-15) is rewritten as:

[0135]

[0136] in

[0137] Therefore, an optimization problem P2 can be constructed to maximize the profit of SUs, as follows:

[0138]

[0139]

[0140] Model Solving

[0141] In this section, we propose a convex optimization method based on the Stackelberg game model and the supermodel game model to solve problems (3-14) and (3-17), with the goal of finding the equilibrium point between PU and SUs.

[0142] make It is the NE solution to the optimization problem P1. It is a NE solution to the optimization problem P2. Therefore,

[0143] The equilibrium solution of the Stackelberg game is given by the following equation:

[0144]

[0145] Therefore, the Stackelberg game strategy proposed in this invention can be obtained by solving optimization problems P1 and P2. In the Stackelberg game, PU, ​​as the sole leader, can obtain the equilibrium disturbance price of SUs by solving optimization problem P1, which can be defined as... As followers, SUs can obtain the balanced spectrum-sensing time coefficient and the balanced power allocation scheme by solving the optimization problem P2, which can be defined as follows:

[0146] Spectrum sensing time coefficient

[0147] In the spectrum sensing phase, P is first... 0,i and P 1,i If the value is fixed to any positive value satisfying equation (3-17), then the optimization problem of the spectrum sensing time coefficient τ can be expressed as:

[0148]

[0149]

[0150] in φ3=a i F i (k) p tot .

[0151] Next, prove that when At that time, U s1,i (τ) is a quasi-concave function.

[0152] The proof is as follows: Calculate U respectively s1,i The first and second partial derivatives of (τ) with respect to τ are expressed as follows:

[0153]

[0154]

[0155] Where p f The first and second partial derivatives with respect to τ can be expressed as follows:

[0156]

[0157]

[0158] in

[0159] From equation (3-20), it can be seen that when τ→1, When τ→0, Therefore, there exists a value Make When p f When ≤0.5, due to According to equation (3-23), we can obtain Therefore, from equation (3-21), we know that Therefore, when At that time, U s1,i (τ) is quasi-concave.

[0160] Due to U s1,i (τ) is quasi-concave, therefore Therefore, the equalization spectrum sensing time coefficient τ * By maximizing Therefore, Newton's iteration algorithm can be used to solve it, as shown in the following equation:

[0161]

[0162] Where k represents the number of iterations, as can be seen from equation (3-7) Therefore, the balanced spectrum sensing time coefficient τ can be obtained. * As shown in the following formula:

[0163]

[0164] Solving the model based on the secondary user network

[0165] In secondary user networks, SUs maximize their utility by adjusting their transmit power. This is due to the fairness factor F. i (k) Then the relationships between SUs become complex. To solve the optimization problem in (3-17), in the secondary user network, the interactions between SUs are modeled as G = {S, {P}. 0,i ,P 1,i},{U s,i The supermodel game of}}, where S represents the set of SUs, {P 0,i ,P 1,i} represents the policy space of SUs, {U s,i} represents the utility function of SUs.

[0166] Next, we will prove that G = {S, {P} 0,i ,P 1,i},{U s,i This is a typical supermodel game.

[0167] The proof is as follows: Calculate U respectively s1,i (τ) about P 0,i The first and second partial derivatives are expressed as follows:

[0168]

[0169]

[0170] From equation (3-27), we can see that U s,i It concerns the policy space P. 0,iA second-order continuously differentiable function.

[0171]

[0172] Similarly, calculate U separately. s1,i (τ) about P 1,i The first and second partial derivatives are expressed as follows:

[0173]

[0174]

[0175] From equation (3-30), we can see that U s,i It concerns the policy space P. 1,i A second-order continuously differentiable function.

[0176]

[0177] From equations (3-28) and (3-31), we can obtain Therefore, G is a typical hypermodal game. Existing techniques have proven that a typical hypermodal game has only one NE solution.

[0178] Since equation (3-17) satisfies the Slater condition, the optimal response in equation (3-17) is... and The solution can be obtained by constructing the Lagrange function, which is expressed as follows:

[0179]

[0180] Where λ1, λ2, λ3, λ4 > 0 represent Lagrange multipliers.

[0181] Therefore, the optimal response in equation (3-17) and It can be obtained based on the KKT conditions. Calculate L(P) 0,i ,P 1,i ,λ1,λ2,λ3,λ4) about P 0,i The first partial derivative of , and setting this first partial derivative to 0, can be expressed as follows:

[0182]

[0183] Therefore, we can obtain the following formula:

[0184]

[0185] To simplify equation (3-34), it can be rewritten as:

[0186]

[0187] Therefore, the best response can be obtained. for:

[0188]

[0189] Where A 0,i B 0,i C 0,i D 0,i It is expressed as follows:

[0190]

[0191] Similarly, L(P) is calculated. 0,i ,P 1,i ,λ1,λ2,λ3,λ4) about P 1,i The first partial derivative of , and setting this first partial derivative to 0, can be expressed as follows:

[0192]

[0193] Therefore, we can obtain the following formula:

[0194]

[0195] To simplify equation (3-39), it can be rewritten as:

[0196]

[0197] Therefore, the best response can be obtained. for:

[0198]

[0199] Where A 1,i B 1,i C 1,i D 1,i It is expressed as follows:

[0200]

[0201] Then, λ1, λ2, λ3, and λ4 can be obtained using the subgradient descent method, as shown in the following equation:

[0202]

[0203] Where μ1, μ2, μ3, and μ4 represent the iteration step size. Therefore, the NE solution of the supermode game can be obtained through Algorithm 3.1. The equations are given by equations (3-25), (3-36), and (3-41), respectively.

[0204] Solving the model based on the primary user network

[0205] In the primary user network, SUs need to choose a balanced interference power pricing to maximize PU revenue. Therefore, the optimization problem of PU revenue can be expressed as:

[0206]

[0207]

[0208]

[0209] Problem P1 can be solved using Lagrange duality; therefore, its Lagrange function can be expressed as:

[0210]

[0211] Next, calculate L(a) i ,τ,P 0,i ,P 1,i ,ν) about a i The first partial derivative of , and setting this first partial derivative equal to 0, can be expressed as follows:

[0212]

[0213] Therefore, we can obtain the following formula:

[0214]

[0215] From equation (3-47), the equilibrium interference power pricing a can be obtained. i , means as follows:

[0216]

[0217] Therefore, the NE solution of the Stackelberg game The equations are given by equations (3-25), (3-36), (3-41), and (3-48), respectively.

[0218] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0219] This patent is not limited to the above-described preferred embodiments. Anyone can derive other forms of joint time and power allocation methods for energy harvesting cognitive wireless networks based on two-layer game theory under the guidance of this patent. All equivalent changes and modifications made within the scope of the claims of this invention shall fall within the scope of this patent.

Claims

1. A method for joint time and power allocation in a two-layer game-theoretic energy harvesting cognitive wireless network, characterized in that: Energy harvesting (EH) is introduced into the CR network to construct an EH-CR network, and an "harvest-use" energy harvesting architecture is applied to harvest and use energy. The interaction between PU and SUs is modeled as a Stackelberg game, and the interaction between SUs is modeled as a supermodel game. A fairness evaluation coefficient is introduced, and the equilibrium spectrum sensing time coefficient and the equilibrium power allocation scheme are obtained by solving the Nash equilibrium NE solution of the supermodel game. In the Stackelberg game, leaders and followers are used to describe the hierarchical structure of behavior; the PU is the leader, which guarantees its own communication quality by pricing interference from SUs; the PU sets a set of prices for each SU's unit interference power to maximize its revenue; the SUs are the followers, who pay for the interference they cause to the PU; in the supermodel game, the SUs choose an equilibrium spectrum-aware time coefficient and an equilibrium power allocation scheme to maximize the utility of the secondary user network.

2. The method for joint time and power allocation of energy harvesting cognitive wireless networks based on two-layer game theory according to claim 1, characterized in that: The EH-CR network system model consists of a primary user network and a secondary user network; the primary user network includes a pair of primary transmitters (PTs) and primary receivers (PRs); the secondary user network consists of... It consists of several units (SUs); the SUs communicate with each other via SBS; it is assumed that the EH-CR network can use shared PUs. There are 10 licensed frequency bands, and all SUs access these bands for communication. When the PT sends data to the PR, the SUs collect the RF signal energy emitted by the PT and use the collected energy for spectrum sensing and data transmission. Assume that the PT and SUs... i The gain between , , Indicates energy harvesting efficiency. This indicates the transmit power of PT, SBS, and SU. i The gain between The gain between PT and SBS is , Indicates the bandwidth of the licensed frequency band; Time frame It is divided into two time slots, namely the spectrum sensing time slot. and data transmission time slots ,in Represents the spectrum sensing time coefficient; assuming the entire time frame Internal substations (SUs) can collect RF energy from the PU signal, and the energy collected by each SU is over the entire time frame. Internal depletion; During the energy harvesting phase, PT uses power Data is sent to the PR, while the SUs collect wireless RF energy from the PU signal; assuming each SU is equipped with a separate antenna for EH, then the... The energy collected by each SU is represented as follows: SUs employ cooperative spectrum sensing to detect whether PUs are operating in licensed frequency bands. SUs use energy detection for spectrum sensing and then report the average energy level of the received signal to the SBS. That is, in a given frequency band, there are two possibilities: This indicates that the licensed frequency band is not occupied. This indicates that the licensed frequency band is occupied; in It is receiving signals. It's a PU signal. It is channel gain. It is Gaussian noise; and These represent the idle and busy states of the licensed frequency band, respectively; the local detection of each SU The decision statistic is calculated as follows: in, The number of perceived samples is represented by Give, This is the sampling frequency; the average energy level of SUs is expressed as: Next, SBS will With preset threshold A comparison is made to determine whether the PU's state exists in the licensed frequency band; two metrics are used to evaluate the performance of the spectrum sensing process: detection probability. and false alarm probability ; To correctly determine the probability of the presence of PU, To determine the probability of erroneous determination of the existence of PU; since PU predefines a target. Therefore, a preset threshold is set. and false alarm probability They are represented as follows: in It is noise power. It's the signal-to-noise ratio of the PU. and These are complementary error functions and ; During the data transmission phase, SUs access licensed frequency bands in Underlay mode; SUs employ a two-layer power allocation strategy, namely: in the absence of a PU, SUs use high power. Transmitting data; in the presence of the PU, the SUs operate at low power. Transmit data; Assumption and Let represent the probabilities of the licensed frequency bands being unused and used, respectively, and let SUs satisfy the minimum target detection probability. The goal is to find a NE solution that maximizes the utility of the primary and secondary user networks while satisfying all constraints in the EH-CR network.

3. The method for joint time and power allocation of energy harvesting cognitive wireless networks based on two-layer game theory according to claim 2, characterized in that: In an EH-CR network, the energy used for spectrum sensing and data transmission cannot exceed the collected energy; the energy constraint is given by the following equation: in This represents the power of the cooperative spectrum sensing. and These represent the energy consumed by spectrum sensing and data transmission, respectively. When the licensed frequency band is idle and the SU can correctly detect the absence of the PU, the SU can access the licensed frequency band and operate at high power. Data is transmitted; in this case, the effective data rate of SUs is: When the licensed frequency band is busy and the SUs cannot properly detect the presence of the PU, the SUs can access the licensed frequency band and operate at low power. Data is transmitted; in this case, the effective data rate of SUs is: The throughput of SUs is expressed as: SU i The throughput limit is expressed as follows: in , , SU i The throughput threshold; A fairness evaluation coefficient is introduced to assess the fairness among SUs, given by the following formula: in , , and They are the first Second and third In the next iteration, SU i The fairness evaluation coefficient; d is the fairness evaluation standard. This indicates the case where all SUs achieve the same throughput; Indicates the sum of SU in each iteration i Changes; Represents the speed control coefficient, control The rate of change; if in the last iteration, SU j of Increase, then SU i Will increase or To avoid The reduction; In a primary user network, the PU acts as the leader, and the PU's utility function is given by the following equation: in , SU i The utility cost of interfering with PU units; Given that PU can tolerate the interference from SUs, SUs chooses the equilibrium interference price to maximize PU's revenue; the revenue problem of PU is defined as optimization problem P1; under the constraint of SUs' interference, maximizing PU's revenue is the objective of optimization problem P1, as follows: in This indicates the maximum interference power that the PU can tolerate; In the secondary user network, SU i The utility function includes the revenue function and the payoff function, i.e. In the above formula, the first and second terms represent the gains obtained from the throughput of SUs. Let SUs represent the utility gain per unit rate; the third term in the above equation represents the payoff function; to simplify the calculation, equation (3-15) is rewritten as: in , ; We construct an optimization problem P2 to maximize the profit of SUs, as follows: 。 4. The method for joint time and power allocation of energy harvesting cognitive wireless networks based on two-layer game theory according to claim 3, characterized in that: The proposed convex optimization method based on the Stackelberg game model and the supermodel game model is used to solve problems (3-14) and (3-17), with the goal of finding the equilibrium point between PU and SUs. make It is the NE solution to the optimization problem P1. It is a NE solution to the optimization problem P2; therefore, The equilibrium solution of the Stackelberg game is given by the following equation: In a Stackelberg game, PU, ​​as the sole leader, can obtain the equilibrium disturbance price of SUs by solving the optimization problem P1, defined as... Meanwhile, SUs, as followers, obtains the balanced spectrum sensing time coefficient and the balanced power allocation scheme by solving the optimization problem P2, defined as... ; In the spectrum sensing phase, firstly... and Fixed to any positive value satisfying equation (3-17), therefore, the spectrum sensing time coefficient The optimization problem is expressed as: in , , ; when hour, It is a quasi-concave function; because It is quasi-concave, therefore Therefore, the equalization of the spectrum sensing time coefficient By maximizing Therefore, Newton's iteration algorithm is used to solve this problem, as shown in the following equation: in This represents the number of iterations, yielding the equalized spectrum sensing time coefficient. As shown in the following formula: In secondary user networks, SUs maximize their utility by adjusting their transmit power; this is due to consideration of fairness factors. Then the relationships between SUs become complex; in order to solve the optimization problem in (3-17), in the secondary user network, the interactions between SUs are modeled as The supermodel game, in which Denotes the set of SUs, Represents the policy space of SUs. The utility function of SUs; It is a typical supermodal game, and a typical supermodal game has only one NE solution; Since equation (3-17) satisfies the Slater condition, the optimal response in equation (3-17) is... and The optimal response is obtained by constructing the Lagrange function. for: Best Response for: in It is expressed as follows: Achieving balanced pricing of interference power , means as follows: in Represents the Lagrange multiplier, and the NE solution of the Stackelberg game. The equations are given by equations (3-25), (3-36), (3-41), and (3-48), respectively.

Images