A resource management and optimization method for multiple users and a single eavesdropper based on Stackelberg game

Abstract

The application discloses a resource management and optimization method for multiple users and a single eavesdropper based on Stackelberg game. In a network scene with an eavesdropping device, although each user can improve the data transmission rate by increasing the transmission power, the data rate of the eavesdropping device is also increased. How to effectively model the resource allocation of the data transmission power of the user is a key problem to be solved by the application. Based on the above problem, the application provides a resource management and optimization method for multiple users and a single eavesdropper based on Stackelberg game. The power allocation of multiple users and the limited eavesdropping rate of the eavesdropper are combined to form a game model, and Taylor expansion is adopted to convert the original non-convex optimization problem into a convex optimization problem for modeling.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory. Background Technology

[0002] Data eavesdropping techniques are diverse. Besides traditional wired and wireless eavesdropping, new technologies such as microwaves, infrared, lasers, and networks are also widely used. For example, voice eavesdropping can be achieved using wireless communication technologies such as Wi-Fi and RFID. Mobile phone eavesdropping has also become common, as the openness of the wireless channels used by mobile phones allows third parties to intercept call information. This invention focuses on the power allocation problem of limited total eavesdropping rate for multiple users and a single eavesdropper. To protect the security of user data in the network, the total data rate that an eavesdropping device can eavesdrop on should be limited. At the same time, it should be noted that while each user can increase their own data transmission rate by increasing their transmission power, this also increases the eavesdropping data rate of the eavesdropping device.

[0003] Based on the above analysis, the key problem this invention aims to solve is how to effectively model and optimize the data transmission power allocation problem for each user. To address this problem, this invention proposes a resource management and optimization method for multiple users with a single eavesdropper based on Stackelberg game theory. This method combines the multi-user power allocation problem and the eavesdropper's limited eavesdropping rate problem into a game model, and uses Taylor expansion to transform the original non-convex optimization problem into a convex optimization problem for solution. This invention aims to provide a unique solution that physically conforms to real-world application scenarios and can be effectively applied to engineering practice. Summary of the Invention

[0004] Purpose of the invention: To address the game-theoretic allocation of data transmission power among multiple users in a multi-user scenario, under the premise of limited total eavesdropping rate, this invention proposes a resource management and optimization method for a single eavesdropper in a multi-user scenario based on Stackelberg game theory.

[0005] Technical solution: A resource management and optimization method for multi-user single eavesdropper based on Stackelberg game theory, including:

[0006] Construct a multi-user, single-eavesdropper wireless communication network; the multi-user, single-eavesdropper wireless communication network is composed of... The network model consists of a user terminal and a single eavesdropping device; each user sends uplink data to the base station, and the eavesdropping device eavesdrops on the uplink data of multiple users; in the network model... Each user establishes an uplink radio link with a single base station. The user set is represented as follows: Because users need to send wireless data to the base station on the uplink, there is an eavesdropping device in the network that receives the data uploaded by users through the wireless link.

[0007] Based on the multi-user single-eavesdropper wireless communication network, a Stackelberg game model is constructed; in the Stackelberg game model, the base station acts as the leader of the game model, while the user terminal that only has partial information acts as the follower.

[0008] For each user terminal, the objective function is to maximize its own utility function; for the base station, the objective function is to maximize the total cost paid by all user terminals for purchasing eavesdropping rates; for each user terminal, its own utility function is the difference between the data transmission rate to the base station generated by the transmission power obtained from the purchased eavesdropping rate and the eavesdropping rate obtained by the eavesdropping device.

[0009] The original non-convex optimization problem is transformed into a convex optimization problem and solved iteratively. In each iteration, the optimal pricing per unit eavesdropping rate is obtained by solving the Stackelberg game model.

[0010] In each iteration, each user terminal determines the number of eavesdropping rates to purchase based on the optimal pricing per unit of eavesdropping rate, thereby obtaining the magnitude of its respective transmission power.

[0011] The iteration ends when the conditions are met.

[0012] Furthermore, for each user terminal, the objective function is to maximize its own utility function, expressed as:

[0013]

[0014] In the formula, For the communication bandwidth of a single user, For receiver noise, For set The first in Data upload transmission power per user, For the first Channel gain of the uplink from each user to the base station For the first Channel gain from user to eavesdropping device and This represents the unit price that the leader sets for the rate at which a user can eavesdrop in a resource game.

[0015] Furthermore, the utility function for each user terminal is the difference between the data transmission rate to the base station generated by the transmission power obtained from the purchased eavesdropping rate as a benefit function and the eavesdropping rate obtained by the eavesdropping device as a cost function.

[0016] Furthermore, for the base station, the objective function, which maximizes the total cost incurred by all user terminals in purchasing eavesdropping rates, is expressed as:

[0017]

[0018] In the formula, This represents the unit price that the leader sets for the rate at which a user can eavesdrop in a resource game.

[0019] Furthermore, the constraints on the objective function of the base station in the game problem include:

[0020] The total eavesdropping rate obtained by an eavesdropper from all users on a network should be less than or equal to a threshold. , is represented as:

[0021]

[0022] In the formula, This represents the threshold of the total eavesdropping rate obtained by the eavesdropper.

[0023] Furthermore, the total rate of eavesdropping by a single eavesdropper is used as a limited resource in the Stackelberg game to play among multiple users.

[0024] Furthermore, sets The Middle The game optimization problem involving individual users is a non-convex optimization problem, which uses the logarithmic function. At point Perform a first-order Taylor expansion as

[0025]

[0026] in, For the first In the next iteration, the set The Middle Transmit power of each user;

[0027] Then, in the first In this iteration, the optimization problem for constructing the user terminal is:

[0028]

[0029] in, In the first The set in the next iteration The Middle Optimization variables for transmit power of each user;

[0030] Remove the first After the constant term in the next iteration, the set will be... The Middle The original non-convex game optimization problem for individual users is transformed into a convex game optimization problem.

[0031]

[0032] in, and The first Second and third In the next iteration, the set The Middle Transmit power of each user.

[0033] Furthermore, the first step is to obtain the th... The optimal solution in the next iteration ,at this time Pricing per unit eavesdropping rate in a game theory model The function; secondly, the game leader based on Find the optimal pricing per unit eavesdropping rate The final game follower based on It is possible to obtain the first In the next iteration The optimal value.

[0034] Furthermore, when The iteration ends at that time.

[0035] In the formula The threshold value is used as the termination condition for the iteration. For the follower in the game, in the first The optimal transmit power value obtained in the next iteration.

[0036] The beneficial effects of this invention are as follows: This invention discloses a resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory. To protect the security of user data in the network, the total data rate that the eavesdropping device can eavesdrop on should be limited. Simultaneously, it should be noted that while each user can increase their own data transmission rate by increasing their transmission power, this also increases the eavesdropping data rate of the eavesdropping device. Based on the above analysis, how to effectively manage the data transmission power of each user is the key problem that this invention needs to solve. Based on the above problem, this invention proposes a resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory. The multi-user power allocation and the limited eavesdropping rate problem are combined into a game model, and Taylor expansion is used to transform the original non-convex optimization problem into a convex optimization problem for solution. This invention aims to provide a unique solution. It physically conforms to real-world application scenarios and can be effectively applied to engineering practice. Attached Figure Description

[0037] Figure 1 This is a scenario diagram illustrating a resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory proposed in this invention.

[0038] Figure 2 This is a system block diagram of a multi-user single-eavesdropper resource management and optimization method based on Stackelberg game theory proposed in this invention. Detailed Implementation

[0039] Now combined with the appendix Figure 1 and attached Figure 2 The technical solutions of the present invention are further illustrated by the embodiments.

[0040] This embodiment proposes a resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory, which mainly includes the following steps:

[0041] Step 1: Construct a network model with multiple users and a single eavesdropper, such as... Figure 1 As shown, in this network model, it is assumed that... Each user establishes an uplink radio link with a single base station. The user set is represented as follows: Because users need to transmit wireless data to the base station on the uplink, there is an eavesdropping device in the network that receives the data uploaded by users through the wireless link.

[0042] Assuming the user communicates with the base station using Orthogonal Frequency Division Multiple Access (OFDMA), then in the set The first in The data upload rate for each user is

[0043]

[0044] in, For the communication bandwidth of a single user, For receiver noise, For set The first in Data upload transmission power per user, For the first Channel gain of the uplink from a user to the base station.

[0045] Because there are eavesdropping devices in the network, these devices can target the entire network. The Middle The eavesdropping data rate per user is expressed as:

[0046]

[0047] in, For the first Channel gain from the user to the eavesdropping device.

[0048] Based on a multi-user single eavesdropper network model, ensemble The Middle The confidentiality rate for an individual user can be expressed as:

[0049]

[0050] In this example, to protect the security of user data in the network, the total data rate that the eavesdropping device can eavesdrop on should be limited. At the same time, it should be noted that while individual users can increase their own data transmission rate by increasing their transmission power, this also increases the data transmission rate that the eavesdropping device can intercept. Based on the above analysis, how to effectively model, manage, and optimize the data transmission power of each user is the key problem that this invention needs to solve.

[0051] Considering that user terminals all desire to use high power for data transmission, the higher the power of user data transmission, the faster the data transmission rate. However, this also increases the eavesdropping rate for network eavesdroppers. Therefore, to limit the total eavesdropping rate, user terminals with different channel gains compete with each other in the allocation of uplink transmission power. The Steinberg game is a pure-strategy, non-cooperative sequential game model in economics. Based on the priority of actions and the completeness of information possessed, the participants can be divided into leaders and followers. Followers possess only partial information and act first; while the leader possesses all the information of the followers and acts subsequently. The leader needs to consider the optimal response of the followers when setting the game strategy, and the followers determine their optimal resource purchase size based on the leader's optimal decision. In this embodiment, since the base station possesses global information, it acts as the leader in the game model, while the user terminals, possessing only partial information, act as followers.

[0052] In this example, each follower in the game mechanism purchases eavesdropping rate with the aim of increasing its data transmission speed. Therefore, the utility function of the user terminal as a follower consists of two parts: a payoff function and a cost function. The payoff function is the data transmission rate to the base station generated by the transmission power gained from the purchased eavesdropping rate, while the cost function is the eavesdropping rate obtained by the eavesdropping device. Therefore, the user terminal's utility function is the difference between the payoff function and the cost function, expressed as:

[0053]

[0054] in, This represents the unit price that the leader sets for the rate at which a user can eavesdrop in a resource game.

[0055] Therefore, in game theory, sets The The higher the transmit power of an individual user, the greater the data transmission rate it achieves, but the greater the cost. For a set... The Middle The game optimization problem for individual users is modeled as follows:

[0056]

[0057] In this game theory relationship, the leader, i.e., the base station, sells a limited total data rate for eavesdropping to multiple competing users for their data transmission. Therefore, its objective function is defined as maximizing the total cost incurred by all user terminals in purchasing the eavesdropping rate. Thus, the optimization problem for the leader in this game theory is modeled as follows:

[0058]

[0059] st

[0060] in, The upper limit of the total data rate that the eavesdropping device can eavesdrop on; objective function This represents the total revenue a leader receives from selling a limited total data rate of eavesdropping resources to multiple competing users.

[0061] The objective functions of both the follower and the leader constitute the Stackelberg game. By following certain rules and engaging in game action, the two sides can reach the final Stackelberg equilibrium, which represents the optimal pricing per unit of eavesdropping rate. Then, each user terminal is priced according to the optimal rate per unit of eavesdropping. This allows us to determine the amount of eavesdropping data purchased, and thus obtain the uplink data transmission power of each user.

[0062] Step 2: However, due to the set The Middle The game optimization problem for a single user is a non-convex optimization problem (the difference between two concave functions). In this example, Taylor expansion is used, that is, a first-order approximation (linearization) is used to approximate the second logarithmic function.

[0063] First, for the second logarithmic function At point Perform a first-order Taylor expansion as

[0064]

[0065] in, For the first In the next iteration, the set The Middle Transmit power of each user.

[0066] Then, in the first In this iteration, the optimization problem for constructing the user terminal is approximated as follows:

[0067]

[0068] in, In the first The set in the next iteration The Middle The optimized variable for each user is transmit power.

[0069] Remove the constant term The set can be The Middle The game optimization problem for individual users is simplified to:

[0070]

[0071] The objective function of the above optimization problem is a concave function minus a linear function; therefore, the above optimization problem is a convex optimization problem. In the The constant value in the nth iteration can be obtained using convex optimization theory. The optimal solution in the next iteration ,in Pricing per unit eavesdropping rate in a game theory model The function.

[0072] According to game theory, the leader obtains the optimal sales revenue only when all resources are sold. Therefore, the constraint of the leader optimization problem should hold equality at the optimum. Thus, we have...

[0073]

[0074] The first The optimal solution in the next iteration (at this time, The pricing per unit eavesdropping rate in the game theory model remains the same. Substituting the function into the above equation yields the optimal pricing per unit eavesdropping rate. Therefore, it is possible to obtain the first In the next iteration The optimal value.

[0075] when When the iteration ends, the iteration is complete. The threshold is the condition for terminating the iteration. For the follower in the game, in the first The optimal transmit power value obtained in the next iteration.

Claims

1. A resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory, characterized in that, include: Construct a wireless communication network with multiple users and a single eavesdropper; The multi-user single-eavesdropper wireless communication network is composed of It consists of a user terminal and a single eavesdropping device; each user sends uplink data to the base station, and the eavesdropping device eavesdrops on the uplink data of multiple users; Each user establishes an uplink radio link with a single base station. The user set is represented as follows: Because users need to send wireless data to the base station on the uplink, there is an eavesdropping device in the network that receives the data uploaded by users through the wireless link. Based on the multi-user single-eavesdropper wireless communication network, a Stackelberg game model is constructed; in the Stackelberg game model, the base station acts as the leader of the game model, while the user terminal that only has partial information acts as the follower. For each user terminal, maximizing its own utility function is its objective function; for the base station, maximizing the total cost incurred by all user terminals in purchasing eavesdropping rates is its objective function; for each user terminal, its own utility function is the difference between the data transmission rate to the base station generated by the transmission power obtained from the purchased eavesdropping rate and the eavesdropping rate obtained by the eavesdropping device, i.e. in, For the communication bandwidth of a single user, For receiver noise, For set The first in Data upload transmission power per user, For the first Channel gain of the uplink from each user to the base station For the first Channel gain from user to eavesdropping device and This represents the unit price that the leader sets for the rate at which a user can eavesdrop in a resource game. Due to the above set The Middle The game optimization problem for each user is the difference between two concave functions, which is a non-convex optimization problem. It is transformed into a convex optimization problem and solved iteratively. In each iteration, the optimal pricing per unit eavesdropping rate is obtained by solving the Stackelberg game model. In each iteration, each user terminal determines the number of eavesdropping rates to purchase based on the optimal pricing per unit of eavesdropping rate, thereby obtaining the magnitude of its respective transmission power. The iteration ends when the conditions are met.

2. The resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory as described in claim 1, characterized in that: For the base station, the objective function is to maximize the total cost incurred by all user terminals in purchasing eavesdropping rates, expressed as: 。 3. The resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory as described in claim 2, characterized in that: The constraints on the objective function of the base station in the game theory problem include: The total eavesdropping rate obtained by an eavesdropper from all users on a network should be less than or equal to a threshold. , represented as: In the formula, This represents the threshold of the total eavesdropping rate obtained by the eavesdropper.

4. The resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory as described in claim 3, characterized in that: The total rate at which a single eavesdropper eavesdrops is used as a limited resource in a Stackelberg game, which is then played among multiple users.

5. A resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory as described in claim 1, characterized in that, gather The Middle The game optimization problem involving individual users is a non-convex optimization problem, which uses the logarithmic function. At point Perform a first-order Taylor expansion as in, For the first In the next iteration, the set The Middle Transmit power of each user; Then, in the first In this iteration, the optimization problem for constructing the user terminal is: in, In the first The set in the next iteration The Middle Optimization variables for transmit power of each user; Remove the first After the constant term in the next iteration, the set will be... The Middle The original non-convex game optimization problem for individual users is transformed into a convex game optimization problem. .

6. The resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory as described in claim 5, characterized in that, First, the convex optimization theory is used to obtain the... The optimal solution in the next iteration ,in For the first In the next iteration, the set The Middle The transmit power of each user at this time Pricing per unit eavesdropping rate in a game theory model The function; secondly, the game leader based on Find the optimal pricing per unit eavesdropping rate The final game follower based on It is possible to obtain the first In the next iteration The optimal value, where Indicates the first In the next iteration, the set The Middle The optimal value of transmit power for each user.

7. A resource management and optimization method for a multi-user single eavesdropper based on Stackelberg game theory as described in claim 6, characterized in that, when The iteration ends at that time. In the formula The threshold is the termination condition for the iteration; Indicates the first In the next iteration, the set The Middle The optimal value of transmit power for each user.

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