An intelligent reflecting surface resource allocation method based on game theory

Abstract

The present invention provides a method for allocating intelligent reflective surface resources based on game theory, comprising the following steps: Step 1: Calculate the utility function V of user k k ; Step 2: Calculate the utility function w of IRS k ; Step 3: Calculate the optimal number of IRS unit allocations b k * ; Step 4: Calculate the optimal IRS pricing Pr k * ; Step 5: Calculate the price update function I (Pr k ); Step 6: Given the initial price pr k , substitute it into the price update function I(Pr k ), determine whether the IRS pricing obtained in each iteration is equal to Pr k * , if they are not equal, return to step 5. Step 7: The intelligent reflective surface resource allocation method ends. The above technical solution quotes the relevant theories of non-cooperative game theory and uses the Stackelberg game to propose a pricing mechanism to solve the problem of allocating the number of IRS reflective units, thereby achieving the goal of improving user utility and maximizing IRS benefits.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to an intelligent reflecting surface resource allocation method based on game theory. Background Art

[0002] In recent years, the development of wireless communication has been rapid. The application traffic of mobile users has increased exponentially, and the demand for wireless resources for various applications has also increased accordingly. Different applications have different resource requirements, so it is very important to rationally allocate limited wireless resources. Game theory is a branch of applied mathematics and can be used as a tool to solve conflicts and cooperation. It can provide a suitable analysis framework for the interaction between users. It mainly studies the problem of multiple rational decision-makers with conflicting interests to obtain corresponding equilibriums for all participants under the conditions of mutual influence and restriction.

[0003] Intelligent reflecting surface (IRS) has developed rapidly in industrial promotion because it can flexibly control the electromagnetic characteristics in the channel environment and is considered a promising new technology for future high-efficiency spectrum wireless communication systems. The intelligent reflecting surface has the characteristics of low cost, low energy consumption, programmable, easy to deploy, etc. It is usually composed of a large number of carefully designed electromagnetic units arranged. By applying control signals to the adjustable elements on the electromagnetic units, the electromagnetic properties of these electromagnetic units can be dynamically controlled, and then the active intelligent regulation of spatial electromagnetic waves can be realized in a programmable manner, forming an electromagnetic field with controllable parameters such as amplitude, phase, polarization, and frequency.

[0004] The introduction of IRS will bring new changes to the channel characteristics, and there is an opportunity to realize the reconstruction of the wireless channel and break through the limitations of the traditional network wireless propagation channel. IRS can actively enrich the channel scattering conditions and enhance the multiplexing gain of the wireless communication system. IRS can also realize signal propagation direction control and in-phase superposition in three-dimensional space, increase the received signal strength, and improve the transmission performance between communication devices.

[0005] There are mainly two existing IRS resource allocation methods: fixed allocation method and dynamic allocation method. If the IRS resources are allocated to a specific position through the solid-state allocation method, it is impossible to flexibly adjust for different users or different network requirements. When the network topology or user location changes, it is necessary to re-adjust the IRS resource allocation, increasing the management and maintenance costs. The dynamic allocation method has a high computational complexity and needs to consider multiple factors, such as channel state, user location, etc. At the same time, there may be a problem of excessive competition for IRS resources, resulting in performance degradation. Therefore, a suitable intelligent reflecting surface resource allocation method is very important for IRS-assisted wireless communication. Based on this, the present invention proposes an intelligent reflecting surface resource allocation method based on game theory. Summary of the Invention

[0006] In view of the deficiencies of the prior art, the present invention proposes an intelligent reflecting surface resource allocation method based on game theory, which achieves the goals of improving user utility and maximizing IRS revenue.

[0007] To solve the above technical problems, the technical solution of the present invention is as follows:

[0008] An intelligent reflecting surface resource allocation method based on game theory, comprising the following steps:

[0009] Step 1: Calculate the utility function V of user k k

[0010] Step 2: Calculate the utility function w of the IRS k

[0011] Step 3: Calculate the optimal number b of IRS unit allocations k *

[0012] Step 4: Calculate the optimal IRS pricing Pr k *

[0013] Step 5: Calculate the price update function I(Pr k ):

[0014] Step 6: Given the initial pricing pr k , substitute it into the price update function I(Pr k ), and determine whether the IRS pricing obtained from each iteration is equal to Pr k * . If not, return to Step 5.

[0015] Step 7: The intelligent reflecting surface resource allocation method ends.

[0016] Preferably, Step 1 is specifically as follows:

[0017] The utility function V of user k k is calculated as follows:

[0018] V k = Blog 2 (1 + γ k ) - Pr k b k

[0019] where B is the channel bandwidth, k is the number of users, γ k is the signal-to-noise ratio received by user k, Pr k is the price that user k pays for the IRS unit, and b kThe number of IRS units allocated to user k. In the MU-SISO-OFDM system, each user is allocated a set of independent orthogonal subcarriers for parallel transmission, which can avoid interference between users. Therefore, the signal-to-noise ratio γ k can be written in the following form:

[0020]

[0021] In the above formula, P t is the base station transmission power, ∑ is the summation symbol, N is the number of IRS units, is the baseband equivalent channel from the nth IRS unit to the user, β n is the amplitude value of the nth IRS unit, 0 ≤ β n ≤ 1, θ n is the phase value of the nth IRS unit, mod represents the modulo operation, φ n , η n , are respectively g n , 's phase, g n is the baseband equivalent channel from the base station to the nth IRS unit, is the baseband equivalent channel from the base station to the user, σ k 2 is the variance of the Gaussian noise on the receiver of user k.

[0022] Preferably, step 2 is specifically as follows:

[0023] w k =(Pr k -c)b k

[0024] where Pr k is the price that user k pays for the IRS unit, c is the cost price of the IRS unit, b k is the number of IRS units allocated to user k.

[0025] Preferably, step 3 is specifically as follows:

[0026] Use the non-linear least squares method for power function fitting to fit the utility function of user k into the following form:

[0027] V k =ab k e +d - pr k b k

[0028] where a, d, e are the parameters of the fitting curve, bk The number of IRS units allocated to user k, Pr k The price that user k pays for the IRS units.

[0029] Solve for the optimal number b of IRS units allocated by using the first-order partial derivative of the user's utility function k * :

[0030] Let Then

[0031] The optimal number of IRS units allocated can be solved as follows:

[0032] Preferably, step 4 is specifically as follows:

[0033] Using b k * and the first-order partial derivative of the utility function of the IRS to solve for the optimal IRS pricing Pr k * ,

[0034] Let Then

[0035] The optimal IRS pricing can be solved as follows:

[0036] Preferably, step 5 is specifically as follows:

[0037] The calculation method of the price update function is as follows:

[0038]

[0039] where c is the cost price of the IRS unit, Pr k is the price that user k pays for the IRS unit, and e is the parameter of the fitting curve.

[0040] Preferably, step 6 is specifically as follows:

[0041] Given the initial pricing: pr k = c, substitute the price pr k into the price update function I(Pr k ), and update the user's bid until after multiple iterations, I n (Pr k ) converges to the optimal IRS pricing Pr k * , and the IRS can obtain its maximum revenue, and the user can also purchase the optimal number of IRS units accordingly.

[0042] The present invention has the following characteristics and beneficial effects:

[0043] Adopting the above technical solution, the present invention incorporates the "utility theory" in "decision theory", the "Nash equilibrium" theory in non - cooperative game theory, and the idea of "best response dynamics", and uses the Stackelberg game to propose a pricing mechanism to solve the problem of reasonable allocation of the number of IRS reflection units. The price update function obtained by calculation can converge to the optimal IRS pricing, achieving the goals of reasonable allocation of IRS resources and maximization of IRS revenue. Brief Description of the Drawings

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following - described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0045] Figure 1 It is the flowchart of the method for the embodiment of the present invention. Detailed Embodiments

[0046] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0047] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0048] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installation", "connection", and "linkage" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0049] The present invention provides an intelligent reflecting surface resource allocation method based on game theory, as Figure 1 shown, specifically including the following steps:

[0050] Step 1: Based on the "utility theory" in "decision theory", calculate the utility function V of user k k

[0051] V k = Blog 2 (1 + γ k ) - Pr k b k

[0052] where B is the channel bandwidth, k is the number of users, γ k is the signal-to-noise ratio received by user k, Pr k is the price that user k pays for the IRS unit, and b k is the number of IRS units allocated to user k. In the MU - SISO - OFDM system, each user is allocated a set of independent orthogonal sub - carriers for parallel transmission, which can avoid interference between users. Therefore, the signal - to - noise ratio γ k can be written in the following form:

[0053]

[0054] In the above formula, P t is the base station transmission power, ∑ is the summation symbol, N is the number of IRS units, is the baseband equivalent channel from the nth IRS unit to the user, β n is the amplitude value of the nth IRS unit, 0 ≤ β n ≤ 1, θ n is the phase value of the nth IRS unit, mod represents the modulo operation, φ n , η n , are respectively g n , 's phase, g n is the baseband equivalent channel from the base station to the nth IRS unit, is the baseband equivalent channel from the base station to the user, and σ k 2 is the variance of the Gaussian noise at the receiver of user k.

[0055] Step 2: Based on the "Utility Theory" in "Decision Theory", calculate the utility function w of the IRS k

[0056] w k =(Pr k -c)b k

[0057] where Pr k is the price that user k pays for the IRS unit, c is the cost price of the IRS unit, and b k is the number of IRS units allocated to user k.

[0058] Step 3: Based on the "Nash Equilibrium Theory" in "Game Theory", calculate the optimal number b of IRS units allocated k *

[0059] Use the non - linear least - squares method for power function fitting to fit the utility function of user k into the following form:

[0060] V k =ab k e +d - pr k b k

[0061] where a, d, e are the parameters of the fitting curve. b k is the number of IRS units allocated to user k, and Pr k is the price that user k pays for the IRS unit.

[0062] Solve for the optimal number b of IRS units allocated using the first - order partial derivative of the user's utility function k * :

[0063] Let Then

[0064] The optimal number of IRS units allocated can be solved as:

[0065] Step 4: Based on the "Nash Equilibrium Theory" in "Game Theory", calculate the optimal IRS pricing Pr k *

[0066] Using b k* Solve for the optimal IRS pricing Pr by taking the first-order partial derivative of the utility functions of the IRS and the user k * ,

[0067] Let Then

[0068] The optimal IRS pricing can be solved as follows:

[0069] Step 5: Calculate the price update function I(Pr based on the Shapley-Shubik theorem in "game theory" k )

[0070]

[0071] where c is the cost price of the IRS unit, Pr k is the price paid by user k for the IRS unit, and e is the parameter of the fitting curve.

[0072] Step 6: Given the initial pricing: pr k = c, substitute the price pr k into the price update function I(Pr k ), and update the user's bid until I n (Pr k ) converges to the optimal IRS pricing Pr k * . The IRS can obtain its maximum revenue, and the user can also purchase the optimal number of IRS units accordingly.

[0073] Step 7: The intelligent reflecting surface resource allocation method ends.

[0074] The above has described the embodiments of the present invention in detail in conjunction with the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, without departing from the principles and spirit of the present invention, various changes, modifications, substitutions, and variations to these embodiments including components still fall within the protection scope of the present invention.

Claims

1. An intelligent reflecting surface resource allocation method based on game theory, characterized in that, it includes the following steps: S1. Calculate the utility function V of user k k ; S2. Calculate the utility function w of the IRS k ; S3. Calculate the optimal number b of IRS unit allocations k * S3-1. Use the non-linear least squares method to perform a power function fitting on the utility function V of user k k ; S3-2. Solve for the optimal number of IRS unit allocations \(b\) using the first-order partial derivative of the utility function after fitting with the user's power function k * ; S4. Calculate the optimal IRS pricing Pr k * The utility function w of the IRS k and the optimal number b of IRS unit allocations k * Solve for the optimal IRS pricing Pr using the first-order partial derivatives k * ; S5. Calculate the price update function I(Pr k ), and the expression is as follows: where c is the cost price of the IRS unit, Pr k is the price that user k pays for the IRS unit, pr k is the given initial pricing, and e is the parameter of the fitting curve; S6. Given the initial price pr k , substitute it into the price update function I(Pr k ), and determine whether the IRS price obtained in each iteration is equal to Pr k * . If they are not equal, return to step 5; S7. After completing the iteration, the intelligent reflecting surface resource allocation method ends.

2. The intelligent reflecting surface resource allocation method according to claim 1, characterized in that, In the step S1, the utility function V of user k k is calculated as follows: V k = Blog 2 (1 + γ k ) - Pr k b k where B is the channel bandwidth, k is the number of users, and γ k is the signal-to-noise ratio received by user k, Pr k is the price that user k pays for the IRS unit, and b k is the number of IRS units allocated to user k.

3. The intelligent reflecting surface resource allocation method according to claim 2, characterized in that, In the step S1, in the MU-SISO-OFDM system, each user is assigned a set of independent orthogonal subcarriers for parallel transmission, and the signal-to-noise ratio γ k is written in the following form: where P t is the base station transmission power, ∑ is the summation symbol, N is the number of IRS units, is the baseband equivalent channel from the n-th IRS unit to the user, β n is the amplitude value of the n-th IRS unit, 0 ≤ β n ≤ 1, θ n is the phase value of the n-th IRS unit, mod represents the modulo operation, φ n , η n , are respectively the phase of g n , g n is the baseband equivalent channel from the base station to the n-th IRS unit, is the baseband equivalent channel from the base station to the user, σ k 2 is the variance of the Gaussian noise at the receiver of user k.

4. The intelligent reflecting surface resource allocation method according to claim 1, characterized in that, In the said step S1, the utility function w of the IRS k is calculated as follows: w k = (Pr k - c)b k where Pr k is the price paid by user k for the IRS unit, c is the cost price of the IRS unit, and b k is the number of IRS units allocated to user k.

5. The intelligent reflecting surface resource allocation method according to claim 3, characterized in that, in the step S3-1, power function fitting is performed, and the expression is as follows: V k = ab k e + d - pr k b k where a, d, e are the parameters of the fitting curve, and b k is the number of IRS units allocated to user k, and Pr k is the price that user k pays for the IRS units.

6. The intelligent reflecting surface resource allocation method according to claim 5, characterized in that, In the step S3-2, solve for the optimal number b of IRS unit allocations k * , and the expression is as follows: Let Then Solve for the optimal number of IRS unit allocations:

7. The intelligent reflecting surface resource allocation method according to claim 6, characterized in that, In step S4, the optimal IRS price Pr is solved k * , and the expression is as follows: Let Then Obtain the optimal IRS pricing:

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