CN112543498B - Power self-adaptive distribution method based on layered game model - Google Patents

Power self-adaptive distribution method based on layered game model Download PDF

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CN112543498B
CN112543498B CN202011325015.7A CN202011325015A CN112543498B CN 112543498 B CN112543498 B CN 112543498B CN 202011325015 A CN202011325015 A CN 202011325015A CN 112543498 B CN112543498 B CN 112543498B
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陈赓
邵睿
马璐瑶
曾庆田
姚文静
徐先杰
张旭
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Shandong University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/06—TPC algorithms
    • H04W52/14—Separate analysis of uplink or downlink
    • H04W52/146—Uplink power control
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    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/04—Inference or reasoning models
    • G06N5/042—Backward inferencing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/243—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account interferences
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

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Abstract

The invention discloses a power self-adaptive distribution method based on a layered game model, belongs to the technical field of mobile communication, and solves the problem of power self-adaptive distribution in wireless resources. The theory of the layered game is introduced into a 5G heterogeneous convergence network, and a three-layer heterogeneous network model consisting of an RNC (radio network controller), a base station and base station users is established. A SteinKelberg game model is adopted between the RNC and the base station; and the base station users further play the game by adopting a non-cooperative game mode according to the power distributed by the respective corresponding base station. The method firstly distributes power to each base station managed by the RNC, and then users contained in the base stations perform further distribution according to the power distributed by the base stations to which the users belong, so that the aims of primary distribution, secondary distribution and user side power distribution of the power are achieved, interference can be reduced, and system capacity is improved.

Description

Power self-adaptive distribution method based on layered game model
Technical Field
The invention belongs to the technical field of mobile communication, and particularly relates to a power self-adaptive distribution method based on a layered game model.
Background
The network densification in the 5G heterogeneous network is a trend of 5G development, and it is very important to research the problems of resource allocation and the like in the 5G heterogeneous convergence network under the condition of massive deployment of base stations.
Generally, a plurality of femto base stations are arranged around a macro base station, so that the coverage area can be enlarged, the femto base stations can supplement places which cannot be covered by the macro base station, the femto base stations and the macro base station share frequency spectrum resources, and meanwhile, the mobile equipment and the data traffic are greatly increased to cause resource shortage. In consideration of the increasing data traffic and mobile communication devices, a large number of femto base stations are deployed in a heterogeneous network, so that communication quality can be enhanced, communication speed can be increased, but network resources in the future will become very precious, resource allocation problems cannot be ignored, problems between resource supply and resource demand need to be solved, resources are reasonably allocated to maintain the stability of the whole communication system, interference can be reduced to improve the service quality of users, system capacity can be improved, and efficient utilization of resources can be achieved.
Disclosure of Invention
The invention provides a power self-adaptive distribution method based on a layered game model, which solves the problem of power distribution in a 5G heterogeneous fusion network by introducing a power control method based on a SteinKerberg game and a non-cooperative game and a power distribution algorithm based on a layered game from the viewpoint of power distribution.
In order to achieve the purpose, the invention adopts the following technical scheme:
a power self-adaptive distribution method based on a layered game model comprises the following steps:
(1) in a 5G heterogeneous convergence network area, a three-layer heterogeneous convergence network model consisting of an RNC (radio network controller), a base station and base station users is constructed by adopting the theoretical basis of a game theory;
(2) obtaining optimal transmitting power by adopting a power control method based on a Steckelberg game and a non-cooperative game;
(3) the equilibrium solution of the SteinKerberg game is obtained through analyzing the equilibrium solution of the layered game;
(4) and adopting a power distribution algorithm based on a layered game to obtain a converged power value and optimal pricing of each base station.
Preferably, in the step (2), a stanzeberg game is adopted between the RNC and the base station, the RNC is a game leader, and the base station is a follower; obtaining respective optimal transmitting power among base station users by adopting a non-cooperative game;
the specific process of the Stenkerberg game is as follows:
in a given time slot, the RNC prices the unit power of the base station i to be lambdaiThe transmission bandwidth of base station i is wiThen, the link transmission rate of the base station i is as follows:
Figure BDA0002794051800000021
wherein p isiRepresenting the transmission power, p, of base station ijRepresenting the transmit power, p, of base station j0Denotes the transmission power, h, of the RNCiiRepresenting the power gain, h, of the link channel of base station i with its usersi0Represents the interference link gain, h, between the RNC and base station iijRepresenting the interference link gain of a base station i and a user j, wherein N is the total number of the base stations, i is any base station and belongs to {1,2,3 …, N };
utility function U of base station iiThe following were used:
Figure BDA0002794051800000022
utility function U of RNCRNCThe following were used:
Figure BDA0002794051800000023
wherein h is0iThe interference link gain of the base station i to the base station user is obtained;
in summary, the optimization problem of the RNC is as follows:
Figure BDA0002794051800000024
wherein,
Figure BDA0002794051800000025
the upper and lower bounds of the link transmission rate are respectively;
the optimization problem of the base station is as follows:
Figure BDA0002794051800000026
the formulas (5) and (6) jointly form a Stannkralberg game process, the RNC prices the power of the base station under the condition that the optimal strategy of the base station is mastered, and the base station takes corresponding strategy action by observing the pricing of the RNC to adjust the self transmitting power;
the non-cooperative game process among the base station users is to solve the formula (6), then the result is substituted into the formula (5), the optimization problem of the RNC is solved, and finally the whole system reaches SteinKelberg equilibrium;
wherein the equilibrium solution (lambda) of the Stanckberg game equilibrium is achieved*，
Figure BDA0002794051800000027
) The following conditions are satisfied:
URNC(λ*,p*)≥URNC(λ,p*) (7)
Figure BDA0002794051800000031
wherein λ is*The optimal pricing set of the RNC is p, the optimal transmitting power strategy set of the RNC is p, the pricing of the RNC to the unit power of the base station is lambda,
Figure BDA0002794051800000032
for the optimal pricing set of base station i,
Figure BDA0002794051800000033
is the optimal transmit power strategy set for base station i.
Preferably, the specific process of step (3) is as follows:
firstly, the optimal transmitting power when the base station user non-cooperative game reaches Nash equilibrium is solved by utilizing a back-stepping method, and the specific process is as follows:
for a given pricing, equation (6) has an optimal solution, i.e., the optimal transmit power of the base station, as follows:
Figure BDA0002794051800000034
wherein (a)+Max { a,0 };
secondly, writing the obtained optimal transmitting power into a matrix form, and substituting the matrix form into a utility function of the RNC for simplification;
and finally, researching the relation between the utility function and the pricing, further simplifying the optimization problem, and solving the optimal pricing of the RNC when the system model reaches SteinKelberg equilibrium, wherein the optimal pricing of the RNC is lambda*The following were used:
Figure BDA0002794051800000035
wherein,
Figure BDA0002794051800000036
is λiUpper bound of (1), n0Noise interference for RNC;
the optimal transmission power and optimal pricing obtained from equations (10) and (32) form the equilibrium solution (p) of the Stanckberg gamei(λ*),λ*)。
Preferably, the specific process of step (4) is as follows:
firstly, the RNC calculates the pricing of each base station according to the initial transmitting power of the base station, and broadcasts the obtained pricing to the corresponding base station through the RNC;
secondly, the base station adjusts the self transmitting power according to the iterative function after receiving the pricing,
the iteration function is as follows:
Figure BDA0002794051800000037
and finally, setting iteration times to obtain the optimal transmitting power of each base station and the optimal pricing of the RNC to each base station.
The invention has the following beneficial technical effects:
according to the power self-adaptive distribution method based on the layered game model, from the power distribution perspective, a power control method based on the SteinKerberg game and the non-cooperative game and a power distribution algorithm based on the layered game are introduced to solve the power distribution problem in the 5G heterogeneous fusion network, so that the interference can be effectively reduced, the communication quality can be improved, and the overall performance of a communication system can be improved.
Drawings
FIG. 1 is a block diagram of the method of the present invention;
FIG. 2 is a schematic diagram of a three-tier heterogeneous network model according to the present invention;
FIG. 3 is a schematic diagram of power allocation technique classification according to an embodiment of the present invention;
fig. 4 is a flow chart of a power allocation algorithm of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
fig. 1 shows a block diagram of the method of the present invention, which includes the following four processes: constructing a system model by adopting the theoretical basis of game theory; obtaining the optimal transmitting power by adopting a power control method based on a SteinKerberg game and a non-cooperative game; the equilibrium solution of the game is obtained through analyzing the equilibrium solution of the layered game; and adopting a power distribution algorithm based on a layered game to obtain a converged power value and optimal pricing of each base station. The concrete expression is as follows: a three-layer heterogeneous Network model formed by a Radio Network Controller (RNC), a base station and base station users is established, the interference problem in a heterogeneous fusion Network is not ignored, the base station needs to improve the transmitting power for improving the self throughput, but more interference can be generated, so that the system performance is influenced, a layered game method is adopted and the interference problem is considered, the whole system is analyzed based on a Steckelberg game model, a cost function is set in a utility function of the base station, a stable state is achieved in a non-cooperative game mode, the RNC obtains pricing collected by the base station according to the transmitting power when the base station is in a balanced state, and the whole system achieves Steckelberg balance. Meanwhile, a power distribution algorithm is designed, the convergence is proved, the power distribution processing is realized, and the pricing of the RNC to the base station, the utility function of the base station and the like are obtained.
Each process is described in further detail below.
(1) Game theory-based three-layer heterogeneous fusion network model
Games can be divided into cooperative games and non-cooperative games, i.e. games are classified according to whether players in the game can achieve a consensus, i.e. a binding agreement. If the consensus can be achieved, it is a cooperative game, otherwise it is a non-cooperative game. The mutual cooperation process of people in the cooperative game key research bureau emphasizes the overall benefit, and the cooperation enables people in each bureau to obtain the own benefit so as to improve the overall benefit; in the non-cooperative game process, people in the game office can not reach a consensus, and the people in the game office adopt a corresponding strategy scheme by taking own benefits as a starting point, and the emphasis is on pursuing maximization of personal benefits.
The SteinKerberg game is a branch of a non-cooperative game, a person in a game in the game process can be divided into a Leader (Leader) and a Follower (Follower) according to the level sequence of the game, the SteinKerberg game is in a steady state of SteinKerberg game Equilibrium (SE, Stackelberg Equilibrium), the Leader moves in advance and then the Follower moves in the game, the SteinKerberg game can be regarded as a double-layer game process, the game high layer, namely the Leader grasps the game information of the Follower to select own strategy behaviors, and the Follower in the lower layer of the game selects a strategy suitable for the player after seeing the strategy taken by the Leader.
Fig. 2 is a schematic diagram of a three-layer heterogeneous network model according to the present invention, in which a three-layer heterogeneous convergence network model composed of a radio network controller RNC, a base station and a base station user is established, and the radio network controller allocates power to the base station, and then further allocates power to implement power allocation of a user terminal.
In a communication network, an Orthogonal Frequency Division Multiple Access (OFDMA) technology is adopted, base station users share one Frequency band for data transmission, and it is assumed that a sub-channel allocation work is completed in a system, and multiple users belonging to the same base station cannot simultaneously occupy one channel resource, so that the base station has only one active user in a certain specific time slot, and the active user transmits data information to the base station in the time slot.
There are N base stations, i being any base station and i ∈ {1,2,3 …, N }, i ═ 0 representing RNC. The received Signal To Interference and Noise Ratio (SINR) of the user served by the base station is:
Figure BDA0002794051800000051
wherein p isiRepresenting the transmission power, p, of base station ijRepresenting the transmit power, p, of base station j0Denotes the transmission power, h, of the RNCiiRepresenting the power gain, h, of the link channel of base station i with its usersi0Represents the interference link gain, h, between the RNC and base station iijRepresenting the interfering link gain, n, of base station i and user j0Representing noise interference of the RNC.
(2) Power control method based on Stenkerberg game and non-cooperative game
For the power allocation problem in the resource allocation problem in the 5G heterogeneous converged network, the following three allocation techniques are mainly used:
centralized power distribution: in the centralized allocation technology, a centralized control center is arranged for searching and storing relevant information in the aspects of channels, power, signal-to-noise ratio and the like, resources of a communication system, such as frequency spectrum resources, power resources and the like, are allocated through the centralized control center, the resource utilization and allocation problems of the whole network are reasonably analyzed and taken charge, and the benefit maximization of the system is realized on the basis of mutual cooperation of the centralized control center and user terminal equipment.
In the centralized power distribution process, a centralized control center needs to store and manage information provided by users in a unified manner, and then power resources of a system are distributed in a unified manner according to the obtained information, a large amount of information is needed in the process, and a user side needs to continuously interact with the centralized control center, so that a certain amount of basic equipment needs to be ensured to realize the functions of the centralized control center, but the centralized power distribution process is difficult to realize in an actual application scene, and is complex and tedious in process, so that a centralized power distribution method is rarely used in an actual communication system.
Distributed power allocation: the distributed power distribution process has no centralized control center, compared with the centralized power distribution technology, users do not need to provide and transmit own data information to the centralized control center, user terminals in the network system do not need to interact with other users, only the transmission rate of the users needs to be considered, the transmission power of the users needs to be improved for improving the transmission rate, the relevant theory of the game theory is usually applied for research, a model of mutual game among the users is constructed, the game is carried out by taking the transmission rate maximization as a game target, so that the stable state of the whole system is achieved, and the optimal performance of the user terminals can be realized. The distributed power allocation technique is simpler and less expensive than the centralized technique, and thus, the distributed power allocation technique is widely applied in practice.
Thirdly, semi-distributed power distribution: the centralized power distribution and the distributed power distribution are combined to form semi-distributed power distribution, the centralized control center and the base station perform unified centralized distribution processing, and then the base station realizes further power distribution on the respective managed areas.
The research of the power distribution problem is carried out based on a 5G heterogeneous fusion network model constructed by the power distribution technology of fig. 3, in the Stannberg game, an RNC serves as a game leader, a base station serves as a follower to make corresponding strategies according to the action of the RNC, and users obtain respective optimal strategies, namely optimal transmitting power, through a non-cooperative game method.
In order to reduce the interference to the user, the RNC prices the base station, if the pricing is too low, the power obtained by the base station is too much, interference can be generated on the RNC, the pricing of the RNC can be improved for the effectiveness and benefits of the RNC, the power obtained by the base station can be correspondingly reduced, the pricing of the RNC and the power of the base station are mutually influenced to jointly form a SteinKelberg game, the base station can select the optimal transmitting power of the base station according to the pricing of the RNC, Nash balance can be achieved among users through a non-cooperative game, the optimal transmitting power is obtained, then the obtained optimal transmitting power is utilized to conduct the research of the optimal pricing of the RNC, at the moment, the whole system achieves the SteinKerberg balance, the set of the optimal pricing and the optimal transmitting power is the balanced solution of the SteinKerberg game, at the moment, the game parties can not continuously increase own benefits by changing own strategies, and the game achieves a stable state.
Stenkberg game between RNC and base station
In a given time slot, the pricing of the RNC to the unit power of the base station i is set as lambdaiThe transmission bandwidth of base station i is wiThen the link transmission rate of base station i can be expressed as:
Figure BDA0002794051800000061
let the utility function of base station i be UiIt can be expressed as:
Figure BDA0002794051800000062
the utility function of the base station consists of two parts, wherein the first part is a gain function of a user in a logarithmic form based on the signal-to-noise ratio, the second part is a cost function set by the RNC for the power of the base station, and the utility function is the difference between the two parts.
Meanwhile, RNC sets reasonable pricing to reduce interference to users, and sets utility function of RNC as URNCIt can be expressed as:
Figure BDA0002794051800000071
wherein h is0iThe interfering link gain for base station i to the user.
In summary, the optimization problem of the RNC can be expressed as:
Figure BDA0002794051800000072
wherein,
Figure BDA0002794051800000073
the upper and lower bounds of the link transmission rate are respectively used to ensure the Quality of Service (QoS) when the base station i and the user perform data transmission.
The optimization problem for a base station can be expressed as:
Figure BDA0002794051800000074
the formulas (5) and (6) jointly form a Stannberg game process, the RNC prices the power of the base station under the condition that the optimal strategy of the base station is mastered, the base station takes corresponding strategy action after observing the behavior of the RNC, namely pricing, and adjusts the self-emission power to maximize the self-benefit, and the Stannberg balance in the process is defined as follows:
λ*for the optimal pricing set of the RNC,
Figure BDA0002794051800000075
and if the optimal transmission power strategy set of the base station i meets the following conditions:
URNC(λ*,p*)≥URNC(λ,p*) (7)
Figure BDA0002794051800000076
(λ*，
Figure BDA0002794051800000077
) Is an equilibrium solution to the above-described stan-kerberg gaming process.
② non-cooperative gaming between users
For the solution of the equilibrium point of the SteinKerberg game, a backward method can be adopted, the NE is achieved among the given pricing users in a non-cooperative game mode, the optimal transmitting power of the users is obtained, namely, the formula (6) is solved, then the result is substituted into the formula (5), the optimization problem of the RNC is solved, and finally the whole system reaches SE.
(3) Analyzing the equilibrium solution of the layered game to obtain the equilibrium solution of the SteinKelberg game
When the optimization problem is solved, firstly, an equilibrium solution when the user non-cooperative game reaches Nash equilibrium is solved by utilizing a back-stepping method, namely, the optimal transmitting power is solved, the existence and the uniqueness of the solved equilibrium solution are proved, next, the solved optimal transmitting power is written into a matrix form and substituted into a utility function of the RNC for simplification, the relation between the utility function and pricing is further researched, the optimization problem is further simplified, the optimal pricing of the RNC is solved when the system model reaches Steinklerberg equilibrium, and the solved optimal transmitting power and the optimal pricing form the equilibrium solution of the Steinklerberg game.
Analysis of Nash equilibrium solution in non-cooperative game
For a given pricing, equation (6) has an optimal solution, i.e., the optimal transmit power of the base station is:
Figure BDA0002794051800000081
since the power value is not negative, when data is not transmitted, the power value is 0, so that the following form can be written:
Figure BDA0002794051800000082
wherein (a)+Representing max a, 0.
The following was demonstrated:
the first derivative is obtained by applying equation (3):
Figure BDA0002794051800000083
the second derivative is obtained by applying equation (3):
Figure BDA0002794051800000084
let the first derivative be 0, get:
Figure BDA0002794051800000085
the optimal transmission power of the base station can be obtained by equation (13):
Figure BDA0002794051800000086
for a given time slot when
Figure BDA0002794051800000087
Then, the obtained value is substituted into formula (3) to obtain lambdaiThe upper bound of (A) is:
Figure BDA0002794051800000088
theorem 1 is: when in use
Figure BDA0002794051800000091
Then, the Nash equilibrium that the non-cooperative game among the users achieves exists, and the Nash equilibrium solution can be expressed as:
p*＝H-1m (16)
wherein,
Figure BDA0002794051800000092
Figure BDA0002794051800000093
the following was demonstrated:
for Nash equilibrium of non-cooperative game, the existence of equilibrium solution thereof needs to satisfy that p is non-empty convex set and UiA continuous convex function with respect to p.
For the first condition, p should satisfy p ∈ { p ∈ }min，pmaxAnd p isminAnd if the power is not less than 0, each base station can obtain the distributed power, so that the p is known to be a non-empty set and meets the first condition.
For the second condition, according to the utility function U of base station iiThe formula given is relative to piAs a continuous function, U is known from the formula (12)iRelative to piIs less than 0, UiRelative to piThe second condition is satisfied for a continuous convex function.
In conclusion, the nash equilibrium point is proved to exist.
For lambda within the range of conditionsiEquation (10) can be developed:
Figure BDA0002794051800000094
write it in matrix form:
Hp*＝m (20)
formula (20) further provides formula (16).
Analysis of Stenkerberg equilibrium solutions
Substituting the obtained optimal transmitting power into the optimization problem of the RNC to obtain:
Figure BDA0002794051800000095
because the base stations are very densely distributed in the 5G heterogeneous convergence network, the interference link gain from any one base station to other base station users is the same, and the interference fading from the base station i to the base station user j is much smaller than the fading from the base station j to the base station user j, h can be reducedijConsidering a constant h, the utility function (21) of the RNC can be expressed as:
Figure BDA0002794051800000101
theorem 2 is URNC(λi) Is aboutiIs a monotonically increasing function ofiA convex function of (a).
The following was demonstrated:
h is to beijTaken as a constant h, and hii>>H, the link gain matrix H can be written as follows:
Figure BDA0002794051800000102
wherein, due to hii>>hijH, let:
Figure BDA0002794051800000103
solving an inverse matrix of H according to the existing method to obtain:
Figure BDA0002794051800000104
wherein,
Figure BDA0002794051800000105
due to the fact that
Figure BDA0002794051800000111
So alphaiαj0, then H-1The following can continue to be written:
Figure BDA0002794051800000112
the obtained H-1Substituting formula (21) to obtain:
Figure BDA0002794051800000113
the first derivative is obtained by applying equation (28):
Figure BDA0002794051800000114
u is shown by formula (29)RNC(λi) Is aboutiIs a monotonically increasing function of.
The second derivative is calculated for equation (28):
Figure BDA0002794051800000115
u is shown by the formula (30)RNC(λi) Is aboutiA convex function of (a).
The optimization problem of the RNC can be simplified as follows according to theorem 2:
Figure BDA0002794051800000116
Figure BDA0002794051800000117
that is, the solution of the optimization problem of the RNC can be simplified to the solution formula (31), the optimal pricing λ of the RNC*Comprises the following steps:
Figure BDA0002794051800000118
as is apparent from the formulae (10) and (32), (p)i(λ*),λ*) Is an equilibrium solution to the Stanckreberg game.
(4) And adopting a power distribution algorithm based on a layered game to obtain a converged power value and optimal pricing of each base station.
An iteration function is set, based on the power of the iteration function, the power can be gradually converged to an equilibrium point, the system reaches a stable state, and the iteration function is as follows:
Figure BDA0002794051800000121
theorem 3 is a standard function, and satisfies positive qualitative, monotonous and measurable properties.
The following was demonstrated:
positive qualitative: power value is not negative, i (p) > 0.
Monotonicity:
according to formula (16):
Figure BDA0002794051800000122
the first derivative is taken from equation (34):
Figure BDA0002794051800000123
from formula (35) it follows that I (p) is
Figure BDA0002794051800000124
Is aboutiIs a monotonically decreasing function of (a).
Testability:
according to the variant of formula (14):
Figure BDA0002794051800000125
for any beta is more than or equal to 1, there are
Figure BDA0002794051800000131
For any beta.gtoreq.1, beta I (p) -I (beta p) >0, I (p) is measurable.
The convergence of the power allocation algorithm can be proved by theorem 3, and table 1 is an algorithm pseudo code table.
TABLE 1 Algorithm pseudocode Table
Figure BDA0002794051800000132
The algorithm adopts a Steckelberg game model, an RNC serves as a game leader, a base station serves as a follower, and the algorithm mainly comprises the following steps:
firstly, the RNC calculates the pricing of each base station according to the initial transmitting power of the base station, and broadcasts the obtained pricing to the corresponding base station through the RNC;
secondly, the base station adjusts the self transmitting power according to the iterative formula after receiving the pricing;
and thirdly, setting iteration times to obtain the optimal transmitting power of each base station and the optimal pricing of the RNC to each base station.
According to the power allocation algorithm shown in the algorithm flow chart of fig. 4, the base station receives the pricing lambda of the RNCiThen carrying out power iteration to converge to the optimal transmitting power
Figure BDA0002794051800000141
And then the RNC updates self pricing according to the converged power value and obtains optimal pricing, and the obtained optimal pricing of the RNC and the optimal transmitting power of the base station jointly form a balanced solution of the game.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (1)

1. A power self-adaptive distribution method based on a layered game model is characterized by comprising the following steps:
(1) in a 5G heterogeneous convergence network area, a three-layer heterogeneous convergence network model consisting of an RNC (radio network controller), a base station and base station users is constructed by adopting the theoretical basis of a game theory;
(2) obtaining optimal transmitting power by adopting a power control method based on a Steckelberg game and a non-cooperative game;
(3) the equilibrium solution of the SteinKerberg game is obtained through analyzing the equilibrium solution of the layered game;
(4) adopting a power distribution algorithm based on a layered game to obtain a converged power value and optimal pricing of each base station;
in the step (2), a SteinKelberg game is adopted between the RNC and the base station, the RNC is a game leader, and the base station is a follower; obtaining respective optimal transmitting power among base station users by adopting a non-cooperative game;
the specific process of the Stenkerberg game is as follows:
in a given time slot, the RNC prices the unit power of the base station i to be lambdaiThe transmission bandwidth of base station i is wiThen, the link transmission rate of the base station i is as follows:
Figure FDA0003496908400000011
wherein p isiRepresenting the transmission power, p, of base station ijIndicating a base stationTransmission power of j, p0Denotes the transmission power, h, of the RNCiiRepresenting the power gain, h, of the link channel of base station i with its usersi0Represents the interference link gain, h, between the RNC and base station iijRepresenting the interference link gain of a base station i and a user j, wherein N is the total number of the base stations, i is any base station and belongs to {1,2,3 …, N };
utility function U of base station iiThe following were used:
Figure FDA0003496908400000012
utility function U of RNCRNCThe following were used:
Figure FDA0003496908400000013
wherein h is0iThe interference link gain of the base station i to the base station user is obtained;
in summary, the optimization problem of the RNC is as follows:
Figure FDA0003496908400000014
wherein,
Figure FDA0003496908400000015
the upper and lower bounds of the link transmission rate are respectively;
the optimization problem of the base station is as follows:
Figure FDA0003496908400000021
the formulas (5) and (6) jointly form a Stannkralberg game process, the RNC prices the power of the base station under the condition that the optimal strategy of the base station is mastered, and the base station takes corresponding strategy action by observing the pricing of the RNC to adjust the self transmitting power;
the non-cooperative game process among the base station users is to solve the formula (6), then the result is substituted into the formula (5), the optimization problem of the RNC is solved, and finally the whole system reaches SteinKelberg equilibrium;
wherein the equalization solution when the Stanckberg game equalization is achieved
Figure FDA0003496908400000022
The following conditions are satisfied:
URNC(λ*,p*)≥URNC(λ,p*) (7)
Figure FDA0003496908400000023
wherein λ is*The optimal pricing set of the RNC is p, the optimal transmitting power strategy set of the RNC is p, the pricing of the RNC to the unit power of the base station is lambda,
Figure FDA0003496908400000024
for the optimal pricing set of base station i,
Figure FDA0003496908400000025
setting an optimal transmission power strategy set for a base station i;
the specific process of the step (3) is as follows:
firstly, the optimal transmitting power when the base station user non-cooperative game reaches Nash equilibrium is solved by utilizing a back-stepping method, and the specific process is as follows:
for a given pricing, equation (6) has an optimal solution, i.e., the optimal transmit power of the base station, as follows:
Figure FDA0003496908400000026
wherein (a)+Max { a,0 };
secondly, writing the obtained optimal transmitting power into a matrix form, and substituting the matrix form into a utility function of the RNC for simplification;
and finally, researching the relation between the utility function and the pricing, further simplifying the optimization problem, and solving the optimal pricing of the RNC when the system model reaches SteinKelberg equilibrium, wherein the optimal pricing of the RNC is lambda*The following were used:
Figure FDA0003496908400000027
wherein,
Figure FDA0003496908400000028
is λiUpper bound of (1), n0Noise interference for RNC;
the optimal transmission power and optimal pricing obtained from equations (10) and (32) form the equilibrium solution (p) of the Stanckberg gamei(λ*),λ*)；
The specific process of the step (4) is as follows:
firstly, the RNC calculates the pricing of each base station according to the initial transmitting power of the base station, and broadcasts the obtained pricing to the corresponding base station through the RNC;
secondly, the base station adjusts the self transmitting power according to the iterative function after receiving the pricing,
the iteration function is as follows:
Figure FDA0003496908400000031
and finally, setting iteration times to obtain the optimal transmitting power of each base station and the optimal pricing of the RNC to each base station.
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