CN111194043B - Power distribution method based on non-perfect serial interference elimination - Google Patents
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Abstract
The invention belongs to the technical field of communication, and particularly relates to a power distribution method based on non-perfect serial interference elimination, which comprises the following steps: the base station sets the price of unit power and sends the set price to the user terminal; the user side determines the power quantity purchased from the base station according to the price set by the base station and sends the purchased power quantity to the base station; the base station readjusts the updated price according to the power purchase amount of the user side; the base station and the users play games continuously until the power price of the base station and the power purchase amount of the users reach a balanced state; obtaining the balanced user power and finishing the power distribution; the invention adopts the power distribution method of the imperfect serial interference elimination on the premise of ensuring the service quality and the user fairness, so that the algorithm is simpler and more accurate.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a power distribution method based on non-perfect serial interference elimination.
Background
With the development of mobile communication technology, a simple voice service has been expanded to a mobile internet service. Due to the rapid development of the internet of things, the mobile traffic is exponentially increased. The spectrum efficiency and access-allowed users of conventional orthogonal multiple access are limited and this explosive user growth has not been met. Different from the orthogonal multiple access method, the non-orthogonal multiple access method can superpose and multiplex a plurality of users in the same frequency band, and eliminate the Interference caused by other users through a Successive Interference Cancellation (SIC) technology. A Non-Orthogonal Multiple Access (NOMA) technology is one of the 5G (5th-Generation) key technologies, and can meet the requirements of low delay, high reliability, mass Access and the like in the age of 5G internet of things.
Currently, a Multiple-Input Multiple-Output (MIMO) technology is a hot spot of recent research, and is used in 4G (4th-Generation) to improve the spectral efficiency of a communication system, and is a key technology of 4G, and also appears as a key technology in 5G. For example, patent application No. CN201811267625.9, "interference suppression based multi-cell MIMO-NOMA optimal power allocation method" discloses: constructing a multi-cell MIMO-NOMA system model; eliminating cell interference through an interference technology to obtain a mathematical model of power distribution; constructing a tight lower bound coefficient and corresponding substitution, and converting the original power distribution problem into a convex optimization problem; and (5) solving the optimal power through iteration. The method enables the system to transmit data more quickly.
However, the method adopts the power distribution algorithm of the convex difference planning when the optimal power is obtained, and the algorithm has large calculation amount and complex calculation process and is not beneficial to data transmission.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a power allocation method based on non-perfect serial interference cancellation, which includes: the base station sets the price of unit power and sends the set price to the user terminal; the user side determines the power quantity purchased from the base station according to the price set by the base station and sends the purchased power quantity to the base station; the base station readjusts the updated price according to the power purchase amount of the user side; the base station and the users play games continuously until the power price of the base station and the power purchase amount of the users reach a balanced state; obtaining the balanced user power and finishing the power distribution;
the amount of power purchased by the user side includes: the base station acquires effective channel gain of users, and a system throughput maximization model is constructed according to the signal-to-interference-and-noise ratio and the Shannon formula of each user; according to the connection relation between a user side and a base station, a plurality of one-master-one-slave Steckelberg game models are constructed, the user is defined as a buyer, and the base station is defined as a seller; determining power limit of users, maximum power constraint of the system, fairness constraint among users and user service quality constraint conditions according to the system throughput maximization model to obtain a utility optimization model of a buyer; calculating a utility optimization model of the buyer by adopting a Lagrange multiplier method and a sub-gradient iteration method, and obtaining the purchased power quantity of the user side according to the utility optimization model;
the base station sets a price per unit power: obtaining a utility function of a seller according to the power price and the cost of selling unit power of the base station, and constructing a utility optimization model of the seller according to the maximized utility function; and calculating the price of the unit power according to the utility optimization model.
Preferably, the system throughput maximization model is as follows:
preferably, the system is a MIMO-NOMA system, the number of base station antennas in the system is M1, the number of user antennas is N, and N is more than or equal to M1; the users are divided into M clusters, each cluster has L users, and the number of users in a cell is G (M multiplied by L); each cluster of users uses a non-orthogonal multiple access technique.
Further, the transmission signal at the base station is:
preferably, the Stanckreberg gaming model comprises:
each user side purchases power from the base station according to the price set by the base station, and the utility function of the buyer is as follows:
wherein λ ism,lFor the base station to the UEm,lA price at which the user sells power;
the base station sells power to each user terminal, and the utility function of the seller is as follows: u shapeBS m,l＝(λm,l-cm,l)pm,l。
Preferably, the utility optimization model of the buyer is as follows:
Subject to:
preferably, the utility optimization model of the seller obtained according to the seller maximized self utility function is as follows:
preferably, the optimal purchasing strategy of the user comprises:
the utility maximization problem of the buyer is as follows:
lagrange function pair pm,lThe derivation can be:
order to
Solve to obtain UEm,lThe optimum power of (2):
θm,l＝um,l+ωm,l+βm,l-γm,l
preferably, the process of obtaining the purchased power amount of the user terminal includes:
and bringing the optimal power solution into the optimal problem of the seller to obtain the optimal problem solution of the seller:
lambda to seller's optimal problem solutionm,lAnd (5) derivation to obtain:
order to
Obtaining the optimal price:
preferably, the process of gaming between the base station and the user comprises: the base station sets unit power price and sells power to each user, and each user purchases power from the base station according to the price set by the base station so as to maximize the benefit of the user; the user makes a strategy according to the optimal price
Calculating the power price at the moment, and substituting the result into the optimal power purchase amount pm,l *And updating the amount of power purchased by the user, and continuously circulating the process until the power and the price reach balance.
According to the invention, SIC residue is considered in the MIMO-NOMA system, the algorithm can adjust the power price and the power distribution value of a user along with the size of SIC residue factors, so that the result is closer to the optimal power; according to the invention, a plurality of Stanckrebs game models with one master and one slave are established in MIMO-NOMA, so that the throughput performance of the invention is more excellent on the premise of ensuring the service quality and the user fairness, and the algorithm complexity is lower than that of a power distribution algorithm based on the convex difference planning.
Drawings
FIG. 1 is a downlink MIMO-NOMA system model of the present invention;
FIG. 2 is a flow chart of a throughput-optimized power allocation algorithm based on game theory according to the present invention;
FIG. 3 is a comparison of algorithm complexity of the proposed algorithm and power allocation based on convex difference planning;
FIG. 4 is a graph of system throughput versus total base station power for the present invention;
fig. 5 is a comparison of throughput of the proposed algorithm and power allocation based on the convex difference program.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, and the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
The invention relates to a power distribution method based on non-perfect serial interference cancellation, as shown in fig. 2, comprising:
the base station sets the price of unit power and sends the set price to the user terminal; the user side determines the power quantity purchased from the base station according to the price set by the base station and sends the purchased power quantity to the base station; the base station readjusts the updated price according to the power purchase amount of the user side; the base station and the users play games continuously until the power price of the base station and the power purchase amount of the users reach a balanced state; obtaining the balanced user power and finishing the power distribution;
the amount of power purchased by the user side includes: the base station acquires effective channel gain of users, and a system throughput maximization model is constructed according to the signal-to-interference-and-noise ratio and the Shannon formula of each user; according to the connection relation between a user side and a base station, a plurality of one-master-one-slave Steckelberg game models are constructed, the user is defined as a buyer, and the base station is defined as a seller; determining power limit of users, maximum power constraint of the system, fairness constraint among users and user service quality constraint conditions according to the system throughput maximization model to obtain a utility optimization model of a buyer; calculating a utility optimization model of the buyer by adopting a Lagrange multiplier method and a sub-gradient iteration method, and obtaining the purchased power quantity of the user side according to the utility optimization model;
the base station sets a price per unit power: obtaining a utility function of a seller according to the power price and the cost of selling unit power of the base station, and constructing a utility optimization model of the seller according to the maximized utility function; and calculating the price of the unit power according to the utility optimization model.
As shown in FIG. 1, in the embodiment of the present invention, it is considered that in the MIMO-NOMA network, the number of base station antennas is M1, and the total power of the base station is PtotThere are G users in the cell, the number of antennas of each user is N (N ≧ M1), and if users are already divided into M clusters, and each cluster has L users, then G is mxl. In thatIn the MIMO-NOMA network, each cluster of users uses a non-orthogonal multiple access technology, that is, all users are sent by superposition at a base station, and a serial interference cancellation technology is used at a receiving end to perform multi-user detection so as to cancel interference brought by other users in the same cluster. The transmitted signals at the base station are:
wherein,
superimposed signals for mth cluster of users, pm，lRepresenting the power value, S, allocated by the base station to the ith user in the mth clusterm，lTransmitting symbol, S, representing the l-th user in the m-th clusterMA superimposed signal representing the mth cluster of users.
Marking the ith user in the mth cluster as UEm，l，UEm，lThe received signal is represented as:
wherein,
representing a user UEm，lBy conjugate transpose of the detection matrix, ym，lIndicating a matrix of signals received at the receiving end without user detection, Hm，lRepresenting a UEm，lChannel gain with the base station, C denotes a precoding matrix used by the base station, S denotes a transmission signal of the base station, n denotes a Gaussian white noise vector, CmRepresents the m-th column, S, of the precoding matrix CmSuperimposed signal representing mth cluster of users, cjRepresents the jth column, S, of the precoding matrix CjA superimposed signal representing the j-th cluster of users,
indicating the base station as the mth clusterThe power value allocated by the ith user in (1),
indicating the power value allocated by the base station to the kth user in the mth cluster.
If order
The interference of the signals sent by other clusters to the signal of the cluster can be eliminated theoretically.
The desired signal may be obtained by successive interference cancellation techniques and signal detection techniques. Suppose that the effective channel gain ordering of the mth cluster of users at the receiving end is:
at the receiving end, using successive interference cancellation techniques, let η bem，l(0≤ηm，lLess than or equal to 1) is UEm，lSuccessive interference residual coefficient in mth cluster, representing UEm，lOf series interference cancellation capability, etam，lWhen the value is 0, it indicates that the receiving end is ideal for serial interference cancellation. Then the UE is subjected to successive interference cancellationm，lThe received signal may be expressed as:
UE after serial interference eliminationm，lThe signal to interference plus noise ratio (SINR) of (1) can be expressed as:
wherein, the SINRm，lRepresenting a user UEm，lSignal to interference plus noise ratio (SINR).
Order to
Then by shannonFormula-derived UEm，lThe rates of (a) and (b) are:
the result of the above equation calculation is the throughput per unit spectrum (1 Hz). The total throughput of all users in the system can be expressed as:
the system power is evenly distributed among the users in each cluster, and the total power distributed to the users in each cluster by the base station is Ptot/M。
The system throughput maximization model is as follows:
wherein M represents total user clusteringNumber ofL denotes the number of users per cluster, Rm，lRepresenting a user UEm，lThroughput of pm，lIndicating the l user UE in the m cluster of the base stationm，lThe value of the power to be allocated is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm，lDenotes the channel gain of the i-th user in the i-th cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm，kIndicating the k-th user UE in the m-th cluster of the base stationm，kAssigned power value, ηm，lRepresenting a user UEm，lSuccessive interference residual coefficient, p, in mth clusterm，iIndicating the ith user UE in the mth cluster of the base stationm，iValue of the power allocated, δ2Representing the variance value of gaussian white noise.
To solve the throughput optimization problem of the present invention, a power allocation strategy based on throughput optimization is given below:
the process of constructing the SteinKerberg game model includes: the users in the cell are defined as buyers (slaves), the base station is defined as sellers (masters), the base station sets unit power price and sells power to each user, and each user purchases power from the base station according to the price set by the base station so as to maximize the benefit of the user.
The utility optimization model of the buyer is as follows:
wherein, Um，lRepresenting a user UEm，lThe utility function of (a) is determined,
representing a user UEm，lThe equivalent channel gain of (a) is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm，lDenotes the channel gain of the ith user in the mth cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm，lIndicating the l user UE in the m cluster of the base stationm，lAssigned power value, hm，lIndicating the base station and the l user UE in the m clusterm，lEquivalent channel gain, p, betweenm，kIndicating the k-th user UE in the m-th cluster of the base stationm，kAssigned power value, pm，iIndicating the ith user UE in the mth cluster of the base stationm，iAssigned power value, ηm，lRepresenting a UEm，lSuccessive interference cancellation residual coefficient of (d)2Representing the variance value, λ, of Gaussian white noisem，lFor the base station to the UEm，lThe price at which the user sells power.
Subject to：
Wherein, Um，lRepresenting a user UEm，lThe utility function of (a) is determined,
representing a user UEm，lThe equivalent channel gain of (a) is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm，lDenotes the channel gain of the ith user in the mth cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm，lIndicating the l user UE in the m cluster of the base stationm，lAssigned power value, hm，lIndicating the base station and the l user UE in the m clusterm，lEquivalent channel gain, p, betweenm，kIndicating the k-th user UE in the m-th cluster of the base stationm，kAssigned power value, pm，iIndicating the ith user UE in the mth cluster of the base stationm，iAssigned power value, ηm，lRepresenting a UEm，lSuccessive interference cancellation residual coefficient of (d)2Representing the variance value, λ, of Gaussian white noisem，lFor the base station to the UEm，lPrice of power sold by user, M represents number label of user clustering number, L represents number label of user number, M represents total number of user clustering, L represents number of user in each cluster, p represents total number of user clusteringm，kIndicates the mth cluster of base stationk User Equipments (UEs)m，kAssigned power value, Rm，lRepresenting a user UEm，lThroughput of ROMAFor the throughput, P, of this user in an orthogonal multiple access system under the constraint of the total power of the same systemtotFor the total power value of the base station, G represents the total number of users in the system, delta2Representing the variance value of Gaussian white noise, wherein the constraint condition C1 represents that the power distribution value of a single user must be greater than 0, the constraint condition C2 represents the total power constraint of a base station, the constraint conditions C3 and C4 represent the fairness constraint among users, and C5 represents the service quality requirement of the users.
Constraint C1 indicates that the power allocation value of a single user must be greater than 0, constraint C2 indicates the total power constraint of the base station, constraints C3 and C4 are the fairness constraints among users, and constraint C5 is the quality of service requirement of the user.
The utility model for the seller is:
wherein, UBS m，lIndicating that the base station is towards the user UEm，lUtility function of sales power, λm，lIndicating base station to user UEm，lPrice of sold power, cm，lIndicating base station to UEm，lCost per unit of power sold, pm，lIndicating the base station as the l user UE in the m clusterm，lThe assigned power value.
The optimal purchasing strategy of the user comprises the following steps:
the invention adopts a Lagrange multiplier method to solve the optimization problem of the buyer, constructs a Lagrange function for the utility function of the buyer, and converts the utility maximization problem of the buyer into the following problems:
lagrange function pair pm，lThe derivation can be:
order to
Solve to obtain UEm，lThe optimum power of (2):
wherein L ism，lRepresenting a user UEm，lLagrangian functions with utility function under constraint,
representing a user UEm，lThe equivalent channel gain of (a) is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm，lDenotes the channel gain of the ith user in the mth cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm，lIndicating the l user UE in the m cluster of the base stationm，lAssigned power value, hm，lIndicating the base station and the l user UE in the m clusterm，lEquivalent channel gain, p, betweenm，kIndicating the k-th user UE in the m-th cluster of the base stationm，kAssigned power value, pm，iIndicating the ith user UE in the mth cluster of the base stationm，iAssigned power value, ηm，lRepresenting a UEm，lSuccessive interference cancellation residual coefficient of (d)2Representing the variance value, λ, of Gaussian white noisem，lFor the base station to the UEm，lPrice of power sold by the user, um，lLagrange multiplier, P, representing constraint C2totFor the base station total power value, ωm，lLagrange multiplier, β, representing constraint C3m，lLagrange multiplier, gamma, representing constraint C4m，lLagrange multiplier representing constraint C5, G representing the systemThe number of the total number of users in the house,
lagrange function pair p representing user utility functionm，lDerivative, thetam，lRepresents um，l+ωm，l+βm，l-γm，l，pm，l *Representing a user UEm，lOf the optimum power value, λm，lIndicating base station to UEm，lThe price at which the user sells power.
The process of finding the optimal purchasing strategy of the user comprises the following steps:
substituting the optimal power solution into the seller optimization problem, and obtaining the seller optimization problem as follows:
UBS m，lfor lambdam，lTaking the derivative, we can get:
order to
Solving to obtain an optimal price:
wherein, UBS m，lIndicating base station to UEm，lA utility function ofm，lIndicating the base station as a UEm，lPrice per unit power set, cm，lIndicating base station to UEm，lCost per unit of power sold, pm，l *Representing a UEm，lThe optimum value of the power,
lagrange function pair lambda representing base station utility functionm，lDerivative, thetam，lFor a determined value um，l+ωm，l+βm，l-γm，l，hm，lRepresenting a UEm，lEffective channel gain of pm，kRepresents the power, η, of the kth user in the mth clusterm，lRepresenting a UEm，lSerial interference cancellation residual coefficient of (p)m，iRepresents the power of the ith user in the mth cluster,
representing a UEm，lBy conjugate transposing of the channel detection matrix, delta2Represents the variance of white gaussian noise and,
indicating the base station as a UEm，lThe set optimal price.
The process of gaming between the base station and the user comprises the following steps: the base station sets unit power price and sells power to each user, and each user purchases power from the base station according to the price set by the base station so as to maximize the benefit of the user. Assume quoted secondary cost c of base stationm，lInitially, the user's power purchase amount pm，lStarting from 0, a strategy is firstly made according to the optimal price
Calculating the power price at the moment, and substituting the result into the optimal power purchase amount pm，l *And updating the amount of power purchased by the user, and continuously circulating the process until the power and the price reach balance.
Assuming that the number of user clusters is M and the number of users per cluster is L, the total number G of users in the cell is mxl. In the algorithm provided by the invention, each user determines the optimal power distribution strategy according to the price of the unit power set by the base station, and in each cycle, one user responds based on the price set by the base station, and the optimal power distribution strategy at the moment is obtained by 1-time calculation. By taking into account the worst case of the proposed power allocation algorithmTo analyze its computational complexity. Assuming that all users still do not reach equilibrium state when the algorithm reaches the maximum iteration number in the worst case, K × M × I is performedmaxI.e. GxImaxAnd (5) secondary calculation. So when the maximum iteration number of the algorithm is ImaxThe time complexity of the algorithm is O (G × I)max). For the power distribution algorithm based on the convex difference planning, when the maximum iteration number is NmaxWhen the time complexity is O (N)max×G3)。
As shown in FIG. 3, when N ismax＝Imax30, time complexity comparison of the two algorithms is carried out, and complexity analysis shows that the complexity of the distributed power allocation algorithm based on the Steckelberg game is obviously lower than that of a power allocation strategy based on a convex difference program.
In order to further illustrate that the performance of the power allocation algorithm based on the game theory in the MIMO-NOMA network is better than that of the fractional order power allocation algorithm, the power allocation algorithm of the invention is subjected to simulation verification.
As shown in fig. 4, the simulation parameters are set as follows: base station antenna number M is 2, user antenna number N is 2, cell radius R is 500M, and minimum distance d between user and base stationminThe number of users in the cell is 8 at 50m, the users are randomly distributed in the cell, and the channel noise power is-70 dBm. The channel estimation is ideal, the path loss exponent is 3, the total power range of the base station is 24dBm to 40dBm, and the successive interference cancellation residue is η 0.001 and η 0.002, respectively. Simulation results show that the performance of the power distribution algorithm is superior to that of a fractional order power distribution algorithm. Under the condition that the total power of the base station is the same, the total throughput of the system of the algorithm is always higher than that of a fractional order power allocation algorithm, and the total rate of the system is increased with the increase of the total power of the system, but the increasing speed is gradually slowed down, because for the algorithm provided by the invention, the power allocated to the user by the base station does not increase without limit with the increase of the total power of the system.
As shown in fig. 5, when the total number of users in a cell is set to 8, the performance of the algorithm provided by the present invention in terms of the total system throughput is compared with the power allocation algorithm based on the convex difference planning. Simulation results show that the total system rate of the power distribution algorithm based on the convex difference planning is slightly higher than that of the algorithm provided by the invention, and the complexity of the algorithm is reduced on the basis of performance similar to that of the power distribution algorithm based on the convex difference planning.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by instructions associated with hardware via a program, which may be stored in a computer-readable storage medium, and the storage medium may include: ROM, RAM, magnetic or optical disks, and the like.
The above-mentioned embodiments, which further illustrate the objects, technical solutions and advantages of the present invention, should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. A power allocation method based on imperfect serial interference cancellation is characterized by comprising the following steps:
the base station sets the price of unit power and sends the set price to the user terminal; the user side determines the power quantity purchased from the base station according to the price set by the base station and sends the purchased power quantity to the base station; the base station readjusts the updated price according to the power purchase amount of the user side; the base station and the users play games continuously until the power price of the base station and the power purchase amount of the users reach a balanced state; obtaining the balanced user power and finishing the power distribution;
the amount of power purchased by the user side includes: the base station acquires effective channel gain of users, and a system throughput maximization model is constructed according to the signal-to-interference-and-noise ratio and the Shannon formula of each user; according to the connection relation between a user side and a base station, a plurality of one-master-one-slave Steckelberg game models are constructed, the user is defined as a buyer, and the base station is defined as a seller; determining power limit of users, maximum power constraint of the system, fairness constraint among users and user service quality constraint conditions according to the system throughput maximization model to obtain a utility optimization model of a buyer; calculating a utility optimization model of the buyer by adopting a Lagrange multiplier method and a sub-gradient iteration method, and obtaining the purchased power quantity of the user side according to the utility optimization model;
the base station setting the price of unit power includes: obtaining a utility function of a seller according to the power price and the cost of selling unit power of the base station, and constructing a utility optimization model of the seller according to the maximized utility function; calculating a unit power price according to the utility optimization model;
the system throughput maximization model is as follows:
wherein M represents the total number of user clusters, L represents the number of users per cluster, and Rm,lRepresenting a user UEm,lThroughput of pm,lIndicating the l user UE in the m cluster of the base stationm,lThe value of the power to be allocated is,
denotes the conjugate transpose of the detection matrix used by the receiving end, denotes the channel gain of the l-th user in the m-th cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm,kIndicating the k-th user UE in the m-th cluster of the base stationm,kAssigned power value, ηm.lRepresenting a user UEm,lSuccessive interference residual coefficient, p, in mth clusterm,iIndicating the ith user UE in the mth cluster of the base stationm,iValue of the power allocated, δ2A variance value representing white gaussian noise;
the Stanckreberg gaming model includes: each user side purchases power from the base station according to the price set by the base station, and the utility function of the buyer is as follows:
wherein, Um,lRepresenting a user UEm,lThe utility function of (a) is determined,
representing a user UEm,lThe equivalent channel gain of (a) is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm.lDenotes the channel gain of the ith user in the mth cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm,lIndicating the base station as the l user UE in the m clusterm,lAssigned power value, hm,lIndicating the base station and the l user UE in the m clusterm,lEquivalent channel gain, p, betweenm,kIndicating the base station as the k user UE in the m clusterm,kAssigned power value, pm,iIndicating the base station as the ith user UE in the mth clusterm,kAssigned power value, ηm,lRepresenting a user UEm,lResidual coefficient of successive interference, δ, at mth cluster2Representing the variance value, λ, of Gaussian white noisem,lFor the base station to the UEm,lA price at which the user sells power;
the base station sells power to each user terminal, and the utility function of the seller is as follows:
UBS m,l＝(λm,l-cm,l)pm,l
wherein, UBS m,lIndicating base station to user UEm,lUtility function of sales power, pm,lIndicating the base station as the l user UE in the m clusterm,lAssigned power value, cm,lIndicating base station to UEm,lCost of selling unit power; the utility optimization model of the buyer is as follows:
Subject to:
C1:
C2:
C3:
C4:
wherein, Um,lRepresenting a user UEm,lThe utility function of (a) is determined,
representing a user UEm,lThe equivalent channel gain of (a) is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm.lDenotes the channel gain of the ith user in the mth cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm,lIndicating the base station as the l user UE in the m clusterm,lAssigned power value, hm,lIndicating the base station and the l user UE in the m clusterm,lEquivalent channel gain, p, betweenm,kIndicating the base station as the k user UE in the m clusterm,kAssigned power value, pm,iIndicating the base station as the ith user UE in the mth clusterm,iAssigned power value, ηm,lRepresenting a user UEm,lResidual coefficient of successive interference, δ, at mth cluster2Representing the variance value, λ, of Gaussian white noisem,lFor the base station to the UEm,lPrice of power sold by user, M represents number label of user clustering number, L represents number label of user number, M represents total number of user clustering, L represents number of user in each cluster, R represents total number of user clusteringm,lRepresenting a user UEm,lThroughput of ROMAFor the throughput, P, of this user in an orthogonal multiple access system under the constraint of the total power of the same systemtotFor the total power value of the base station, G represents the total number of users in the system, delta2Representing a variance value of Gaussian white noise, wherein a constraint condition C1 represents that a power distribution value of a single user must be greater than 0, a constraint condition C2 represents total power constraint of a base station, constraint conditions C3 and C4 represent fairness constraint among users, and C5 represents service quality requirements of the users;
the utility optimization model of the seller is obtained according to the seller maximized self utility function, and the model is as follows:
wherein, UBS m,lIndicating that the base station is towards the user UEm,lUtility function of sales power, λm,lIndicating base station to user UEm,lPrice of sold power, cm,lIndicating base station to UEm,lCost per unit of power sold, pm,lIndicating the base station as the l user UE in the m clusterm,lAn assigned power value;
the optimal purchasing strategy of the user comprises the following steps: the utility maximization problem of the buyer is as follows:
lagrange function pair pm,lThe derivation can be:
order to
Solve to obtain UEm,lThe optimum power of (2):
θm,l＝um,l+ωm,l+βm,l-γm,l
wherein L ism,lRepresenting a user UEm,lLagrangian functions with utility function under constraint,
representing a user UEm,lThe equivalent channel gain of (a) is,
conjugate transpose of detection matrix, H, representing the use of the receiving endm.lDenotes the channel gain of the i-th user in the i-th cluster and the base station, cmRepresenting the m-th column, p, of the precoding matrix Cm,lIndicating the base station as the l user UE in the m clusterm,lAssigned power value, hm,lIndicating the base station and the l user UE in the m clusterm,lEquivalent channel gain, p, betweenm,kIndicating the base station as the k user UE in the m clusterm,kAssigned power value, pm,iIndicating the base station as the ith user UE in the mth clusterm,iAssigned power value, ηm,lRepresenting a user UEm,lResidual coefficient of successive interference, δ, at mth cluster2Representing the variance value, λ, of Gaussian white noisem,lFor the base station to the UEm,lPrice of power sold by the user, um,lLagrange multiplier, P, representing constraint C2totFor the total power value of the base station, M represents the total clustering number of users, omegam,lLagrange multiplier, β, representing constraint C3m,lLagrange multiplier, gamma, representing constraint C4m,lThe lagrange multiplier, which represents the constraint C5, G,
representing the lagrange function pair pm,lDerivative, thetam,lFor a determined value um,l+ωm,l+βm,l-γm,l，pm,l *Representing a user UEm,lOf the optimum power value, λm,lIndicating base station to UEm,lA price at which the user sells power;
the process of obtaining the amount of power purchased at the user end comprises: bringing the optimal power solution into the optimal problem of the seller to obtain the optimal problem solution of the seller:
lambda to seller's optimal problem solutionm,lAnd (5) derivation to obtain:
order to
Obtaining the optimal price:
wherein, UBS m,lIndicating base station to UEm,lA utility function ofm,lIndicating the base station as a UEm,lPrice per unit power set, cm,lIndicating base station to UEm,lCost per unit of power sold, pm,l *Representing a UEm,lThe optimum value of the power,
is represented by thetam,lIs a determined valueum,l+ωm,l+βm,l-γm,l，um,lLagrange multiplier, ω, representing constraint C2m,lLagrange multiplier, β, representing constraint C3m,lLagrange multiplier, gamma, representing constraint C4m,lLagrange multiplier, h, representing constraint C5m,lRepresenting a UEm,lEffective channel gain of pm,kRepresenting the power, η, of the base station for the kth user in the mth clusterm,lRepresenting a UEm,lSerial interference cancellation residual coefficient of (p)m,iIndicating the power of the base station for the ith user in the mth cluster,
representing a UEm,lBy conjugate transposing of the channel detection matrix, delta2Represents the variance of white gaussian noise and,
indicating the base station as a UEm,lThe set optimal price;
the process of gaming between the base station and the user comprises the following steps: the base station sets unit power price and sells power to each user, and each user purchases power from the base station according to the price set by the base station so as to maximize the benefit of the user; the user makes a strategy according to the optimal price
Calculating the power price at the moment, and substituting the result into the optimal power purchase amount pm,l *And updating the amount of power purchased by the user, and continuously circulating the process until the power and the price reach balance.
2. The method of claim 1, wherein the system is a MIMO-NOMA system, the number of base station antennas in the system is M1, the number of user antennas is N, and N is greater than or equal to M1; the users are divided into M clusters, each cluster has L users, and the number of users in a cell is G (M multiplied by L); each cluster of users uses a non-orthogonal multiple access technology;
wherein, MIMO-NOMA represents MIMO non-orthogonal multiple access, M1 represents the number of base station antennas, N represents the number of user antennas, L represents the number of users in each cluster, and G represents the number of users in a cell.
3. The method of claim 2, wherein the transmission signals at the base station are:
wherein,
superimposed signals for mth cluster of users, pm,lRepresenting the power value, s, allocated by the base station to the ith user in the mth clusterm,lTransmitting symbol, S, representing the l-th user in the m-th clusterMA superimposed signal representing the mth cluster of users.
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