CN111194043B - Power distribution method based on non-perfect serial interference elimination - Google Patents

Abstract

The invention belongs to the field of communication technologies, and in particular relates to a power allocation method based on imperfect serial interference elimination. The method includes: a base station sets a unit power price, and sends the set price to a user; The price determines the amount of power purchased from the base station, and sends the purchased power amount to the base station; the base station readjusts the update price according to the power purchase amount of the user end; the base station and the user continue to compete until the power price of the base station and the power purchase amount of the user reach Equilibrium state; obtain equalized user power to complete power distribution; the present invention adopts the power distribution method of non-perfect serial interference elimination under the premise of ensuring service quality and user fairness, so that the algorithm is simpler and more accurate.

Description

A Power Allocation Method Based on Imperfect Serial Interference Cancellation

technical field

The invention belongs to the technical field of communications, and in particular relates to a power distribution method based on imperfect serial interference cancellation.

Background technique

With the development of mobile communication technology, it has expanded from pure voice services to mobile Internet services. Mobile traffic is growing exponentially due to the rapid development of the Internet of Things. The spectral efficiency of the traditional orthogonal multiple access and the users allowed to access are limited, and can no longer meet this explosive user growth. Different from the orthogonal multiple access method, the non-orthogonal multiple access can superimpose multiple users in the same frequency band, and eliminate the interference caused by other users through the serial interference cancellation (Successive Interference Cancellation, SIC) technology. As one of the key technologies of 5G (5th-Generation), Non-Orthogonal Multiple Access (NOMA) can meet the requirements of low latency, high reliability and massive access in the era of 5G IoT.

At present, the Multiple-Input Multiple-Output (MIMO) technology is a hot research topic in recent years. It is used to improve the spectral efficiency of the communication system in 4G (4th-Generation) and is the key technology of 4G. It will also appear as a key technology in 5G. For example, the patent application number CN201811267625.9 "Multi-cell MIMO-NOMA optimal power allocation method based on interference suppression" discloses: building a multi-cell MIMO-NOMA system model; eliminating cell interference through interference technology to obtain a mathematical model of power allocation ; Construct tight lower bound coefficients and corresponding substitutions to transform the original power distribution problem into a convex optimization problem; find the optimal power through iteration. This method enables the system to transmit data faster.

However, this method adopts the power allocation algorithm of convex difference planning when obtaining the optimal power, which requires a large amount of calculation and complicated calculation process, which is not conducive to data transmission.

SUMMARY OF THE INVENTION

In order to solve the above problems of the prior art, the present invention proposes a power allocation method based on imperfect serial interference cancellation, including: the base station sets a unit power price, and sends the set price to the user; the user sets the price according to the base station. Determine the amount of power purchased from the base station and send the purchased power amount to the base station; the base station readjusts the update price according to the power purchase amount of the user end; the base station and the user continue to compete until the power price of the base station and the power purchase amount of the user The equilibrium state is reached; the balanced user power is obtained, and the power allocation is completed;

The amount of power purchased by the user terminal includes: the base station obtains the effective channel gain of the user, and constructs a system throughput maximization model according to the signal-to-interference noise ratio of each user and the Shannon formula; The Steinkelberg game model of one master and one slave defines the user as the buyer and the base station as the seller; according to the system throughput maximization model, the user's power limit, system maximum power constraint, inter-user fairness constraint and user service quality constraint are determined The buyer's utility optimization model is obtained; the Lagrange multiplier method and the sub-gradient iteration method are used to calculate the buyer's utility optimization model, and the purchased power amount of the user terminal is obtained according to the utility optimization model;

The base station sets the unit power price: obtains the seller's utility function according to the power price and the cost of selling unit power of the base station, constructs the seller's utility optimization model according to the maximized utility function; calculates the unit power price according to the utility optimization model.

Preferably, the system throughput maximization model is:

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≥M1; the users have been divided into M clusters, there are L users in each cluster, and the number of users in the cell is L. The number of users is G=M×L; each cluster of users uses non-orthogonal multiple access technology.

Further, the transmitted signal at the base station is:

Preferably, the Steinkelberg game model includes:

Each client purchases power from the base station according to the price set by the base station, and the buyer's utility function is:

where λ _m,l is the price at which the base station sells power to UE _m,l users;

The base station sells power to each user, and the seller's utility function is: U _BS ^m,l =(λ _m,l -c _m,l )p _m,l .

Preferably, the buyer's utility optimization model is:

Subject to:

Preferably, the seller's utility optimization model is obtained according to the seller's maximization of its own utility function:

Preferably, the user's optimal purchase strategy includes:

The buyer's utility maximization problem is:

The Lagrangian function can be derived from p _m,l to get:

求解得UE_m,l的最优功率：make

Solve the optimal power of UE _m,l :

θ _m,l =u _m,l +ω _m,l +β _m,l -γ _m,l

Preferably, the process of obtaining the purchased power amount of the user terminal includes:

The optimal power solution is brought into the seller's optimal problem, and the seller's optimal solution is obtained:

Taking the derivative of λ _m,l of the seller's optimal problem solution, we get:

得到最优价格：make

Get the best price:

计算此时功率价格，并将结果代入最优功率购买量p_m,l ^*，更新用户购买功率的数量，此过程不断循环，直至功率和价格达到均衡。Preferably, the game process between the base station and the user includes: the base station sets a unit power price and sells power to each user, and each user buys power from the base station according to the price set by the base station to maximize their own benefits; Develop strategies

Calculate the power price at this time, and substitute the result into the optimal power purchase amount p _m,l ^* to update the amount of power purchased by the user. This process loops continuously until the power and price reach equilibrium.

The present invention considers the SIC residual in the MIMO-NOMA system, and the algorithm adjusts the power price and the user's power allocation value according to the size of the SIC residual factor, so that the result is closer to the optimal power; the present invention is based on the establishment of multiple The one-master-one-slave Steinkelberg game model, under the premise of ensuring service quality and user fairness, makes the throughput performance of the present invention more superior, and the algorithm complexity is lower than that of the power allocation algorithm based on convex difference planning.

Description of drawings

Fig. 1 is the downlink MIMO-NOMA system model of the present invention;

Fig. 2 is the flow chart of the throughput optimization power allocation algorithm based on game theory of the present invention;

Fig. 3 is the algorithm complexity comparison of the proposed algorithm and the power allocation based on convex difference programming;

4 is the relationship between the system throughput of the present invention and the total power of the base station;

Figure 5 shows the throughput comparison between the proposed algorithm and the power allocation based on convex difference planning.

Detailed ways

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or 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 part of the implementation of the present invention. examples, but not all examples. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The present invention is a power allocation method based on imperfect serial interference cancellation, as shown in Figure 2, including:

The base station sets the unit power price, and sends the set price to the user terminal; the user terminal determines the amount of power purchased from the base station according to the price set by the base station, and sends the purchased power amount to the base station; the base station purchases the amount of power according to the user terminal. Re-adjust the update price; the base station and the user continue to compete until the power price of the base station and the user's power purchase amount reach an equilibrium state; obtain the balanced user power and complete the power allocation;

The amount of power purchased by the user terminal includes: the base station obtains the effective channel gain of the user, and constructs a system throughput maximization model according to the signal-to-interference noise ratio of each user and the Shannon formula; The Steinkelberg game model of one master and one slave defines the user as the buyer and the base station as the seller; according to the system throughput maximization model, the user's power limit, system maximum power constraint, inter-user fairness constraint and user service quality constraint are determined The buyer's utility optimization model is obtained; the Lagrange multiplier method and the sub-gradient iteration method are used to calculate the buyer's utility optimization model, and the purchased power amount of the user terminal is obtained according to the utility optimization model;

The base station sets the unit power price: obtains the seller's utility function according to the power price and the cost of selling unit power of the base station, constructs the seller's utility optimization model according to the maximized utility function; calculates the unit power price according to the utility optimization model.

As shown in FIG. 1 , in the embodiment of the present invention, consider that in a MIMO-NOMA network, the number of base station antennas is M1, the total power of the base station is P _tot , there are G users in the cell, and the number of antennas of each user is N ( N≥M1), assuming that users have been divided into M clusters, and there are L users in each cluster, then G=M×L. In the above-mentioned MIMO-NOMA network, each cluster of users uses non-orthogonal multiple access technology, that is, all users superimpose transmission at the base station, and use serial interference cancellation technology to perform multi-user detection at the receiving end to eliminate the same cluster. interference from other users within. The transmitted signal at the base station is:

为第m簇用户的叠加信号，p_m，l表示基站为第m簇中的第l个用户分配的功率值，S_m，l表示第m簇中的第l个用户的发送符号，S_M表示第M簇用户的叠加信号。in,

is the superimposed signal of the mth cluster user, p _m,l represents the power value allocated by the base station for the lth user in the mth cluster, S _m,l represents the transmitted symbol of the lth user in the mth cluster, S _M represents the superimposed signal of the Mth cluster of users.

Mark the lth user in the mth cluster as UE _m,l , and the signal received by UE _m,l is expressed as:

表示用户UE_m，l的检测矩阵的共轭转置，y_m，l表示表示在接收端收到的未进行用户检测的信号矩阵，H_m，l表示UE_m，l与基站的信道增益，C表示基站使用的预编码矩阵，S表示基站的发送信号，n表示高斯白噪声向量，c_m表示预编码矩阵C的第m列，S_m表示第m簇用户的叠加信号，c_j表示预编码矩阵C的第j列，S_j表示第j簇用户的叠加信号，

表示基站为第m簇中的第l个用户分配的功率值的开方，

表示基站为第m簇中的第k个用户分配的功率值。in,

represents the conjugate transpose of the detection matrix of user UE _m,l , y _m,l represents the signal matrix received at the receiver without user detection, H _m,l represents the channel gain of UE _m,l and the base station, C represents the precoding matrix used by the base station, S represents the transmitted signal of the base station, _n represents the Gaussian white noise vector, cm represents the _mth column of the precoding matrix C, Sm represents the superimposed signal of the _mth cluster of users, and cj represents the precoding matrix. The jth column of the coding matrix C, S _j represents the superimposed signal of the jth cluster of users,

represents the square root of the power value allocated by the base station to the lth user in the mth cluster,

Indicates the power value allocated by the base station to the kth user in the mth cluster.

理论上可消除其他簇发送的信号对本簇信号所造成的干扰。Ruo Ling

In theory, the interference caused by the signals sent by other clusters to the signals of this cluster can be eliminated.

The desired signal can be obtained by serial interference cancellation technology and signal detection technology. Assume that the effective channel gain ranking of the mth cluster users at the receiving end is:

The serial interference cancellation technique is used at the receiving end, assuming that n _m,l (0≤n _m, l≤1) is the serial interference residual coefficient of UE _m,l in the mth cluster, which represents the serial interference of UE _m,l Cancellation capability, when η _{m, l} = 0, it indicates that the serial interference cancellation at the receiving end is ideal. Then the signal received by UE _{m, l} after serial interference cancellation can be expressed as:

After serial interference cancellation, the signal-to-interference-noise ratio of UE _{m and l} can be expressed as:

Among them, SINR _{m, l} represents the signal-to-interference and noise ratio of user UE _{m, l} .

则由香农公式可得UE_m，l的速率为：make

Then the rate of UE _{m, l} can be obtained from Shannon's formula:

The result calculated by the above formula 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 each cluster of users, and the total power allocated by the base station to each cluster of users is P _tot /M.

The system throughput maximization model is:

表示接收端使用的检测矩阵的共轭转置，H_m，l表示第i簇中的第l个用户与基站的信道增益，c_m表示预编码矩阵C的第m列，p_m，k表示基站第m簇中的第k个用户UE_m，k分配的功率值，η_m，l表示用户UE_m，l在第m簇的串行干扰残留系数，p_m，i表示基站第m簇中的第i个用户UE_m，i分配的功率值，δ²表示高斯白噪声的方差值。Among them, M represents the total number of clusters of users, L represents the number of users in each cluster, R _m,l represents the throughput of user UE _m,l , p _m,l represents the lth user UE _{m in the mth cluster of the base station, l} Power value assigned,

Represents the conjugate transpose of the detection matrix used by the receiving end, H _m,l represents the channel gain of the l-th user in the i-th cluster and the base station, cm represents the m-th column of the precoding matrix C, p _{m ,k} represents The power value allocated by the kth user UE _m,k in the mth cluster of the base station, η _m,l denotes the serial interference residual coefficient of the user UE _m,l in the mth cluster, p _m,i denotes the mth cluster of the base station The power value assigned by the i-th user UE _{m, i} , δ ² represents the variance value of Gaussian white noise.

In order 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 Steinkelberg game model includes: defining the user in the cell as the buyer (slave side), the base station as the seller (master side), the base station setting the unit power price and selling the power to each user, each user according to the base station. The price buys power from the base station to maximize its own benefits.

The buyer's utility optimization model is:

表示用户UE_m，l的等效信道增益，

表示接收端使用的检测矩阵的共轭转置，H_m，l表示第m簇中的第l个用户与基站的信道增益，c_m表示预编码矩阵C的第m列，p_m，l表示基站第m簇中的第l个用户UE_m，l分配的功率值，h_m，l表示基站与第m簇中的第l个用户UE_m，l之间的等效信道增益，p_m，k表示基站第m簇中的第k个用户UE_m，k分配的功率值，p_m，i表示基站第m簇中的第i个用户UE_m，i分配的功率值，η_m，l表示UE_m，l的串行干扰消除残留系数，δ²表示高斯白噪声的方差值，λ_m，l为基站向UE_m，l用户出售功率的价格。Among them, U _{m, l} represents the utility function of user UE _{m, l} ,

represents the equivalent channel gain of user UE _{m, l} ,

Represents the conjugate transpose of the detection matrix used by the receiving end, H _m,l represents the channel gain of the lth user in the mth cluster and the base station, cm represents the mth column of the precoding matrix C, p _{m ,l} represents Power value allocated by the lth user UE _m,l in the mth cluster of the base station, h _m,l represents the equivalent channel gain between the base station and the lth user UE _m,l in the mth cluster, p _{m, k} represents the power value allocated by the kth user UE _m,k in the mth cluster of the base station, p _m,i represents the power value allocated by the ith user UE _m,i in the mth cluster of the base station, η _m,l represents The serial interference cancellation residual coefficient of UE _{m, l} , δ ² represents the variance value of white Gaussian noise, and λ _{m, l} is the price that the base station sells power to UE _{m, l} users.

Subject to:

表示用户UE_m，l的等效信道增益，

表示接收端使用的检测矩阵的共轭转置，H_m，l表示第m簇中的第l个用户与基站的信道增益，c_m表示预编码矩阵C的第m列，p_m，l表示基站第m簇中的第l个用户UE_m，l分配的功率值，h_m，l表示基站与第m簇中的第l个用户UE_m，l之间的等效信道增益，p_m，k表示基站第m簇中的第k个用户UE_m，k分配的功率值，p_m，i表示基站第m簇中的第i个用户UE_m，i分配的功率值，η_m，l表示UE_m，l的串行干扰消除残留系数，δ²表示高斯白噪声的方差值，λ_m，l为基站向UE_m，l用户出售功率的价格，m表示用户分簇数标号，l表示用户数标号，M表示用户总分簇数，L表示每簇中的用户数，p_m，k表示基站第m簇中的第k个用户UE_m，k分配的功率值，R_m，l表示用户UE_m，l的吞吐量，R_OMA为相同系统总功率约束下此用户在正交多址系统中的吞吐量，P_tot为基站总功率值，G表示系统内用户总数，δ²表示高斯白噪声的方差值，约束条件C1表示单个用户的功率分配值必须大于0，约束条件C2表示基站的总功率约束，约束条件C3和C4为用户间公平性约束，C5为用户的服务质量要求。Among them, U _{m, l} represents the utility function of user UE _{m, l} ,

represents the equivalent channel gain of user UE _{m, l} ,

Represents the conjugate transpose of the detection matrix used by the receiving end, H _m,l represents the channel gain of the lth user in the mth cluster and the base station, cm represents the mth column of the precoding matrix C, p _{m ,l} represents Power value allocated by the lth user UE _m,l in the mth cluster of the base station, h _m,l represents the equivalent channel gain between the base station and the lth user UE _m,l in the mth cluster, p _{m, k} represents the power value allocated by the kth user UE _m,k in the mth cluster of the base station, p _m,i represents the power value allocated by the ith user UE _m,i in the mth cluster of the base station, η _m,l represents The residual coefficient of serial interference cancellation of UE _{m, l} , δ ² is the variance value of white Gaussian noise, λ _{m, l} is the price that the base station sells power to UE _{m, l} users, m is the label of the number of user clusters, and l is the User number label, M represents the total number of user clusters, L represents the number of users in each cluster, p _{m, k} represents the power value allocated by the kth user UE _{m, k} in the mth cluster of the base station, R _{m, l} represents The throughput of user UE _{m, l} , _ROMA is the throughput of this user in the orthogonal multiple access system under the same total system power constraint, _Ptot is the total power value of the base station, G is the total number of users in the system, δ ² is Gaussian The variance value of white noise, the constraint C1 indicates that the power allocation value of a single user must be greater than 0, the constraint C2 is the total power constraint of the base station, the constraints C3 and C4 are the fairness constraints between users, and C5 is the user's service quality requirements. .

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 fairness constraints between users, and C5 is the user's QoS requirement.

The seller's utility model is:

Among them, U _BS ^m,l denotes the utility function that the base station sells power to the user UE _m,l , λ _m,l denotes the price at which the base station sells the power to the user UE _m,l , cm, _l denotes the base station sells the power to the UE _m,l The cost of selling unit power, p _m,l represents the power value allocated by the base station to the lth user UE _m,l in the mth cluster.

The user's optimal purchasing strategy includes:

The invention adopts the Lagrange multiplier method to solve the buyer's optimization problem, constructs a Lagrangian function for the buyer's utility function, and transforms the buyer's utility maximization problem into:

The derivative of the Lagrangian function with respect to p _{m, l} can be obtained:

求解得UE_m，l的最优功率：make

Solve the optimal power of UE _{m, l} :

表示用户UE_m，l的等效信道增益，

表示接收端使用的检测矩阵的共轭转置，H_m，l表示第m簇中的第l个用户与基站的信道增益，c_m表示预编码矩阵C的第m列，p_m，l表示基站第m簇中的第l个用户UE_m，l分配的功率值，h_m，l表示基站与第m簇中的第l个用户UE_m，l之间的等效信道增益，p_m，k表示基站第m簇中的第k个用户UE_m，k分配的功率值，p_m，i表示基站第m簇中的第i个用户UE_m，i分配的功率值，η_m，l表示UE_m，l的串行干扰消除残留系数，δ²表示高斯白噪声的方差值，λ_m，l为基站向UE_m，l用户出售功率的价格，u_m，l表示约束条件C2的拉格朗日乘子，P_tot为基站总功率值，ω_m，l表示约束条件C3的拉格朗日乘子，β_m，l表示约束条件C4的拉格朗日乘子，γ_m，l表示约束条件C5的拉格朗日乘子，G表示系统内总用户数，

表示用户效用函数的拉格朗日函数对p_m，l求导，θ_m，l表示u_m，l+ω_m，l+β_m，l-γ_m，l，p_m，l ^*表示用户UE_m，l的最优功率值，λ_m，l表示基站向UE_m，l用户出售功率的价格。Among them, L _{m, l} represents the Lagrangian function of the user UE _{m, l} utility function under the constraint condition,

represents the equivalent channel gain of user UE _{m, l} ,

Represents the conjugate transpose of the detection matrix used by the receiving end, H _m,l represents the channel gain of the lth user in the mth cluster and the base station, cm represents the mth column of the precoding matrix C, p _{m ,l} represents Power value allocated by the lth user UE _m,l in the mth cluster of the base station, h _m,l represents the equivalent channel gain between the base station and the lth user UE _m,l in the mth cluster, p _{m, k} represents the power value allocated by the kth user UE _m,k in the mth cluster of the base station, p _m,i represents the power value allocated by the ith user UE _m,i in the mth cluster of the base station, η _m,l represents The residual coefficient of serial interference cancellation of UE _{m, l} , δ ² is the variance value of white Gaussian noise, λ _{m, l} is the price that the base station sells power to UE _{m, l} users, _{um, l} is the pull of the constraint condition C2 Grange multiplier, P _tot is the total power value of the base station, ω _{m, l} represents the Lagrangian multiplier of the constraint C3, β _{m, l} represents the Lagrangian multiplier of the constraint C4, γ _{m, l} represents the Lagrange multiplier of the constraint C5, G represents the total number of users in the system,

The Lagrangian function representing the user's utility function is derived with respect to pm _,l , θm _,l denotes _um,l +ωm _,l +βm _,l −γm _,l ,pm _,l ^* denotes the user The optimal power value of UE _m,l , λ _m,l represents the price at which the base station sells power to UE _m,l users.

The process of finding the user's optimal purchasing strategy includes:

Substituting the optimal power solution into the seller's optimization problem, the seller's optimization problem can be obtained as:

Taking the derivative of U _BS ^{m, l} with respect to λ _{m, l} , we can get:

求解可得最优价格：make

Solve for the optimal price:

表示基站效用函数的拉格朗日函数对λ_m，l求导，θ_m，l为一个确定值u_m，l+ω_m，l+β_m，l-γ_m，l，h_m，l表示UE_m，l的有效信道增益，p_m，k表示第m簇中第k个用户的功率，η_m，l表示UE_m，l的串行干扰消除残留系数，p_m，i表示第m簇中第i个用户的功率，

表示UE_m，l的信道检测矩阵的共轭转置，δ²表示高斯白噪声的方差，

表示基站为UE_m，l设置的的最优价格。Among them, U _BS ^m,l denotes the utility function of the base station for UE _m,l , λm _,l denotes the unit power price set by the base station for UE _m,l , cm _,l denotes the price of unit power sold by the base station to UE _m,l cost, p _m,l ^* denotes the optimal power value of UE _m,l ,

The Lagrangian function representing the utility function of the base station is derived from λ _{m, l} , θ _{m, l} is a certain value _{um, l} + ω _{m, l} + β _{m, l} −γ _{m, l} , h _{m, l} is the effective channel gain of UE _{m, l} , pm _{, k} is the power of the k-th user in the m-th cluster, η _m, l is the serial interference cancellation residual coefficient of UE _{m, l} , pm _{, i} is the m-th user the power of the ith user in the cluster,

represents the conjugate transpose of the channel detection matrix of UE _m,l , δ ² represents the variance of white Gaussian noise,

Indicates the optimal price set by the base station for UE _m,l .

计算此时功率价格，并将结果代入最优功率购买量p_m，l ^*，更新用户购买功率的数量，此过程不断循环，直至功率和价格达到均衡。The game process between the base station and the user includes: the base station sets a unit power price and sells power to each user, and each user buys power from the base station according to the price set by the base station to maximize their own benefits. Assuming that the base station's quotation starts from the cost cm _{, l} , and the user's power purchase quantity p _{m, l} starts from 0, first formulate the strategy according to the optimal price

Calculate the power price at this time, and substitute the result into the optimal power purchase quantity pm _{, l} ^* , and update the quantity of power purchased by the user. This process loops continuously until the power and price reach equilibrium.

Assuming that the number of user clusters is M, and the number of users in each cluster is L, the total number of users in the cell is G=M×L. In the algorithm proposed in the present invention, each user decides the optimal power allocation strategy according to the unit power price set by the base station. In each cycle, one user will respond based on the price set by the base station, and pass one The optimal power allocation strategy at this time is obtained by calculation. By considering the worst case of the proposed power allocation algorithm, its computational complexity can be analyzed. It is assumed that in the worst case, all users have not reached the equilibrium state when the algorithm reaches the maximum number of iterations. At this time, K×M×I _max , that is, G×I _max calculations, are performed. Therefore, when the maximum number of iterations of the algorithm is I _max , the time complexity of the algorithm is O(G×I _max) . For the power allocation algorithm based on convex difference programming, when the maximum number of iterations is N _max , its time complexity is O(N _max ×G ³ ).

As shown in Figure 3, when N _max =I _max =30, the time complexity of the two algorithms is compared, and the complexity analysis shows that the complexity of the distributed power allocation algorithm based on the Steinkelberg game is significantly lower For the power allocation strategy based on convex difference planning.

In order to further illustrate that the performance of the power allocation algorithm based on game theory in the MIMO-NOMA network is better than the fractional order power allocation algorithm, the power allocation algorithm of the present invention is simulated and verified below.

As shown in Figure 4, the simulation parameters are set as follows: the number of base station antennas M=2, the number of user antennas N=2, the cell radius R=500m, the minimum distance between the user and the base station _dmin =50m, the number of users in the cell is 8, the user Randomly distributed in the cell, the channel noise power is -70dBm. The channel estimation is ideal, the path loss index is 3, the total power range of the base station is 24dBm to 40dBm, and the serial interference cancellation residuals are η=0.001 and η=0.002, respectively. The simulation results show that the performance of the proposed power allocation algorithm is better than that of the fractional-order power allocation algorithm. When the total power of the base station is the same, the total system throughput of the proposed algorithm is always higher than that of the fractional power allocation algorithm, and with the increase of the total system power, the total system rate also increases, but the speed of increase gradually slows down, which is As for the algorithm proposed in the present invention, the power allocated by the base station to the user does not increase unlimitedly with the increase of the total system power.

As shown in FIG. 5 , when the total number of users in the cell is set to 8, the performance comparison between the algorithm proposed in the present invention and the power allocation algorithm based on convex difference planning in terms of total system throughput. The simulation results show that the total system rate of the power allocation algorithm based on the convex difference programming is slightly higher than that of the algorithm proposed by the present invention, indicating that the present invention reduces the algorithm complexity on the basis of similar performance to the power allocation algorithm based on the convex difference programming.

Those of ordinary skill in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium, and the storage medium can include: ROM , RAM, disk or CD, etc.

The above-mentioned embodiments further describe the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made to the present invention within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (3)

1. a power allocation method based on non-perfect serial interference cancellation, is characterized in that, comprises: The base station sets the unit power price, and sends the set price to the user terminal; the user terminal determines the amount of power purchased from the base station according to the price set by the base station, and sends the purchased power amount to the base station; the base station purchases the amount of power according to the user terminal. Re-adjust the update price; the base station and the user continue to compete until the power price of the base station and the user's power purchase amount reach an equilibrium state; obtain the balanced user power and complete the power allocation; The amount of power purchased by the user terminal includes: the base station obtains the effective channel gain of the user, and constructs a system throughput maximization model according to the signal-to-interference noise ratio of each user and the Shannon formula; The Steinkelberg game model of one master and one slave defines the user as the buyer and the base station as the seller; according to the system throughput maximization model, the user's power limit, system maximum power constraint, inter-user fairness constraint and user service quality constraint are determined The buyer's utility optimization model is obtained; the Lagrange multiplier method and the sub-gradient iteration method are used to calculate the buyer's utility optimization model, and the purchased power amount of the user terminal is obtained according to the utility optimization model; The setting of the unit power price by the base station includes: obtaining the seller's utility function according to the power price and the cost of the unit power sold by the base station, constructing the seller's utility optimization model according to the maximized utility function; calculating the unit power price according to the utility optimization model; The system throughput maximization model is:

Among them, M represents the total number of clusters of users, L represents the number of users in each cluster, R _m,l represents the throughput of user UE _m,l , p _m,l represents the lth user UE _{m in the mth cluster of the base station, l} Power value assigned,

represents the conjugate transpose of the detection matrix used by the receiver, represents the channel gain between the l-th user in the _m -th cluster and the base station, cm represents the m-th column of the precoding matrix C, and p _m,k represents the m-th cluster of the base station The power value allocated by the kth user UE _m,k in , η _ml represents the serial interference residual coefficient of the user UE _m,l in the mth cluster, p _m,i represents the ith user UE in the mth cluster of the base station The power value assigned by _{m, i} , δ ² represents the variance value of Gaussian white noise; The Steinkelberg game model includes: each client purchases power from the base station according to the price set by the base station, and the buyer's utility function is:

Among them, U _m,l represents the utility function of user UE _m,l ,

represents the equivalent channel gain of user UE _m,l ,

Represents the conjugate transpose of the detection matrix used by the receiver, H _ml represents the channel gain of the l-th user in the _m -th cluster and the base station, cm represents the m-th column of the precoding matrix C, and p _m,l represents that the base station is The power value allocated by the lth user UE _m,l in the mth cluster, h _m,l represents the equivalent channel gain between the base station and the lth user UE _m,l in the mth cluster, p _m,k represents the power value allocated by the base station to the kth user UE _m,k in the mth cluster, p _m,i represents the power value allocated by the base station to the ith user UE _m,k in the mth cluster, η _m,l represents the serial interference residual coefficient of user UE _m,l in the mth cluster, δ ² represents the variance value of white Gaussian noise, and λ _m,l is the price that the base station sells power to UE _m,l user; The base station sells power to each user, and the seller's utility function is: U _BS ^m,l =(λ _m,l -c _m,l )p _m,l where U _BS ^m,l denotes the utility function of the base station selling power to user UE _m,l , p _m,l denotes the power value allocated by the base station to the lth user UE _m,l in the mth cluster, _cm,l Represents the cost of the base station selling unit power to UE _m,l ; the buyer's utility optimization model is:

Subject to: C1:

C2:

C3:

C4:

Among them, U _m,l represents the utility function of user UE _m,l ,

represents the equivalent channel gain of user UE _m,l ,

Represents the conjugate transpose of the detection matrix used by the receiver, H _ml represents the channel gain of the l-th user in the _m -th cluster and the base station, cm represents the m-th column of the precoding matrix C, and p _m,l represents that the base station is The power value allocated by the lth user UE _m,l in the mth cluster, h _m,l represents the equivalent channel gain between the base station and the lth user UE _m,l in the mth cluster, p _m,k represents the power value allocated by the base station to the kth user UE _m,k in the mth cluster, p _m,i represents the power value allocated by the base station to the ith user UE _m,i in the mth cluster, η _m,l is the serial interference residual coefficient of user UE _m,l in the mth cluster, δ ² is the variance value of white Gaussian noise, λ _m,l is the price that the base station sells power to UE _m,l users, m is the user clustering Number label, l represents the number of users, M represents the total number of clusters of users, L represents the number of users in each cluster, R _m,l represents the throughput of user UE _m,l , and _ROMA is the total power constraint of the same system. The throughput of users in the orthogonal multiple access system, P _tot is the total power value of the base station, G is the total number of users in the system, δ ² is the variance value of white Gaussian noise, and the constraint C1 indicates that the power allocation value of a single user must be greater than 0, the constraint C2 represents the total power constraint of the base station, the constraints C3 and C4 are the fairness constraints between users, and C5 is the user's service quality requirement; According to the seller's maximization of its own utility function, the seller's utility optimization model is obtained as:

Among them, U _BS ^m,l denotes the utility function representing the power sold by the base station to the user UE _m,l , λ _m,l denotes the price at which the base station sells the power to the user UE _m,l , and _cm,l denotes the base station to the UE _m,l The cost of selling unit power, p _m,l represents the power value allocated by the base station for the lth user UE _m,l in the mth cluster; The user's optimal purchase strategy includes: the buyer's utility maximization problem is:

The Lagrangian function can be derived from p _m,l to get:

make

Solve the optimal power of UE _m,l : θ _m,l =u _m,l +ω _m,l +β _m,l -γ _m,l

Among them, L _m,l represents the Lagrangian function of the user UE _m,l utility function under the constraint condition,

represents the equivalent channel gain of user UE _m,l ,

represents the conjugate transpose of the detection matrix used by the receiver, H _ml represents the channel gain of the l-th user in the i-th cluster and the base station, cm represents the _m -th column of the precoding matrix C, and p _m,l represents that the base station is The power value allocated by the lth user UE _m,l in the mth cluster, h _m,l represents the equivalent channel gain between the base station and the lth user UE _m,l in the mth cluster, p _m,k represents the power value allocated by the base station to the kth user UE _m,k in the mth cluster, p _m,i represents the power value allocated by the base station to the ith user UE _m,i in the mth cluster, η _m,l represents the residual coefficient of serial interference of user UE _m,l in the mth cluster, δ ² represents the variance value of white Gaussian noise, λ _m,l is the price that the base station sells power to UE _m,l user, u _m,l represents Lagrangian multiplier of constraint C2, P _tot is the total power value of the base station, M represents the total number of user clusters, ω _m,l represents the Lagrangian multiplier of constraint C3, β _m,l represents the constraint Lagrange multiplier of C4, γ _m,l represents the Lagrange multiplier of constraint C5, G represents,

Represents the derivation of the Lagrangian function to p _m,l , θ _m,l is a certain value _um,l +ω _m,l +β _m,l -γ _m,l , p _m,l ^* represents The optimal power value of user UE _m,l , λ _m,l represents the price at which the base station sells power to UE _m,l user; The process of obtaining the purchased power amount of the user terminal includes: bringing the optimal power solution into the seller's optimal problem, and obtaining the seller's optimal problem solution:

Taking the derivative of λ _m,l of the seller's optimal problem solution, we get:

make

Get the best price:

Among them, U _BS ^m,l _{represents the} utility function of the base station for UE _{m ,l ;} cost, p _m,l ^* represents the optimal power value of UE _m,l ,

represents, θ _m,l is a certain value u _m,l +ω _m,l +β _m,l -γ _m,l , u _m,l denotes the Lagrange multiplier of constraint C2, ω _{m, l} represents the Lagrangian multiplier of constraint C3, β _m,l represents the Lagrangian multiplier of constraint C4, γ _m,l represents the Lagrange multiplier of constraint C5, h _m,l represents Effective channel gain of UE _m,l , p _m,k denotes the power of the base station as the kth user in the mth cluster, η _m,l denotes the serial interference cancellation residual coefficient of UE _m,l , p _m,i denotes the base station is the power of the i-th user in the m-th cluster,

represents the conjugate transpose of the channel detection matrix of UE _m,l , δ ² represents the variance of white Gaussian noise,

Indicates the optimal price set by the base station for UE _m,l ; The process of the game between the base station and the user includes: the base station sets the unit power price and sells power to each user, and each user buys power from the base station according to the price set by the base station to maximize their own benefits; users formulate strategies according to the optimal price

Calculate the power price at this time, and substitute the result into the optimal power purchase amount p _m,l ^* to update the amount of power purchased by the user. This process loops continuously until the power and price reach equilibrium. 2. a kind of power allocation method based on imperfect serial interference elimination according to claim 1, is characterized in that, described system is MIMO-NOMA system, in the system, the number of base station antennas is M1, and the number of antennas of users is N, And N≥M1; users have been divided into M clusters, there are L users in each cluster, and the number of users in the cell is G=M×L; each cluster of users uses non-orthogonal multiple access technology; Among them, MIMO-NOMA represents multiple-input multiple-output 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 per cluster, and G represents the number of cell users. 3. a kind of power allocation method based on imperfect serial interference cancellation according to claim 2, is characterized in that, the transmission signal at the base station is:

in,

is the superimposed signal of the mth cluster user, p _m,l represents the power value allocated by the base station for the lth user in the mth cluster, s _m,l represents the transmitted symbol of the lth user in the mth cluster, S _M represents the superimposed signal of the Mth cluster of users.

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