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CN106211178B - Frequency spectrum auction bid optimization method based on fractional order frequency reuse - Google Patents

Frequency spectrum auction bid optimization method based on fractional order frequency reuse Download PDF

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CN106211178B
CN106211178B CN201610542004.1A CN201610542004A CN106211178B CN 106211178 B CN106211178 B CN 106211178B CN 201610542004 A CN201610542004 A CN 201610542004A CN 106211178 B CN106211178 B CN 106211178B
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赵峰
聂化芝
陈宏滨
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Guilin University of Electronic Technology
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Abstract

The invention discloses a frequency spectrum auction bid optimization method based on fractional order frequency reuse, which comprises the following steps: s1, establishing a frequency spectrum auction model with fractional order frequency reuse, submitting frequency band information to be rented to an auction broker by a seller, summarizing and sorting frequency spectrum resources to be auctioned by the auction broker, and putting the frequency spectrum resources into a frequency spectrum pool for bidding by buyers with frequency spectrum requirements; s2, establishing a target function of the maximum profit of the main user end, interfering the optimization design of price factors, and broadcasting the optimization to the secondary users in the auction; s3, through optimized interference price factor omegak *Performing joint pre-coding and power distribution design under a fractional order frequency multiplexing scene, dividing secondary users into cell center secondary users and cell edge secondary users, and analyzing the cell center secondary users and the cell edge secondary users respectively; and S4, carrying out optimization design on the bids of the secondary users in the auction. The method is easy to realize, convenient to expand and closer to practical application, and the frequency spectrum auction method also has higher distribution efficiency and interference suppression effect.

Description

Frequency spectrum auction bid optimization method based on fractional order frequency reuse
Technical Field
The invention relates to the technical field of cognitive radio, in particular to a frequency spectrum auction bid optimization method based on fractional order frequency reuse.
Background
With the rapid development of scientific technology and the continuous improvement of communication requirements of people, the wireless spectrum is increasingly short of resources, meanwhile, the existing frequency band is unreasonable in use, spectrum congestion and idle spectrum coexist, and in addition, mutual interference necessarily exists in the information transmission process, so that the communication quality needs to be improved urgently. Therefore, how to improve the allocation efficiency and the usage efficiency of the existing spectrum resources as much as possible and effectively suppress the mutual interference between users is a long-standing research focus.
Fractional order frequency reuse is an effective frequency reuse technology, a cellular cell is divided into a cell center part and a cell edge part, and the interference suppression of the cell center and the cell edge is realized by allocating different frequency bands to the cell center part and the cell edge part, so that the communication quality of users is guaranteed. Fractional order frequency reuse studies with reuse factors of 3 or 7 are currently in widespread use. The spectrum auction can effectively help to solve the problem of low spectrum resource allocation efficiency and low use efficiency, and the application of the auction theory to the improvement of the spectrum resource utilization rate has become a research hotspot. The auction system has the advantages that the performance of personal rationality, budget balance, incentive compatibility, auction authenticity and the like in the auction design is continuously improved, and the real bidirectional spectrum auction which guarantees economic robustness, profitability and service quality is continuously developed. However, most bidding methods in the existing spectrum auction schemes adopt random values in a certain interval, and factors such as the preference of buyers to the spectrum and the signal-to-interference-and-noise ratio are not fully considered, so that the method is not reasonable.
The joint pre-coding and power distribution in the cognitive heterogeneous network can effectively inhibit the interference of unauthorized users to authorized users and the mutual interference between the unauthorized users, and improve the throughput. The present invention therefore allows for the improvement of the bidding for spectrum auctions with joint pre-coding and power allocation design in a fractional order frequency reuse scenario.
Disclosure of Invention
The invention aims to provide a frequency spectrum auction bid optimization method based on fractional order frequency reuse, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
a frequency spectrum auction bid optimization method based on fractional order frequency reuse comprises the following steps:
s1, establishing a frequency spectrum auction model with fractional order frequency reuse, wherein the system model comprises a seller with a frequency spectrum renting requirement, an auction broker controlling the whole auction process and a buyer with a frequency spectrum resource requirement, the seller submits information of a frequency band to be rented to the auction broker, and the auction broker collects and arranges the frequency spectrum resources to be auctioned and places the frequency spectrum resources into a frequency spectrum pool for bidding of the buyer with the frequency spectrum requirement;
s2, according to the interference situation when the primary user and the secondary user share the frequency spectrum resource, optimizing an interference price factor omegak *Establishing a target function of maximum profit of the main user end for connecting links, carrying out optimization design on interference price factors, and broadcasting the optimized interference price factors to secondary users in the auction;
s3, through optimized interference price factor omegak *Performing joint pre-coding and power distribution design in a fractional order frequency multiplexing scene, dividing secondary users into cell center secondary users and cell edge secondary users according to a fractional order frequency multiplexing model, and analyzing the secondary users respectively, wherein a signal vector S to be transmitted at a macro base station end is S [ [ S ] ]1，s2,...,sM]TWherein T represents transposition, and a vector of a signal to be transmitted of the secondary user side obtained through precoding is X ═ FPS, where F ═ F1,f2,......,fk]Is a precoding vector, fkPrecoding matrix (1 × M), f, representing kth secondary user endm||＝1，
Figure GDA0002313518660000021
Is a transmit power matrix, pkAfter the transmission power vector corresponding to the kth secondary user is sent through a channel and sent through the channel at a secondary user side, the receiving signal of the kth secondary user, the receiving signal of a main user and the signal-to-interference ratio of the kth secondary user can be obtained, and the throughput expression of the secondary user is obtained according to the Shannon formula: c is Bklog2(1+SINRk)；
S4, carrying out optimization design on the bids of the secondary users in the auction, wherein the expression of bid optimization is as follows: v ═ γkBklog2(1+SINRk) Wherein γ iskIndicating the preference of the secondary user k for a certain spectrum.
Preferably, in step S2, the objective function of the primary user side for pursuing the maximum benefit Up under the interference constraint generated by the secondary user sharing spectrum resource is expressed as:
Figure GDA0002313518660000022
Figure GDA0002313518660000023
wherein ω iskRepresenting the interference price factor, I, between primary and secondary users kkRepresenting interference from a secondary user k, for a given interference cost function omegakAnd a unit utility gain λkAnd obtaining a power distribution expression optimized by the secondary user through the KKT condition:
Figure GDA0002313518660000024
p is to bekSubstituting the income expression of the main user and the constraint condition to obtain an optimized cost function omegak *：
Figure GDA0002313518660000031
Wherein HkIndicating the channel state information, g, from the macro base station to the secondary user kkIndicating the channel state information, σ, from the home base station to the secondary user k2Representing the variance of additive white gaussian noise.
Preferably, in step S3, when the secondary user k is distributed in the center of the cell, he is interfered by other secondary users except for himself, interference of the primary user, and noise interference, so that the signal to interference plus noise ratio expression thereof can be obtained as follows:
Figure GDA0002313518660000032
wherein p iskPower vector representing the kth secondary user, fkPrecoding vector, H, representing the kth secondary userkIndicating the channel state information, g, from the macro base station to the secondary user kkHome base station to secondaryThe variance of the channel state information of the user k and the additive white Gaussian noise is sigma2The secondary user and the primary user share frequency spectrum resources and will certainly bring interference to the communication of the primary user, so the utility U of the secondary user in the center of the cellCThe reward paid to the primary user needs to be subtracted, specifically expressed as:
UC＝log2(1+SINRk)-ωkIk
＝log2(1+SINRk)-ωkpk|Hpfk|2
wherein the SINRkRepresents the SINR, ω, of the kth secondary userkIkIndicating that the secondary user k needs to pay the primary user a reward, whereby the optimal interference price factor omega is obtained by the primary user endk *The design target G for performing joint precoding and power allocation considering the maximization of the benefits of the primary user and the effectiveness of the secondary user under the constraints of transmitting power, interference and the signal-to-interference-and-noise ratio of a single user can be obtained as follows:
Figure GDA0002313518660000033
Figure GDA0002313518660000041
UCindicating the utility of secondary users in the center of the cell, wherein the first constraint condition indicates that the interference generated by all the secondary users to the primary user should be lower than the interference threshold I tolerable by the primary userthThe second constraint being that the transmission power of the secondary users is lower than the maximum value p of the transmission powermaxThe third constraint indicates that the signal-to-interference-and-noise ratio of a single secondary user should be higher than the threshold value gammathIn the same way, when the secondary users are distributed at the edge of the cell, because the fractional order frequency reuse can effectively suppress the same frequency interference, the secondary users only receive the interference from the noise at the moment, other interference can be ignored, and we can obtain the signal to interference plus noise ratio expression of the edge secondary users:
Figure GDA0002313518660000042
final utility U of cell edge secondary userEThe reward paid to the primary user needs to be subtracted, specifically expressed as:
UE＝log2(1+SINRk)-ωkIk
＝log2(1+SINRk)-ωkpk|Hpfk|2
giving an optimal interference price factor omegak *The optimization objective function G for performing joint precoding and power distribution by considering the maximum effect of the primary user and the secondary user under the transmission power constraint, the interference constraint and the signal-to-interference-and-noise ratio constraint of a single user by the edge secondary user can be obtained as follows:
Figure GDA0002313518660000043
Figure GDA0002313518660000051
wherein the first constraint condition indicates that the interference generated by all secondary users to the primary user should be lower than the interference threshold I tolerable by the primary userthThe second constraint being that the transmission power of the secondary users is lower than the maximum value p of the transmission powermaxThe third constraint indicates that the signal-to-interference-and-noise ratio of a single secondary user should be higher than the threshold value gammath。
Compared with the prior art, the invention has the beneficial effects that: the method fully considers the factors such as the preference, the bandwidth, the signal-to-interference-and-noise ratio and the like of the secondary user during actual bidding, simultaneously considers the requirements of the benefit maximization of the primary user side and the utility maximization of the secondary user side, and combines a fractional order frequency reuse model with the reuse factor of 3 to carry out detailed analysis and precoding and power distribution design on the secondary users distributed at the center and the edge of the cell. The method provided by the invention is easy to realize and convenient to expand, is closer to practical application compared with the frequency spectrum auction bidding method, and has higher distribution efficiency and interference suppression effect.
Drawings
FIG. 1 is a schematic diagram of a system model for conducting a spectrum auction under a fractional frequency reuse scenario according to the present invention;
FIG. 2 is a model schematic of a cognitive MIMO system of the present invention;
fig. 3 is a schematic diagram of communication interference in a fractional order frequency reuse scenario according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-3, the present invention provides a technical solution:
a frequency spectrum auction bid optimization method based on fractional order frequency reuse comprises the following steps:
s1, establishing a frequency spectrum auction model with fractional order frequency reuse, wherein the system model comprises a seller with a frequency spectrum renting requirement, an auction broker controlling the whole auction process and a buyer with a frequency spectrum resource requirement, the seller submits information of a frequency band to be rented to the auction broker, and the auction broker collects and arranges the frequency spectrum resources to be auctioned and places the frequency spectrum resources into a frequency spectrum pool for bidding of the buyer with the frequency spectrum requirement;
s2, according to the interference situation when the primary user and the secondary user share the frequency spectrum resource, optimizing an interference price factor omegak *In order to link the links, an objective function of maximum revenue of the primary user end is established, the interference price factor is optimized and designed, the optimized interference price factor is broadcasted to the secondary users in the auction, and in the step S2, the primary user end pursues the maximum revenue Up under the interference constraint generated by the secondary users sharing the frequency spectrum resourcesThe objective function is expressed as:
Figure GDA0002313518660000061
Figure GDA0002313518660000062
wherein ω iskRepresenting the interference price factor, I, between primary and secondary users kkRepresenting interference from a secondary user k, for a given interference cost function omegakAnd a unit utility gain λkAnd obtaining a power distribution expression optimized by the secondary user through the KKT condition:
Figure GDA0002313518660000063
p is to bekSubstituting the income expression of the main user and the constraint condition to obtain an optimized cost function omegak *：
Figure GDA0002313518660000064
S3, through optimized interference price factor omegak *Performing joint pre-coding and power distribution design in a fractional order frequency multiplexing scene, dividing secondary users into cell center secondary users and cell edge secondary users according to a fractional order frequency multiplexing model, and analyzing the secondary users respectively, wherein a signal vector S to be transmitted at a macro base station end is S [ [ S ] ]1，s2,...,sM]TWherein T represents transposition, and a vector of a signal to be transmitted of the secondary user side obtained through precoding is X ═ FPS, where F ═ F1,f2,......,fk]Is a precoding vector, fkPrecoding matrix (1 × M), f, representing kth secondary user endm||＝1，
Figure GDA0002313518660000071
Is a transmit power matrix, pkIs the transmission power corresponding to the k-th secondary userAfter the data is sent through the channel, at a secondary user side, after the data is sent through the channel, a receiving signal of a kth secondary user, a receiving signal of a primary user and a signal-to-interference ratio of the kth secondary user can be obtained, and a throughput expression of the secondary user is obtained according to a shannon formula: c is Bklog2(1+SINRk) When the secondary user k is distributed in the center of the cell in step S3, it receives interference from other secondary users except for itself, interference from the primary user, and noise interference, so that its signal to interference plus noise ratio expression can be obtained as follows:
Figure GDA0002313518660000072
wherein p iskPower vector representing the kth secondary user, fkPrecoding vector, H, representing the kth secondary userkIndicating the channel state information, g, from the macro base station to the secondary user kkThe variance of additive white Gaussian noise is sigma2The secondary user and the primary user share frequency spectrum resources and will certainly bring interference to the communication of the primary user, so the utility U of the secondary user in the center of the cellCThe reward paid to the primary user needs to be subtracted, specifically expressed as:
UC＝log2(1+SINRk)-ωkIk
＝log2(1+SINRk)-ωkpk|Hpfk|2
wherein the SINRkRepresents the SINR, ω, of the kth secondary userkIkIndicating that the secondary user k needs to pay the primary user a reward, whereby the optimal interference price factor omega is obtained by the primary user endk *The design target G for performing joint precoding and power allocation considering the maximization of the benefits of the primary user and the effectiveness of the secondary user under the constraints of transmitting power, interference and the signal-to-interference-and-noise ratio of a single user can be obtained as follows:
Figure GDA0002313518660000073
Figure GDA0002313518660000081
wherein the first constraint condition indicates that the interference generated by all secondary users to the primary user should be lower than the interference threshold I tolerable by the primary userthThe second constraint being that the transmission power of the secondary users is lower than the maximum value p of the transmission powermaxThe third constraint indicates that the signal-to-interference-and-noise ratio of a single secondary user should be higher than the threshold value gammathIn the same way, when the secondary users are distributed at the edge of the cell, because the fractional order frequency reuse can effectively suppress the same frequency interference, the secondary users only receive the interference from the noise at the moment, other interference can be ignored, and we can obtain the signal to interference plus noise ratio expression of the edge secondary users:
Figure GDA0002313518660000082
final utility U of cell edge secondary userEThe reward paid to the primary user needs to be subtracted, specifically expressed as:
UE＝log2(1+SINRk)-ωkIk
＝log2(1+SINRk)-ωkpk|Hpfk|2
giving an optimal interference price factor omegak *The optimization objective function G for performing joint precoding and power distribution by considering the maximum effect of the primary user and the secondary user under the transmission power constraint, the interference constraint and the signal-to-interference-and-noise ratio constraint of a single user by the edge secondary user can be obtained as follows:
Figure GDA0002313518660000083
Figure GDA0002313518660000091
wherein the first constraint condition indicates that the interference generated by all secondary users to the primary user should be lower than the interference threshold I tolerable by the primary userthThe second constraint being that the transmission power of the secondary users is lower than the maximum value p of the transmission powermaxThe third constraint indicates that the signal-to-interference-and-noise ratio of a single secondary user should be higher than the threshold value gammath；
S4, carrying out optimization design on the bids of the secondary users in the auction, wherein the expression of bid optimization is as follows:
v＝γkBklog2(1+SINRk) Wherein γ iskIndicating the preference of the secondary user k for a certain spectrum.
Factors such as preference, bandwidth and signal-to-interference-and-noise ratio when secondary users bid actually are fully considered, the requirements of benefit maximization of a primary user side and utility maximization of a secondary user side are considered, and detailed analysis and precoding and power distribution design are performed on the secondary users distributed in the center and the edge of a cell by combining a fractional order frequency reuse model with a reuse factor of 3. The method provided by the invention is easy to realize and convenient to expand, is closer to practical application compared with the frequency spectrum auction bidding method, and has higher distribution efficiency and interference suppression effect.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (3)

1.一种分数阶频率复用的频谱拍卖出价优化方法，其特征在于，包括如下步骤：1. a spectrum auction bidding optimization method of fractional frequency reuse, is characterized in that, comprises the steps: S1.建立分数阶频率复用的频谱拍卖模型，系统模型中包括有频谱出租需求的卖家、控制整个拍卖过程的拍卖中间人和有频谱资源需求的买家，卖家将自己待出租的频段信息提交给拍卖中间人，拍卖中间人将待拍卖的频谱资源汇总整理后放入频谱池中供有频谱需求的买家竞标；S1. Establish a spectrum auction model for fractional frequency reuse. The system model includes sellers with spectrum rental needs, auction middlemen who control the entire auction process, and buyers with spectrum resource needs. The seller submits the frequency band information to be rented to the Auction intermediary, the auction intermediary aggregates the spectrum resources to be auctioned and puts them into the spectrum pool for bidders with spectrum needs; S2.根据主用户和次用户共享频谱资源时的干扰情况，以最优干扰价格因子ωk *为联系纽带，建立主用户端收益最大化的目标函数，进行干扰价格因子的优化设计，并将这一最优化的干扰价格因子广播给拍卖中的次用户；S2. According to the interference situation when the primary user and the secondary user share spectrum resources, the optimal interference price factor ω k * is used as the link to establish the objective function of maximizing the revenue of the primary user terminal, and the optimal design of the interference price factor is carried out. This optimized interference price factor is broadcast to secondary users in the auction; S3.通过最优干扰价格因子ωk *在分数阶频率复用场景下进行联合预编码与功率分配设计，根据分数阶频率复用模型，将次用户划分为小区中心次用户和小区边缘次用户并分别进行分析，宏基站端待发射信号向量S＝[s1，s2,...,sM]T,其中T表示转置，经过预编码后得到次用户端待发射信号向量为X＝FPS，其中F＝[f1,f2,......,fk]是预编码向量，fk表示第k个次用户端的预编码矩阵(1×M)，||fm||＝1，
Figure FDA0002317040680000011
是发射功率矩阵，pk是对应第k个次用户的发射功率向量，经信道发送后，在次用户端，经信道发送后，求得第k个次用户的接收信号，主用户的接收信号，第k个次用户的信干比，并根据香农公式求得次用户的吞吐量表达式：C＝Bklog2(1+SINRk)；S3. Carry out joint precoding and power allocation design in fractional frequency reuse scenario through the optimal interference price factor ω k * , and divide secondary users into cell center secondary users and cell edge secondary users according to the fractional frequency reuse model And analyze them respectively, the signal vector to be transmitted at the macro base station is S=[s 1 , s 2 , ..., s M ] T , where T represents the transposition, and after precoding, the signal vector to be transmitted at the secondary user end is X = FPS, where F = [f 1 , f 2 , . ||=1,
Figure FDA0002317040680000011
is the transmit power matrix, and p k is the transmit power vector corresponding to the kth secondary user. After transmission through the channel, at the secondary user end, after transmission through the channel, the received signal of the kth secondary user and the received signal of the primary user are obtained. , the signal-to-interference ratio of the kth sub-user, and the throughput expression of the sub-user is obtained according to the Shannon formula: C=B k log 2 (1+SINR k ); S4.对拍卖中次用户的出价进行优化设计，出价优化的表达为：v＝γkBklog2(1+SINRk)其中γk表示次用户k对某段频谱的喜好度。S4. Optimally design the bid of the secondary user in the auction. The expression of bid optimization is: v=γ k B k log 2 (1+SINR k ), where γ k represents the preference of the secondary user k to a certain spectrum. 2.根据权利要求1所述的分数阶频率复用的频谱拍卖的出价优化方法，其特征在于：所述步骤S2中主用户端在次用户共享频谱资源产生的干扰约束下追求收益Up最大化目标函数表示为：2. the bidding optimization method of the spectrum auction of fractional-order frequency reuse according to claim 1, is characterized in that: in described step S2, the primary user end pursues profit Up maximization under the interference constraint that secondary users share the spectrum resource that produces The objective function is expressed as:
Figure FDA0002317040680000012
Figure FDA0002317040680000012
Figure FDA0002317040680000013
Figure FDA0002317040680000013
 其中ωk表示主用户与次用户k之间的干扰价格因子，Ik表示来自次用户k的干扰，Ith表示主用户忍受的干扰门限，对于一个给定的干扰价格因子ωk和单位效用增益λk，通过KKT条件，求得次用户优化的功率分配表达式：where ω k is the interference price factor between the primary user and secondary user k, I k is the interference from secondary user k, and I th is the interference threshold tolerable by the primary user. For a given interference price factor ω k and unit utility Gain λ k , through the KKT condition, the power distribution expression for sub-user optimization is obtained:
Figure FDA0002317040680000021
Figure FDA0002317040680000021
 Hk表示宏基站到次用户k的信道状态信息，gk表示家庭基站到次用户k的信道状态信息，σ2表示加性高斯白噪声的方差；H k represents the channel state information from the macro base station to the secondary user k, g k represents the channel state information from the home base station to the secondary user k, and σ 2 represents the variance of the additive white Gaussian noise; 将pk代入主用户收益表达式和约束条件，从而得出最优干扰价格因子ωk *：Substitute p k into the main user revenue expression and constraints to obtain the optimal interference price factor ω k * :
Figure FDA0002317040680000022
Figure FDA0002317040680000022
 其中Hk表示宏基站到次用户k的信道状态信息，gk表示家庭基站到次用户k的信道状态信息，σ2表示加性高斯白噪声的方差。Wherein H k represents the channel state information from the macro base station to the secondary user k, g k represents the channel state information from the home base station to the secondary user k, and σ 2 represents the variance of the additive white Gaussian noise. 3.根据权利要求1所述的分数阶频率复用的频谱拍卖的出价优化方法，其特征在于：所述步骤S3中当次用户k分布在小区中心时，它受到来自除了它本身之外的其他次用户的干扰、主用户的干扰以及噪声干扰，从而得到它的信干噪比表达式为：3. The bidding optimization method of the spectrum auction of fractional-order frequency reuse according to claim 1, characterized in that: in the step S3, when the secondary user k is distributed in the center of the cell, it is subject to a The interference of other secondary users, the interference of the primary user and the noise interference, so its signal-to-interference-noise ratio expression is:
Figure FDA0002317040680000023
Figure FDA0002317040680000023
 其中pk表示第k个次用户的功率向量，fk表示第k个次用户的预编码向量，Hk表示宏基站到次用户k的信道状态信息，gk表示家庭基站到次用户k的信道状态信息，加性高斯白噪声的方差为σ2，次用户与主用户共享频谱资源，势必会给主用户的通信带来干扰，因此小区中心次用户的效用UC需要减去支付给主用户的报酬，具体表示为：where p k represents the power vector of the k-th secondary user, f k represents the precoding vector of the k-th secondary user, H k represents the channel state information from the macro base station to the secondary user k, and g k represents the signal from the home base station to the secondary user k Channel state information, the variance of the additive white Gaussian noise is σ 2 , the secondary user and the primary user share spectrum resources, which will inevitably cause interference to the primary user's communication, so the utility U C of the secondary user in the cell center needs to be subtracted from the payment to the primary user. The user's remuneration, specifically expressed as: UC＝log2(1+SINRk)-ωkIk U C =log 2 (1+SINR k )-ω k I k ＝log2(1+SINRk)-ωkpk|Hpfk|2 =log 2 (1+SINR k )-ω k p k |H p f k | 2 其中SINRk表示第k个次用户的信干噪比，ωkIk表示次用户k需要支付给主用户的报酬，由此，通过主用户端得到的最优干扰价格因子ωk *，得出在发射功率约束、干扰约束和单个用户的信干噪比约束下，兼顾主用户收益和次用户效用最大化进行联合预编码和功率分配的设计目标G为：where SINR k represents the signal-to-interference-to-noise ratio of the k-th secondary user, and ω k I k represents the remuneration that secondary user k needs to pay to the primary user. Therefore, through the optimal interference price factor ω k * obtained by the primary user, we can obtain Under the constraints of transmit power, interference and signal-to-interference-noise ratio of a single user, the design goal G of joint precoding and power allocation taking into account the benefits of primary users and the maximization of secondary users' utility is:
Figure FDA0002317040680000031
Figure FDA0002317040680000031
Figure FDA0002317040680000032
Figure FDA0002317040680000032
 UC表示小区中心次用户的效用，Up表示主用户总收益，其中第一个约束条件表示所有次用户对主用户产生的干扰低于主用户忍受的干扰门限Ith，第二个约束条件表示次用户的发射功率要低于发射功率的最大值pmax，第三个约束条件表示单个次用户的信干噪比高于门限值γth，同理，当次用户分布在小区边缘时，由于分数阶频率复用有效抑制同频干扰，因此此时次用户只接收到来自噪声的干扰，其他的干扰忽略，得到边缘次用户的信干噪比表达式：U C represents the utility of the secondary user in the center of the cell, U p represents the total revenue of the primary user, where the first constraint indicates that the interference caused by all secondary users to the primary user is lower than the interference threshold I th tolerated by the primary user, and the second constraint It means that the transmit power of the secondary user is lower than the maximum value p max of the transmit power, and the third constraint indicates that the signal-to-interference-noise ratio of a single secondary user is higher than the threshold γ th . Similarly, when the secondary users are distributed at the edge of the cell , since fractional-order frequency reuse effectively suppresses co-channel interference, the secondary user only receives interference from noise at this time, and other interference is ignored, and the signal-to-interference-noise ratio expression of the edge secondary user is obtained:
Figure FDA0002317040680000033
Figure FDA0002317040680000033
 小区边缘次用户的最终效用UE需要减去支付给主用户的报酬，具体表示为：The final utility UE of the secondary user at the edge of the cell needs to deduct the remuneration paid to the primary user, which is specifically expressed as: UE＝log2(1+SINRk)-ωkIk U E =log 2 (1+SINR k )-ω k I k ＝log2(1+SINRk)-ωkpk|Hpfk|2 =log 2 (1+SINR k )-ω k p k |H p f k | 2 给定最优干扰价格因子ωk *，得出边缘次用户在发射功率约束、干扰约束和单个用户的信干噪比约束下，兼顾主用户收益和次用户效用最大化进行联合预编码和功率分配的优化目标函数G为：Given the optimal interference price factor ω k * , it is obtained that under the constraints of transmit power, interference and signal-to-interference-noise ratio of a single user, the edge secondary users take into account the primary user's benefit and the secondary user's utility maximization for joint precoding and power The assigned optimization objective function G is:
Figure FDA0002317040680000034
Figure FDA0002317040680000034
Figure FDA0002317040680000041
Figure FDA0002317040680000041
 UE表示小区边缘次用户的最终效用，其中第一个约束条件表示所有次用户对主用户产生的干扰低于主用户忍受的干扰门限Ith，第二个约束条件表示次用户的发射功率要低于发射功率的最大值pmax，第三个约束条件表示单个次用户的信干噪比高于门限值γth。U E represents the final utility of the secondary users at the cell edge, where the first constraint indicates that the interference caused by all secondary users to the primary user is lower than the interference threshold I th tolerated by the primary user, and the second constraint indicates that the transmit power of the secondary users should be Below the maximum value p max of the transmit power, the third constraint indicates that the signal-to-interference-to-noise ratio of a single secondary user is higher than the threshold γ th .
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