CN102149203B

CN102149203B - Power allocation method in cognition orthogonal frequency division multiple access (OFDMA) system based on proportional fairness and interference constraints

Info

Publication number: CN102149203B
Application number: CN201110098565.4A
Authority: CN
Inventors: 叶露; 张朝阳; 张志鹏; 王联响; 宫本康
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2011-04-14
Filing date: 2011-04-14
Publication date: 2014-09-17
Anticipated expiration: 2031-04-14
Also published as: CN102149203A

Abstract

The invention discloses a power allocation method based on proportional fairness and interference constraints in a cognitive OFDMA system. Its steps are as follows: firstly, according to the proportional fairness factor of cognitive users, the total power constraint and the fixed rate value, the power allocation between cognitive users is carried out, and then each cognitive user uses the fast water injection method to carry out carrier power allocation, if each cognitive user If none of the carrier power exceeds the power constraint value, the algorithm ends. Otherwise, modify the allocated power of the carrier that exceeds the power constraint to the power constraint value, calculate the rate of the carrier and add it to the fixed rate value of the user, and remove the carrier from the carrier set of the user. If each cognitive user If all carrier sets are empty, the algorithm ends, otherwise, the total power value is subtracted from the power constraint value allocated in this round, and the above steps are repeated until the algorithm ends. The invention has good performance in both system capacity and proportional fairness among cognitive users, and the complexity of the algorithm is low, which is suitable for engineering application.

Description

Power Allocation Method Based on Proportional Fairness and Interference Constraints in Cognitive OFDMA Systems

技术领域 technical field

本发明涉及无线通信领域，具体涉及一种认知OFDMA系统中基于比例公平和干扰约束的功率分配方法。The invention relates to the field of wireless communication, in particular to a power allocation method based on proportional fairness and interference constraints in a cognitive OFDMA system.

背景技术 Background technique

认知无线电技术是解决当前频谱资源匮乏、频谱利用率低的关键技术。在认知无线电中，认知用户通过动态地调整发射功率、频率和调制方式等参数，在不干扰授权用户的前提下使用空闲的频段，从而有效地提高了频谱的利用效率。正交频分复用接入(OFDMA)技术是目前公认的易于实现频谱资源控制的传输技术。OFDMA技术能够通过频谱的组合与裁剪灵活地在用户间分配系统资源，这使得它可以和认知系统很好地结合起来。在认知OFDMA系统中，如何在满足各种约束条件(干扰约束、比例公平约束、总功率约束等)的前提下，有效地将资源(载波、功率等)合理地分配给各个认知用户，成为了提高认知OFDMA系统性能的关键。Cognitive radio technology is a key technology to solve the current shortage of spectrum resources and low spectrum utilization. In cognitive radio, cognitive users can use idle frequency bands without interfering with licensed users by dynamically adjusting parameters such as transmission power, frequency, and modulation mode, thereby effectively improving spectrum utilization efficiency. Orthogonal Frequency Division Multiple Access (OFDMA) technology is currently recognized as a transmission technology that is easy to implement spectrum resource control. OFDMA technology can flexibly allocate system resources among users through spectrum combination and tailoring, which makes it a good combination with cognitive systems. In a cognitive OFDMA system, how to effectively allocate resources (carriers, power, etc.) to each cognitive user under the premise of satisfying various constraints (interference constraints, proportional fair constraints, total power constraints, etc.), It becomes the key to improve the performance of cognitive OFDMA system.

现有的资源分配方法主要分为两大类：静态的资源分配法(见“MultiuserOFDM，”in IEEE International Symposium on Signal Processing and itsApplications，1999)和动态的资源分配法(见“On the Use of Liner Programming forDynamic Subchannel and Bit Allocation in Multiuser OFDM，”in IEEE GLOBECOM，2001)。静态的资源分配法，如TDMA、FDMA等，虽然简单但是由于没有合理地利用认知用户和信道的动态变化信息而使得这种资源分配法的性能受限。相反，动态的分配资源法则可以合理地利用认知用户间的分集增益而使性能比静态的资源分配法有很大的提高，因而得到了很大的关注。目前关于认知OFDMA系统的动态资源分配方法有很多，但是基本存在两个问题，一是算法比较复杂，不适合于工程运用；二是很少考虑比例公平的约束，很多工作都集中于考虑整体容量的优化，而忽略了认知用户间的公平性问题。当将认知用户间的公平性约束加入到认知OFDMA系统的资源分配问题中时，问题的复杂度会大大提高。The existing resource allocation methods are mainly divided into two categories: static resource allocation method (see "MultiuserOFDM," in IEEE International Symposium on Signal Processing and its Applications, 1999) and dynamic resource allocation method (see "On the Use of Liner Programming for Dynamic Subchannel and Bit Allocation in Multiuser OFDM," in IEEE GLOBECOM, 2001). Static resource allocation methods, such as TDMA and FDMA, are simple, but the performance of this resource allocation method is limited because they do not make reasonable use of the dynamic change information of cognitive users and channels. On the contrary, the dynamic resource allocation method can reasonably use the diversity gain among cognitive users to greatly improve the performance compared with the static resource allocation method, so it has received a lot of attention. At present, there are many dynamic resource allocation methods for cognitive OFDMA systems, but there are basically two problems. One is that the algorithm is complex and not suitable for engineering applications; capacity optimization, while ignoring the issue of fairness among cognitive users. When the fairness constraint among cognitive users is added to the resource allocation problem of cognitive OFDMA system, the complexity of the problem will be greatly increased.

我们通过对考虑比例公平约束的认知OFDMA系统功率分配问题进行建模分析，利用模型中非线性方程的结构特征进行了合理的简化推导，从而将认知用户间的功率分配问题化简为求单一变量的方程求解过程，大大简化了该问题的求解。同时，对于单用户的载波功率分配，为了克服传统的注水算法需要迭代计算获得一个合理的注水门限的缺陷，我们提出了一种建立在载波信噪比排序基础上的快速注水算法，该算法可以一步获得注水门限。忽略载波信噪比排序的计算复杂度(该过程可以在载波分配的过程中实现)，该快速注水算法的复杂度为O(N)，仅相当于传统注水算法一次迭代的复杂度。We modeled and analyzed the cognitive OFDMA system power allocation problem considering proportional fairness constraints, and made a reasonable simplified derivation using the structural characteristics of the nonlinear equation in the model, thus reducing the power allocation problem among cognitive users to The process of solving the equation of a single variable greatly simplifies the solution of the problem. At the same time, for single-user carrier power allocation, in order to overcome the defect that the traditional water-filling algorithm needs iterative calculation to obtain a reasonable water-filling threshold, we propose a fast water-filling algorithm based on carrier signal-to-noise ratio sorting, which can Get the water injection threshold in one step. Neglecting the computational complexity of carrier signal-to-noise ratio sorting (this process can be realized in the process of carrier allocation), the complexity of the fast water filling algorithm is O(N), which is only equivalent to the complexity of one iteration of the traditional water filling algorithm.

发明内容 Contents of the invention

本发明的目的是克服现有技术的不足，提出一种认知OFDMA系统中基于比例公平和干扰约束的功率分配方法。The purpose of the present invention is to overcome the deficiencies of the prior art, and propose a power allocation method based on proportional fairness and interference constraints in a cognitive OFDMA system.

认知OFDMA系统中基于比例公平与干扰约束的功率分配方法的步骤如下：The steps of the power allocation method based on proportional fairness and interference constraints in the cognitive OFDMA system are as follows:

1)对如下变量进行初始化，P_k，total＝0，R_k，fixed＝0，Ω_k，left＝Ω_k，for k＝2，3，...，K，其中P_total表示总的功率约束值，表示当前的总功率约束值，P_k，total表示分配给第k个认知用户的功率，Ω_k表示分配给第k个认知用户的载波集合，Ω_k，fixed表示属于第k个认知用户的固定速率的载波集合，Ω_k，left表示Ω_k中除去Ω_k，fixed中的元素后剩下的元素集合，K为认知用户个数；1) Initialize the following variables, Pk _,total =0, R _{k, fixed} = 0, Ω _{k, left} = Ω _k , for k = 2, 3, ..., K, where P _total represents the total power constraint value, Indicates the current total power constraint value, P _{k, total} indicates the power allocated to the k-th cognitive user, Ω _k indicates the carrier set allocated to the k-th cognitive user, Ω _{k, fixed} indicates that it belongs to the k-th cognitive user The fixed-rate carrier set of the user, Ω _{k, left} represents the set of elements left after the elements in Ω _k _{, fixed are removed from Ω k} , and K is the number of cognitive users;

2)根据认知用户速率的比例公平因子γ₁∶γ₂...∶γ_K、Ω_k，left中的载波信道噪声比、当前的固定速率R_k，fixed以及当前的总功率计算出分配给各认知用户的功率P_k，total；2) According to the proportional fairness factor of cognitive user rate γ ₁ : γ ₂ ...: γ _K , Ω _{k, the CNR in left} , the current fixed rate R _{k, fixed} and the current total power Calculate the power P _k,total allocated to each cognitive user;

3)各认知用户根据分得的功率值P_k，total，利用快速注水法对Ω_k，left中的载波进行功率分配；3) Each cognitive user performs power allocation to the carrier in Ω _{k, left} according to the allocated power value P _{k, total} ;

4)各认知用户检测Ω_k，left中的载波功率是否均满足干扰约束条件：P_k，n≤P_k，max，n∈Ω_k，left，其中P_k，n表示第k个认知用户在第n个载波上分配的功率，P_k，max表示集合Ω_k，left中载波的功率约束值，若所有认知用户的载波功率分配均满足功率约束条件，则算法结束，否则，检测到P_k，n＞P_k，max的第k个认知用户将第n个载波划入到固定速率的载波集合Ω_k，fixed中，并将第n个载波从集合Ω_k，left中删除，更新第k个认知用户固定速率R_k，fixed为：R_k，fixed＝R_k，fixed+log₂(1+P_k，maxH_k，n)，其中H_k，n＝|h_k，n|²/(N₀BN^-1)，h_k，n为Ω_k，left中第n个载波的载波增益，N₀为信道噪声功率谱密度，B为总的带宽，N为总的载波个数，更新当前的总功率约束值为：其中N_k，fixed为集合Ω_k，fixed中载波个数，转入步骤2)，直至算法结束。4) Each cognitive user checks whether the carrier power in Ω _{k, left} satisfies the interference constraint condition: P _{k, n} ≤ P _{k, max} , n ∈ Ω _{k, left} , where P _{k, n} represents the kth cognitive user The power allocated by the user on the nth carrier, P _{k, max} represents the power constraint value of the carrier in the set Ω _{k, left} , if the carrier power allocation of all cognitive users satisfies the power constraint condition, the algorithm ends, otherwise, the detection The k-th cognitive user until P _k,n >P _k,max divides the n-th carrier into the fixed-rate carrier set Ω _k,fixed , and deletes the n-th carrier from the set Ω _k,left , update the fixed rate R _{k of the kth cognitive user, fixed} is: R _{k, fixed} = R _{k, fixed} + log ₂ (1+P _{k, max} H _{k, n} ), where H _{k, n} =|h _{k , n} | ² /(N ₀ BN ^-1 ), h _{k, n} is Ω _{k, the carrier gain of the nth carrier in left} , N ₀ is the channel noise power spectral density, B is the total bandwidth, N is the total The number of carriers, update the current total power constraint value for: Where N _{k, fixed} is the set Ω _{k, the number of carriers in fixed} , go to step 2) until the algorithm ends.

步骤2)中所述的根据认知用户速率的比例公平因子γ₁∶γ₂...∶γ_K、Ω_k，left中的载波信道噪声比、当前的固定速率R_k，fixed以及当前的总功率计算出分配给各认知用户的功率P_k，total步骤为：According to the proportional fairness factor γ ₁ : γ ₂ ...: γ _K , Ω _{k, left} in step 2), the current fixed rate R _{k, fixed} and the current total power Calculate the power P _{k allocated to each cognitive user, and the total} steps are:

认知用户的功率P_k，total计算公式如下The power P _{k of the cognitive user, the total} calculation formula is as follows

$F f (({P P}_{11,, total total})) = = {Σ Σ}_{k k = = 11}^{K K} {a a}_{k k} {(({P P}_{11,, total total}))}^{{b b}_{k k}} - - {\overset{~ ~}{P P}}_{total total} = = 00$

${P P}_{k k,, total total} = = {a a}_{k k} {(({P P}_{11,, total total}))}^{{b b}_{k k}}$

其中，in,

${a a}_{k k} = = \{\begin{matrix} 11,, & k k = = 11 \\ {((\frac{{H h}_{11,, mid middle} {M m}_{11,, left left}}{{N N}_{11,, left left}} 22^{\frac{{R R}_{11,, fixed fixed}}{{N N}_{11__left left}}}))}^{\frac{{N N}_{11,, left left} {γ γ}_{k k}}{{N N}_{k k,, left left} {γ γ}_{11}}} \cdot &Center Dot; \frac{{N N}_{k k,, left left}}{{H h}_{k k,, mid middle} {M m}_{k k,, left left}} 22^{\frac{{R R}_{k k,, fixed fixed}}{{N N}_{k k,, left left}}},, & k k = = 2,3 2,3,, . . . . . .,, K K \end{matrix}$

${b b}_{k k} = = \{\begin{matrix} 11,, & k k = = 11 \\ \frac{{N N}_{11,, left left} {γ γ}_{k k}}{{N N}_{k k,, left left} {γ γ}_{11}},, & k k = = 2,3 2,3,, . . . . . .,, K K \end{matrix},,$

a_k与b_k中的变量说明：H_k，mid＝|h_k，mid|²/(N₀BN^-1)，h_k，mid为Ω_k，left中载波增益的中间值，N₀为信道噪声功率谱密度，B为总的带宽，N为总的载波个数。N_k，left为Ω_k，left中载波个数。Description of the variables in a _k and b _k : H _{k, mid} =|h _{k, mid} | ² /(N ₀ BN ^-1 ), h _{k, mid} is Ω _{k, the middle value of the carrier gain in left} , N ₀ is Channel noise power spectral density, B is the total bandwidth, N is the total number of carriers. N _{k, left} is Ω _{k, the number of carriers in left} .

步骤3)中所述的各认知用户根据分得的功率值P_k，total，利用快速注水法对Ω_k，left中的载波进行功率分配步骤为：Each cognitive user described in step 3) uses the fast water injection method to perform power allocation to the carrier in Ω _{k, left} according to the assigned power value P _{k, total} as follows:

(1)确定区间[α_n，α_n+1]，其中该区间满足从而得到集合Ф_k＝{i|i≤n，i∈Ω_k，left}，若第一次对Ω_k，left中的载波进行快速功率注水，且Ω_k，left中的载波信道噪声比满足则根据区间左边界值α_n和区间右边界值α_n+1的定义直接计算出满足P_k，total∈[α_n，α_n+1]要求的载波序号n，若不是第一次对Ω_k，left中的载波进行快速功率注水，则只需在前一次的基础上对区间左边界值α_n和区间右边界值α_n+1进行调整，不需要重新计算，假设在上一次的快速注水过程中第l个载波的注水功率超出了功率约束值，则第l个载波将从集合Ω_k，left中剔除，不参加本轮的快速注水过程，则对区间左边界值α_n和区间右边界值α_n+1进行调整：首先修改区间左边界值α_n的值为修改区间右边界值α_n+1的值为判断条件是否仍然满足，是则区间左边界值α_n和区间右边界值α_n+1的值修改完毕，否则若则将第n+1个载波加入集合Φ_k中，即Φ_k＝{i|i≤n+1，i∈Ω_k，left}修改区间左边界值α_n的值为修改区间右边界值α_n+1的值为重复以上步骤直至条件满足；(1) Determine the interval [α _n , α _n+1 ], where This interval satisfies Thus, the set Ф _k ={i|i≤n, i∈Ω _{k, left} } is obtained. If the carrier in Ω _{k, left} is subjected to fast power water injection for the first time, and the carrier-to-channel-noise ratio in Ω _{k, left} satisfies Then, according to the definition of interval left boundary value α _n and interval right boundary value α _n+1, directly calculate the carrier number n that meets the requirements of P _{k, total} ∈ [α _n , α _n+1 ], if it is not the first time for Ω If the carrier in _{k, left} performs fast power injection, it only needs to adjust the interval left boundary value α _n and the interval right boundary value α _n+1 on the basis of the previous time, without recalculation, assuming that in the last fast During the water injection process, the water injection power of the l-th carrier exceeds the power constraint value, then the l-th carrier will be removed from the set Ω _{k, left} , and will not participate in the current round of fast water injection process, then the interval left boundary value α _n and the interval right Adjust the boundary value α _n+1 : first modify the value of the left boundary value α _n of the interval to be Modify the value of the right boundary value of the interval α _n+1 to be Analyzing conditions Whether it is still satisfied, if yes, the values of the interval left boundary value α _n and the interval right boundary value α _n+1 have been modified, otherwise if Then add the n+1th carrier to the set Φ _k , that is, Φ _k = {i|i≤n+1, i∈Ω _{k, left} } modify the value of the left boundary value α _n of the interval to be Modify the value of the right boundary value of the interval α _n+1 to be Repeat the above steps until the condition satisfy;

(2)计算快速功率注水门限：其中M_k为集合Φ_k中元素的个数。(2) Calculate the fast power water injection threshold: Among them, M _k is the number of elements in the set Φ _k .

本发明充分利用比例公平和干扰约束下的认知用户间功率分配的模型特点，将认知用户间的功率分配有效地化简为单一变量的方程求解过程，大大降低了该问题的计算复杂度。同时针对于单用户的载波功率分配问题提出的快速注水法也避免了迭代过程，通过一次计算即可确定注水门限。The present invention makes full use of the model characteristics of power distribution among cognitive users under proportional fairness and interference constraints, effectively simplifies the power distribution among cognitive users into a single-variable equation solving process, and greatly reduces the computational complexity of the problem . At the same time, the fast water injection method proposed for the single-user carrier power allocation problem also avoids the iterative process, and the water injection threshold can be determined by one calculation.

附图说明 Description of drawings

图1是认知OFDMA系统中基于比例公平与干扰约束的功率分配方法的流程图；Fig. 1 is a flowchart of a power allocation method based on proportional fairness and interference constraints in a cognitive OFDMA system;

图2是认知用户间的比例公平性随总功率约束值的变化情况，仿真图中比较了本发明的算法与遍历解(遍历所有情况得到的最优解)、TDMA算法及参考算法(“Increasing in Capacity of Multiuser OFDM System Using DynamicSubchannel Allocation”，in Proc.IEEE VTC，2000)的公平性性能，Fig. 2 is the variation situation of the proportional fairness between cognitive users with the total power constraint value, in the simulation figure, the algorithm of the present invention is compared with the ergodic solution (the optimal solution obtained by traversing all situations), the TDMA algorithm and the reference algorithm (" Increasing in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation", in Proc.IEEE VTC, 2000) fairness performance,

图3是认知用户的系统容量增益随总功率约束值的变化情况，仿真图中比较了本发明的算法与遍历解(遍历所有情况得到的最优解)、参考算法(“Increasing in Capacity of Multiuser OFDM System Using Dynamic SubchannelAllocation”，in Proc.IEEE VTC，2000)相对于TDMA算法的容量增益，其值由各算法的系统容量除以同等条件下的TDMA算法的容量得到。Fig. 3 is the change situation of the system capacity gain of the cognitive user with the total power constraint value. In the simulation diagram, the algorithm of the present invention is compared with the ergodic solution (the optimal solution obtained by traversing all situations), and the reference algorithm ("Increasing in Capacity of Multiuser OFDM System Using Dynamic SubchannelAllocation", in Proc.IEEE VTC, 2000) relative to the capacity gain of the TDMA algorithm, its value is obtained by dividing the system capacity of each algorithm by the capacity of the TDMA algorithm under the same conditions.

具体实施方式 Detailed ways

1)对如下变量进行初始化，P_k，total＝0，R_k，fixed＝0，Ω_k，left＝Ω_k，fork＝2，3，...，K，其中P_total表示总的功率约束值，表示当前的总功率约束值，P_k，total表示分配给第k个认知用户的功率，Ω_k表示分配给第k个认知用户的载波集合，Ω_k，fixed表示属于第k个认知用户的固定速率的载波集合，Ω_k，left表示Ω_k中除去Ω_k，fixed中的元素后剩下的元素集合，K为认知用户个数；1) Initialize the following variables, Pk _,total =0, R _{k, fixed} = 0, Ω _{k, left} = Ω _k , fork = 2, 3, ..., K, where P _total represents the total power constraint value, Indicates the current total power constraint value, P _{k, total} indicates the power allocated to the k-th cognitive user, Ω _k indicates the carrier set allocated to the k-th cognitive user, Ω _{k, fixed} indicates that it belongs to the k-th cognitive user The fixed-rate carrier set of the user, Ω _{k, left} represents the set of elements left after the elements in Ω _k _{, fixed are removed from Ω k} , and K is the number of cognitive users;

其中，in,

${a a}_{k k} = = \{\begin{matrix} 11,, & k k = = 11 \\ {((\frac{{H h}_{11,, mid middle} {M m}_{11,, left left}}{{N N}_{11,, left left}} 22^{\frac{{R R}_{11,, fixed fixed}}{{N N}_{11__left left}}}))}^{\frac{{N N}_{11,, left left} {γ γ}_{k k}}{{N N}_{k k,, left left} {γ γ}_{11}}} \cdot \cdot \frac{{N N}_{k k,, left left}}{{H h}_{k k,, mid middle} {M m}_{k k,, left left}} 22^{\frac{{R R}_{k k,, fixed fixed}}{{N N}_{k k,, left left}}},, & k k = = 2,3 2,3,, . . . . . .,, K K \end{matrix}$

(1)确定区间[α_n，α_n+1]，其中该区间满足从而得到集合Φ_k＝{i|i≤n，i∈Ω_k，left}，若第一次对Ω_k，left中的载波进行快速功率注水，且Ω_k，left中的载波信道噪声比满足则根据区间左边界值α_n和区间右边界值α_n+1的定义直接计算出满足P_k，total∈[α_n，α_n+1]要求的载波序号n，若不是第一次对Ω_k，left中的载波进行快速功率注水，则只需在前一次的基础上对区间左边界值α_n和区间右边界值α_n+1进行调整，不需要重新计算，假设在上一次的快速注水过程中第l个载波的注水功率超出了功率约束值，则第l个载波将从集合Ω_k，left中剔除，不参加本轮的快速注水过程，则对区间左边界值α_n和区间右边界值α_n+1进行调整：首先修改区间左边界值α_n的值为修改区间右边界值α_n+1的值为判断条件是否仍然满足，是则区间左边界值α_n和区间右边界值α_n+1的值修改完毕，否则若则将第n+1个载波加入集合Φ_k中，即Ф_k＝{i|i≤n+1，i∈Ω_k，left}修改区间左边界值α_n的值为修改区间右边界值α_n+1的值为重复以上步骤直至条件满足；(1) Determine the interval [α _n , α _n+1 ], where This interval satisfies Thus, the set Φ _k = {i|i≤n, i∈Ω _{k, left} } is obtained. If the carrier in Ω _{k, left} is subjected to fast power water injection for the first time, and the carrier-to-channel-noise ratio in Ω _{k, left} satisfies Then, according to the definition of interval left boundary value α _n and interval right boundary value α _n+1, directly calculate the carrier number n that meets the requirements of P _{k, total} ∈ [α _n , α _n+1 ], if it is not the first time for Ω If the carrier in _{k, left} performs fast power injection, it only needs to adjust the interval left boundary value α _n and the interval right boundary value α _n+1 on the basis of the previous time, without recalculation, assuming that in the last fast During the water injection process, the water injection power of the l-th carrier exceeds the power constraint value, then the l-th carrier will be removed from the set Ω _{k, left} , and will not participate in the current round of fast water injection process, then the interval left boundary value α _n and the interval right Adjust the boundary value α _n+1 : first modify the value of the left boundary value α _n of the interval to be Modify the value of the right boundary value of the interval α _n+1 to be Analyzing conditions Whether it is still satisfied, if yes, the values of the interval left boundary value α _n and the interval right boundary value α _n+1 have been modified, otherwise if Then add the n+1th carrier to the set Φ _k , that is, Φ _k ＝{i|i≤n+1, i∈Ω _{k, left} } modify the value of the left boundary value α _n of the interval to be Modify the value of the right boundary value of the interval α _n+1 to be Repeat the above steps until the condition satisfy;

(2)计算快速功率注水门限：其中M_k为集合Ф_k中元素的个数。(2) Calculate the fast power water injection threshold: Where M _k is the number of elements in the set Ф _k .

实施例Example

本实施例中的载波分配过程不属于本算法的研究范围，采用参考算法(“Increasing in Capacity of Multiuser OFDM System Using Dynamic SubchannelAllocation”，in Proc.IEEE VTC，2000)中的载波分配方式，只是将载波分配过程中每个载波上的功率由参考算法(“Increasing in Capacity of Multiuser OFDMSystem Using Dynamic Subchannel Allocation”，in Proc.IEEE VTC，2000)中的平均分配改为本例中的载波功率约束值。为了方便理解，现将修改后的参考文献(“Increasing in Capacity of Multiuser OFDM System Using Dynamic SubchannelAllocation”，in Proc.IEEE VTC，2000)中的载波分配方式简单阐述如下：The carrier allocation process in this embodiment does not belong to the research scope of this algorithm. The carrier allocation method in the reference algorithm ("Increasing in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation", in Proc.IEEE VTC, 2000) is adopted, and only the carrier During the allocation process, the power on each carrier is changed from the average allocation in the reference algorithm ("Increasing in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation", in Proc. IEEE VTC, 2000) to the carrier power constraint value in this example. For the convenience of understanding, the carrier allocation method in the revised reference ("Increasing in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation", in Proc.IEEE VTC, 2000) is briefly described as follows:

(1)初始化各个认知用户的载波集合初始化各个认知用户的速率R_k＝0，k＝1，2，...K，Ω为总的可用载波集合，其中共有N＝14个可用载波，认知用户1的载波增益h_1，n在[0.84，0.99]之间随机产生，认知用户2的载波增益h_2，n在[0.85，1.04]之间随机产生，各载波的噪声功率谱密度N₀＝1mW，总带宽B的值设为1；(1) Initialize the carrier set of each cognitive user Initialize each cognitive user's rate R _k =0, k=1, 2, ... K, Ω as the total set of available carriers, wherein there are N=14 available carriers, and the carrier gain h _{1 of cognitive user 1, n} is randomly generated between [0.84, 0.99], the carrier gain h 2 of cognitive user 2 _{, n} is randomly generated between [0.85, 1.04], the noise power spectral density of each carrier N ₀ =1mW, the total bandwidth B set the value to 1;

(2)找出认知用户k，满足由认知用户k挑选载波n满足：H_k，n≥H_k，m，n∈Ω，H_k，n＝|h_k，n|²/(N₀BN^-1)，更新认知用户k的速率为R_k＝R_k+Blog₂(1+H_k，nP_k，max)，更新认知用户k的载波集合Ω_k为Ω_k＝Ω_k∪{n}；(2) Find cognitive user k, satisfy Carrier n selected by cognitive user k satisfies: H _k,n ≥ _{H k,m} , n∈Ω, H _{k, n} = |h _{k, n} | ² /(N ₀ BN ^-1 ), the update rate of cognitive user k is R _k = R _k +Blog ₂ (1+H _{k, n} P _{k , max} ), update the carrier set Ω _k of cognitive user k as Ω _k = Ω _k ∪{n};

(3)将载波n从集合Ω中剔除。若则载波分配完毕，否则回到步骤(2)，直至载波分配完毕，得到各认知用户的载波集合Ω_k，k＝1，2，...K。(3) Eliminate the carrier n from the set Ω. like Then the carrier is allocated, otherwise go back to step (2), until the carrier is allocated, the carrier set Ω _k of each cognitive user is obtained, k=1, 2, . . . K.

认知OFDMA系统中基于比例公平和干扰约束的功率分配方法的步骤如下：The steps of the power allocation method based on proportional fairness and interference constraints in the cognitive OFDMA system are as follows:

1)初始化变量：P_k，total＝0，R_k，fixed＝0，Ω_k，left＝Ω_k，for k＝2，3，...，K。其中P_total表示总的功率约束值，取值从10mW到15mW分别观察不同总功率约束下算法的性能，表示当前的总功率约束值，P_k，total表示分配给第k个认知用户的功率，Ω_k表示分配给第k个认知用户的载波集合，由前面所述的载波分配过程得到，Ω_k，fixed表示属于第k个认知用户的固定速率的载波集合，Ω_k，left表示Ω_k中除去Ω_k，fixed中的元素后剩下的元素集合，K＝2为认知用户个数，认知用户的载波功率约束值P_1，max＝P_2，max＝1mW；1) Initialize the variable: Pk _,total =0, R _{k, fixed} = 0, Ω _{k, left} = Ω _k , for k = 2, 3, . . . , K. Among them, P _total represents the total power constraint value, and the value ranges from 10mW to 15mW to observe the performance of the algorithm under different total power constraints. Represents the current total power constraint value, P _{k, total} represents the power allocated to the k-th cognitive user, Ω _k represents the carrier set allocated to the k-th cognitive user, obtained from the carrier allocation process described above, Ω _{k, fixed} means the fixed-rate carrier set belonging to the kth cognitive user, Ω _{k, left} means the set of elements left after removing the elements in Ω _k _{, fixed from Ω k,} K=2 is the number of cognitive users , the carrier power constraint value of cognitive users P _1,max =P _2,max =1mW;

2)根据认知用户速率的比例公平因子γ₁∶γ₂＝1∶1、Ω_k，left中的载波信道噪声比、当前的固定速率R_k，fixed以及当前的总功率计算出分配给各认知用户的功率P_k，total；2) According to the proportional fairness factor of cognitive user rate γ ₁ : γ ₂ =1:1, Ω _{k, the CNR in left} , the current fixed rate R _{k, fixed} and the current total power Calculate the power P _k,total allocated to each cognitive user;

4)各认知用户检测Ω_k，left中的载波的分配功率是否均满足干扰约束条件：P_k，n≤P_k，max，n∈Ω_k，left，其中P_k，n表示第k个认知用户在第n个载波上分配的功率，P_k，max表示集合Ω_k，left中载波的功率约束值。若所有认知用户的载波功率分配均满足功率约束条件，则算法结束，否则，检测到P_k，n＞P_k，max的第k个认知用户将第n个载波划入到固定速率的载波集合Ω_k，fixed中，并将第n个载波从集合Ω_k，left中删除，更新第k个认知用户固定速率R_k，fixed为：R_k，fixed＝R_k，fixed+log₂(1+P_k，maxH_k，n)，H_k，n＝|h_k，n|²/(N₀BV^-1)，h_k，n为认知用户k的第n个载波的载波增益值，认知用户1的载波增益h_1，n在[0.84，0.99]之间随机产生，认知用户2的载波增益h_2，n在[0.85，1.04]之间随机产生。N₀＝1mW为信道噪声功率谱密度，B为总的带宽，其值假设为1，N＝14为总的载波个数。更新当前的总功率约束值为：其中N_k，fixed为集合Ω_k，fixed中载波个数，转入步骤2)，直至算法结束。4) Each cognitive user detects whether the allocated power of the carrier in Ω _{k, left} satisfies the interference constraint condition: P _{k, n} ≤ _{P k, max} , n ∈ Ω _{k, left} , where P _{k, n} represents the kth The power allocated by cognitive users on the nth carrier, P _k,max represents the power constraint value of the carrier in the set Ω _k,left . If the carrier power allocation of all cognitive users satisfies the power constraints, the algorithm ends; otherwise, the kth cognitive user that detects that P _k,n >P _k,max divides the nth carrier into the fixed rate In the carrier set Ω _{k, fixed} , delete the nth carrier from the set Ω _{k, left} , and update the fixed rate R _{k of the k-th cognitive user, fixed} : R _{k, fixed} = R _{k, fixed} + log ₂ (1+P _{k, max} H _{k, n} ), H _{k, n} = |h _{k, n} | ² /(N ₀ BV ^-1 ), h _{k, n} is the carrier of the nth carrier of cognitive user k For the gain value, the carrier gain h _{1, n} of cognitive user 1 is randomly generated between [0.84, 0.99], and the carrier gain h _{2, n} of cognitive user 2 is randomly generated between [0.85, 1.04]. N ₀ =1mW is the channel noise power spectral density, B is the total bandwidth, its value is assumed to be 1, and N=14 is the total number of carriers. Update the current total power constraint value for: Where N _{k, fixed} is the set Ω _{k, the number of carriers in fixed} , go to step 2) until the algorithm ends.

步骤2)中所述的根据认知用户速率的比例公平因子γ₁∶γ₂＝1、Ω_k，left中的载波信道噪声比、当前的固定速率R_k，fixed以及当前的总功率计算出分配给各认知用户的功率P_k，total步骤为：解方程The proportional fairness factor γ ₁ : γ ₂ =1 according to the cognitive user rate described in step 2), the carrier-channel-to-noise ratio in Ω _k,left , the current fixed rate R _k,fixed and the current total power Calculate the power P _{k allocated to each cognitive user, the total} step is: solve the equation

$F f (({P P}_{11,, total total})) = = {Σ Σ}_{k k = = 11}^{22} {a a}_{k k} {(({P P}_{11,, total total}))}^{{b b}_{k k}} - - {\overset{~ ~}{P P}}_{total total} = = 00$

${P P}_{22,, total total} = = {a a}_{22} {(({P P}_{11,, total total}))}^{{b b}_{22}}$

其中，in,

${a a}_{k k} = = \{\begin{matrix} 11,, & k k = = 11 \\ {((\frac{{H h}_{11,, mid middle} {M m}_{11,, left left}}{{N N}_{11,, left left}} 22^{\frac{{R R}_{11,, fixed fixed}}{{N N}_{11,, left left}}}))}^{\frac{{N N}_{11,, left left}}{{N N}_{k k,, left left}}} \cdot \cdot \frac{{N N}_{k k,, left left}}{{H h}_{k k,, mid middle} {M m}_{k k,, left left}} 22^{\frac{{R R}_{k k,, fixed fixed}}{{N N}_{k k,, left left}}},, & k k = = 22 \end{matrix}$

${b b}_{k k} = = \{\begin{matrix} 11,, & k k = = 11 \\ \frac{{N N}_{11,, left left}}{{N N}_{k k,, left left}},, & k k = = 22 \end{matrix},,$

a_k与b_k中的变量说明：H_k，mid＝|h_k，mid|²/(N₀BN^-1)，h_k，mid为Ω_k，left中载波增益的中间值，认知用户1的载波增益h_1，n在[0.84，0.99]之间随机产生，认知用户2的载波增益h_2，n在[0.85，1.04]之间随机产生。N₀＝1mW为信道噪声功率谱密度，B为总的带宽，其值假设为1，N＝14为总的载波个数。N_k，left为Ω_k，left中载波个数。Description of variables in a _k and b _k : H _{k, mid} =|h _{k, mid} | ² /(N ₀ BN ^-1 ), h _{k, mid} is Ω _{k, the middle value of the carrier gain in left} , cognitive user The carrier gain h 1 _{, n} of 1 is randomly generated between [0.84, 0.99], and the carrier gain h _{2, n} of cognitive user 2 is randomly generated between [0.85, 1.04]. N ₀ =1mW is the channel noise power spectral density, B is the total bandwidth, its value is assumed to be 1, and N=14 is the total number of carriers. N _{k, left} is Ω _{k, the number of carriers in left} .

该步骤中方程的求解可以利用牛顿法或试位法(见“Handbook ofMathematical Functions with Formulas，Graphs，and Mathematical Tables”，9^thprinting.New York：Dover，1972.)The solution of the equation in this step can use Newton's method or trial position method (see "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables", 9 ^th printing. New York: Dover, 1972.)

(1)确定区间[α_n，α_n+1]，其中该区间满足从而得到集合Ф_k＝{i|i≤n，i∈Ω_k，left}，若第一次对Ω_k，left中的载波进行快速功率注水，且Ω_k，left中的载波信道噪声比满足则根据区间左边界值α_n和区间右边界值α_n+1的定义直接计算出满足P_k，total∈[α_n，α_n+1]要求的载波序号n。若不是第一次对Ω_k，left中的载波进行快速功率注水，则只需在前一次的基础上对区间左边界值α_n和区间右边界值α_n+1进行调整，不需要重新计算。假设在上一次的快速注水过程中第l个载波的注水功率超出了功率约束值，则第l个载波将从集合Ω_k，left中剔除，不参加本轮的快速注水过程，因此修改区间左边界值α_n的值为修改区间右边界值α_n+1的值为判断条件是否仍然满足，是，则区间左边界值α_n和区间右边界值α_n+1的值修改完毕，否则若则将第n+1个载波加入集合Φ_k中，即Ф_k＝{i|i≤n+1，i∈Ω_k，left}，修改区间左边界值α_n的值为修改区间右边界值α_n+1的值为重复以上步骤直至条件满足。(1) Determine the interval [α _n , α _n+1 ], where This interval satisfies Thus, the set Ф _k ={i|i≤n, i∈Ω _{k, left} } is obtained. If the carrier in Ω _{k, left} is subjected to fast power water injection for the first time, and the carrier-to-channel-noise ratio in Ω _{k, left} satisfies Then, according to the definition of the interval left boundary value α _n and the interval right boundary value α _n+1, the carrier number n satisfying the requirement of P _{k, total} ∈ [α _n , α _n+1 ] is directly calculated. If it is not the first time to perform rapid power injection on the carrier in Ω _{k, left} , it is only necessary to adjust the interval left boundary value α _n and the interval right boundary value α _n+1 on the basis of the previous one, without recalculation . Assuming that the water injection power of the l-th carrier exceeds the power constraint value in the last fast water injection process, the l-th carrier will be removed from the set Ω _{k, left} , and will not participate in the current round of fast water injection process, so modify the left boundary of the interval The value of α _n is Modify the value of the right boundary value of the interval α _n+1 to be Analyzing conditions Whether it is still satisfied, if yes, then the value of the interval left boundary value α _n and the interval right boundary value α _n+1 has been modified, otherwise if Then add the n+1th carrier to the set Φ _k , that is, Φ _k ＝{i|i≤n+1, i∈Ω _{k, left} }, modify the value of the left boundary value α _n of the interval to be Modify the value of the right boundary value of the interval α _n+1 to be Repeat the above steps until the condition satisfy.

(2)计算快速注水法的注水门限：其中M_k为集合Φ_k中元素的个数。(2) Calculate the water injection threshold of the rapid water injection method: Among them, M _k is the number of elements in the set Φ _k .

图2是认知用户间的比例公平性随总功率的变化情况，仿真图中比较了本发明的方法与遍历解(遍历所有情况得到的最优解)、TDMA方法及参考方法(“Increasing in Capacity of Multiuser OFDM System Using Dynamic SubchannelAllocation”，in Proc.IEEE VTC，2000)的比例公平性性能，从图中可以看出，当总的功率约束值低于14mW时本发明的方法相比较于TDMA方法以及参考方法，能很好的保证认知用户间的比例公平要求。当总的功率约束值超出14mW时，由于所有的载波功率均超出了载波功率约束值，每个认知用户的容量由载波功率约束值决定，从而导致了遍历解、本发明方法和参考方法三者曲线的重合。而TDMA方法由于其载波分配方式与前三者不同，从而认知用户的比例公平性能也与前三者不同。此外，当总的功率约束值小于12.5mW时，从仿真结果可以看出，本发明的方法能够很好地逼近遍历解，但是由于遍历解的求解过程是通过遍历所有情况得到的，因此复杂度远远高于本发明的方法。当总的功率约束值大于12.5mW小于14mW时，由于部分载波的分配功率超出了载波的功率约束值，需要利用本发明的方法对其进行更新求解，方法过程中为了简化计算而采用的部分近似计算导致了结果有一些偏离遍历解，但是综合来看，本发明的方法在比例公平性能和方法复杂度上有一个很好的折衷。图3是认知用户的系统容量增益随总功率的变化情况，仿真图中比较了本发明的方法与遍历解(遍历所有情况得到的最优解)、参考方法(“Increasing in Capacity of Multiuser OFDMSystem Using Dynamic Subchannel Allocation”，in Proc.IEEE VTC，2000)相对于TDMA方法的容量增益，其值由各方法的系统容量除以同等条件下的TDMA方法的容量得到，曲线的下降趋势是因为容量差值随着总功率约束的增大而减小。从图中曲线可以看出，当总的功率约束值低于14mW时，本发明方法在系统容量上优于TDMA方法及参考方法。当总的功率约束值高于14mW时，由于所有的载波功率均超出了载波的功率约束值，每个认知用户的容量由载波功率约束值决定，从而导致了遍历解、本发明方法和参考方法三者曲线的重合。虽然本发明方法的系统容量相比于遍历解有所下降，但是本发明方法的复杂度远远低于遍历解的复杂度，更适合于工程运用。Fig. 2 is the variation situation of proportional fairness between cognitive users with the total power, in the simulation figure, the method of the present invention and the ergodic solution (the optimal solution obtained by traversing all situations), the TDMA method and the reference method ("Increasing in Capacity of Multiuser OFDM System Using Dynamic SubchannelAllocation", in Proc.IEEE VTC, 2000) proportional fairness performance, as can be seen from the figure, when the total power constraint value is lower than 14mW, the method of the present invention is compared with the TDMA method As well as the reference method, it can well guarantee the proportional fairness requirements among cognitive users. When the total power constraint value exceeds 14mW, since all carrier powers all exceed the carrier power constraint value, the capacity of each cognitive user is determined by the carrier power constraint value, thus resulting in the ergodic solution, the method of the present invention and the reference method three the coincidence of curves. The TDMA method is different from the former three in its carrier allocation method, so the proportional fair performance of cognitive users is also different from the former three. In addition, when the total power constraint value is less than 12.5mW, it can be seen from the simulation results that the method of the present invention can approach the ergodic solution well, but since the solution process of the ergodic solution is obtained by traversing all situations, the complexity Far higher than the method of the present invention. When the total power constraint value is greater than 12.5mW and less than 14mW, since the allocated power of some carriers exceeds the power constraint value of the carrier, it is necessary to use the method of the present invention to update and solve it. The partial approximation adopted in the method process to simplify the calculation The calculation results in some deviations from the ergodic solution, but overall, the method of the present invention has a good compromise between proportional fairness performance and method complexity. Fig. 3 is the variation of the system capacity gain of the cognitive user with the total power. In the simulation diagram, the method of the present invention is compared with the ergodic solution (the optimal solution obtained by traversing all situations), and the reference method ("Increasing in Capacity of Multiuser OFDM System") Using Dynamic Subchannel Allocation", in Proc.IEEE VTC, 2000) relative to the capacity gain of the TDMA method, its value is obtained by dividing the system capacity of each method by the capacity of the TDMA method under the same conditions. The downward trend of the curve is due to the capacity difference The value decreases as the total power constraint increases. It can be seen from the curve in the figure that when the total power constraint value is lower than 14mW, the method of the present invention is superior to the TDMA method and the reference method in terms of system capacity. When the total power constraint value is higher than 14mW, since all carrier powers exceed the power constraint value of the carrier, the capacity of each cognitive user is determined by the carrier power constraint value, thus resulting in the ergodic solution, the method of the present invention and the reference The method is the coincidence of the three curves. Although the system capacity of the method of the present invention is lower than that of the ergodic solution, the complexity of the method of the present invention is far lower than that of the ergodic solution, and is more suitable for engineering application.

Claims

1. A power distribution method based on proportional fairness and interference constraint in a cognitive OFDMA system is characterized by comprising the following steps:

1) the following variables are initialized as follows and,P_k，total=0，R_k，fixed=0，Ω_k，left=Ω_kk =2, 3, …, K, wherein P_totalA value representing the total power constraint is indicated,representing the current total power constraint value, P_k，totalRepresents the power, Ω, allocated to the kth cognitive user_kRepresents the set of carriers, Ω, allocated to the kth cognitive user_k，fixedRepresents a set of carriers of fixed rate, Ω, belonging to the kth cognitive user_k，leftRepresents omega_kRemoving omega_k，fixedThe elements left after the elements in the list are collected, and K is the number of the cognitive users;

2) proportional fairness factor gamma based on cognitive user rate₁∶γ₂…∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，total；

3) Each cognitive user is according to the divided power value P_k，totalUsing rapid water injection method to adjust omega_k，leftCarrying out power distribution on the carrier waves in the group;

4) each cognitive user detects omega_k，leftWhether the carrier power in (1) all meets the interference constraint condition: o is_k，n≤P_k，max，n∈Ω_k，leftIn which P is_k，nRepresents the power, P, allocated by the k cognitive user on the n carrier_k，maxRepresents the set omega_k，leftIf the power distribution of the carrier of all cognitive users meets the power constraint condition, the algorithm is ended, otherwise, P is detected_k，n>P_k，maxThe k-th cognitive user divides the n-th carrier into a carrier set omega with a fixed rate_k，fixedAnd the nth carrier is selected from the set omega_k，leftDeleting and updating the fixed rate R of the kth cognitive user_k，fixedComprises the following steps: r_k，fixed=R_k，fixed+log₂(1+P_k，maxH_k，n) In which H is_k，n＝|h_k，n|²/(N₀BN^-1)，h_k，nIs omega_k，leftCarrier gain of the nth carrier, N₀Updating the current total power constraint value for the channel noise power spectral density, B for the total bandwidth and N for the total number of carriersComprises the following steps:wherein N is_k，fixedIs a set omega_k，fixedThe number of the medium carriers is transferred to the step 2) until the algorithm is finished;

proportional fairness factor gamma according to cognitive user rate in step 2)₁∶γ₂…∶γ_K、Ω_k，leftCarrier to channel noise ratio, current fixed rate R_k，fixedAnd the current total powerCalculating power P distributed to each cognitive user_k，totalThe method comprises the following steps:

power P of cognitive user_k，totalThe calculation formula is as follows

<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>Σ</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>a</mi> <mi>k</mi> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mi>k</mi> </msub> </msup> <mo>-</mo> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mi>total</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math>

P_{k, total} = a_{k} {(P_{1, total})}^{b_{k}}

Wherein,

<math> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> <msup> <mn>2</mn> <mfrac> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> <msub> <mi>γ</mi> <mi>k</mi> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <msub> <mi>γ</mi> <mn>1</mn> </msub> </mrow> </mfrac> </msup> <mo>·</mo> <mfrac> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> <mrow> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>mid</mi> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mn>2</mn> <mfrac> <mrow> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>fixed</mi> </mrow> </msub> </mrow> <msub> <mi>N</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>left</mi> </mrow> </msub> </mfrac> </msup> <mo>,</mo> </mtd> <mtd> <mi>k</mi> <mo>=</mo> <mn>2,3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>K</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

a_kand b_kThe variables in (1) describe: h_k，mid=|h_k，mid|²／(N₀BN^-1)，h_k，midIs omega_k，leftIntermediate value of intermediate carrier gain, N₀For the channel noise power spectral density, B is the total bandwidth and N is the total number of carriers.N_k，leftIs omega_k，leftThe number of medium carriers, j is a carrier counting variable;

each cognitive user in the step 3) according to the divided power value P_k，tatolUsing rapid water injection method to adjust omega_k，leftThe power allocation step of the carrier wave in (1) is as follows:

(1) determining the interval [ alpha ]_n，α_n+1]Wherein

The interval satisfiesThereby obtaining a set phi_k={i|i≤n，i∈Ω_k，leftIf it is aligned with Ω for the first time_k，leftThe carrier wave in (1) carries out rapid power water injection and omega_k，leftHas a carrier to channel noise ratio ofN_k，leftThe number of the carriers is determined according to the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1Is directly calculated to satisfy P_k，total∈[α_n，α_n+1]The required carrier number n is not the first time to Ω_k，leftThe carrier wave in the interval is subjected to rapid power water injection, and only the left boundary value alpha of the interval needs to be subjected to rapid power water injection on the basis of the previous time_nAnd interval right boundary value alpha_n+1Adjusting without recalculation, and assuming that the water injection power of the ith carrier exceeds the power constraint value in the last rapid water injection process, the ith carrier will be from the set omega_k，leftRemoving the middle part, not participating the fast water injection process of the round, and then carrying out the left boundary value alpha of the interval_nAnd interval right boundary value alpha_n+1And (3) adjusting: first, the left boundary value alpha of the interval is modified_nHas a value ofModified interval right boundary value alpha_n+1Has a value of

Judgment of conditions

<math> <mrow> <msub> <mover> <mi>P</mi> <mo>~</mo> </mover> <mrow> <mi>k</mi> <mo>,</mo> <mi>total</mi> </mrow> </msub> <mo>&Element;</mo> <mo>[</mo> <msub> <mi>α</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>]</mo> </mrow> </math>

If it is still satisfied, if yes, the left boundary value of the interval is alpha_nAnd interval right boundary value alpha_n+1If not, ifThen add the n +1 th carrier to the set phi_kOf medium, i.e. phi_k={i|i≤n+1，i∈Ω_k，leftThe left boundary value alpha of the modification interval_nHas a value ofModified interval right boundary value alpha_n+1Has a value of

<math> <mrow> <msub> <mi>α</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>α</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>&NotEqual;</mo> <mi>l</mi> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </munderover> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>3</mn> </mrow> </msub> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>H</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>

Repeating the above steps until the conditions

Meets the requirements;

(2) calculating a fast power water filling threshold:wherein M is_kAs a set of phi_kThe number of the elements in (B).