CN113423141A - Bilateral matching-based downlink multi-carrier NOMA system resource allocation method - Google Patents

Bilateral matching-based downlink multi-carrier NOMA system resource allocation method Download PDF

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CN113423141A
CN113423141A CN202110600160.XA CN202110600160A CN113423141A CN 113423141 A CN113423141 A CN 113423141A CN 202110600160 A CN202110600160 A CN 202110600160A CN 113423141 A CN113423141 A CN 113423141A
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CN113423141B (en
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徐鼎
黎家慧
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0453—Resources in frequency domain, e.g. a carrier in FDMA
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/03—Protecting confidentiality, e.g. by encryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/12—Detection or prevention of fraud
    • H04W12/121—Wireless intrusion detection systems [WIDS]; Wireless intrusion prevention systems [WIPS]
    • H04W12/122—Counter-measures against attacks; Protection against rogue devices
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/542—Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/543—Allocation or scheduling criteria for wireless resources based on quality criteria based on requested quality, e.g. QoS
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/56—Allocation or scheduling criteria for wireless resources based on priority criteria
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention discloses a downlink multi-carrier NOMA system resource allocation method based on bilateral matching, and aims to solve the problem that safety-oriented multi-carrier NOMA system resource allocation research is lacked in the prior art. The invention is different from a single carrier NOMA system which only uses one carrier to carry out information transmission, considers the downlink transmission of the multi-carrier NOMA system, and provides a user and sub-carrier matching method based on a bilateral matching algorithm and a sub-carrier power distribution method based on a binary search algorithm under the requirements of the user reachable rate and the total power limit and with the aim of maximizing the system secret throughput. The invention can obviously improve the safety performance of the system while ensuring that the service quality of all users is met.

Description

基于双边匹配的下行多载波NOMA系统资源分配方法Resource allocation method for downlink multi-carrier NOMA system based on bilateral matching

技术领域technical field

本发明涉及一种基于双边匹配的下行多载波NOMA系统资源分配方法，属于无线通信技术领域。The invention relates to a downlink multi-carrier NOMA system resource allocation method based on bilateral matching, and belongs to the technical field of wireless communication.

背景技术Background technique

多载波接入系统将多总频段带宽进行子载波划分并分配给用户，能够优化频谱利用率，此外，各种无线终端设备爆炸式增长，海量连接性的要求日益迫切，这些都促使多载波NOMA系统研究受到越来越多的关注。对于多载波NOMA系统，要充分利用NOMA技术优势，关键是如何将功率、子载波等资源最优地分配给用户，使系统性能最大化。现有的针对NOMA系统的研究多用系统的吞吐量或者能量效率作为优化目标，针对安全性能的优化考虑较少，但NOMA技术中一个载波上传输的是若干用户的叠加信号，窃听者拦截信号后对簇内所有用户都有影响，因此NOMA系统的安全性是值得考虑的。The multi-carrier access system divides and allocates sub-carriers of multiple total frequency bands to users, which can optimize spectrum utilization. In addition, the explosive growth of various wireless terminal equipment and the increasingly urgent requirements for massive connectivity have prompted multi-carrier NOMA Systems research has received more and more attention. For a multi-carrier NOMA system, to make full use of the technical advantages of NOMA, the key is how to optimally allocate resources such as power and sub-carriers to users to maximize system performance. The throughput or energy efficiency of the multi-purpose system in the existing research on NOMA system is taken as the optimization goal, and the optimization of security performance is less considered. However, in NOMA technology, a carrier transmits the superimposed signals of several users. It affects all users in the cluster, so the security of NOMA system is worth considering.

此外，目前关于NOMA系统的安全性讨论集中在单载波NOMA系统上，面向安全的多载波NOMA系统资源分配问题仅对特定中继场景做了讨论，不利于多载波NOMA系统的发展和应用。In addition, the current security discussions on NOMA systems focus on single-carrier NOMA systems, and the security-oriented multi-carrier NOMA system resource allocation problem is only discussed in specific relay scenarios, which is not conducive to the development and application of multi-carrier NOMA systems.

发明内容SUMMARY OF THE INVENTION

针对现有技术中缺乏面向安全的多载波NOMA系统资源分配研究的问题，本发明提出了一种基于双边匹配的下行多载波NOMA系统资源分配方法，能够在用户可达速率要求和总功率限制下最大化系统的保密吞吐量，以提升多载波NOMA系统的安全性能。Aiming at the problem of lack of security-oriented multi-carrier NOMA system resource allocation research in the prior art, the present invention proposes a downlink multi-carrier NOMA system resource allocation method based on bilateral matching, which can meet the requirements of user achievable rate and total power limit. Maximize the security throughput of the system to improve the security performance of multi-carrier NOMA systems.

为解决上述技术问题，本发明采用了如下技术手段：In order to solve the above-mentioned technical problems, the present invention adopts the following technical means:

本发明提出了基于双边匹配的下行多载波NOMA系统资源分配方法，包括如下步骤：The present invention proposes a downlink multi-carrier NOMA system resource allocation method based on bilateral matching, including the following steps:

在用户可达速率和基站传输功率约束下，以下行多载波NOMA系统的保密吞吐量作为目标函数，获取用户子载波匹配和用户功率分配的联合优化问题；Under the constraints of user achievable rate and base station transmission power, the secrecy throughput of the downlink multi-carrier NOMA system is taken as the objective function to obtain the joint optimization problem of user subcarrier matching and user power allocation;

对下行多载波NOMA系统中的用户进行用户配对，获得用户对集，并获得用户对集中每个用户对的子载波优先级列表；Perform user pairing on users in the downlink multi-carrier NOMA system, obtain a user pair set, and obtain a subcarrier priority list of each user pair in the user pair set;

基于联合优化问题，根据子载波优先级列表对用户对集中每个未匹配的用户对进行资源匹配，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。Based on the joint optimization problem, resource matching is performed for each unmatched user pair in the user pair set according to the subcarrier priority list, and the user subcarrier matching and user power allocation that maximize the security throughput are obtained.

进一步的，所述下行多载波NOMA系统包括一个基站、K个用户和1个窃听者，下行多载波NOMA系统中共有M个子载波，K＝2M。Further, the downlink multi-carrier NOMA system includes one base station, K users and one eavesdropper, and there are M sub-carriers in the downlink multi-carrier NOMA system, K=2M.

进一步的，用户子载波匹配和用户功率分配的联合优化问题的表达式如下：Further, the expression of the joint optimization problem of user subcarrier matching and user power allocation is as follows:

Figure BDA0003092454760000021
Figure BDA0003092454760000021

Figure BDA0003092454760000031
Figure BDA0003092454760000031

Figure BDA0003092454760000032
Figure BDA0003092454760000032

其中，{UCn，m}表示用户子载波匹配，UCn，m表示第m个子载波上的第n个用户，{pn，m}表示用户功率分配，pn，m表示用户UCn，m用户的功率，

Figure BDA0003092454760000033
表示用户UCn，m的保密容量，Rn，m表示用户UCn，m的可达速率，
Figure BDA0003092454760000034
表示用户UCn，m的窃听速率，Rmin表示下行多载波NOMA系统中的可达速率最小值，P表示下行多载波NOMA系统中基站的最大总发射功率，
Figure BDA0003092454760000035
为下行多载波NOMA系统的总用户集，
Figure BDA0003092454760000036
为下行多载波NOMA系统的子载波集合，UCn′，m′表示第m′个子载波上的第n′个用户，m＝1，2，…，M，M为下行多载波NOMA系统中子载波的总数。Among them, {UC n, m } represents the user subcarrier matching, UC n, m represents the nth user on the mth subcarrier, { pn, m } represents the user power allocation, pn, m represents the user UC n, the power of m users,
Figure BDA0003092454760000033
is the secret capacity of user UC n, m , R n, m is the reachable rate of user UC n, m ,
Figure BDA0003092454760000034
Represents the eavesdropping rate of user UC n, m , R min represents the minimum achievable rate in the downlink multi-carrier NOMA system, P represents the maximum total transmit power of the base station in the downlink multi-carrier NOMA system,
Figure BDA0003092454760000035
is the total user set of the downlink multi-carrier NOMA system,
Figure BDA0003092454760000036
is the subcarrier set of the downlink multi-carrier NOMA system, UC n', m' represents the n'th user on the m'th subcarrier, m=1, 2, ..., M, M is the neutron of the downlink multi-carrier NOMA system The total number of carriers.

进一步的，获得用户对集和用户对集中每个用户对的子载波优先级列表的方法为：Further, the method for obtaining the user pair set and the subcarrier priority list of each user pair in the user pair set is:

根据下行多载波NOMA系统中每个用户的信道，获取信道降序配列的总用户集

Figure BDA0003092454760000037
其中，K为下行多载波NOMA系统中的用户总数；According to the channel of each user in the downlink multi-carrier NOMA system, obtain the total user set of channels in descending order
Figure BDA0003092454760000037
Among them, K is the total number of users in the downlink multi-carrier NOMA system;

将总用户集

Figure BDA0003092454760000039
中的前K/2个用户与后K/2个用户两两配对，获得用户对集
Figure BDA0003092454760000038
其中，Ui表示第i个用户对，Ui＝{i，i+M}，i＝1，2，…，M，M＝K/2，M为下行多载波NOMA系统中子载波的总数；total user set
Figure BDA0003092454760000039
The first K/2 users are paired with the last K/2 users to obtain a user pair set
Figure BDA0003092454760000038
Among them, U i represents the i-th user pair, U i ={i,i+M}, i=1,2,...,M, M=K/2, M is the total number of subcarriers in the downlink multi-carrier NOMA system ;

针对用户对Ui，根据用户对Ui在各个子载波上的信道对下行多载波NOMA系统中的所有子载波进行降序排列，获得用户对Ui的子载波优先级列表。For the user pair U i , according to the channel of the user pair U i on each sub-carrier, all sub-carriers in the downlink multi-carrier NOMA system are sorted in descending order to obtain the sub-carrier priority list of the user pair U i .

进一步的，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配的方法包括如下步骤：Further, the method for obtaining user subcarrier matching and user power allocation that maximizes the security throughput includes the following steps:

(1)初始化随机数λ，令未匹配用户对集

Figure BDA0003092454760000041
子载波匹配集合
Figure BDA0003092454760000042
和子载波匹配容量
Figure BDA0003092454760000043
其中，λ为正整数，m＝1，2，…，M；(1) Initialize the random number λ, so that the set of unmatched user pairs
Figure BDA0003092454760000041
Subcarrier matching set
Figure BDA0003092454760000042
and subcarrier matching capacity
Figure BDA0003092454760000043
Among them, λ is a positive integer, m=1, 2, ..., M;

(2)当

Figure BDA0003092454760000044
时，{U_un}中所有用户对同时向各自子载波优先级列表中优先级最高的子载波发送匹配请求，计算每个未匹配的用户对在每个子载波上的功率，并获得每个未匹配的用户对在每个子载波上的保密容量；(2) When
Figure BDA0003092454760000044
When , all user pairs in {U_un} simultaneously send matching requests to the subcarrier with the highest priority in their respective subcarrier priority lists, calculate the power of each unmatched user pair on each subcarrier, and obtain each unmatched user pair secrecy capacity on each subcarrier;

(3)根据用户对在子载波上的保密容量、子载波匹配集合和子载波匹配容量进行匹配判断，确定每个子载波的匹配用户对，并更新子载波匹配集合、子载波优先级列表和未匹配用户对集；(3) According to the user's matching judgment on the secrecy capacity, sub-carrier matching set and sub-carrier matching capacity on the sub-carrier, determine the matching user pair of each sub-carrier, and update the sub-carrier matching set, sub-carrier priority list and unmatched user pair set;

(4)根据更新后的子载波匹配集合、子载波优先级列表和未匹配用户对集重复步骤(2)、(3)，直到

Figure BDA0003092454760000045
(4) Repeat steps (2) and (3) according to the updated subcarrier matching set, subcarrier priority list and unmatched user pairing set, until
Figure BDA0003092454760000045

(5)根据匹配用户对更新每个子载波上的数据，完成子载波与用户对的匹配操作；(5) update the data on each subcarrier according to the matched user pair, and complete the matching operation of the subcarrier and the user pair;

(6)根据预设的更新步长更新随机数λ，并判断λ是否收敛，当λ未收敛时，返回步骤(1)，否则，结束迭代，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。(6) Update the random number λ according to the preset update step size, and judge whether λ converges. When λ does not converge, return to step (1), otherwise, end the iteration to obtain the user subcarrier matching that maximizes the security throughput and user power allocation.

进一步的，步骤(2)中，用户对Ui在第m个子载波上的功率的计算公式如下：Further, in step (2), the user's formula for calculating the power of U i on the mth subcarrier is as follows:

Figure BDA0003092454760000051
Figure BDA0003092454760000051

p2，m＝pm-p1，m (3)p 2,m = p m -p 1,m (3)

Figure BDA0003092454760000052
Figure BDA0003092454760000052

其中，p1，m表示用户对Ui中第1个用户在第m个子载波上的功率，

Figure BDA0003092454760000053
Rmin表示下行多载波NOMA系统中的可达速率最小值，Bsc表示子载波的带宽，
Figure BDA0003092454760000054
Figure BDA0003092454760000055
表示基站到第m个子载波上第n个用户的信道系数，n∈{1，2}，σ2表示子载波上的信道噪声方差，pm表示第m个子载波的功率，p2，m表示用户对Ui中第2个用户在第m个子载波上的功率，
Figure BDA0003092454760000056
Figure BDA0003092454760000057
gm表示基站到窃听者的信道系数，
Figure BDA0003092454760000058
表示第m个子载波的最小功率。Among them, p 1, m represents the power of the user to the 1st user in U i on the mth subcarrier,
Figure BDA0003092454760000053
R min represents the minimum achievable rate in the downlink multi-carrier NOMA system, B sc represents the subcarrier bandwidth,
Figure BDA0003092454760000054
Figure BDA0003092454760000055
represents the channel coefficient from the base station to the nth user on the mth subcarrier, n∈{1, 2 }, σ2 represents the channel noise variance on the subcarrier, p m represents the power of the mth subcarrier, p2 , m represents The power of the user to the second user in U i on the mth subcarrier,
Figure BDA0003092454760000056
Figure BDA0003092454760000057
g m represents the channel coefficient from the base station to the eavesdropper,
Figure BDA0003092454760000058
Indicates the minimum power of the mth subcarrier.

进一步的，步骤(2)中，用户对Ui在第m个子载波上的保密容量的计算方法为：Further, in step (2), the calculation method of the secret capacity of U i on the mth subcarrier by the user is:

根据用户对Ui在第m个子载波上的功率计算用户对Ui中每个用户的可达速率和窃听速率；Calculate the reachable rate and the eavesdropping rate of each user in U i according to the power of the user pair U i on the mth subcarrier;

根据用户的可达速率和窃听速率计算用户对Ui中每个用户的保密速率：Calculate the secret rate for each user in U i according to the user's reachable rate and eavesdropping rate:

Figure BDA0003092454760000059
Figure BDA0003092454760000059

其中，

Figure BDA00030924547600000510
表示用户对Ui中第n个用户在第m个子载波上的保密速率，n∈{1，2}，Rn，m表示用户对Ui中第n个用户在第m个子载波上的可达速率，
Figure BDA0003092454760000061
表示用户对Ui中第n个用户在第m个子载波上的窃听速率；in,
Figure BDA00030924547600000510
Represents the secrecy rate of the user to the nth user in U i on the mth subcarrier, n∈{1,2}, R n,m represents the availability of the user to the nth user in Ui on the mth subcarrier reach rate,
Figure BDA0003092454760000061
represents the eavesdropping rate of the user on the mth subcarrier for the nth user in U i ;

根据每个用户的保密速率计算用户对Ui在第m个子载波上的保密容量：Calculate the secrecy capacity of the user for U i on the mth subcarrier according to the secrecy rate of each user:

Figure BDA0003092454760000062
Figure BDA0003092454760000062

进一步的，步骤(3)的具体操作如下：Further, the concrete operation of step (3) is as follows:

当第m个子载波SCm的子载波匹配集合

Figure BDA0003092454760000063
时，认为SCm未匹配，从向SCm发送匹配请求的所有用户对中选择保密容量最大的用户对Ui作为SCm的匹配用户对，将用户对Ui加入{SC_m(m)}，将SCm从其他未匹配的用户对的子载波优先级列表中删除，并将用户对Ui从未匹配用户对集{U_un}中删除；When the subcarriers of the mth subcarrier SC m match the set
Figure BDA0003092454760000063
When SC m is considered unmatched, the user pair U i with the largest secret capacity is selected from all user pairs that send matching requests to SC m as the matching user pair for SC m , and the user pair U i is added to {SC_m(m)}, delete SC m from the subcarrier priority list of other unmatched user pairs, and delete user pair U i from the set of unmatched user pairs {U_un};

当第m个子载波SCm的子载波匹配集合

Figure BDA0003092454760000064
时，认为SCm已与用户对Uj匹配，j=1，2，…，M且j≠i，从向SCm发送匹配请求的所有用户对中选择保密容量最大的用户对Ui，将用户对Ui在SCm上的保密容量
Figure BDA0003092454760000065
与SCm的子载波匹配容量
Figure BDA0003092454760000066
比较，当
Figure BDA0003092454760000067
时，SCm拒绝用户对Ui的匹配请求，将SCm从用户对Ui的子载波优先级列表PL_SC(Ui)中删除；当
Figure BDA0003092454760000068
时，选择用户对Ui作为SCm的匹配用户对，SCm拒绝用户对Uj的匹配请求，利用用户对Ui替换{SC_m(m)}中的用户对Uj，将SCm从用户对Uj的子载波优先级列表PL_SC(Uj)中删除，并将用户对Uj加入未匹配用户对集{U_un}中。When the subcarriers of the mth subcarrier SC m match the set
Figure BDA0003092454760000064
When , it is considered that SC m has been matched with user pair U j , j =1, 2 , . User's secret capacity for U i on SC m
Figure BDA0003092454760000065
Subcarrier matching capacity with SC m
Figure BDA0003092454760000066
compare when
Figure BDA0003092454760000067
, SC m rejects the user's matching request for U i , and deletes SC m from the user's subcarrier priority list PL_SC(U i ) for U i ; when
Figure BDA0003092454760000068
When the user pair U i is selected as the matching user pair of SC m , SC m rejects the user’s matching request for U j , replaces the user pair U j in {SC_m(m)} with the user pair U i , and replaces SC m from the user pair U j with the user pair U i. Delete the sub-carrier priority list PL_SC(U j ) for U j , and add the user pair U j to the unmatched user pair set {U_un}.

进一步的，设用户对Ui为第m个子载波SCm的匹配用户对，则步骤(5)的具体操作为：Further, suppose that the user pair U i is the matching user pair of the mth subcarrier SC m , then the specific operation of step (5) is:

将用户对Ui与第m个子载波SCm匹配，

Figure BDA0003092454760000069
并根据用户对Ui依次更新子载波SCm的匹配用户对、子载波匹配容量和用户功率分配，其中，子载波SCm的匹配用户对如下：Match the user pair U i with the mth subcarrier SC m ,
Figure BDA0003092454760000069
And according to the user pair U i , the matched user pair, subcarrier matching capacity and user power allocation of subcarrier SC m are updated in turn, wherein, the matched user pair of subcarrier SC m is as follows:

Figure BDA0003092454760000071
Figure BDA0003092454760000071

其中，

Figure BDA0003092454760000072
表示子载波SCm的匹配用户对，UC1，m表示第m个子载波上的第1个用户，UC2，m表示第m个子载波上的第2个用户。in,
Figure BDA0003092454760000072
represents the matched user pair of subcarrier SC m , UC 1,m represents the 1st user on the mth subcarrier, and UC2 ,m represents the 2nd user on the mth subcarrier.

进一步的，步骤(6)中，根据预设的更新步长更新随机数λ的公式如下：Further, in step (6), the formula for updating the random number λ according to the preset update step size is as follows:

Figure BDA0003092454760000073
Figure BDA0003092454760000073

其中，θ为更新步长，P表示下行多载波NOMA系统中基站的最大总发射功率。Among them, θ is the update step size, and P represents the maximum total transmit power of the base station in the downlink multi-carrier NOMA system.

采用以上技术手段后可以获得以下优势：After adopting the above technical means, the following advantages can be obtained:

本发明提出了一种基于双边匹配的下行多载波NOMA系统资源分配方法，不同于单载波NOMA系统仅使用一个载波进行信息传播，本发明充分考虑多载波NOMA系统下行传输，在多载波传输的场景中，以用户可达速率要求和总功率作为约束，以最大化系统保密吞吐量为目标进行子载波匹配和功率分配的联合优化，本发明基于双边匹配算法获得用户对集，并按照子载波优先级对每个用户对进行子载波匹配，才外，基于二分搜索算法为每个用户对进行子载波功率分配，最终获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。本发明方法可以在保证满足所有用户服务质量的同时显著提高系统安全性能。The present invention proposes a downlink multi-carrier NOMA system resource allocation method based on bilateral matching. Unlike the single-carrier NOMA system that only uses one carrier for information dissemination, the present invention fully considers the downlink transmission of the multi-carrier NOMA system, and in the scenario of multi-carrier transmission In the method, the user's reachable rate requirement and total power are used as constraints, and the joint optimization of sub-carrier matching and power allocation is carried out with the goal of maximizing the system security throughput. The subcarrier matching is performed for each user pair at the first level, and the subcarrier power allocation is performed for each user pair based on the binary search algorithm, and finally the user subcarrier matching and user power allocation that maximize the security throughput are obtained. The method of the invention can significantly improve the security performance of the system while ensuring that the service quality of all users is satisfied.

附图说明Description of drawings

图1为本发明基于双边匹配的下行多载波NOMA系统资源分配方法的步骤流程图；Fig. 1 is the step flow chart of the downlink multi-carrier NOMA system resource allocation method based on bilateral matching of the present invention;

图2为本发明实施例中下行多载波NOMA系统的模型示意图；2 is a schematic diagram of a model of a downlink multi-carrier NOMA system in an embodiment of the present invention;

图3为本发明实施例中用户子载波匹配和用户功率分配的步骤流程图；3 is a flowchart of steps for user subcarrier matching and user power allocation in an embodiment of the present invention;

图4为本发明实施例中不同多址方式和用户总数下的保密吞吐量相对于P的变化示意图；FIG. 4 is a schematic diagram of the variation of the security throughput with respect to P under different multiple access modes and the total number of users in an embodiment of the present invention;

图5为本发明实施例中不同发射功率和用户总数下的保密吞吐量相对于Rmin的变化示意图；FIG. 5 is a schematic diagram of the variation of the security throughput with respect to R min under different transmit powers and the total number of users in an embodiment of the present invention;

图6为本发明实施例中不同多址方式和发射功率下的保密吞吐量相对于de的变化示意图。FIG. 6 is a schematic diagram illustrating the variation of the security throughput with respect to de under different multiple access modes and transmit powers according to an embodiment of the present invention.

具体实施方式Detailed ways

下面结合附图对本发明的技术方案作进一步说明：Below in conjunction with accompanying drawing, technical scheme of the present invention is further described:

本发明提出了基于双边匹配的下行多载波NOMA系统资源分配方法，如图1所示，包括如下步骤：The present invention proposes a downlink multi-carrier NOMA system resource allocation method based on bilateral matching, as shown in Figure 1, including the following steps:

步骤A、在用户可达速率和基站传输功率约束下，以下行多载波NOMA系统的保密吞吐量作为目标函数，获取用户子载波匹配和用户功率分配的联合优化问题；Step A, under user reachable rate and base station transmission power constraints, obtain the joint optimization problem of user subcarrier matching and user power allocation as the objective function of the security throughput of the downstream multi-carrier NOMA system;

步骤B、对下行多载波NOMA系统中的用户进行用户配对，获得用户对集，并获得用户对集中每个用户对的子载波优先级列表；Step B, performing user pairing on users in the downlink multi-carrier NOMA system, obtaining a user pair set, and obtaining a subcarrier priority list of each user pair in the user pair set;

步骤C、基于联合优化问题，根据子载波优先级列表对用户对集中每个未匹配的用户对进行资源匹配，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。Step C: Based on the joint optimization problem, resource matching is performed on each unmatched user pair in the user pair set according to the subcarrier priority list to obtain user subcarrier matching and user power allocation that maximizes the security throughput.

本发明方法考虑的场景如图2所示，在一个下行多载波NOMA系统中包括一个基站、K个用户和1个窃听者，系统的总用户集

Figure BDA0003092454760000081
Figure BDA0003092454760000091
中从用户1到用户K信道降序排列。下行多载波NOMA系统中共有M个子载波，K＝2M。本发明实施例中的下行多载波NOMA系统的总频谱带宽为B，被平分为M个子载波，每个子载波的带宽为Bsc＝B/M，这些子载波的集合为
Figure BDA0003092454760000092
本发明方法用SCm代表第m个子载波。The scenario considered by the method of the present invention is shown in Figure 2. A downlink multi-carrier NOMA system includes a base station, K users and an eavesdropper, and the total user set of the system
Figure BDA0003092454760000081
Figure BDA0003092454760000091
The channels are arranged in descending order from user 1 to user K. There are totally M sub-carriers in the downlink multi-carrier NOMA system, K=2M. The total spectrum bandwidth of the downlink multi-carrier NOMA system in the embodiment of the present invention is B, which is equally divided into M sub-carriers, the bandwidth of each sub-carrier is B sc =B/M, and the set of these sub-carriers is
Figure BDA0003092454760000092
The method of the present invention uses SC m to represent the mth subcarrier.

在本发明方法中，假设每个用户只占用一个子载波，每个子载波上有2个用户，则K＝2M，用UC1，m和UC2，m分别代表子载波SCm上的两个用户，SCm上的用户对可以表示为UCm＝{UC1，m，UC2，m}，

Figure BDA0003092454760000093
n∈{1，2}，并且
Figure BDA0003092454760000094
表示基站到SCm上第1个用户的信道系数，
Figure BDA0003092454760000095
表示基站到SCm上第2个用户的信道系数，UC1，m和UC2，m功率分别是p1，m和p2，m。下行多载波NOMA系统基站的最大总发射功率为P，所有用户发射功率总和不能大于P，即需满足
Figure BDA0003092454760000096
在接收端，考虑保守的窃听情况，窃听者也能成功进行SIC来解码用户信息。In the method of the present invention, it is assumed that each user occupies only one sub-carrier, and there are 2 users on each sub-carrier, then K=2M, and UC 1,m and UC 2,m respectively represent the two sub-carriers on the sub-carrier SC m User, user pair on SC m can be expressed as UC m ={UC 1,m ,UC 2,m },
Figure BDA0003092454760000093
n ∈ {1, 2}, and
Figure BDA0003092454760000094
represents the channel coefficient from the base station to the first user on SC m ,
Figure BDA0003092454760000095
Represents the channel coefficient from the base station to the second user on SC m , the powers of UC 1,m and UC 2,m are p 1,m and p 2,m respectively. The maximum total transmit power of the downlink multi-carrier NOMA system base station is P, and the total transmit power of all users cannot be greater than P, that is, it needs to meet the
Figure BDA0003092454760000096
At the receiving end, considering the conservative eavesdropping situation, the eavesdropper can also successfully perform SIC to decode the user information.

在步骤A中，基于下行多载波NOMA系统，用户子载波匹配和用户功率分配的联合优化问题的表达式如下：In step A, based on the downlink multi-carrier NOMA system, the expression of the joint optimization problem of user subcarrier matching and user power allocation is as follows:

Figure BDA0003092454760000097
Figure BDA0003092454760000097

其中，{UCn，m}表示用户子载波匹配，UCn，m表示第m个子载波上的第n个用户，{pn，m}表示用户功率分配，pn，m表示用户UCn，m用户的功率，

Figure BDA0003092454760000101
表示用户UCn，m的保密容量，Rn，m表示用户UCn，m的可达速率，
Figure BDA0003092454760000102
表示用户UCn，m的窃听速率，Rmin表示下行多载波NOMA系统中的可达速率最小值，
Figure BDA0003092454760000103
为下行多载波NOMA系统的总用户集，
Figure BDA0003092454760000104
为下行多载波NOMA系统的子载波集合，UCn′，m′表示第m′个子载波上的第n′个用户，m＝1，2，…，M，M为下行多载波NOMA系统中子载波的总数。Among them, {UC n, m } represents the user subcarrier matching, UC n, m represents the nth user on the mth subcarrier, { pn, m } represents the user power allocation, pn, m represents the user UC n, the power of m users,
Figure BDA0003092454760000101
is the secret capacity of user UC n, m , R n, m is the reachable rate of user UC n, m ,
Figure BDA0003092454760000102
represents the eavesdropping rate of user UC n, m , R min represents the minimum achievable rate in the downlink multi-carrier NOMA system,
Figure BDA0003092454760000103
is the total user set of the downlink multi-carrier NOMA system,
Figure BDA0003092454760000104
is the subcarrier set of the downlink multi-carrier NOMA system, UC n', m' represents the n'th user on the m'th subcarrier, m=1, 2, ..., M, M is the neutron of the downlink multi-carrier NOMA system The total number of carriers.

在本发明实施例中，步骤B的具体操作如下：In the embodiment of the present invention, the specific operation of step B is as follows:

步骤B01、根据下行多载波NOMA系统中每个用户的信道，获取信道降序配列的总用户集

Figure BDA0003092454760000105
其中，K为下行多载波NOMA系统中的用户总数。Step B01, according to the channel of each user in the downlink multi-carrier NOMA system, obtain the total user set of the channel arrangement in descending order
Figure BDA0003092454760000105
Among them, K is the total number of users in the downlink multi-carrier NOMA system.

步骤B02、将总用户集

Figure BDA00030924547600001011
中的前K/2个用户与后K/2个用户两两配对，获得用户对集
Figure BDA0003092454760000106
其中，Ui表示第i个用户对，Ui＝{i，i+M}，i＝1，2，…，M，M＝K/2。Step B02, set the total user set
Figure BDA00030924547600001011
The first K/2 users are paired with the last K/2 users to obtain a user pair set
Figure BDA0003092454760000106
Wherein, U i represents the i-th user pair, U i ={i, i+M}, i=1, 2, ..., M, M=K/2.

步骤B03、针对用户对Ui，根据用户对Ui在各个子载波上的信道对下行多载波NOMA系统中的所有子载波进行降序排列，获得用户对Ui的子载波优先级列表PL_SC(Ui)。Step B03, for the user to U i , according to the channel of the user to U i on each sub-carrier, all sub-carriers in the downlink multi-carrier NOMA system are arranged in descending order to obtain the sub-carrier priority list PL_SC (U i ).

在本发明实施例中，如图3所示，步骤C的具体操作如下：In the embodiment of the present invention, as shown in FIG. 3, the specific operation of step C is as follows:

步骤C01、初始化随机数λ，令未匹配用户对集

Figure BDA0003092454760000107
子载波匹配集合
Figure BDA0003092454760000108
和子载波匹配容量
Figure BDA0003092454760000109
其中，λ为正整数。Step C01, initialize the random number λ, so that the unmatched user pair set
Figure BDA0003092454760000107
Subcarrier matching set
Figure BDA0003092454760000108
and subcarrier matching capacity
Figure BDA0003092454760000109
where λ is a positive integer.

步骤C02、当

Figure BDA00030924547600001010
时，{U_un}中所有用户对同时向各自子载波优先级列表中优先级最高的子载波发送匹配请求，计算每个未匹配的用户对在每个子载波上的功率，并获得每个未匹配的用户对在每个子载波上的保密容量。Step C02, when
Figure BDA00030924547600001010
When , all user pairs in {U_un} simultaneously send matching requests to the subcarrier with the highest priority in their respective subcarrier priority lists, calculate the power of each unmatched user pair on each subcarrier, and obtain each unmatched The user pair secrecy capacity on each subcarrier.

201、未匹配的用户对Ui在第m个子载波上的功率的计算公式如下：201. The formula for calculating the power of U i on the mth subcarrier by the unmatched users is as follows:

Figure BDA0003092454760000111
Figure BDA0003092454760000111

p2，m＝pm-p1，m (11)p 2,m = p m -p 1,m (11)

Figure BDA0003092454760000112
Figure BDA0003092454760000112

其中，p1，m表示用户对Ui中第1个用户在第m个子载波上的功率，

Figure BDA0003092454760000113
表示基站到第m个子载波上第n个用户的信道系数，n∈{1，2}，σ2表示子载波上的信道噪声方差，pm表示第m个子载波的功率，p2，m表示用户对Ui中第2个用户在第m个子载波上的功率，
Figure BDA0003092454760000114
Figure BDA0003092454760000115
gm表示基站到窃听者的信道系数，
Figure BDA0003092454760000116
表示第m个子载波的最小功率。Among them, p 1, m represents the power of the user to the 1st user in U i on the mth subcarrier,
Figure BDA0003092454760000113
represents the channel coefficient from the base station to the nth user on the mth subcarrier, n∈{1, 2 }, σ2 represents the channel noise variance on the subcarrier, p m represents the power of the mth subcarrier, p2 , m represents The power of the user to the second user in U i on the mth subcarrier,
Figure BDA0003092454760000114
Figure BDA0003092454760000115
g m represents the channel coefficient from the base station to the eavesdropper,
Figure BDA0003092454760000116
Indicates the minimum power of the mth subcarrier.

202、根据用户对Ui在第m个子载波上的功率(p1，m和p2，m)计算用户对Ui中每个用户的可达速率和窃听速率，具体计算公式如下：202. Calculate the reachable rate and the eavesdropping rate of each user in U i according to the power (p 1, m and p 2, m ) of the user to U i on the mth subcarrier, and the specific calculation formula is as follows:

Figure BDA0003092454760000117
Figure BDA0003092454760000117

Figure BDA0003092454760000118
Figure BDA0003092454760000118

其中，Rn，m表示用户对Ui中第n个用户在第m个子载波上的可达速率，

Figure BDA0003092454760000121
表示用户对Ui中第n个用户在第m个子载波上的窃听速率，
Figure BDA0003092454760000122
表示第m个子载波上第
Figure BDA0003092454760000123
个用户的功率。Among them, R n, m represents the achievable rate of the user to the n-th user in U i on the m-th subcarrier,
Figure BDA0003092454760000121
represents the eavesdropping rate of the user on the mth subcarrier for the nth user in U i ,
Figure BDA0003092454760000122
represents the mth subcarrier on the mth subcarrier
Figure BDA0003092454760000123
power of each user.

203、根据用户的可达速率和窃听速率计算用户对Ui中每个用户的保密速率：203. Calculate the secret rate of the user for each user in U i according to the user's reachable rate and the eavesdropping rate:

Figure BDA0003092454760000124
Figure BDA0003092454760000124

其中，

Figure BDA0003092454760000125
表示用户对Ui中第n个用户在第m个子载波上的保密速率。in,
Figure BDA0003092454760000125
Indicates the secrecy rate of the user to the n-th user in U i on the m-th subcarrier.

204、根据每个用户的保密速率计算用户对Ui在第m个子载波上的保密容量：204. Calculate the security capacity of the user for U i on the mth subcarrier according to the security rate of each user:

Figure BDA0003092454760000126
Figure BDA0003092454760000126

步骤C03、根据用户对在子载波上的保密容量、子载波匹配集合和子载波匹配容量进行匹配判断，确定每个子载波的匹配用户对，并更新子载波匹配集合、子载波优先级列表和未匹配用户对集。Step C03, according to the user's matching judgment on the secrecy capacity on the subcarrier, the subcarrier matching set and the subcarrier matching capacity, determine the matching user pair of each subcarrier, and update the subcarrier matching set, the subcarrier priority list and the unmatched User pair set.

在本发明中，所有未匹配的用户对会同时向各自最优子载波发送匹配请求，如果子载波还未匹配，只收到一个请求就与该用户对匹配，若有多个请求则选择保密容量最大的用户对匹配，如果子载波在前面阶段已经匹配了用户对，则请求的用户对需要与已匹配的用户对一起比较，选择其中保密容量最大的用户对进行匹配。成功匹配的用户对从{U_un}中删除，被拒绝请求的用户对仍归入{U_un}，不断进行匹配直至全匹配完毕，

Figure BDA0003092454760000127
In the present invention, all unmatched user pairs will send matching requests to their respective optimal subcarriers at the same time. If the subcarriers have not yet been matched, only one request is received to match the user pair, and if there are multiple requests, it will be kept secret. The user pair with the largest capacity is matched. If the subcarrier has already matched the user pair in the previous stage, the requested user pair needs to be compared with the matched user pair, and the user pair with the largest privacy capacity is selected for matching. User pairs that are successfully matched will be deleted from {U_un}, and user pairs that have been rejected are still classified as {U_un}, and will continue to match until all matches are completed.
Figure BDA0003092454760000127

步骤C03的具体操作如下：The specific operation of step C03 is as follows:

301、当第m个子载波SCm的子载波匹配集合

Figure BDA0003092454760000128
时，认为SCm未匹配，从向SCm发送匹配请求的所有用户对中选择保密容量最大的用户对Ui作为SCm的匹配用户对，将用户对Ui加入{SC_m(m)}，将SCm从其他未匹配的用户对的子载波优先级列表中删除，并将用户对Ui从未匹配用户对集{U_un}中删除。301. When the subcarriers of the mth subcarrier SC m match the set
Figure BDA0003092454760000128
When SC m is considered unmatched, the user pair U i with the largest secret capacity is selected from all user pairs that send matching requests to SC m as the matching user pair for SC m , and the user pair U i is added to {SC_m(m)}, Remove SC m from the subcarrier priority list of other unmatched user pairs, and remove user pair U i from the set of unmatched user pairs {U_un}.

302、当第m个子载波SCm的子载波匹配集合

Figure BDA0003092454760000131
时，认为SCm已与用户对Uj匹配，j＝1，2，…，M且j≠i，从向SCm发送匹配请求的所有用户对中选择保密容量最大的用户对Ui，将用户对Ui在SCm上的保密容量
Figure BDA0003092454760000132
与SCm的子载波匹配容量
Figure BDA0003092454760000133
比较，当
Figure BDA0003092454760000134
时，SCm拒绝用户对Ui的匹配请求，将SCm从用户对Ui的子载波优先级列表PL_SC(Ui)中删除；当
Figure BDA0003092454760000135
时，选择用户对Ui作为SCm的匹配用户对，SCm拒绝用户对Uj的匹配请求，利用用户对Ui替换{SC_m(m)}中的用户对Uj，将SCm从用户对Uj的子载波优先级列表PL_SC(Uj)中删除，并将用户对Uj加入未匹配用户对集{U_un}中。302. When the subcarriers of the mth subcarrier SC m match the set
Figure BDA0003092454760000131
When , it is considered that SC m has been matched with user pair U j , j =1, 2 , . User's secret capacity for U i on SC m
Figure BDA0003092454760000132
Subcarrier matching capacity with SC m
Figure BDA0003092454760000133
compare when
Figure BDA0003092454760000134
, SC m rejects the user's matching request for U i , and deletes SC m from the user's subcarrier priority list PL_SC(U i ) for U i ; when
Figure BDA0003092454760000135
When the user pair U i is selected as the matching user pair of SC m , SC m rejects the user’s matching request for U j , replaces the user pair U j in {SC_m(m)} with the user pair U i , and replaces SC m from the user pair U j with the user pair U i. Delete the sub-carrier priority list PL_SC(U j ) for U j , and add the user pair U j to the unmatched user pair set {U_un}.

步骤C04、根据更新后的子载波匹配集合、子载波优先级列表和未匹配用户对集重复步骤(2)、(3)，直到

Figure BDA0003092454760000136
将所有用户对于子载波建立匹配关系。Step C04: Repeat steps (2) and (3) according to the updated subcarrier matching set, the subcarrier priority list and the unmatched user pair set, until
Figure BDA0003092454760000136
All users are matched with subcarriers.

步骤C05、根据匹配用户对更新每个子载波上的数据，完成子载波与用户对的匹配操作。设用户对Ui为第m个子载波SCm的匹配用户对，则步骤C05的具体操作为：Step C05: Update the data on each subcarrier according to the matched user pair, and complete the matching operation of the subcarrier and the user pair. Let the user pair U i be the matched user pair of the mth subcarrier SC m , then the specific operation of step C05 is:

将用户对Ui与第m个子载波SCm匹配，

Figure BDA0003092454760000137
并根据用户对Ui依次更新子载波SCm的匹配用户对、子载波匹配容量和用户功率分配，其中，更新子载波SCm的匹配用户对的操作如下：Match the user pair U i with the mth subcarrier SC m ,
Figure BDA0003092454760000137
And according to the user pair U i , the matching user pair, the subcarrier matching capacity and the user power allocation of the subcarrier SC m are updated in turn, wherein, the operation of updating the matching user pair of the subcarrier SC m is as follows:

Figure BDA0003092454760000141
Figure BDA0003092454760000141

其中，

Figure BDA0003092454760000142
表示子载波SCm的匹配用户对，UC1，m表示第m个子载波上的第1个用户，UC2，m表示第m个子载波上的第2个用户。in,
Figure BDA0003092454760000142
represents the matched user pair of subcarrier SC m , UC 1,m represents the 1st user on the mth subcarrier, and UC2 ,m represents the 2nd user on the mth subcarrier.

更新子载波匹配容量和用户功率分配的操作为：

Figure BDA0003092454760000143
Figure BDA0003092454760000144
其中，
Figure BDA0003092454760000145
和
Figure BDA0003092454760000146
分别表示第m个子载波SCm上第1个用户和第2个用户的功率分配值。The operations to update the subcarrier matching capacity and user power allocation are:
Figure BDA0003092454760000143
Figure BDA0003092454760000144
in,
Figure BDA0003092454760000145
and
Figure BDA0003092454760000146
respectively represent the power allocation values of the first user and the second user on the mth subcarrier SC m .

步骤C06、根据预设的更新步长更新随机数λ，并判断λ是否收敛，当λ未收敛时，返回步骤C01，进行迭代运算；当λ收敛时，结束迭代，根据最终的

Figure BDA0003092454760000147
和
Figure BDA0003092454760000148
获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。Step C06, update the random number λ according to the preset update step size, and judge whether λ converges, when λ does not converge, return to step C01, and perform iterative operation; when λ converges, end the iteration, according to the final
Figure BDA0003092454760000147
and
Figure BDA0003092454760000148
User subcarrier matching and user power allocation are obtained that maximize security throughput.

在步骤C06中，根据预设的更新步长更新随机数λ的公式如下：In step C06, the formula for updating the random number λ according to the preset update step size is as follows:

Figure BDA0003092454760000149
Figure BDA0003092454760000149

其中，θ为更新步长。Among them, θ is the update step size.

为了验证本发明方法的效果，给出了如下对比实验：In order to verify the effect of the inventive method, the following comparative experiments are provided:

下行多载波NOMA系统的总传输带宽B为5MHz，每个子载波上的信道噪声方差均为

Figure BDA00030924547600001410
其中，噪声功率谱密度N0＝-70dBm。在子载波SCm上，从基站到第k个用户的信道增益定义为
Figure BDA00030924547600001411
α是路径损失指数，
Figure BDA00030924547600001412
是瑞利衰落信道增益，
Figure BDA00030924547600001413
是用户k与基站之间的距离，基站到窃听者的信道增益定义为
Figure BDA00030924547600001414
de是窃听者与基站之间的距离，默认
Figure BDA00030924547600001415
The total transmission bandwidth B of the downlink multi-carrier NOMA system is 5MHz, and the channel noise variance on each subcarrier is
Figure BDA00030924547600001410
Among them, the noise power spectral density N 0 =-70dBm. On subcarrier SC m , the channel gain from the base station to the kth user is defined as
Figure BDA00030924547600001411
α is the path loss index,
Figure BDA00030924547600001412
is the Rayleigh fading channel gain,
Figure BDA00030924547600001413
is the distance between user k and the base station, and the channel gain from the base station to the eavesdropper is defined as
Figure BDA00030924547600001414
d e is the distance between the eavesdropper and the base station, the default
Figure BDA00030924547600001415

对比实验分别在用户集

Figure BDA00030924547600001416
总数目K＝10、K＝20下仿真了本发明NOMA方案和OFDMA参考方案，对比讨论不同方案中系统保密吞吐量Rs
Figure BDA0003092454760000151
随着基站发射功率P、最小可达速率Rmin和基站与窃听者的距离de的变化，具体方针结果如图4～6所示。Comparative experiments were performed on the user set
Figure BDA00030924547600001416
The NOMA scheme of the present invention and the OFDMA reference scheme are simulated under the total number K=10 and K=20, and the system security throughput R s in different schemes is compared and discussed.
Figure BDA0003092454760000151
As the base station transmit power P, the minimum reachable rate R min and the distance d e between the base station and the eavesdropper change, the specific policy results are shown in Figures 4-6.

图4表明了在不同用户总数下，NOMA和OFDMA两种下行多载波资源分配方案中系统保密吞吐量Rs与基站发射功率P之间的关系，其中，设置用户最小可达速率Rmin＝1Mbps，基站到窃听者的距离de＝50m。从图4可以看出，保密吞吐量Rs随着基站发射功率P的增大而增大，并且随着P持续增大，保密吞吐量Rs的增长速度逐渐变缓且趋于平稳，这是因为基站的发射功率越大，经过路径损耗后用户和窃听者接收到的信号的功率就越大，用户保密容量是关于功率单调递增的；此外，子载波SCm上用户UCn，m的保密容量

Figure BDA0003092454760000152
的是关于P的两个对数函数之差，其导数随着P的增大而减小，趋近于0但大于0，故当P增大时，系统保密吞吐量Rs的增长速率会变缓且趋于稳定。从图4显然看出，在用户集
Figure BDA0003092454760000153
总数目K＝10、K＝20下，本发明的NOMA方案都优于OFDMA方案，因为OFDMA方案一个子载波上传输一个用户的信息，频谱效率更低，而本发明设置的NOMA传输中一个子载波传输两个用户，具有分集优势，而且本发明联合用户子载波匹配和功率分配，在用户QoS限制下，能以最大限度地提高多载波NOMA安全性能。Figure 4 shows the relationship between the system secrecy throughput R s and the base station transmit power P in the two downlink multi-carrier resource allocation schemes of NOMA and OFDMA under different total numbers of users, where the minimum user achievable rate R min =1Mbps is set , the distance from the base station to the eavesdropper de =50m. It can be seen from Fig. 4 that the security throughput R s increases with the increase of the transmit power P of the base station, and as P continues to increase, the growth rate of the security throughput R s gradually slows down and tends to be stable. It is because the greater the transmit power of the base station, the greater the power of the signal received by the user and the eavesdropper after the path loss, and the user privacy capacity is monotonically increasing with respect to the power; in addition, the user UC n, m on the subcarrier SC m has a higher power. Confidential capacity
Figure BDA0003092454760000152
is the difference between the two logarithmic functions of P, and its derivative decreases with the increase of P, approaching 0 but greater than 0, so when P increases, the growth rate of the system security throughput R s will be slowed down and stabilized. It is evident from Figure 4 that in the user set
Figure BDA0003092454760000153
Under the total number K=10 and K=20, the NOMA scheme of the present invention is superior to the OFDMA scheme, because the OFDMA scheme transmits information of one user on one subcarrier, and the spectral efficiency is lower, while the NOMA transmission set by the present invention has a subcarrier in one subcarrier. The carrier transmits two users, which has the advantage of diversity, and the invention combines user subcarrier matching and power allocation, and can maximize the multi-carrier NOMA security performance under the user QoS restriction.

图5表明了在不同用户总数和不同最大发射功率下，本发明方法中系统保密吞吐量Rs与用户最小可达速率Rmin之间的关系，其中，最大基站发射功率P取10dBm、30dBm，基站到窃听者的距离de＝50m。图5展示了QoS要求对系统保密吞吐量Rs的影响，随着Rmin的增加，Rs减小，这是因为Rmin的增加需要发射机利用额外的功率来提高信道条件较差的用户的数据速率，因此，当Rmin变得非常大时，此时P不能满足所有用户的QoS要求，基站不向用户发送消息，Rs＝0。从图5还可以看出，用户数目相同时，P越大Rs下降得越晚，因为P越大能够提供更高的用户QoS要求，并且功率相同时，用户数目越少下降得越晚，因为用户少则有限的功率能够满足这些少数人更高的QoS要求。Figure 5 shows the relationship between the system security throughput R s and the minimum reachable rate R min of users in the method of the present invention under different total numbers of users and different maximum transmit powers, wherein the maximum base station transmit power P is 10dBm, 30dBm, The distance from the base station to the eavesdropper de =50m. Figure 5 shows the effect of QoS requirements on the system security throughput R s , R s decreases as R min increases, because an increase in R min requires the transmitter to utilize additional power to boost users with poor channel conditions Therefore, when R min becomes very large, at this time, P cannot meet the QoS requirements of all users, the base station does not send messages to users, and R s =0. It can also be seen from Figure 5 that when the number of users is the same, the larger the P is, the later the R s declines, because the larger the P is, the higher the user QoS requirements can be. Because the limited power of users can meet the higher QoS requirements of these few people.

图6表明了在不同用户总数和不同最大发射功率下，本发明NOMA方案和OFDMA方案中系统保密吞吐量Rs与基站到窃听者的距离de之间的关系，其中，设置用户最小可达速率Rmin＝1Mbps，基站发射功率P取20dBm、30dBm。图6可以看出，随着基站到窃听者的距离de的增大，保密吞吐量Rs攀升十分快速，这是因为距离越远，基站到窃听者间的路径损耗越大，信道增益gm越差，窃听者接收到的信号功率就越小，窃听速率越小，子载波SCm上用户UCn，m的保密容量

Figure BDA0003092454760000161
就越大，系统保密吞吐量Rs就越大，同时，在不同功率下，NOMA方案的保密吞吐量Rs都高于OFDMA方案，因此本发明方法具有更高的安全性能。图6中，P＝30dBm时，NOMA和OFDMA下的系统保密吞吐量Rs在de＝1000m时开始平稳，而P＝20dBm时，Rs在de＝500m时开始平稳，总发射功率阈值更小能更早保持稳定，这是因为功率越大，在经过路径损耗后窃听者接收到的功率也就越大，窃听速率也就越大，窃听的风险就越大，而小功率情况更容易达到窃听风险趋于0的状态。从图6还可以看出，NOMA和OFDMA两种方案中，当基站到窃听者的距离de持续增大时，保密吞吐量Rs最终都会保持平稳，这是因为距离足够远时，窃听者拦截的信号经过了较大路径损耗，功率会很小，系统会不断趋近于一种无窃听者状态，导致窃听者的速率趋向于0，保密速率趋向于可达速率，保密吞吐量趋向于无窃听者下的吞吐量，因此当基站到窃听者的距离de非常大时，NOMA和OFDMA两种方案的保密吞吐量都会保持在无窃听的总吞吐量数值附近Figure 6 shows the relationship between the system security throughput R s and the distance d e from the base station to the eavesdropper in the NOMA scheme and OFDMA scheme of the present invention under different total numbers of users and different maximum transmit powers, wherein the minimum user reachable The rate R min =1 Mbps, and the transmit power P of the base station is 20 dBm and 30 dBm. It can be seen from Fig. 6 that with the increase of the distance de from the base station to the eavesdropper, the security throughput R s rises very rapidly. This is because the longer the distance, the greater the path loss between the base station and the eavesdropper , and the channel gain g The worse m is, the lower the signal power received by the eavesdropper and the lower the eavesdropping rate, the lower the security capacity of the user UC n, m on the subcarrier SC m .
Figure BDA0003092454760000161
The larger the value is, the larger the system security throughput R s is. At the same time, under different powers, the security throughput R s of the NOMA scheme is higher than that of the OFDMA scheme, so the method of the present invention has higher security performance. In Fig. 6, when P=30dBm, the system security throughput R s under NOMA and OFDMA starts to stabilize at d e =1000m, and when P=20dBm, R s starts to stabilize at d e =500m, and the total transmit power threshold Smaller can be stabilized earlier, because the higher the power, the more power the eavesdropper receives after the path loss, the greater the eavesdropping rate, the greater the risk of eavesdropping, and the lower the power. It is easy to reach a state where the eavesdropping risk tends to zero. It can also be seen from Figure 6 that in the NOMA and OFDMA schemes, when the distance de from the base station to the eavesdropper continues to increase, the secrecy throughput Rs will eventually remain stable, because when the distance is far enough, the eavesdropper The intercepted signal has undergone a large path loss, the power will be very small, and the system will continue to approach a state of no eavesdropper, resulting in the eavesdropper's rate tending to 0, the security rate tending to the reachable rate, and the security throughput tending to be The throughput without eavesdropping, so when the distance d e from the base station to the eavesdropper is very large, the secrecy throughput of both NOMA and OFDMA schemes will remain close to the total throughput value without eavesdropping

与现有技术相比，本发明方法可以在保证满足所有用户服务质量的同时显著提高系统安全性能。Compared with the prior art, the method of the present invention can significantly improve the system security performance while ensuring that the service quality of all users is satisfied.

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变形，这些改进和变形也应视为本发明的保护范围。The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the technical principle of the present invention, several improvements and modifications can also be made. These improvements and modifications It should also be regarded as the protection scope of the present invention.

Claims (10)

1.基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，包括如下步骤：1. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching, is characterized in that, comprises the steps: 在用户可达速率和基站传输功率约束下，以下行多载波NOMA系统的保密吞吐量作为目标函数，获取用户子载波匹配和用户功率分配的联合优化问题；Under the constraints of user achievable rate and base station transmission power, the secrecy throughput of the downlink multi-carrier NOMA system is taken as the objective function to obtain the joint optimization problem of user subcarrier matching and user power allocation; 对下行多载波NOMA系统中的用户进行用户配对，获得用户对集，并获得用户对集中每个用户对的子载波优先级列表；Perform user pairing on users in the downlink multi-carrier NOMA system, obtain a user pair set, and obtain a subcarrier priority list of each user pair in the user pair set; 基于联合优化问题，根据子载波优先级列表对用户对集中每个未匹配的用户对进行资源匹配，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。Based on the joint optimization problem, resource matching is performed for each unmatched user pair in the user pair set according to the subcarrier priority list, and the user subcarrier matching and user power allocation that maximize the security throughput are obtained. 2.根据权利要求1所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，所述下行多载波NOMA系统包括一个基站、K个用户和1个窃听者，下行多载波NOMA系统中共有M个子载波，K＝2M。2. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 1, is characterized in that, described downlink multi-carrier NOMA system comprises a base station, K users and 1 eavesdropper, downlink multi-carrier NOMA There are totally M subcarriers in the system, K=2M. 3.根据权利要求1所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，用户子载波匹配和用户功率分配的联合优化问题的表达式如下：3. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 1, is characterized in that, the expression of the joint optimization problem of user subcarrier matching and user power allocation is as follows:
Figure FDA0003092454750000011
Figure FDA0003092454750000011
Figure FDA0003092454750000012
Figure FDA0003092454750000012
Figure FDA0003092454750000013
Figure FDA0003092454750000013
 pn，m≥0p n, m ≥ 0
Figure FDA0003092454750000021
Figure FDA0003092454750000021
Figure FDA0003092454750000022
Figure FDA0003092454750000022
 其中，{UCn，m}表示用户子载波匹配，UCn，m表示第m个子载波上的第n个用户，{pn，m}表示用户功率分配，pn，m表示用户UCn，m用户的功率，
Figure FDA0003092454750000023
表示用户UCn，m的保密容量，Rn，m表示用户UCn，m的可达速率，
Figure FDA0003092454750000024
表示用户UCn，m的窃听速率，Rmin表示下行多载波NOMA系统中的可达速率最小值，P表示下行多载波NOMA系统中基站的最大总发射功率，
Figure FDA0003092454750000025
为下行多载波NOMA系统的总用户集，
Figure FDA0003092454750000026
为下行多载波NOMA系统的子载波集合，UCn′，m′表示第m′个子载波上的第n′个用户，m＝1，2，…，M，M为下行多载波NOMA系统中子载波的总数。Among them, {UC n, m } represents the user subcarrier matching, UC n, m represents the nth user on the mth subcarrier, { pn, m } represents the user power allocation, pn, m represents the user UC n, the power of m users,
Figure FDA0003092454750000023
is the secret capacity of user UC n, m , R n, m is the reachable rate of user UC n, m ,
Figure FDA0003092454750000024
Represents the eavesdropping rate of user UC n, m , R min represents the minimum achievable rate in the downlink multi-carrier NOMA system, P represents the maximum total transmit power of the base station in the downlink multi-carrier NOMA system,
Figure FDA0003092454750000025
is the total user set of the downlink multi-carrier NOMA system,
Figure FDA0003092454750000026
is the subcarrier set of the downlink multi-carrier NOMA system, UC n', m' represents the n'th user on the m'th subcarrier, m=1, 2, ..., M, M is the neutron of the downlink multi-carrier NOMA system The total number of carriers. 4.根据权利要求1所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，获得用户对集和用户对集中每个用户对的子载波优先级列表的方法为：4. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 1, is characterized in that, the method that obtains the subcarrier priority list of each user pair in user pair set and user pair set is: 根据下行多载波NOMA系统中每个用户的信道，获取信道降序配列的总用户集
Figure FDA0003092454750000027
其中，K为下行多载波NOMA系统中的用户总数；According to the channel of each user in the downlink multi-carrier NOMA system, obtain the total user set of channels in descending order
Figure FDA0003092454750000027
Among them, K is the total number of users in the downlink multi-carrier NOMA system; 将总用户集
Figure FDA0003092454750000028
中的前K/2个用户与后K/2个用户两两配对，获得用户对集
Figure FDA0003092454750000029
其中，Ui表示第i个用户对，Ui＝{i，i+M}，i＝1，2，…，M，M＝K/2，M为下行多载波NOMA系统中子载波的总数；total user set
Figure FDA0003092454750000028
The first K/2 users are paired with the last K/2 users to obtain a user pair set
Figure FDA0003092454750000029
Among them, U i represents the i-th user pair, U i ={i,i+M}, i=1,2,...,M, M=K/2, M is the total number of subcarriers in the downlink multi-carrier NOMA system ; 针对用户对Ui，根据用户对Ui在各个子载波上的信道对下行多载波NOMA系统中的所有子载波进行降序排列，获得用户对Ui的子载波优先级列表。For the user pair U i , according to the channel of the user pair U i on each sub-carrier, all sub-carriers in the downlink multi-carrier NOMA system are sorted in descending order to obtain the sub-carrier priority list of the user pair U i . 5.根据权利要求1或4所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配的方法包括如下步骤：5. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 1 or 4, is characterized in that, obtaining the method for user subcarrier matching and user power allocation that maximizes the secrecy throughput comprises the steps: (1)初始化随机数λ，令未匹配用户对集
Figure FDA0003092454750000031
子载波匹配集合
Figure FDA0003092454750000032
和子载波匹配容量
Figure FDA0003092454750000033
其中，λ为正整数，m＝1，2，…，M；(1) Initialize the random number λ, so that the set of unmatched user pairs
Figure FDA0003092454750000031
Subcarrier matching set
Figure FDA0003092454750000032
and subcarrier matching capacity
Figure FDA0003092454750000033
Among them, λ is a positive integer, m=1, 2, ..., M; (2)当
Figure FDA0003092454750000034
时，{U_un}中所有用户对同时向各自子载波优先级列表中优先级最高的子载波发送匹配请求，计算每个未匹配的用户对在每个子载波上的功率，并获得每个未匹配的用户对在每个子载波上的保密容量；(2) When
Figure FDA0003092454750000034
When , all user pairs in {U_un} simultaneously send matching requests to the subcarrier with the highest priority in their respective subcarrier priority lists, calculate the power of each unmatched user pair on each subcarrier, and obtain each unmatched user pair secrecy capacity on each subcarrier; (3)根据用户对在子载波上的保密容量、子载波匹配集合和子载波匹配容量进行匹配判断，确定每个子载波的匹配用户对，并更新子载波匹配集合、子载波优先级列表和未匹配用户对集；(3) According to the user's matching judgment on the secrecy capacity, sub-carrier matching set and sub-carrier matching capacity on the sub-carrier, determine the matching user pair of each sub-carrier, and update the sub-carrier matching set, sub-carrier priority list and unmatched user pair set; (4)根据更新后的子载波匹配集合、子载波优先级列表和未匹配用户对集重复步骤(2)、(3)，直到
Figure FDA0003092454750000035
(4) Repeat steps (2) and (3) according to the updated subcarrier matching set, subcarrier priority list and unmatched user pairing set, until
Figure FDA0003092454750000035
 (5)根据匹配用户对更新每个子载波上的数据，完成子载波与用户对的匹配操作；(5) update the data on each subcarrier according to the matched user pair, and complete the matching operation of the subcarrier and the user pair; (6)根据预设的更新步长更新随机数λ，并判断λ是否收敛，当λ未收敛时，返回步骤(1)，否则，结束迭代，获得令保密吞吐量最大化的用户子载波匹配和用户功率分配。(6) Update the random number λ according to the preset update step size, and judge whether λ converges. When λ does not converge, return to step (1), otherwise, end the iteration to obtain the user subcarrier matching that maximizes the security throughput and user power allocation. 6.根据权利要求5所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，步骤(2)中，用户对Ui在第m个子载波上的功率的计算公式如下：6. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 5, is characterized in that, in step (2), the calculation formula of the power of user to U i on the mth subcarrier is as follows:
Figure FDA0003092454750000041
Figure FDA0003092454750000041
 p2，m＝pm-p1，m p 2,m =p m -p 1,m
Figure FDA0003092454750000042
Figure FDA0003092454750000042
 其中，p1，m表示用户对Ui中第1个用户在第m个子载波上的功率，
Figure FDA0003092454750000043
Rmin表示下行多载波NOMA系统中的可达速率最小值，Bsc表示子载波的带宽，
Figure FDA0003092454750000044
Figure FDA0003092454750000045
表示基站到第m个子载波上第n个用户的信道系数，n∈{1，2}，σ2表示子载波上的信道噪声方差，pm表示第m个子载波的功率，p2，m表示用户对Ui中第2个用户在第m个子载波上的功率，
Figure FDA0003092454750000046
Figure FDA0003092454750000047
gm表示基站到窃听者的信道系数，
Figure FDA0003092454750000048
表示第m个子载波的最小功率。Among them, p 1, m represents the power of the user to the 1st user in U i on the mth subcarrier,
Figure FDA0003092454750000043
R min represents the minimum achievable rate in the downlink multi-carrier NOMA system, B sc represents the subcarrier bandwidth,
Figure FDA0003092454750000044
Figure FDA0003092454750000045
represents the channel coefficient from the base station to the nth user on the mth subcarrier, n∈{1, 2 }, σ2 represents the channel noise variance on the subcarrier, p m represents the power of the mth subcarrier, p2 , m represents The power of the user to the second user in U i on the mth subcarrier,
Figure FDA0003092454750000046
Figure FDA0003092454750000047
g m represents the channel coefficient from the base station to the eavesdropper,
Figure FDA0003092454750000048
Indicates the minimum power of the mth subcarrier. 7.根据权利要求5所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，步骤(2)中，用户对Ui在第m个子载波上的保密容量的计算方法为：7. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 5, is characterized in that, in step (2), the calculation method of the secret capacity of user to U i on the mth subcarrier is: 根据用户对Ui在第m个子载波上的功率计算用户对Ui中每个用户的可达速率和窃听速率；Calculate the reachable rate and the eavesdropping rate of each user in U i according to the power of the user pair U i on the mth subcarrier; 根据用户的可达速率和窃听速率计算用户对Ui中每个用户的保密速率：Calculate the secret rate for each user in U i according to the user's reachable rate and eavesdropping rate:
Figure FDA0003092454750000051
Figure FDA0003092454750000051
 其中，
Figure FDA0003092454750000052
表示用户对Ui中第n个用户在第m个子载波上的保密速率，n∈{1，2}，Rn，m表示用户对Ui中第n个用户在第m个子载波上的可达速率，
Figure FDA0003092454750000053
表示用户对Ui中第n个用户在第m个子载波上的窃听速率；in,
Figure FDA0003092454750000052
Represents the secrecy rate of the user to the nth user in U i on the mth subcarrier, n∈{1,2}, R n,m represents the availability of the user to the nth user in Ui on the mth subcarrier reach rate,
Figure FDA0003092454750000053
represents the eavesdropping rate of the user on the mth subcarrier for the nth user in U i ; 根据每个用户的保密速率计算用户对Ui在第m个子载波上的保密容量：Calculate the secrecy capacity of the user for U i on the mth subcarrier according to the secrecy rate of each user:
Figure FDA0003092454750000054
Figure FDA0003092454750000054
 8.根据权利要求5所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，步骤(3)的具体操作如下：8. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 5, is characterized in that, the concrete operation of step (3) is as follows: 当第m个子载波SCm的子载波匹配集合
Figure FDA0003092454750000055
时，认为SCm未匹配，从向SCm发送匹配请求的所有用户对中选择保密容量最大的用户对Ui作为SCm的匹配用户对，将用户对Ui加入{SC_m(m)}，将SCm从其他未匹配的用户对的子载波优先级列表中删除，并将用户对Ui从未匹配用户对集{U_un}中删除；When the subcarriers of the mth subcarrier SC m match the set
Figure FDA0003092454750000055
When SC m is considered unmatched, the user pair U i with the largest secret capacity is selected from all user pairs that send matching requests to SC m as the matching user pair for SC m , and the user pair U i is added to {SC_m(m)}, delete SC m from the subcarrier priority list of other unmatched user pairs, and delete user pair U i from the set of unmatched user pairs {U_un}; 当第m个子载波SCm的子载波匹配集合
Figure FDA0003092454750000056
时，认为SCm已与用户对Uj匹配，j＝1，2，…，M且j≠i，从向SCm发送匹配请求的所有用户对中选择保密容量最大的用户对Ui，将用户对Ui在SCm上的保密容量
Figure FDA0003092454750000057
与SCm的子载波匹配容量
Figure FDA0003092454750000058
比较，当
Figure FDA0003092454750000059
时，SCm拒绝用户对Ui的匹配请求，将SCm从用户对Ui的子载波优先级列表PL_SC(Ui)中删除；当
Figure FDA00030924547500000510
时，选择用户对Ui作为SCm的匹配用户对，SCm拒绝用户对Uj的匹配请求，利用用户对Ui替换{SC_m(m)}中的用户对Uj，将SCm从用户对Uj的子载波优先级列表PL_SC(Uj)中删除，并将用户对Uj加入未匹配用户对集{U_un}中。When the subcarriers of the mth subcarrier SC m match the set
Figure FDA0003092454750000056
When , it is considered that SC m has been matched with user pair U j , j =1, 2 , . User's secrecy capacity for U i on SC m
Figure FDA0003092454750000057
Subcarrier matching capacity with SC m
Figure FDA0003092454750000058
compare when
Figure FDA0003092454750000059
, SC m rejects the user's matching request for U i , and deletes SC m from the user's subcarrier priority list PL_SC(U i ) for U i ; when
Figure FDA00030924547500000510
When the user pair U i is selected as the matching user pair of SC m , SC m rejects the user’s matching request for U j , replaces the user pair U j in {SC_m(m)} with the user pair U i , and replaces SC m from the user pair U j with the user pair U i. Delete the sub-carrier priority list PL_SC(U j ) for U j , and add the user pair U j to the unmatched user pair set {U_un}. 9.根据权利要求5所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，设用户对Ui为第m个子载波SCm的匹配用户对，则步骤(5)的具体操作为：9. the downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 5, is characterized in that, suppose that user pair U i is the matched user pair of mth subcarrier SC m , then the concrete of step (5) The operation is: 将用户对Ui与第m个子载波SCm匹配，
Figure FDA0003092454750000061
并根据用户对Ui依次更新子载波SCm的匹配用户对、子载波匹配容量和用户功率分配，其中，子载波SCm的匹配用户对如下：Match the user pair U i with the mth subcarrier SC m ,
Figure FDA0003092454750000061
And according to the user pair U i , the matched user pair, subcarrier matching capacity and user power allocation of subcarrier SC m are updated in turn, wherein, the matched user pair of subcarrier SC m is as follows:
Figure FDA0003092454750000062
Figure FDA0003092454750000062
 其中，
Figure FDA0003092454750000063
表示子载波SCm的匹配用户对，UC1，m表示第m个子载波上的第1个用户，UC2，m表示第m个子载波上的第2个用户。in,
Figure FDA0003092454750000063
represents the matched user pair of subcarrier SC m , UC 1,m represents the 1st user on the mth subcarrier, and UC2 ,m represents the 2nd user on the mth subcarrier. 10.根据权利要求5所述的基于双边匹配的下行多载波NOMA系统资源分配方法，其特征在于，步骤(6)中，根据预设的更新步长更新随机数λ的公式如下：10. The downlink multi-carrier NOMA system resource allocation method based on bilateral matching according to claim 5, is characterized in that, in step (6), the formula for updating random number λ according to preset update step size is as follows:
Figure FDA0003092454750000064
Figure FDA0003092454750000064
 其中，θ为更新步长，P表示下行多载波NOMA系统中基站的最大总发射功率。Among them, θ is the update step size, and P represents the maximum total transmit power of the base station in the downlink multi-carrier NOMA system.
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