WO2023231165A1 - 一种基于Stackelberg博弈的多频段群智频谱感知方法 - Google Patents
一种基于Stackelberg博弈的多频段群智频谱感知方法 Download PDFInfo
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- H—ELECTRICITY
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- the invention belongs to the field of communication technology, and specifically relates to a multi-frequency group intelligence spectrum sensing method based on Stackelberg game.
- Cognitive Radio technology can greatly improve spectrum utilization through spectrum sharing.
- Spectrum sensing is an important part of cognitive radio technology.
- Spectrum holes refer to idle frequency bands that are legally used but not occupied by authorized users (AU).
- Cognitive radio can allow secondary users (SU) to access the spectrum holes.
- AU authorized users
- SU secondary users
- the process of detecting and confirming the existence of authorized users through spectrum sensing technology is particularly important.
- Secondary user spectrum sensing usually uses the energy detection method, which does not require prior knowledge of the authorized user. It determines whether the authorized user exists by calculating whether the accumulated energy in the frequency band exceeds the threshold value.
- the perception results of a single secondary user on the licensed frequency band are often unreliable, and the collaborative spectrum sensing performance of multiple secondary users is better than that of a single secondary user. User perception performance, therefore multiple secondary users are usually used for collaborative spectrum sensing.
- Literature [10] proposes a cooperative spectrum sensing algorithm based on SU classification, which introduces an incentive mechanism to encourage more SUs to actively participate in detection.
- the algorithm divides secondary users into ordinary secondary users (OSU) and relay secondary users according to channel conditions.
- User (RSU) first each SU decides whether to participate by calculating the utility function, then the OSU sends the detected data to the nearby RSU, and then the RSU sends the received data together with the local detection data to the fusion center.
- the above-mentioned research only focuses on spectrum sensing in a single frequency band. In actual systems, multiple frequency bands often need to be occupied, and this research does not consider the optimization of secondary user perception costs, resulting in high sensing costs.
- the present invention introduces crowd intelligence sensing technology into spectrum sensing, considers multi-band scenarios, and proposes a multi-band group intelligence spectrum sensing method based on Stackelberg game to reduce the sensing cost of cooperative sensing secondary users by optimizing sensing time.
- the purpose of this invention is to overcome the shortcomings of sensing a single frequency band in the existing technology and provide a multi-band crowd intelligence spectrum sensing method based on Stackelberg game.
- the sensing demand is The secondary user recruits appropriate collaborative sensing secondary users to complete the sensing task, improves the enthusiasm for collaborative sensing, optimizes the sensing time of the cooperative sensing secondary user during the game process, saves sensing costs, and improves sensing performance.
- the present invention adopts the following technical solutions.
- Secondary users the set of secondary users with perceived needs is expressed as The set of collaboration-aware secondary users is expressed as
- the method includes the following steps:
- Step 1 Construct a subordinate layer optimization problem and deduce that there is a Nash equilibrium solution for the cooperative sensing secondary user game: comprehensively consider the detection probability and sensing time to define the utility function of the cooperative sensing secondary user to maximize the utility of the cooperative sensing secondary user;
- Step 2 Construct a leadership optimization problem: comprehensively considering the detection probability and task reward after voting and fusion, the utility function of the perceived demand sub-user is defined to maximize the utility of the perceived demand sub-user;
- Step 3 Construct the problem of payment of rewards from the sensing demand secondary users to the collaborative sensing secondary users into a multi-band crowd intelligence spectrum sensing system model based on Stackelberg game.
- the sensing demand secondary users are the leadership layer
- the collaborative sensing secondary users are the subordinate layers.
- each cooperative sensing secondary user can sense all frequency bands, but can only sense one frequency band at the same time;
- Step 4 The sensing demand sub-user releases tasks and initial rewards to the collaborative sensing sub-user for the frequency band to be sensed, and initializes the maximum utility of the sensing demand sub-user. is 0;
- Step 5 All collaborative sensing secondary users calculate their utility under the current reward based on the reward and sensing time, and select the sensing time corresponding to the maximum utility by optimizing the sensing time.
- the collaborative sensing secondary user calculates the corresponding detection probability and cost based on the sensing time. And transmit the data pairs (sensing time, detection probability, cost-based quotation) to the sensing demand secondary users;
- Step 6 The demand-sensing secondary user sends the recruitment intention and the price of payment to the collaboration-sensing secondary user with high detection probability according to its remuneration;
- Step 7 If the collaborative sensing sub-user is recruited by multiple sensing demand sub-users at the same time, by comparing the price options provided by multiple sensing demand sub-users, the sensing task with higher reward can be added;
- Step 8 Perceived demand sub-users calculate utility under current remuneration. If the utility value is higher than Then record the reward, increase the reward value with a step size ⁇ under the limit of the maximum reward B max , release a new reward and repeat Steps 5-Step 8 until the error of the utility value of the user in two consecutive times of perceived demand is less than ⁇ ;
- Step 9 Use the reward corresponding to the optimal utility of the sensing demand sub-user obtained in Step 8 as the final reward.
- the collaborative sensing secondary user determines the final sensing time based on the reward and uploads the sensing data to the sensing demand secondary user to obtain the final judgment. result.
- T j represents the set of collaborative secondary users participating in frequency band sensing task j.
- the cost c ij of collaborative sensing secondary users is:
- ⁇ and ⁇ represent weighting coefficients
- t ij represents the sensing time of cooperative sensing secondary user i in sensing band task j
- d ij represents the distance between cooperative sensing secondary user i and sensing demand secondary user j.
- p ij represents the reward obtained by the collaborative sensing secondary user i
- c ij represents the cost consumed by the collaborative sensing secondary user i to complete the frequency band sensing task j
- B j represents the reward released by sensing demand secondary user j
- ⁇ and ⁇ represent weighting coefficients
- t ij represents the sensing time of cooperative sensing secondary user i sensing band task j
- d ij represents the distance between the collaboration sensing sub-user i and the sensing demand sub-user j.
- the detection probability formula of cooperative sensing secondary user i sensing frequency band j is:
- p f represents the false alarm probability of secondary user i
- ⁇ ij represents the signal-to-noise ratio of secondary user i sensing frequency band j
- t ij represents the sensing time of secondary user i sensing frequency band j
- f s represents the sampling frequency, usually a fixed value
- the Q function is a complementary cumulative distribution function
- ⁇ represents the weighting coefficient
- B j represents the reward released by sensing demand sub-user j.
- the detection probability of sensing task j after the sensing demand secondary users are fused through voting is expressed as:
- the sampling frequency of the cooperative sensing secondary user is 10kHz
- the false alarm probability is 0.1
- Wireless signal transmission considers large-scale fading, and its fading coefficient is 4,
- the decision threshold value of the voting fusion criterion is N/2.
- the present invention has the following advantages and beneficial effects:
- the method of the present invention models the demand-sensing sub-users and the collaboration-sensing sub-users as the leadership and subordinate layers of the Stackelberg game respectively.
- the optimal strategies of the demand-sensing sub-users and the collaboration-sensing sub-users are obtained, and the leadership game is played
- Optimizing the reward in the medium optimizes the utility of the sensing demand sub-users
- optimizing the sensing time in the subordinate layer game optimizes the utility of the collaborative sensing sub-users.
- the present invention combines spectrum sensing with crowd intelligence sensing, considers multiple sensing needs of secondary users working in different frequency bands, and recruits cooperative sensing secondary users to complete tasks to obtain the usage of different frequency bands.
- one cooperative sensing secondary user Only one frequency band can be sensed at the same time.
- the cooperative sensing secondary user sends the sensing result to the sensing demand secondary user.
- the sensing demand secondary user integrates the results of multiple cooperative sensing sub-users to obtain more accurate sensing results.
- the present invention considers that multiple secondary users with sensing needs working in different frequency bands need to sense different frequency bands. Secondary users with sensing needs issue frequency band sensing tasks and recruit cooperative sensing secondary users to obtain the usage of the frequency band.
- the cooperative sensing sub-users recruited by each sensing demand sub-user are not determined in advance, but change with the game process according to the detection probability, sensing time and quotation of the cooperative sensing sub-users.
- the utility of the sensing demand secondary user in the present invention is defined as comprehensive consideration of detection probability and reward.
- the utility of the collaborative sensing secondary user is defined as reward minus cost.
- the reward is related to the detection probability, the cost is related to the sensing time, and the cooperative sensing secondary user and sensing demand. related to the distance between secondary users.
- the present invention considers reverse selection when selecting a collaborative sensing secondary user.
- a collaborative sensing secondary user is only sent a recruitment intention by one sensing needs secondary user, the collaborative sensing secondary user will complete the sensing task.
- a collaboration sensing sub-user is sent recruitment intentions by multiple sensing demand sub-users at the same time, the sub-user can join the task with the highest reward by comparing the remuneration price options given by multiple sensing demand sub-users.
- Figure 1 is a method flow chart of an embodiment of the present invention.
- Figure 2 is a schematic diagram of a Stackelberg game system model according to an embodiment of the present invention.
- the present invention is a multi-band crowd intelligence spectrum sensing method based on Stackelberg game.
- This method models the problem of sensing demand secondary users paying rewards to collaborative sensing secondary users as a Stackelberg game system model, where the sensing demand secondary users are in the game model.
- the leadership layer, collaborative sensing sub-user is the subordinate layer in the game model.
- Sensing demand sub-users publish frequency band sensing tasks and initial rewards.
- Each collaborative sensing sub-user optimizes its own utility by optimizing sensing time and sends sensing data to sensing demand sub-users. Sensing demand sub-users continuously update their rewards to make them more efficient. The utility is optimized and the final judgment result is obtained.
- this method comprehensively considers the detection probability and reward to define the utility of the sensing demand secondary user, and optimizes the reward through the game to obtain the best utility.
- this method comprehensively considers the detection probability and sensing time to define The utility of the secondary users is collaboratively sensed, and the sensing time is optimized according to the rewards released by the sensing needs to obtain the best utility. The derivation proves that there is a Nash equilibrium in the optimization of the sensing time.
- FIG. 2 is a schematic diagram of a Stackelberg game system model according to an embodiment of the present invention.
- the system scene is a circular area with N collaborative sensing sub-users and M sensing demand sub-users randomly distributed.
- the sampling frequency of the cooperative sensing secondary user is 10kHz
- the false alarm probability is 0.1
- wireless signal transmission considers large-scale fading
- the fading coefficient is 4,
- the decision threshold value of the voting fusion criterion is N/2.
- the sensing demand sub-users will pay rewards to the sub-users who provide sensing results.
- the secondary users existing in the system model of the present invention are divided into two parts.
- the first part of the secondary users work on different frequency bands respectively. If they want to use the authorized frequency band without affecting the authorized users, they first need to issue sensing tasks, and then recruit other idle secondary users for collaborative spectrum sensing to obtain the usage of the frequency band.
- the set of these secondary users with needs is called the sensing demand secondary user set, expressed as The other part is the idle secondary users.
- After receiving the tasks issued by the sensing demand secondary users they sense and upload the sensing results through the smart devices they carry.
- the set of these idle secondary users is called the collaborative sensing secondary user set.
- a multi-band crowd intelligence spectrum sensing method based on Stackelberg game of the present invention includes the following steps:
- Step1 Construct a subordinate layer optimization problem, and deduce that there is a Nash equilibrium solution for the collaborative sensing secondary user game: comprehensively considering the detection probability and sensing time, the utility function of the cooperative sensing secondary user is defined, that is, the optimization problem of the subordinate layer is to make the cooperative sensing secondary user Maximize utility.
- T j represents the set of collaborative secondary users participating in frequency band sensing task j.
- Collaboration-aware secondary users Completing the sensing task requires a cost, including the cost of sensing frequency band consumption and the cost of uploading sensing data.
- the cost of sensing frequency band consumption is related to the sensing time t ij .
- the cost of uploading sensing data is related to the cost of collaborative sensing secondary users. and perceived needs sub-users It is related to the distance between them, so the cost c ij of collaborative sensing secondary users is defined as follows:
- ⁇ and ⁇ represent weighting coefficients
- t ij represents the sensing time of cooperative sensing secondary user i in sensing band task j
- d ij represents the distance between cooperative sensing secondary user i and sensing demand secondary user j.
- p ij represents the collaboration-aware secondary user
- the reward obtained, c ij represents the collaboration-aware secondary user
- the cost of completing the frequency band sensing task Represents the detection probability of cooperative sensing secondary user i sensing band task j
- B j represents the reward released by sensing demand secondary user j
- ⁇ and ⁇ represent weighting coefficients
- t ij represents the sensing time of cooperative sensing secondary user i sensing band task j
- d ij represents the distance between the collaboration sensing sub-user i and the sensing demand sub-user j.
- the secondary user senses whether the spectrum of the authorized user is in use through the energy detection method.
- the detection probability formula of cooperative sensing secondary user i sensing frequency band j is expressed as:
- p f represents the false alarm probability of secondary user i
- ⁇ ij represents the signal-to-noise ratio of secondary user i sensing frequency band j
- t ij represents the sensing time of secondary user i sensing frequency band j
- f s represents the sampling frequency, usually a fixed value
- the Q function is a complementary cumulative distribution function
- the signal-to-noise ratio ⁇ ij are all positive values, so the second part of K' Less than 0, third part is less than 0, and because K ⁇ 0, the first part of K' is less than 0, so K' is less than 0, and because U ij is about the first part of the second-order partial derivative of t ij is greater than 0, so it can be seen that the second-order partial derivative of U ij with respect to t ij Right now
- the utility function U ij is a strictly convex function about t ij , and there is a unique optimal solution.
- the first-order partial derivative of U ij with respect to t ij has a positive value.
- Step 2 Construct the leadership optimization problem: comprehensively considering the detection probability and task reward after voting and fusion, the utility function of the perceived demand sub-user is defined, that is, the leadership optimization problem is to maximize the utility of the perceived demand sub-user.
- ⁇ represents the weighting coefficient
- B j represents the reward released by sensing demand sub-user j.
- Each sensing demand secondary user uses the voting fusion criterion to process the sensing results submitted by multiple collaborative sensing secondary users. After voting fusion, the detection probability of sensing task j is expressed as:
- Step3 Construct the problem of payment of rewards from the sensing demand secondary users to the collaborative sensing secondary users into a multi-band crowd intelligence spectrum sensing system model based on Stackelberg game.
- the sensing demand secondary users are the leadership layer and the collaborative sensing secondary users are the subordinate layers.
- each cooperative sensing secondary user can sense all frequency bands, but can only sense one frequency band at the same time;
- Step 4 The sensing demand secondary user issues tasks and initial rewards to the collaborative sensing secondary user for the frequency band to be sensed, and initializes the maximum utility of the sensing demand secondary user. is 0;
- Step5 All cooperative sensing secondary users calculate their utility under the current reward based on the reward and sensing time, and select the sensing time corresponding to the maximum utility by optimizing the sensing time.
- the cooperative sensing secondary user calculates the corresponding detection probability and cost based on the sensing time. And transmit the data (sensing time, detection probability, cost-based quotation) to the sensing demand secondary users;
- Step6 The demand-sensing secondary user sends the recruitment intention and the price of payment to the collaboration-sensing secondary user with high detection probability according to its remuneration;
- Step7 If the collaborative sensing sub-user is recruited by multiple sensing demand sub-users at the same time, by comparing the price options provided by multiple sensing demand sub-users, the sensing task with the highest reward can be added;
- Step8 The perceived demand sub-user calculates the utility under the current remuneration. If the utility value is higher than Then record the reward, increase the reward value with a step size ⁇ under the limit of the maximum reward B max , release a new reward and repeat Steps 5-Step 8 until the error of the utility value of the user in two consecutive times of perceived demand is less than ⁇ ;
- Step9 Use the reward corresponding to the optimal utility of the sensing demand secondary user obtained in Step 8 as the final reward.
- the collaborative sensing secondary user determines the final sensing time based on the reward and uploads the sensing data to the sensing demand secondary user to obtain the final judgment. result.
- the present invention proposes a multi-band crowd intelligence spectrum sensing method based on Stackelberg game for spectrum sensing scenarios, combined with crowd intelligence sensing technology.
- This method models the problem of payment of rewards from sensing demand sub-users to collaboration sensing sub-users as a Stackelberg game model, where sensing demand sub-users are the leadership in the game model and collaboration sensing sub-users are the subordinate layers in the game model.
- the utility of sensing demand sub-users is defined by comprehensive consideration of detection probability and reward, and the reward is optimized through the game to obtain the best utility
- the utility of collaborative sensing secondary users is defined by comprehensive consideration of detection probability and sensing time.
- Utility according to the perceived demand, the rewards released by users are optimized to obtain the best utility by optimizing the sensing time, and the derivation proves that there is a Nash equilibrium in the optimization of sensing time.
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Abstract
本发明公开了一种基于Stackelberg博弈的多频段群智频谱感知方法，将感知需求次用户向协作感知次用户支付报酬问题建模为博弈模型，其中前者是领导层，后者是从属层。感知需求次用户发布频段感知任务与初始报酬，各协作感知次用户通过优化感知时间使自身效用最优并将感知数据发送给感知需求次用户，感知需求次用户不断更新报酬使效用最优并得到最终判决结果。本发明在领导层博弈中综合考虑检测概率和报酬定义了感知需求次用户效用，通过博弈优化报酬获得最佳效用，从属层博弈中综合考虑检测概率和感知时间定义了协作感知次用户效用，根据感知需求次用户发布报酬优化感知时间以获得最佳效用，推导证明了感知时间的优化存在纳什均衡。
Description
本发明属于通信技术领域，具体涉及一种基于Stackelberg博弈的多频段群智频谱感知方法。
随着智能终端设备的急剧增加，频谱资源日益紧缺，认知无线电技术(Cognitive Radio，CR)可以通过频谱共享大大提高频谱利用率，频谱感知是认知无线电技术的重要环节。频谱空洞是指授权用户(Authorized User，AU)合法使用但未被占用的空闲频段，认知无线电可以将次用户(Second User，SU)机会接入到频谱空洞，但要想实现空闲频谱资源的接入，通过频谱感知技术检测确认授权用户是否存在这一过程尤为重要。
次用户频谱感知通常采用能量检测法，不需要知道授权用户的先验知识，通过计算频段积累的能量是否超过门限值来判断授权用户是否存在。然而面对无线环境中阴影效应、多径衰落、噪声不确定等不利因素的影响，单个次用户对授权频段的感知结果往往是不可靠的，而多个次用户协作频谱感知性能优于单个次用户的感知性能，因此通常采用多个次用户协作频谱感知。关于多用户协作频谱感知的许多研究都是默认次用户无偿感知授权用户是否存在，这在生活中是不现实的，因为次用户在感知过程中会消耗时间、能量、内存等计算资源，所以多用户感知结果虽然更准确，但次用户可能不愿意无偿参与频谱感知过程。因此将激励机制引入频谱感知可以有效解决这一问题，激励机制通过支付报酬的方式补偿次用户的成本，鼓励他们积极参与协作频谱感知。
文献[10]提出了一种基于SU分类的协作频谱感知算法，引入激励机制来鼓励更多的SU积极参与检测，该算法根据信道条件将次用户分为普通次用户(OSU)和中继次用户(RSU)，首先每个SU通过计算效用函数决定是否参与，然后OSU将检测到的数据发送给附近的RSU，接着RSU将收到的数据与本地检测数据一同传送给融合中心。
上述研究只针对单个频段进行频谱感知，在实际系统中，往往需要占用多个频段，并且该研究没有考虑次用户感知成本优化问题，造成感知代价较大。本发明将群智感知技术引入到频谱感知中，考虑多频段的场景，提出了一种基于Stackelberg博弈的多频段群智频谱感知方法，通过优化感知时间减少协作感知次用户的感知成本。
[10]LI Peijun,HAN Bo,LI Heng,et al.The research of spectrum sensing based on SU classification in cognitive LTE-A network[C]//2019 IEEE 3rd Information Technology,Networking,Electronic and Automation Control Conference,Chengdu,China.IEEE,2019:1917-1921.
发明内容
本发明的目的在于克服现有技术感知单个频段的缺陷，提供一种基于Stackelberg博弈的多频段群智频谱感知方法，通过领导层感知需求次用户和从属层协作感知次用户各自博弈，为感知需求次用户招募到合适的协作感知次用户完成感知任务，提高协作感知积极性，在博弈过程中优化协作感知次用户感知时间节约感知成本，提高感知性能。
为解决上述技术问题，本发明采用以下技术方案。
一种基于Stackelberg博弈的多频段群智频谱感知方法，将感知需求次用户向协作感知次用户支付报酬的问题建模为Stackelberg博弈系统模型，其中感知需求次用户是博弈模型中的领导层，协作感知次用户是博弈模型中的从属层；所述系统的场景是一个圆形区域，随机分布有N个协作感知次用户和M个感知需求次用户，取M＝2，即存在两个感知需求次用户；所述的感知需求次用户的集合，表示为
所述的协作感知次用户的集合表示为
所述方法包括以下步骤：
Step1、构建从属层优化问题，并推导协作感知次用户博弈存在纳什均衡解：综合考虑检测概率、感知时间定义协作感知次用户的效用函数，使协作感知次用户的效用最大化；
Step2、构建领导层优化问题：综合考虑经表决融合后的检测概率和任务报酬定义了感知需求次用户的效用函数，使感知需求次用户的效用最大化；
Step3、将感知需求次用户向协作感知次用户支付报酬的问题构建成基于Stackelberg博弈的多频段群智频谱感知系统模型，在博弈模型中感知需求次用户是领导层，协作感知次用户是从属层，每个协作感知次用户可以感知所有频段，但同时只能感知一个频段；
Step4、感知需求次用户对于要感知的频段向协作感知次用户发布任务及初始报酬，初始化感知需求次用户的最大效用
为0；
Step5、所有协作感知次用户根据报酬及感知时间计算其在当前报酬下的效用，通过优化感知时间选择效用最大时对应的感知时间，协作感知次用户根据该感知时间计算对应的检测概率与成本，并将数据对(感知时间，检测概率，基于成本产生的报价)传送给感知需求次用户；
Step6、感知需求次用户根据其报酬向检测概率高的协作感知次用户发送招募意愿及支付报酬的价格；
Step7、若协作感知次用户被多个感知需求次用户同时招募时，通过比较多个感知需求次用户提供的价格选择能够获得报酬多的感知任务加入；
Step8、感知需求次用户计算在当前报酬下的效用，如果该效用值高于
则将该报酬记录下来，在最大报酬B
max的限制下以步长μ增加报酬值，发布新的报酬并重复Step5-Step8，直到相邻两次感知需求次用户的效用值误差小于δ；
Step9、将Step8中得到的感知需求次用户效用最优时对应的报酬作为最终的报酬，协作感知次用户根据该报酬确定最终的感知时间并将感知数据上传给感知需求次用户，得到最终的判决结果。
具体的，协作感知次用户
的报酬p
ij为：
其中
表示协作感知次用户i感知频段任务j的检测概率，B
j表示感知需求次用户j发布的报酬，T
j表示参与频段感知任务j的协作次用户集合。
具体的，协作感知次用户的成本c
ij为：
c
ij＝β×t
ij+γ×d
ij (2)
其中β和γ表示加权系数，t
ij表示协作感知次用户i感知频段任务j的感知时间，d
ij表示协作感知次用户i和感知需求次用户j之间的距离。
具体的，协作感知次用户
的效用为：
其中p
ij表示协作感知次用户i获得的报酬，c
ij表示协作感知次用户i完成频段感知任务j消耗的成本，
表示协作感知次用户i感知频段任务j的检测概率，B
j表示感知需求次用户j发布的报酬，β和γ表示加权系数，t
ij表示协作感知次用户i感知频段任务j的感知时间，d
ij表示协作感知次用户i和感知需求次用户j之间的距离。
具体的，协作感知次用户i感知频段j的检测概率公式为：
其中，p
f表示次用户i的虚警概率，γ
ij表示次用户i感知频段j的信噪比，t
ij表示次用户i感知频段j的感知时间，f
s表示采样频率，通常是一个定值，Q函数是一个互补的累积分布函数，表达式为：
具体的，感知需求次用户
通过招募协作感知次用户
完成相应频段感知任务得到的效用表示为：
其中α表示加权系数，
表示感知需求次用户经过表决融合之后得到频段j的检测概率，
表示协作感知次用户i感知频段任务j的检测概率，B
j表示感知需求次用户j发布的报酬。
具体的，所述感知需求次用户经过表决融合后感知任务j的检测概率表示为：
其中
表示次用户i感知频段j的虚警概率，
表示次用户i感知频段j的检测概率。
优选的，所述的协作感知次用户的采样频率取10kHz，虚警概率取0.1，加权系数α＝8，β＝1，γ＝0.3，无线信号传输考虑大尺度衰落，其衰落系数取4，表决融合准则的判决门限值取N/2。
与现有技术相比，本发明具有以下优点和有益效果：
1、本发明方法将感知需求次用户与协作感知次用户分别建模为Stackelberg博弈的领导层和从属层，通过博弈得到感知需求次用户和协作感知次用户各自的最优策略，在领导层博弈中优化报酬使感知需求次用户效用最优，在从属层博弈中优化感知时间使协作感知次用户效用最优。
2、本发明将频谱感知与群智感知结合，考虑工作在不同频段的多个感知需求次用户招募协作感知次用户完成任务来获得不同的频段的使用情况，在该场景中一个协作感知次用户同时只能感知一个频段，协作感知次用户将感知结果发送给感知需求次用户，感知需求次用户融合多个协作感知次用户的结果，得到更准确的感知结果。
3、本发明考虑工作在不同频段的多个感知需求次用户需要对不同的频段进行感知，有感知需求次用户发布频段感知任务，分别招募协作感知次用户获得频段的使用情况。每个感知 需求次用户招募到的协作感知次用户不是事先确定好的，而是根据协作感知次用户的检测概率、感知时间以及报价，随着博弈的过程而变化。
4、本发明感知需求次用户的效用定义为综合考虑检测概率以及报酬，协作感知次用户的效用定义为报酬减去成本，报酬与检测概率有关，成本与感知时间以及协作感知次用户与感知需求次用户之间的距离有关。
5、本发明在协作感知次用户选择时考虑反向选择，当一个协作感知次用户仅被一个感知需求次用户发送招募意愿时，该协作感知次用户就完成该感知任务。当一个协作感知次用户被多个感知需求次用户同时发送招募意愿时，该次用户通过比较多个感知需求次用户给出的报酬价格选择可以使自己获得报酬最多的任务加入。
图1为本发明的一个实施例的方法流程图。
图2为本发明的一个实施例的Stackelberg博弈系统模型示意图。
本发明的一种基于Stackelberg博弈的多频段群智频谱感知方法，该方法将感知需求次用户向协作感知次用户支付报酬的问题建模为Stackelberg博弈系统模型，其中感知需求次用户是博弈模型中的领导层，协作感知次用户是博弈模型中的从属层。感知需求次用户发布频段感知任务与初始报酬，每个协作感知次用户通过优化感知时间使得自身的效用最优并将感知数据发送给感知需求次用户，感知需求次用户通过不断的更新报酬使其效用达到最优，并得到最终的判决结果。在领导层博弈中，该方法综合考虑检测概率和报酬定义了感知需求次用户的效用，通过博弈优化报酬以获得最佳效用，在从属层博弈中，该方法综合考虑检测概率和感知时间定义了协作感知次用户的效用，根据感知需求次用户发布的报酬优化感知时间以获得最佳效用，并且推导证明了感知时间的优化存在纳什均衡。
下面结合附图和实施例对本发明做进一步详细说明。
图2为本发明一个实施例的Stackelberg博弈系统模型示意图。如图2所示，系统的场景是一个圆形区域，随机分布着N个协作感知次用户和M个感知需求次用户，本发明取M＝2，即存在两个感知需求次用户。在本实施例中，协作感知次用户的采样频率取10kHz，虚警概率取0.1，加权系数α＝8，β＝1，γ＝0.3，无线信号传输考虑大尺度衰落，并且衰落系数取4，表决融合准则的判决门限值取N/2。为了激励协作感知次用户完成感知任务，感知需求次用户会向提供感知结果的次用户支付报酬。
本发明在系统模型中存在的次用户分为两部分，第一部分次用户分别工作在不同的频段上，想要在不影响授权用户情况下使用授权频段的次用户，首先需要发布感知任务，然后招 募其他空闲次用户进行协作频谱感知获得频段的使用情况，这些有需求的次用户组成的集合称为感知需求次用户集合，表示为
另外一部分是空闲次用户，在接收到感知需求次用户发布的任务以后，他们通过自身携带的智能设备进行感知并上传感知结果，这些空闲次用户组成的集合称为协作感知次用户集合
如图1所示，本发明的一种基于Stackelberg博弈的多频段群智频谱感知方法，包括以下步骤：
Step1:构建从属层优化问题，并推导协作感知次用户博弈存在纳什均衡解：综合考虑检测概率、感知时间定义了协作感知次用户的效用函数，即从属层的优化问题就是使协作感知次用户的效用最大化。
协作感知次用户
完成频段感知任务可以从感知需求次用户
那里得到报酬，并且得到的报酬与其自身的检测概率有关，所以协作感知次用户
的报酬p
ij定义为：
其中
表示协作感知次用户i感知频段任务j的检测概率，B
j表示感知需求次用户j发布的报酬，T
j表示参与频段感知任务j的协作次用户集合。
协作感知次用户
完成感知任务需要消耗成本，包括感知频段消耗的成本和上传感知数据消耗的成本，感知频段消耗的成本与感知时间t
ij有关，上传感知数据消耗的成本与协作感知次用户
和感知需求次用户
之间距离有关，因此协作感知次用户的成本c
ij的定义如下：
c
ij＝β×t
ij+γ×d
ij (2)
其中β和γ表示加权系数，t
ij表示协作感知次用户i感知频段任务j的感知时间，d
ij表示协作感知次用户i与感知需求次用户j之间的距离。
所以协作感知次用户
的效用定义为：
其中p
ij表示协作感知次用户
获得的报酬，c
ij表示协作感知次用户
完成频段感知任务消耗的成本，
表示协作感知次用户i感知频段任务j的检测概率，B
j表示感知需求次用户j发布的报酬，β和γ表示加权系数，t
ij表示协作感知次用户i感知频段任务j的感知时间，d
ij表示协作感知次用户i与感知需求次用户j之间的距离。
对于协作感知次用户
而言，为了获得更多的报酬，需要向感知需求次用户
提交最佳的检测概率，假设检测概率中只有感知时间是可以由协作感知次用户
自身决定的，为了使得协作感知次用户
效用最优，协作感知次用户
通过博弈可以确定自己最优的感知时间，从而获得最优的检测概率，因此，从属层协作感知次用户
的优化问题表示为：
在认知无线电频谱感知中，次用户通过能量检测法来感知授权用户的频谱是否在使用，协作感知次用户i感知频段j的检测概率公式表示为：
其中，p
f表示次用户i的虚警概率，γ
ij表示次用户i感知频段j的信噪比，t
ij表示次用户i感知频段j的感知时间，f
s表示采样频率，通常是一个定值，Q函数是一个互补的累积分布函数，表达式为：
为了使次用户的检测概率具有参考意义，要求
即
令
则
关于t
ij的一阶偏导数表示为：
进而，U
ij关于t
ij的一阶偏导数表示为：
进而，U
ij关于t
ij的二阶偏导数表示为：
其中，
因为任务预算B
j、感知时间t
ij、采样频率f
s、检测概率
信噪比γ
ij都是正值，所以K'中第二部分
小于0，第三部分
小于0，又因为K<0，所以K'中第一部分
小于0，所以K'小于0，又因为U
ij关于t
ij二阶偏导的前一部分
大于0，从而可知U
ij关于t
ij的二阶偏导数
即
的效用函数U
ij是关于t
ij的严格凸函数，存在唯一的最优解。
由于U
ij关于t
ij的二阶偏导数恒为负值，意味着U
ij关于t
ij的一阶偏导数单调递减，又因为K<0，即
所以有
假设当K＝0时，可得
从而有
即U
ij关于t
ij的一阶偏导数存在正值。
假设当K→-∞时，可得t
ij→∞，从而有
由于β>0，所以当t
ij→∞时，
即U
ij关于t
ij的一阶偏导数存在负值。
因此若
的最大值大于0，则最优的感知时间
可以通过下列方程组得到：
若
的最大值小于0，则
效用最大时对应的感知时间为
因此，
的感知时间博弈存在唯一纳什均衡解，即
检测概率博弈存在唯一纳什均衡解。
Step2:构建领导层优化问题：综合考虑经表决融合后的检测概率和任务报酬定义了感知需求次用户的效用函数，即领导层的优化问题就是使感知需求次用户的效用最大化。
考虑
的效用与发布的报酬以及
感知相应频段的检测概率有关，通过向
发放报酬可以激励更多的协作感知次用户参与感知。感知需求次用户
通过招募
完成相应频段感知任务得到的效用定义为：
其中α表示加权系数，
表示感知需求次用户经过表决融合之后得到频段j的检测概率，
表示协作感知次用户i感知频段任务j的检测概率，B
j表示感知需求次用户j发布的报酬。每个感知需求次用户采用表决融合准则对多个协作感知次用户提交的感知结果进行处理，经过表决融合后感知任务j的检测概率表示为：
其中
表示次用户i感知频段j的虚警概率，
表示次用户i感知频段j的检测概率。因此，领导层感知需求次用户
的优化问题表示为：
假设每个感知需求次用户支付给协作感知次用户的总报酬不超过B
max，那么在0<B
j≤B
max的范围内一定存在一个最优的报酬
使得感知需求次用户的效用函数值最大。
Step3:将感知需求次用户向协作感知次用户支付报酬的问题构建成基于Stackelberg博弈的多频段群智频谱感知系统模型，在博弈模型中感知需求次用户是领导层，协作感知次用户是从属层，每个协作感知次用户可以感知所有频段，但同时只能感知一个频段；
Step4:感知需求次用户对于要感知的频段向协作感知次用户发布任务及初始报酬，初始化感知需求次用户的最大效用
为0；
Step5:所有协作感知次用户根据报酬及感知时间计算其在当前报酬下的效用，通过优化感知时间选择效用最大时对应的感知时间，协作感知次用户根据该感知时间计算对应的检测概率与成本，并将数据对感知时间，检测概率，基于成本产生的报价)传送给感知需求次用户；
Step6:感知需求次用户根据其报酬向检测概率高的协作感知次用户发送招募意愿及支付报酬的价格；
Step7:若协作感知次用户被多个感知需求次用户同时招募时，通过比较多个感知需求次用户提供的价格选择能够获得报酬多的感知任务加入；
Step8:感知需求次用户计算在当前报酬下的效用，如果该效用值高于
则将该报酬记录下来，在最大报酬B
max的限制下以步长μ增加报酬值，发布新的报酬并重复Step5-Step8，直到相邻两次感知需求次用户的效用值误差小于δ；
Step9:将Step8中得到的感知需求次用户效用最优时对应的报酬作为最终的报酬，协作感知次用户根据该报酬确定最终的感知时间并将感知数据上传给感知需求次用户，得到最终的 判决结果。
综上所述，本发明针对频谱感知场景，结合群智感知技术，提出了一种基于Stackelberg博弈的多频段群智频谱感知方法。该方法将感知需求次用户向协作感知次用户支付报酬的问题建模为Stackelberg博弈模型，其中感知需求次用户是博弈模型中的领导层，协作感知次用户是博弈模型中的从属层。在领导层博弈中，综合考虑检测概率和报酬定义了感知需求次用户的效用，通过博弈优化报酬以获得最佳效用；在从属层博弈中，综合考虑检测概率和感知时间定义了协作感知次用户的效用，根据感知需求次用户发布的报酬通过优化感知时间以获得最佳效用，并且推导证明了感知时间的优化存在纳什均衡。
Claims (8)
- 一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，将感知需求次用户向协作感知次用户支付报酬的问题建模为Stackelberg博弈系统模型，其中感知需求次用户是博弈模型中的领导层，协作感知次用户是博弈模型中的从属层；所述系统的场景是一个圆形区域，随机分布有N个协作感知次用户和M个感知需求次用户，取M＝2，即存在两个感知需求次用户；所述的感知需求次用户的集合，表示为所述的协作感知次用户的集合表示为
所述方法包括以下步骤：Step1、构建从属层优化问题，并推导协作感知次用户博弈存在纳什均衡解：综合考虑检测概率、感知时间定义协作感知次用户的效用函数，使协作感知次用户的效用最大化；Step2、构建领导层优化问题：综合考虑经表决融合后的检测概率和任务报酬定义了感知需求次用户的效用函数，使感知需求次用户的效用最大化；Step3、将感知需求次用户向协作感知次用户支付报酬的问题构建成基于Stackelberg博弈的多频段群智频谱感知系统模型，在博弈模型中感知需求次用户是领导层，协作感知次用户是从属层，每个协作感知次用户可以感知所有频段，但同时只能感知一个频段；Step4、感知需求次用户对于要感知的频段向协作感知次用户发布任务及初始报酬，初始化感知需求次用户的最大效用为0；
Step5、所有协作感知次用户根据报酬及感知时间计算其在当前报酬下的效用，通过优化感知时间选择效用最大时对应的感知时间，协作感知次用户根据该感知时间计算对应的检测概率与成本，并将数据对(感知时间，检测概率，基于成本产生的报价)传送给感知需求次用户；Step6、感知需求次用户根据其报酬向检测概率高的协作感知次用户发送招募意愿及支付报酬的价格；Step7、若协作感知次用户被多个感知需求次用户同时招募时，通过比较多个感知需求次用户提供的价格选择能够获得报酬多的感知任务加入；Step8、感知需求次用户计算在当前报酬下的效用，如果该效用值高于则将该报酬记录下来，在最大报酬B max的限制下以步长μ增加报酬值，发布新的报酬并重复Step5-Step8，直到相邻两次感知需求次用户的效用值误差小于δ；
Step9、将Step8中得到的感知需求次用户效用最优时对应的报酬作为最终的报酬，协作感知次用户根据该报酬确定最终的感知时间并将感知数据上传给感知需求次用户，得到最终的判决结果。 - 根据权利要求1所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，协作感知次用户的报酬p ij为：
其中表示协作感知次用户i感知频段任务j的检测概率，B j表示感知需求次用户j发布的报酬，T j表示参与频段感知任务j的协作次用户集合。
- 根据权利要求1所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，协作感知次用户的成本c ij为：c ij＝β×t ij+γ×d ij (2)其中β和γ表示加权系数，t ij表示协作感知次用户i感知频段任务j的感知时间，d ij表示协作感知次用户i和感知需求次用户j之间的距离。
- 根据权利要求1所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，协作感知次用户的效用为：
其中p ij表示协作感知次用户i获得的报酬，c ij表示协作感知次用户i完成频段感知任务j消耗的成本，表示协作感知次用户i感知频段任务j的检测概率，B j表示感知需求次用户j发布的报酬，β和γ表示加权系数，t ij表示协作感知次用户i感知频段任务j的感知时间，d ij表示协作感知次用户i和感知需求次用户j之间的距离。
- 根据权利要求1所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，协作感知次用户i感知频段j的检测概率公式为：
其中，p f表示次用户i的虚警概率，γ ij表示次用户i感知频段j的信噪比，t ij表示次用户i感知频段j的感知时间，f s表示采样频率，通常是一个定值，Q函数是一个互补的累积分布函数， 表达式为：
- 根据权利要求1所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，感知需求次用户通过招募协作感知次用户
完成相应频段感知任务得到的效用表示为：
其中α表示加权系数，表示感知需求次用户经过表决融合之后得到频段j的检测概率，
表示协作感知次用户i感知频段任务j的检测概率，B j表示感知需求次用户j发布的报酬。
- 根据权利要求1所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，所述感知需求次用户经过表决融合后感知任务j的检测概率表示为：
其中表示次用户i感知频段j的虚警概率，
表示次用户i感知频段j的检测概率。
- 根据权利要求1至7任一项所述的一种基于Stackelberg博弈的多频段群智频谱感知方法，其特征在于，所述的协作感知次用户的采样频率取10kHz，虚警概率取0.1，加权系数α＝8，β＝1，γ＝0.3，无线信号传输考虑大尺度衰落，其衰落系数取4，表决融合准则的判决门限值取N/2。
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