CN110798837B - Dynamic bidirectional spectrum allocation method and storage medium for resisting Sybil attack of primary user - Google Patents
Dynamic bidirectional spectrum allocation method and storage medium for resisting Sybil attack of primary user Download PDFInfo
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- 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
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
- H04W16/02—Resource partitioning among network components, e.g. reuse partitioning
- H04W16/10—Dynamic resource partitioning
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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
Abstract
The invention belongs to the technical field of wireless communication, and discloses a dynamic bidirectional spectrum allocation method and an intelligent terminal for resisting Sybil attack of a master user, which defend against the Sybil attack of the innovative master user, dynamically correspond to a bidirectional defense strategy control spectrum auction model for flexible and real evaluation and quote, and determine bidding relations between primary and secondary users in the model; carrying out frequency spectrum auction through a specific bidding strategy; and (3) adopting an auction theory and mechanism to prevent a master user Sybil from attacking, and carrying out frequency spectrum auction on line through a bidding strategy. The invention integrates an auction model in economics, designs an online dynamic spectrum auction mechanism which can meet the flexible requirement of secondary users on channels and prevent Sybil attack of bidding; by the mechanism, primary and secondary users can compete for the frequency spectrum by submitting different requirements of the primary and secondary users on the frequency spectrum and corresponding estimation functions, Sybil attack of illegal primary users is prevented, and a better frequency spectrum sharing mechanism is realized.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a dynamic bidirectional spectrum allocation method and an intelligent terminal for resisting Sybil attack of a master user.
Background
Currently, the closest prior art: radio spectrum is a key but scarce resource for wireless communications. With the advent of software-defined radios (SDR) and wireless devices, the spectrum shortage problem is becoming more severe and a bottleneck for the rapid growth of the wireless communications industry. In conventional static spectrum allocation mechanisms, long-term spectrum licenses are issued to wireless devices, resulting in low spectrum utilization due to traffic fluctuations. To improve spectrum utility, dynamic spectrum access mechanisms have been proposed to reallocate spectrum resources, where spectrum owners are encouraged to lease their licensed, underutilized spectrum to unlicensed devices or users. Auction theory is considered a very popular tool for the allocation of wireless spectrum due to issues related to efficiency and fairness in the spectrum allocation process. A number of auction-based wireless spectrum allocations have been proposed in recent years. They improve the utilization rate of the frequency spectrum to a certain extent, but have a plurality of defects, such as the defense of classical attack means Sybil attack in an auction mechanism. In response to such a problem, some researchers have conducted research on spectrum allocation, and proposed a spectrum auction mechanism for preventing Sybil attack. Meaning that a cheating bidder cannot gain more utility when submitting multiple bids under multiple fictitious identities. However, this mechanism is an offline mechanism and its algorithm is a static algorithm, which is just offline static allocation, which will result in a reduction of spectrum utilization. Such spectrum allocation methods are still deficient.
In summary, the problems of the prior art are as follows:
(1) existing auction-based spectrum allocation mechanisms do not take into account the potential for primary users to gain profit through Sybil attacks, and only some mechanisms take into account the prevention of secondary user Sybil attacks. In the two-way frequency spectrum auction, a master user also needs to auction, and the attack is possibly carried out.
(2) Most of the existing auction-based spectrum allocation mechanisms are static allocation, namely spectrum resources and user applications are regarded as static existence, and the method is not practical regardless of time factors.
(3) There is currently no spectrum allocation mechanism that can all solve the above problems. Namely, the existing algorithm cannot prevent the Sybil attack of the primary user and consider the flexibility of the time dimension of the frequency spectrum.
The difficulty of solving the technical problems is as follows: the main difficulties for solving the above problems are how to prove the existence of the Sybil attack of the master user and how to design an online algorithm capable of resisting the attack.
The significance of solving the technical problems is as follows: at present, only the defense of secondary user Sybil attack is considered in the allocation mechanism in the spectrum auction field, the possibility of primary user Sybil attack is provided, and an online allocation mechanism which resists the attack and meets good fairness and authenticity is provided.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a dynamic bidirectional spectrum allocation method and an intelligent terminal for resisting Sybil attack of a main user.
The invention is realized in such a way that a dynamic bidirectional spectrum allocation method for resisting the Sybil attack of a main user defends against the Sybil attack of the innovative main user so as to dynamically correspond to a bidirectional defense strategy control spectrum auction model for flexible and real evaluation to quote, and the bidding relation between the main user and the secondary user is determined in the model; carrying out frequency spectrum auction through a specific bidding strategy; and (3) adopting an auction theory and mechanism to prevent a master user Sybil from attacking, and carrying out frequency spectrum auction on line through a bidding strategy.
Further, the bidirectional dynamic spectrum allocation mechanism resisting the Sybil attack of the primary user comprises the following steps:
step one, pre-renting frequency band information is about a master user M ═ {1,2, …, M }
Submitting, summarizing and putting the resource information into a spectrum pool, and determining the total distribution time length T, wherein all the subsequent steps are carried out in each time of the time period;
step two, determining all secondary user sets N ═ {1,2, …, N } participating in bidding at the current moment and interference graph G ═<V,E>(ii) a All participating in biddingThe secondary user needs to submit a set of requirement information
The method comprises the steps of respectively obtaining total quoted price, the number of application channels and the length of time occupied by the application; at most, m channels are required, and at most, T time lengths are occupied;
step three, calculating discount quotation and interference discount of each secondary user according to the information of the secondary users at the moment, namely predicting and quantifying interference and loss possibly caused by the secondary users; screening out proper candidate secondary users according to the opportunity cost in the auction process after the participation;
step four, grouping through a grouping algorithm according to the geographical position in the interference graph of the candidate secondary user; and calculating a group offer for each group;
designing a master user sequencing algorithm irrelevant to quotation, and sequencing all master users in sequence; the secondary user groups are sorted according to the group quotation;
step six, according to the sequencing result, the primary users and the secondary users are matched in a one-to-one correspondence mode, the successfully matched primary users and the successfully matched secondary users are used as winners, and the winners of the primary users and the secondary users are respectively determined;
and step seven, searching for a critical node through the matching result to respectively determine the payment price of the primary user and the secondary user.
Further, the interference graph G in the second step is the interference relationship in < V, E >, and the signal-to-noise ratio is indirectly described by calculating the distance between each bidder.
Further, the interference discount in step three is the inverse of the product of the average interference level of the secondary user to the neighboring node and the reusability, indicating a ratio of the loss that the secondary user may cause.
Further, the discount offer in the third step refers to the product of the interference discount and the original offer, namely, the offer after the loss is converted.
Further, the opportunity cost in the third step is a cost price estimated according to information such as a discount offer and an application channel, and if the opportunity cost of the secondary user is smaller than the discount income of the secondary user, namely the income calculated according to the discount offer, the opportunity cost can be selected as a candidate.
Further, the master user in the fifth step is not sequenced through the quotation of the master user directly by a sequencing-independent algorithm; coordinate sorting is used.
Further, the matching process of the primary and secondary users in the sixth step is that the primary and secondary users are matched one by one according to the number of the channels applied by the primary and secondary users, and all the applied channels of the secondary user group are successfully matched only if all the applied channels are required to be matched, otherwise, the group is not allocated with any channel;
the critical nodes in the step seven refer to critical unmatched nodes of the primary user and critical unmatched groups of the secondary users; and respectively taking the quotation of the main user critical node and the quotation of the secondary user critical node group as final prices.
The invention also aims to provide the intelligent terminal for realizing the dynamic bidirectional spectrum allocation method for resisting the Sybil attack of the primary user.
It is another object of the present invention to provide a computer-readable storage medium comprising instructions which, when executed on a computer, cause the computer to perform the method for dynamic bidirectional spectrum allocation against primary user Sybil attacks.
In summary, the advantages and positive effects of the invention are: the invention provides a Sybil attack form based on a master user, and defends against the Sybil attack, so as to dynamically correspond to a flexible real evaluation value to carry out a strategy-preventing operation spectrum auction model of the quotation of a primary user and a secondary user, discuss the bidding relation among the secondary users in the model, and carry out spectrum auction by designing a specific bidding strategy; and (3) adopting an auction theory and mechanism to prevent a master user Sybil from attacking, and carrying out frequency spectrum auction on line through a bidding strategy. The spectrum allocation method of the invention not only can realize individual rationality and authenticity, but also can resist Sybil attack of a master user, and dynamically allocates channels on line, thereby improving spectrum efficiency and reusability; according to the evaluation result, the invention can prevent the bidder from operating the auction and realize good spectrum redistribution performance. The method provided by the invention is easy to realize, is convenient to expand and is closer to practical application compared with the frequency spectrum auction method already provided.
According to the invention, the secondary users can compete for the frequency spectrum by submitting different requirements of the secondary users on the frequency spectrum and corresponding estimation functions, and Sybil attack of the primary user is prevented in the process, so that a better dynamic frequency spectrum sharing mechanism is realized. The method fully considers factors such as signal-to-noise ratio interference of secondary users to spectrum channels in spectrum allocation, simultaneously considers the requirements of spectrum utilization rate maximization and strategy manipulation prevention performance of primary and secondary users, and carries out detailed analysis and design on a spectrum auction mechanism. The method provided by the invention is easy to realize, is convenient to expand and is closer to practical application compared with the frequency spectrum auction method already provided. Compared with the existing spectrum auction method, the method provided by the invention not only defends against Sybil attack of the main user, but also is an online dynamic allocation method, and is the only spectrum allocation method considering the two points at present.
Drawings
Fig. 1 is a flowchart of a dynamic bidirectional spectrum allocation method for resisting a Sybil attack of a primary user according to an embodiment of the present invention.
Fig. 2 is a diagram of a spectrum sharing system model according to an embodiment of the present invention.
Fig. 3 is a block diagram of a system according to an embodiment of the present invention.
Fig. 4 is a flowchart of an implementation of the dynamic bidirectional spectrum allocation method for resisting the Sybil attack of the primary user according to the embodiment of the present invention.
Fig. 5 is a fairness comparison result provided in the embodiment of the present invention, which is compared with fairness of other three bidirectional spectrum auction algorithms, respectively, and the result proves that the algorithm Tsunami has good fairness.
Fig. 6 is a main user Sybil attack existence proof provided by the embodiment of the present invention, and simulation experiments on two bidirectional algorithms are shown in the figure, so that the main user Sybil attack can be proved to exist really.
In the figure: (a) is the result of the Sybil attack experiment of the main user of the bidirectional algorithm DOTA; (b) is the result of the Sybil attack experiment of the main user of the bidirectional algorithm True-MCSA;
fig. 7 is a proof experiment against the Sybil attack of the primary user provided by the embodiment of the present invention. As shown in the figure, the invention can be proved to be resistant to the attack mode through experiments.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a dynamic bidirectional spectrum allocation method and an intelligent terminal for resisting Sybil attack of a main user, and the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the dynamic bidirectional spectrum allocation method for resisting the Sybil attack of the primary user provided by the embodiment of the present invention includes the following steps:
s101: establishing a two-way spectrum auction model, and submitting idle spectrum and auction standard by a master user to an Auctioneer (Auctioneer) to place the idle spectrum and the auction standard into a spectrum pool for bidding by a secondary user;
s102: all secondary users submit channel requirements (including application duration and number, etc.) whose true estimates are bid prices. The auctioneer screens out proper candidate users according to the information simulation dynamic process and sorts the candidate users and the master users according to a sort mode irrelevant to quotation;
s103: and matching the master users with the candidates one by one according to a price calculation algorithm and a distribution algorithm, and determining a final distribution result and a final unit price.
The multi-channel dynamic spectrum allocation method for preventing Sybil attack provided by the embodiment of the invention specifically comprises the following steps:
step one, pre-renting frequency band information is about a master user M ═ {1,2, …, M }
Submitting, summarizing and putting the resource information into a spectrum pool, and determining the total distribution time length T, wherein all the subsequent steps are carried out in each time of the time period;
step two, determining all secondary user sets N ═ {1,2, …, N } participating in bidding at the current moment and interference graph G ═<V,E>(ii) a All secondary users participating in bidding need to submit a set of requirement information
The method comprises the steps that the total quotation, the number of application channels and the length of time occupied by the application are respectively total quotation; at most, m channels are required, and at most, T time lengths are occupied;
and step three, calculating the discount quotation and the interference discount of each secondary user according to the information of the secondary users at the moment, namely predicting and quantifying the interference and the loss possibly caused by the secondary users. And screening out proper candidate secondary users according to the interference discount to participate in the auction process.
Step four, grouping the candidate secondary users through a grouping algorithm such as a coloring algorithm according to the geographic positions in the interference graph of the candidate secondary users so as to improve the reusability of the frequency spectrum; and calculating a group offer for each group;
designing a master user sequencing algorithm irrelevant to quotation, and sequencing all master users in sequence; the secondary user groups are ranked according to their group offers;
and step six, according to the sequencing result, the primary users and the secondary users are matched in a one-to-one correspondence mode, the successfully matched primary users and secondary users are used as winners, and the winners of the primary users and the secondary users are respectively determined.
And step seven, searching for a critical node through the matching result to respectively determine the payment price of the primary user and the secondary user.
In a preferred embodiment of the invention, the spectrum channels are homogeneous, i.e. for bidders, the channels in the spectrum pool are not differentiated, and only the number of application channels is considered at the time of application.
In the preferred embodiment of the present invention, the interference relationship in the interference graph G ═ V, E >, the signal-to-noise ratio is indirectly described in practical application by calculating the distance between each bidder, for example, the outdoor transmission range of IEEE 802.11n is about 250 m, and the interference factor θ is defined as 1.7, so that the same channel can be shared as long as the distance between two bidders is greater than 425 m, and the interference is mutually interfered when the distance is less than 425 m.
In the preferred embodiment of the present invention, the interference discount is the inverse of the product of the average interference level of the secondary user to the neighbor node and the reusability, which indicates a ratio of the loss that the secondary user may cause. The discounted offers refer to the product of the interference discount and the original offer, i.e., the offer after the loss is reduced, so as to facilitate fair distribution. The opportunity cost refers to a cost price estimated according to information such as discount quotation and application channel, and if the opportunity cost of the secondary user is smaller than the discount income of the secondary user, namely the income calculated according to the discount quotation, the opportunity cost can be selected as a candidate.
In the preferred embodiment of the invention, a master user sequencing algorithm irrelevant to quotation is designed, and all master users are sequenced in sequence, namely sequencing is not directly performed through the quotation of the master users, so that the authenticity of the algorithm can be ensured, and methods such as coordinate sequencing and the like can be used.
In the preferred embodiment of the invention, the primary and secondary user matching process is a single one-to-one matching according to the number of the channels applied by the primary and secondary users, and all the applied channels of the secondary user group are required to be completely matched to be successful, otherwise, the group is not allocated with any channel.
In a preferred embodiment of the invention, a critical node is sought and the payment prices of the primary user and secondary users, respectively, are determined. I.e. a critical unmatched node for primary users and a critical unmatched group for secondary users. And respectively taking the quotation of the main user critical node and the quotation of the secondary user critical node group as final prices.
The technical solution of the present invention is further described below with reference to the accompanying drawings.
As shown in fig. 2-4, the method for multi-channel dynamic spectrum allocation against Sybil attack according to the embodiment of the present invention includes the following steps:
(1) and establishing a system model, wherein entities comprise a main user with a spectrum renting requirement, an auctioneer controlling the whole auction process and a secondary user with a spectrum resource requirement, and determining the total distribution time length T. Frequency band pre-rented by primary user M {1,2, …, M }Information
Submitting the resource information to an auctioneer, and putting the resource information into a frequency spectrum pool for bidding of the secondary users after the resource information is collected and sorted by the auctioneer. The spectral channel differs from the conventional thing in that it can be used by several secondary users together, provided that they are able to transmit and transmit signals below a sufficient signal-to-noise ratio (SINR).
(2) Determining the set N of all secondary users participating in bidding at the current moment {1,2, …, N } and an interference map, and using G ═ in the invention<V,E>To represent an interference graph, where V is the set of all secondary users and E is the interference relationship between bidders. All secondary users participating in bidding need to submit a set of requirement information
The method comprises the steps that the total quotation, the number of application channels and the length of time occupied by the application are respectively total quotation; at most, m channels are required, and at most, T time lengths are occupied;
(3) and calculating the discount quotation and the interference discount of each secondary user according to the information of the secondary users at the moment, namely predicting and quantifying the possible interference and loss caused by the secondary users. Wherein the interference discount is the inverse of the product of the average interference degree of the secondary user to the neighbor node and the reusability, and indicates a ratio of losses possibly caused by the secondary user; the discounted offers refer to the product of the interference discount and the original offer, i.e., the offer after the loss is reduced, so as to facilitate fair distribution. The opportunity cost refers to a cost price estimated according to information such as discount quotation and application channel, and if the opportunity cost of the secondary user is smaller than the discount income of the secondary user, namely the income calculated according to the discount quotation, the opportunity cost can be selected as a candidate. And screening out proper candidate secondary users according to the interference discount to participate in the auction process.
(4) And performing candidate secondary user grouping. According to the geographical position in the interference graph of the candidate secondary users, grouping the secondary users which do not generate interference through a grouping algorithm such as a coloring algorithm so as to improve the reusability of the frequency spectrum; and calculating a group offer for each group;
(5) and designing a sequencing algorithm. The master users adopt a sorting algorithm irrelevant to quotation to sort the master users in sequence, namely, the master users do not directly sort through the quotation, so that the authenticity of the algorithm can be ensured, and the coordinate sorting can be used according to an interference graph G; the secondary user groups are ranked from large to small according to their previously calculated group offers;
(6) and designing a matching algorithm. And correspondingly matching the primary users with the secondary users according to the sequencing result, namely, matching the primary users with the secondary users one by one according to the number of the channels applied by the primary users, and meeting the condition that all the applied channels of the secondary user group are required to be completely matched to be successful, otherwise, the group does not allocate any channel. The primary and secondary users that are successfully matched will be winners.
(7) And designing a price determination algorithm. And searching for a critical node through a matching result to respectively determine the payment prices of the primary user and the secondary users. I.e. a critical unmatched node for primary users and a critical unmatched group for secondary users. And respectively taking the quotation of the main user critical node and the quotation of the secondary user critical node group as final prices.
The technical effects of the present invention will be described in detail with reference to experiments.
The algorithm simulation results of the existing two bidirectional spectrum auction mechanisms DOTA and True-MCSA prove that the Sybil attack of the main user really exists in other algorithms; the invention prevents the Sybil attack of the main user, namely, for an attacker, the obtainable benefit after the Sybil attack is less than that of the attacker without the Sybil attack. And by controlling a variable method, comparing a plurality of frequency distribution algorithms, the spectrum fairness is tested. Experimental results show that the invention achieves good efficiency and fairness in distribution.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (3)
1. A dynamic two-way spectrum allocation method for resisting a Sybil attack of a primary user is characterized in that the dynamic two-way spectrum allocation method for resisting the Sybil attack of the primary user defends against the Sybil attack of the innovative primary user, a two-way defense strategy operation spectrum auction model for dynamically corresponding to a flexible real evaluation value to quote is used, and a bidding relation between primary users and secondary users is determined in the model; carrying out frequency spectrum auction through a specific bidding strategy; an auction theory and mechanism are adopted to prevent a master user Sybil from attacking, and the frequency spectrum auction is carried out on line through a bidding strategy;
the dynamic bidirectional spectrum allocation method for resisting Sybil attack of the main user comprises the following steps:
step one, pre-renting frequency band information is about a master user M ═ {1,2, …, M }
Submitting, summarizing and putting the resource information into a spectrum pool, and determining the total distribution time length T, wherein all the subsequent steps are carried out in each time of the time period;
step two, determining all secondary user sets N ═ {1,2, …, N } participating in bidding at the current moment and interference graph G ═<V,E>(ii) a All secondary users participating in bidding need to submit a set of requirement information
The method comprises the steps that the total quotation, the number of application channels and the length of time occupied by the application are respectively total quotation; at most, m channels are required, and at most, T time lengths are occupied;
step three, calculating discount quotation and interference discount of each secondary user according to the information of the secondary users at the moment, namely predicting and quantifying interference and loss possibly caused by the secondary users; screening out proper candidate secondary users according to the opportunity cost in the auction process after the participation;
step four, grouping through a grouping algorithm according to the geographical position in the interference graph of the candidate secondary user; and calculating a group offer for each group;
designing a master user sequencing algorithm irrelevant to quotation, and sequencing all master users in sequence; the secondary user groups are ranked according to their group offers;
step six, according to the sequencing result, the primary users and the secondary users are matched in a one-to-one correspondence mode, the successfully matched primary users and the successfully matched secondary users are used as winners, and the winners of the primary users and the secondary users are respectively determined;
step seven, searching for a critical node through a matching result to respectively determine the payment price of the secondary user of the master user;
the interference discount in the third step is the reciprocal of the product of the average interference degree of the secondary user to the neighbor node and the reusability, and indicates a ratio of the loss which the secondary user may cause;
the discount quotation in the third step is the product of the interference discount and the original quotation, namely the quotation after the conversion loss;
the opportunity cost in the third step is the cost price estimated according to information such as discount quotation and application channel, and if the opportunity cost of the secondary user is smaller than the discount income of the secondary user, namely the income calculated according to the discount quotation, the opportunity cost can be selected as a candidate;
the master user in the fifth step is not sequenced through the quotation of the master user directly by a sequencing-independent algorithm; sorting by using coordinates;
in the step six, the primary and secondary user matching process is that the primary and secondary user application channels are matched one by one according to the number of the primary and secondary user application channels, and all the application channels of the secondary user group are required to be matched completely to be successful, otherwise, the group is not allocated with any channel;
the critical nodes in the step seven refer to critical unmatched nodes of the primary user and critical unmatched groups of the secondary users; and respectively taking the quotation of the main user critical node and the quotation of the secondary user critical node group as final prices.
2. The method for dynamic bidirectional spectrum allocation resistant to Sybil attack as set forth in claim 1, wherein the interference relationship in the interference graph G ═ V, E > in the second step indirectly describes the signal-to-noise ratio by calculating the distance between each bidder.
3. A computer-readable storage medium comprising instructions that, when executed on a computer, cause the computer to perform the method of dynamic bidirectional spectrum allocation against Sybil attacks of primary users according to any one of claims 1-2.
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