JP2018142956A - Management apparatus, program for causing computer to execute, and computer-readable recording medium recording the program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a management device capable of forming an exclusive area of a primary user having a hole. SOLUTION: A calculation means 102 of a management device 10 transmits the transmission power of a transmission station of a secondary user in each of a plurality of areas forming a two-dimensional area with a reception station of a primary user as an origin, and a primary usage. The threshold that the receiving station receives from the transmitting station using the constants that depend on the receiving station's antenna, the fading coefficient between the receiving station and the transmitting station, the Euclidean distance between the transmitting station position and the origin, and the radio wave attenuation constant. The interference power larger than the value is calculated as the probability of interference with the receiving station of the primary user, which is a function of the transmission probability of the transmitting station of the secondary user. The determining means 104 sets the transmission probabilities of the transmitting stations of the secondary users in a plurality of areas in which the calculated interference probability is equal to or less than the target value and maximizes the average number of the transmitting stations of the secondary users transmitting. Decide on each. The determining unit 105 creates the exclusive area of the primary user based on the determined transmission probability. [Selection diagram] Fig. 4

Description

  The present invention relates to a management apparatus, a program to be executed by a computer, and a computer-readable recording medium on which the program is recorded.

  As one of cognitive radio technologies expected in the fifth generation mobile communication system (5G), database-assisted frequency sharing systems (Non-Patent Documents 1 and 2) are known.

  In the database-assisted frequency sharing system, the spectrum database collects the primary user's usage information in advance for the licensed band at each point. Thereafter, frequency sharing conditions are set for the secondary user so that the unlicensed operation of the secondary user does not interfere with the operation of the primary user. Finally, when the secondary user sends an inquiry to this database by sending his / her location information, the secondary user's transmitting station uses the license band determined by the frequency sharing condition.

  Even if the secondary user operates according to the frequency sharing condition, the primary user may be affected by interference. The cause of this problem is an unexpected propagation path caused by changes in real world geography and building information. In order to reduce the probability of the primary user receiving interference, it is necessary to adjust the frequency sharing condition to increase the number of secondary users who are prohibited from transmission. Usage efficiency is significantly reduced.

  Non-Patent Documents 1 and 2 propose frameworks for updating frequency sharing conditions based on emergency information that a primary user has been affected by interference. Non-Patent Documents 3 and 4 consider a circular primary user exclusive region (PER) (Non-Patent Document 5) with a primary receiving station as the frequency sharing condition. Transmission prohibition is notified to the secondary transmitting station in the person exclusive area.

  Non-patent document 6 divides the space into sector areas and optimizes the radius of the sector area as the primary user exclusive area. That is, a non-circular primary user exclusive area is designed.

D. Gurney, G. Buchwald, L. Ecklund, S. Kuffner, and J. Grosspietsch, “Geo-location database techniques for incumbent protection in the TV white space,” Proc. IEEE DySPAN 2008, pp.232-240, Aug . 2008. M. Barrie, S. Delaere, G. Sukareviciene, J. Gesquiere, and I. Moerman, “Geolocation database beyond TV white spaces Matching applications with database requirements,” Proc. IEEE DySPAN 2012, pp.467-478, Oct. 2012 . S. Yamashita, K. Yamamoto, T. Nishio, and M. Morikura, “Knowledge-based update of primary exclusive region for database-driven spectrum sharing towards 5G,” Proc. IEEE WCNC-IWSS 2016, pp.473-476, April 2016. S. Yamashita, K. Yamamoto, T. Nishio, and M. Morikura, “Knowledge-based reestablishment of primary exclusive region in database-driven spectrum sharing,” IEICE Trans. Commun., Vol.E99-B, no.9, pp.2019-2027, Sept. 2016. M. Vu, N. Devroye, and V. Tarokh, “On the primary exclusive region of cognitive networks,” IEEE Trans. Commun., Vol.8, no.7, pp.3380-3385, July 2009. S. Bhattarai, A. Ullah, JMJ Park, JH Reed, D. Gurney, and B. Gao, “Defining incumbent protection zones on the fly: Dynamic boundaries for spectrum sharing,” Proc. IEEE DySPAN 2015, pp.251-262 , Sept. 2015. M. Haenggi, Stochastic Geometry for Wireless Networks, Cambridge University Press, Nov. 2012. D.C. Schleher, “Generalized Gran-Charlier series with application to the sum of normal bariates,” IEEE Trans. Inf. Theory, vol.23, no.2, pp.275-280, May 1977. K.L.Q. Read, “A lognormal approximation for the collector ’s problem,” Amer. Stat., Vol.52, no.2, pp.175-180, May 1998. A. Ghasemi and E.S. Sousa, “Interference aggregation in spectrum-sensing cognitive wireless networks,” IEEE J. Sel. Top. Signal Process., Vol, 2, no.1, pp.41-56, Feb. 2008. W.L.Stutzman and G.A. Thiele, Antenna Theory and Design, 3rd Edition, John Wiley & Sons, Inc., May 2012. M.K Simon and M.S Alouini, Digital Communication over Fading Channels, Johon Wiley & Sons, Inc., 2004. W.E.Hart, C. Laird, J.-P. Watson, and D.L.Woodruff, Pyomo Optimization Modeling in Python, vol.67, Springer Optimization and Its Applications, 2012. A. Wachter and LT Biegler, “On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming,” Math. Program., Vol.106, no.1, pp.25-57, March 2006. The Information and Communication Council, “Technical requirements for Upgrading of use of radio waves for robots, etc. (in Japanese),” Mar. 2016. C. Zhang and W. Zhang, “Spectrum sharing for drone networks,” IEEE J. Sel. Area Commun., Vol.35, no.1, pp.136-144, Nov. 2016. S. Yamashita, K. Yamamoto, T. Nishio, and M. Morikura, “Optimization of primary exclusive region in spatial grid-based spectrum database using stochastic geometry,” Proc. IEEE ICC2017, pp. 1-6, Paris, France, May 2017. K.W. Sung, M. Tercero, and J. Zander, “Aggregate interference in secondary access with interference protection,” IEEE Commun. Lett., Vol. 15, no. 6, pp.629-631, April 2011. M.K.Simon and M.-S.Alouini, Digital Communication over Fading Channels, John Wiley & Sons, Inc., 2004. W.E.Hart, C. Laird, J.-P, Watson, and D.L.Woodruff, Pyomo Optimization Modeling in Python, vol. 67, Springer Science & Business Media, 2012. A. Wachter and LT Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program., Vol. 106, no. 1, pp.25-27, Mar. 2006.

  However, there is a possibility that the actual primary user exclusive area is non-circular and has a hole. In Non-Patent Document 6, it is difficult to form a primary user exclusive area with a hole. is there.

  According to the embodiment of the present invention, a management device capable of forming an exclusive area of a primary user with a hole is provided.

  In addition, according to the embodiment of the present invention, a program for causing a computer to execute formation of an exclusive area of a primary user having a hole is provided.

  Furthermore, according to the embodiment of the present invention, there is provided a computer-readable recording medium on which a program for causing a computer to execute an exclusive area of a primary user having a hole is recorded.

(Configuration 1)
According to the embodiment of the present invention, the management device includes a calculation unit, a determination unit, and a creation unit.

  The calculation means is a non-uniform Poisson point of the secondary user in each of a two-dimensional area or a plurality of areas constituting the three-dimensional area with the receiving station of the primary user having a constant ratio of interference data as the origin. Transmitting power of transmitting stations distributed according to the process, constant on antenna directivity at receiving station of primary user, fading coefficient between receiving station of primary user and transmitting station of secondary user, secondary usage Interference power greater than the threshold received by all the transmitting stations transmitted by the secondary user using the Euclidean distance between the position of the transmitting station of the user and the origin, and the radio wave attenuation constant. Is calculated as an interference probability of the primary user to the receiving station, which is a function of the transmission probability of the transmitting station of the secondary user in each of the plurality of regions.

  The determining means sets the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted, in which the calculated interference probability is equal to or less than the target value, for each of the plurality of regions. To decide on.

  The creation means creates an exclusive area where only the primary user can perform wireless communication based on the transmission probability of the transmission station of the secondary user in each of the determined areas.

  In the management apparatus according to the embodiment of the present invention, in each of a plurality of areas constituting a two-dimensional area with the receiving station of the primary user as the origin, the transmitting station of the secondary user is the receiving station of the primary user. The transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is determined in each of the plurality of regions. Of the plurality of areas, the area where the transmission probability is zero is set as an exclusive area where only the primary user can perform wireless communication. Therefore, in the entire two-dimensional area, a non-circular exclusive area with a hole is provided. An area can be created.

(Configuration 2)
In Configuration 1, each of the plurality of regions has an annular sector shape formed by a plurality of lines extending radially from the origin and a plurality of concentric circles centered on the origin.

  Since each of the plurality of areas has an annular fan shape, the amount of calculation when calculating the interference probability that the secondary user's transmitting station gives to the primary user's receiving station can be reduced.

(Configuration 3)
In Configuration 1 or Configuration 2, the computing means includes: transmission power of the secondary user's transmission station in each of the plurality of regions; antenna directivity in the primary user's reception station; primary user's reception station; A constant that affects the antenna height at the secondary user's transmitter station, the fading coefficient between the primary user's receiver station and the secondary user's transmitter station, and the position and origin of the secondary user's transmitter station. Using the Euclidean distance and the radio wave attenuation constant, the first interference power that the secondary user's transmitting station gives to the primary user's receiving station in each of the plurality of regions is calculated, and the moment of the first interference power is calculated. Using the generating function, the n-th order cumulant (n is a positive integer) of the first interference power is calculated as a function of the transmission probability of the transmission station of the secondary user, and based on the calculated n-th order cumulant, a plurality of All secondary users in the domain The n-th order cumulant of the second interference power, which is the interference power from the transmitting station to the primary user's receiving station, is calculated, and the second interference is calculated based on the calculated n-th order cumulant of the second interference power. A probability density function of power is calculated, and an interference probability is calculated using parameters of the probability density function.

  The n-th order cumulant of the first interference power is the density and transmission power distribution of the secondary user's transmitting station in each of the plurality of regions, the antenna gain between each region and the primary user, and the assumed radio wave It is a statistic that depends on the propagation model. And a more general statistic can be calculated | required by calculating | requiring this n-th order cumulant.

  The n-th order cumulant includes the average of the first interference power, the variance of the first interference power, the skewness of the first interference power, and the kurtosis of the first interference power. The distribution of the second interference power can be approximated to a shifted lognormal distribution by obtaining the average and variance of the power.

  As a result, the probability of interference with the receiving station of the primary user can be easily calculated.

(Configuration 4)
In any one of the configurations 1 to 3, the determining unit may multiply a plurality of multiplication results obtained by multiplying an average number of transmitting stations transmitted by the secondary user in each of the plurality of regions by a transmission probability of the transmitting station of the secondary user. The result of addition for the region is used as an objective function, and the subtraction result obtained by subtracting the target value from the calculated interference probability is zero or less. By determining the transmission probability in each of the plurality of areas, the transmission probability of the secondary user's transmission station that maximizes the average number of transmission stations of the secondary user's transmission is determined.

  Under the constraint that the probability of interference with the primary user is less than or equal to the target value, the transmission probability of the secondary user's transmitting station that maximizes the objective function is obtained. If the transmission probability of the transmitting station is zero, the region where the transmission probability is zero is guaranteed to be an exclusive region of the primary user, and if the transmission probability is not zero, the region where the transmission probability is not zero is It is guaranteed to be a non-exclusive area of the primary user.

  Accordingly, the exclusive area of the primary user can be accurately created in the two-dimensional area.

(Configuration 5)
In Configuration 1, each of the plurality of regions is arranged with a plurality of lines extending radially from the origin, a plurality of concentric circles centered on the origin, a predetermined distance in the height direction from the origin, and a plurality of concentric circles It has a shape formed by a plurality of sets of concentric circles as one set of concentric circles.

  Since each of the plurality of regions has a three-dimensional shape extending in the height direction while maintaining a planar shape having an annular sector shape, the three-dimensional space can be easily divided into a plurality of regions using cylindrical coordinates. As a result, the transmission probability of the secondary user's transmission station can be determined in consideration of the distance in the height direction from the origin in addition to the distance in the plane direction from the origin.

(Configuration 6)
In the configuration 1 or the configuration 5, the calculating means includes a transmission power of a secondary user's transmission station in each of the plurality of areas, a constant related to antenna directivity in the primary user's reception station, and a primary user's reception station. Of the secondary user in each of the plurality of regions using the fading coefficient between the transmission station and the secondary user's transmission station, the Euclidean distance between the position and origin of the secondary user's transmission station, and the radio wave attenuation constant. The first interference power that the transmitting station gives to the receiving station of the primary user is calculated, and the n-th order cumulant of the first interference power (where n is a positive integer) 2 is calculated using Laplace transform of the first interference power. Calculated as a function of the transmission probability of the secondary user's transmitting station, and based on the calculated nth order cumulant, interference power from all the secondary user's transmitting stations to the primary user's receiving station in a plurality of regions The second-order key of the second interference power is Calculates the Muranto, based on the n-order cumulant of the second interference power to the operation, the probability density function of the second interference power calculated, calculates the interference probability with the parameters of the probability density function.

  The n-th order cumulant of the first interference power is the density and transmission power distribution of the secondary user's transmitting station in each of the plurality of regions, the antenna gain between each region and the primary user, and the assumed radio wave It is a statistic that depends on the propagation model. And a more general statistic can be calculated | required by calculating | requiring this n-th order cumulant.

  The n-th order cumulant includes the average of the first interference power, the variance of the first interference power, the skewness of the first interference power, and the kurtosis of the first interference power. The distribution of the second interference power can be approximated to a lognormal distribution by obtaining the average and variance of the power. As a result, the probability of interference with the receiving station of the primary user can be easily calculated.

(Configuration 7)
In the configuration 6, the calculating means calculates the n-th order cumulant of the second interference power by calculating the sum of the second interference power from the first order cumulant to the n-th order cumulant.

  The n-th order cumulant of the second interference power is a Q function of the parameter represented by the first and second order cumulants of the second interference power, and the first and second order cumulants of the second interference power are The n-th order cumulant of the second interference power is calculated using Expression (41) indicating that it is the sum of each cumulant. Therefore, the exclusive region can be obtained based on the transmission probability in consideration of the entire three-dimensional space grid.

(Configuration 8)
In any one of the configurations 5 to 7, the determining means sets a non-transmission probability that is a probability that the secondary user's transmitting station does not transmit to the average number of transmitting stations transmitted by the secondary user in each of the plurality of regions. The transmission result of the secondary user's transmitting station that minimizes the objective function under the constraint that the addition result obtained by multiplying the multiplication results for a plurality of areas is the objective function and the calculated interference probability is less than or equal to the target value. By determining the probability in each of the plurality of areas, the transmission probability of the secondary user's transmission station that maximizes the average number of transmission stations of the secondary user to transmit is determined.

  Under the constraint that the probability of interference with the primary user is less than or equal to the target value, the transmission probability of the secondary user's transmitting station that minimizes the objective function is obtained. If the transmission probability of the transmitting station is zero, the region where the transmission probability is zero is guaranteed to be an exclusive region of the primary user, and if the transmission probability is not zero, the region where the transmission probability is not zero is It is guaranteed to be a non-exclusive area of the primary user. Accordingly, the exclusive area of the primary user can be accurately created in the two-dimensional area.

(Configuration 9)
Further, according to the embodiment of the present invention, a program for causing a computer to execute is
The computing means is distributed according to the non-uniform Poisson point process of the secondary user in each of a plurality of areas constituting the two-dimensional area starting from the receiving station of the primary user having a constant ratio of interference data. Constants that affect the transmission power of the transmitting station, the antenna directivity at the receiving station of the primary user, and the antenna height at the receiving station of the primary user or the transmitting station of the secondary user, the receiving station of the primary user And the secondary user's transmitting station, using the Euclidean distance between the position of the secondary user's transmitting station and the origin, and the radio wave attenuation constant, the receiving station of the primary user The primary user's receiving station, which is a function of the transmission probability of the secondary user's transmitting station in each of the plurality of regions, with interference power greater than the threshold received from all transmitting stations transmitted by the secondary user. Calculated as the probability of interference with And the first step,
The determining means sets the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted, in which the calculated interference probability is equal to or less than the target value, for each of the plurality of regions. A second step of determining in
The creation means creates an exclusive area of the primary user in which only the primary user can perform wireless communication based on the transmission probability of the transmission station of the secondary user in each of the determined areas. A program for causing a computer to execute the third step.

  By executing the program according to the embodiment of the present invention, in each of a plurality of areas constituting a two-dimensional area starting from the receiving station of the primary user, the transmitting station of the secondary user is the primary user. The transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is equal to or less than the target value and the transmission probability of the secondary user's transmission station is in each of the plurality of regions. Among the plurality of areas, the area where the transmission probability is zero is defined as an exclusive area where only the primary user can perform wireless communication. A circular exclusive area can be created.

(Configuration 10)
In Configuration 9, each of the plurality of regions has an annular sector shape formed by a plurality of lines extending radially from the origin and a plurality of concentric circles centered on the origin.

  Since each of the plurality of areas has an annular fan shape, the amount of calculation when calculating the interference probability that the secondary user's transmitting station gives to the primary user's receiving station can be reduced.

(Configuration 11)
In Configuration 9 or Configuration 10, the computing means in the first step, the transmission power of the secondary user's transmitting station in each of the plurality of regions, the antenna directivity and the primary usage in the receiving station of the primary user Constants that affect the antenna altitude at the receiving station of the user and the transmitting station of the secondary user, fading coefficient between the receiving station of the primary user and the transmitting station of the secondary user, and the transmission of the secondary user Using the Euclidean distance between the station position and the origin and the radio wave attenuation constant, the first interference power that the secondary user's transmitting station gives to the primary user's receiving station in each of the plurality of regions is calculated, Using the moment generating function of the first interference power, the n-th order cumulant (n is a positive integer) of the first interference power is calculated as a function of the transmission probability of the transmission station of the secondary user, and the calculated n-th order Based on cumulants, The n-th order cumulant of the second interference power, which is the interference power from all the transmitting stations of the secondary user to the receiving station of the primary user in the region of, is calculated, and the n-th order of the calculated second interference power Based on the cumulant, a probability density function of the second interference power is calculated, and an interference probability is calculated using parameters of the probability density function.

  The n-th order cumulant of the first interference power is the density and transmission power distribution of the secondary user's transmitting station in each of the plurality of regions, the antenna gain between each region and the primary user, and the assumed radio wave It is a statistic that depends on the propagation model. And a more general statistic can be calculated | required by calculating | requiring this n-th order cumulant.

  The n-th order cumulant includes the average of the first interference power, the variance of the first interference power, the skewness of the first interference power, and the kurtosis of the first interference power. The distribution of the second interference power can be approximated to a shifted lognormal distribution by obtaining the average and variance of the power.

  As a result, the probability of interference with the receiving station of the primary user can be easily calculated.

(Configuration 12)
In any one of configurations 9 to 11, in the second step, the determining means sets the transmission probability of the secondary user's transmission station to the average number of transmission stations transmitted by the secondary user in each of the plurality of regions. A quadratic that maximizes the objective function under the constraint that the subtraction result obtained by subtracting the target value from the calculated interference probability is less than or equal to zero, using the addition result obtained by adding the multiplication results for a plurality of regions as the objective function. By determining the transmission probability of the user's transmission station in each of the plurality of areas, the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is determined.

  Under the constraint that the probability of interference with the primary user is less than or equal to the target value, the transmission probability of the secondary user's transmitting station that maximizes the objective function is obtained. If the transmission probability of the transmitting station is zero, the region where the transmission probability is zero is guaranteed to be an exclusive region of the primary user, and if the transmission probability is not zero, the region where the transmission probability is not zero is It is guaranteed to be a non-exclusive area of the primary user.

  Accordingly, the exclusive area of the primary user can be accurately created in the two-dimensional area.

(Configuration 13)
In Configuration 9, each of the plurality of regions is arranged with a plurality of lines extending radially from the origin, a plurality of concentric circles centered on the origin, and a plurality of concentric circles arranged at predetermined intervals in the height direction from the origin. It has a shape formed by a plurality of sets of concentric circles as one set of concentric circles.

  Since each of the plurality of regions has a three-dimensional shape extending in the height direction while maintaining a planar shape having an annular sector shape, the three-dimensional space can be easily divided into a plurality of regions using cylindrical coordinates. As a result, the transmission probability of the secondary user's transmission station can be determined in consideration of the distance in the height direction from the origin in addition to the distance in the plane direction from the origin.

(Configuration 14)
In the configuration 9 or the configuration 13, in the first step, the computing means is a constant relating to the transmission power of the secondary user's transmitting station in each of the plurality of regions, the antenna directivity in the primary user's receiving station, 1 Each of the plurality of areas is determined using a fading coefficient between the receiving station of the secondary user and the transmitting station of the secondary user, the Euclidean distance between the position and the origin of the transmitting station of the secondary user, and the radio wave attenuation constant. The first interference power given by the secondary user's transmitting station to the primary user's receiving station is calculated using the Laplace transform of the first interference power, and n (n is a positive value). (Integer) The next cumulant is calculated as a function of the transmission probability of the transmission station of the secondary user, and based on the calculated n-th order cumulant, the primary user's With interference power to the receiving station And calculating a probability density function of the second interference power based on the calculated n-order cumulant of the second interference power, and calculating a parameter of the probability density function. To calculate the interference probability.

  The n-th order cumulant of the first interference power is the density and transmission power distribution of the secondary user's transmitting station in each of the plurality of regions, the antenna gain between each region and the primary user, and the assumed radio wave It is a statistic that depends on the propagation model. And a more general statistic can be calculated | required by calculating | requiring this n-th order cumulant.

  The n-th order cumulant includes the average of the first interference power, the variance of the first interference power, the skewness of the first interference power, and the kurtosis of the first interference power. The distribution of the second interference power can be approximated to a lognormal distribution by obtaining the average and variance of the power. As a result, the probability of interference with the receiving station of the primary user can be easily calculated.

(Configuration 15)
In the configuration 14, in the first step, the computing means computes the nth order cumulant of the second interference power by computing the sum of the second interference power from the first order cumulant to the nth order cumulant.

  The n-th order cumulant of the second interference power is a Q function of the parameter represented by the first and second order cumulants of the second interference power, and the first and second order cumulants of the second interference power are The n-th order cumulant of the second interference power is calculated using Expression (41) indicating that it is the sum of each cumulant. Therefore, the exclusive region can be obtained based on the transmission probability in consideration of the entire three-dimensional space grid.

(Configuration 16)
In any one of Configurations 13 to 15, the determining means, in the second step, the probability that the secondary user transmitting station does not transmit the average number of transmitting stations transmitted by the secondary user in each of the plurality of regions. The secondary use that minimizes the objective function under the constraint that the calculated interference probability is less than or equal to the target value, with the addition result obtained by multiplying the multiplication results obtained by multiplying the non-transmission probabilities as the objective function. The transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is determined by obtaining the transmission probability of the transmission station of the secondary user in each of the plurality of regions.

  Under the constraint that the probability of interference with the primary user is less than or equal to the target value, the transmission probability of the secondary user's transmitting station that minimizes the objective function is obtained. If the transmission probability of the transmitting station is zero, the region where the transmission probability is zero is guaranteed to be an exclusive region of the primary user, and if the transmission probability is not zero, the region where the transmission probability is not zero is It is guaranteed to be a non-exclusive area of the primary user. Accordingly, the exclusive area of the primary user can be accurately created in the two-dimensional area.

  Further, according to the embodiment of the present invention, the computer-readable recording medium on which the program is recorded is a computer-readable recording medium on which the program according to any one of Configurations 5 to 8 is recorded.

  An exclusive area for a primary user with a hole can be formed. In addition, an exclusive area having a complicated shape can be designed.

It is the schematic which shows the communication apparatus in embodiment of this invention. 1 is a diagram illustrating an example of a system having a spatial grid in Embodiment 1. FIG. It is a figure which shows one annular sector ASR. It is a block diagram in Embodiment 1 of the management apparatus shown in FIG. It is a figure which shows the memory | storage method in the memory | storage means shown in FIG. 5 is a flowchart for explaining a method of creating an exclusive area PER in the first embodiment. It is a flowchart for demonstrating the detailed operation | movement of step S1 of FIG. It is a flowchart for demonstrating the detailed operation | movement of step S2 of FIG. It is a flowchart for demonstrating the detailed operation | movement of step S3 of FIG. It is a figure which shows the setting value of { _gj } in each N ( _theta ). Is a diagram showing the values of randomly generated in the scenario 2 {λ _ij} or _{{P ij}.} It is a figure which shows the optimal solution of the transmission probability _aij in each N ( _theta ). It is a figure which shows the complementary cumulative distribution function (CCDF) of total interference electric power _IS2P in each N ( _theta ). It is a figure which shows the optimal solution of the transmission probability _aij when {(lambda) _ij } or { _Pij } is produced | generated at random. It is a figure which shows the complementary cumulative distribution function (CCDF) of the total interference electric power I _S2P when {λ _ij } or {P _ij } is randomly generated. It is a figure which shows an example of the system which has the space grid in Embodiment 2. FIG. It is a block diagram in Embodiment 2 of the management apparatus shown in FIG. It is a figure which shows the memory | storage method in the memory | storage means shown in FIG. 10 is a flowchart for explaining a method of creating an exclusive area PER in the second embodiment. It is a flowchart for demonstrating the detailed operation | movement of step S1A shown in FIG. It is a flowchart for demonstrating the detailed operation | movement of step S2A of FIG. It is a flowchart for demonstrating the detailed operation | movement of step S3A of FIG. It is a figure which shows the optimal solution of the antenna gain and maximum transmission probability in each altitude. It is a figure which shows the result of having calculated the complementary cumulative distribution function (CCDF) of Formula (45) about the case of an optimal solution.

  Embodiments of the present invention will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are denoted by the same reference numerals and description thereof will not be repeated.

  FIG. 1 is a schematic diagram showing a communication device according to an embodiment of the present invention. Referring to FIG. 1, there are wireless communication systems WLC1 and WLC2. The wireless communication system WLC1 is a licensed wireless communication system and is referred to as a “primary user”. The wireless communication system WLC1 includes a wireless station 1 and terminals 2 and 3. The radio station 1 is a primary user radio station, and the terminals 2 and 3 are primary user terminals. The wireless station 1 and the terminals 2 and 3 perform wireless communication with each other in the licensed frequency band.

  The wireless communication system WLC2 is a wireless communication system that performs wireless communication in the frequency band of the primary user, and is referred to as a “secondary user”. The wireless communication system WLC2 includes a wireless station 11 and terminals 121 to 12s (s is an integer of 2 or more). The wireless station 11 is a secondary user's wireless station, and the terminals 121 to 12s are secondary user terminals. The wireless station 11 and the terminals 121 to 12s perform wireless communication with each other in the primary user frequency band.

  Each of the terminals 2 and 3 may receive a radio signal from the terminals 121 to 12s. Each of the terminals 2 and 3 detects its own position using, for example, GPS (Global Positioning System), and transmits the detected own position to the radio station 1.

  The wireless station 1 receives the positions of the terminals 2 and 3 from the terminals 2 and 3, and transmits the received positions of the terminals 2 and 3 to the wireless station 11.

  The management device 10 is disposed in the wireless station 11. Then, the management device 10 receives the positions of the terminals 2 and 3 from the wireless station 1. Moreover, the management apparatus 10 receives the position and transmission power of the terminals 121 to 12s from the terminals 121 to 12s.

  The management device 10 uses the position of the terminals 2 and 3, the positions of the terminals 121 to 12 s and the transmission power of the terminals 121 to 12 s, and an exclusive area where only the primary user can perform wireless communication by a method described later. Create a PER (Primary Exclusive Region).

  For example, the terminals 121 to 12 s detect their positions using GPS, and transmit the detected positions to the management apparatus 10. In addition, the terminals 121 to 12 s detect transmission power when wireless communication is performed, and transmit the detected transmission power to the management apparatus 10.

[Embodiment 1]
FIG. 2 is a diagram illustrating an example of a system having a spatial grid in the first embodiment. Referring to FIG. 2, the primary user's receiving station PR (Primary Receiver) (one of terminals 2 and 3) is set as origin O (represented by a white square), and spreads from origin O (N _θ +1). Assume a two-dimensional spatial grid composed of a radial line of books and (N _r +1) concentric circles centered on the origin O.

Polar coordinates (r, θ) are used to represent (N _θ +1) radial lines and (N _r +1) concentric circles.

The radial line is expressed as θ = θ _j , j = 0 _,. Here, θ ₀ = 0, θ _Nθ = 2π, and θ ₀ <... <Θ _Nθ .

The concentric circles are expressed as r = R _i , i = 0 _,. Here, R ₀ = 0 and R ₀ <... <R _Nr .

These radial lines and concentric circles are used to divide the space into N _r N _θ annular sector ASR (Annular Sector Region).

FIG. 3 is a diagram showing one annular sector ASR. Referring to FIG. 3, each annular sector ASR _{is, i = 0, ···, N} r -1 and j = 0, · · ·, for _{N θ -1, S ij = {} (r, θ) | R _i ≦ r ≦ R _{i + 1} , θ _j ≦ θ ≦ θ _{j + 1} }. Obviously, {S _ij } is disjoint. The area of each annular sector ASR (S _ij ) is denoted as | S _ij |.

  It is assumed that a secondary user's transmitter station ST (Secondary Transmitter) (represented by a black triangle and one transmitter station ST is composed of any of terminals 121 to 12s) is randomly arranged in a two-dimensional space grid. To do.

  FIG. 4 is a configuration diagram of the management apparatus 10 illustrated in FIG. 1 according to the first embodiment. With reference to FIG. 4, the management apparatus 10 includes a reception unit 101, a calculation unit 102, a storage unit 103, a determination unit 104, and a creation unit 105.

  The receiving unit 101 receives the positions of the terminals 2 and 3 from the wireless station 1 and outputs the received positions of the terminals 2 and 3 to the calculating unit 102. The receiving means 101 receives the positions and transmission power of the terminals 121 to 12 s from the terminals 121 to 12 s and outputs the received positions and transmission power of the terminals 121 to 12 s to the computing means 102.

  The computing means 102 receives the positions of the terminals 2 and 3, the positions of the terminals 121 to 12 s and the transmission power of the terminals 121 to 12 s from the receiving means 101.

The computing means 102 holds in advance the area | S _ij | of the two-dimensional space grid and each circular sector ASR (S _ij ) described in FIG.

  The calculating means 102 arranges any one of the terminals 2 and 3 as the primary user receiving station PR at the origin O of the two-dimensional space grid.

The computing means 102 computes the density λ _ij of the secondary user's transmission station ST existing in the area S _ij of each annular sector ASR based on the positions of the terminals 121 to 12s. Then, the calculation means 102 stores the calculated density λ _ij of the transmission station ST of the secondary user in the storage means 103.

The number of secondary user transmitting stations ST existing in the region S _ij is as follows.

It is assumed that the transmission stations ST of secondary users on the region S _ij are distributed according to a non-uniform Poisson point process (PPP). This PPP and its density function are denoted as Φ _Sij and Λ _ij (r, θ), respectively.

The density function Λ _ij (r, θ) is expressed by the following equation.

In other words, the number of transmission stations ST of secondary users existing on the area S _ij follows the Poisson distribution of the average λ _ij | S _ij |, and the transmission stations ST of these secondary users are on the area S _ij Is uniformly distributed.

Further, the computing means 102 computes a probability density function f _pij (PDF: Probability Density Function) of the transmission power used by the secondary user's transmission station ST based on the transmission power of the terminals 121 to 12s, and computes it. The probability density function f _pij is stored in the storage unit 103.

Further, the calculation means 102 uses an after-mentioned method to determine the interference probability P of the primary user to the receiving station PR, which is a function of the transmission probability a _ij of the secondary user's transmitting station ST in each of the plurality of regions S _ij. (I _S2P > I _th ) is calculated, and the calculated interference probability P (I _S2P > I _th ) is output to the determination unit 104.

Storage means 103, the secondary density lambda _ij of a user of the transmitting station ST and probability density function _{f pij} receiving from the operation unit 102, the density of the transmitting station ST of received secondary user lambda _ij and the probability density function f Store _pij .

The storage unit 103 stores a constant g _ij in advance. The constant g _ij is a constant that affects the antenna directivity of the primary user's receiving station PR and the antenna height of the primary user's receiving station PR or the secondary user's transmitting station ST. It is a value specific to ASR.

The determination unit 104 receives the interference probability P (I _S2P > I _th ) from the calculation unit 102. Then, the determination unit 104 determines that the interference probability P (I _S2P > I _th ) is equal to or less than the target value β _target , and maximizes the average number of transmission stations ST of the secondary users to be transmitted. ST transmission probability a _ij (0 ≦ a _ij ≦ 1) is determined in each of a plurality of regions S _ij . Then, determination unit 104 outputs the transmission probability _{a ij} of the transmitting station ST of the secondary user in each area _{S ij} to create means 105.

The creation unit 105 receives the transmission probability a _ij of the transmission station ST of the secondary user in each area S _ij from the determination unit 104. Then, the creation unit 105 sets an area S _{ij in} which the transmission probability a _ij of the transmission station ST of the secondary user is zero as an exclusive area, and an area S _{ij in} which the transmission probability a _ij of the transmission station ST of the secondary user is not zero. _An exclusive region PER is created on the two-dimensional space grid with _ij as a non-exclusive region.

FIG. 5 is a diagram showing a storage method in the storage means 103 shown in FIG. Referring to FIG. 5, the storage unit 103, the density lambda _ij of the transmitting station ST of the secondary user, the secondary user position x of the transmitting station ST, and transmit power _{p ij} of the probability density function _{f pij,} constant g _ij , the radio wave attenuation constant α, and the fading coefficient h _x are stored in association with the annular sector area S _ij .

The density λ _ij is obtained by dividing the number of secondary user transmitting stations ST existing in the region S _{ij by} the area | S _ij | of the region S _ij by the computing unit 102.

The position x of the transmission station ST of the secondary user is determined by polar coordinates (r, θ). The probability density function _{f pij} of the transmission power _{p ij} are those calculated by the calculation means 102 by using _the transmission power _{p ij} in the transmitting station ST present in each area _{S ij.}

The constant g _ij is a value unique to each region S _ij .

The fading coefficient h _x corresponds to the position x of the transmission station ST of the secondary user.

A method for determining the transmission probability a _ij of the transmission station ST of the secondary user in each of the plurality of regions S _ij will be described.

The transmission stations ST of secondary users transmitting on the region Sij are distributed according to the non-uniform Poisson point process (PPP) Φ _Sij of the density function a _ij Λ _ij (r, θ). Therefore, the number of secondary user transmitting stations ST transmitting on the region S _ij follows a Poisson distribution with an average a _ij λ _ij | S _ij |.

_Assume that the total interference power I _S2P received from the transmitting station ST of all the secondary users transmitting at the receiving station PR of the primary user exceeds the threshold value Ith for the interference to the primary user. The threshold value I _th is set to a value that is 10 dB lower than the noise power, for example. At this time, the probability of interference with the primary user can be expressed as P (I _S2P > I _th ).

When the interference power in the primary user to receive from the transmitting station ST of the secondary user to transmit on one annular sector S _ij is expressed as I _ij, interference power I _ij is expressed by the following equation.

In equation (2), h _x is a fading coefficient between the secondary user's transmitting station ST and the primary user's receiving station at coordinates x∈Φ _Sij , and p _{ij, x} is the coordinate x Is the transmission power of the transmission station ST of the secondary user of ∈Φ _Sij , || x || is the Euclidean distance between the coordinates x∈Φ _Sij and the origin O, and α is the radio wave attenuation constant (α > 2). The transmission power p _{ij, x} is a random variable that follows the probability density function f _pij described above. Based on the information in all the circular sector regions, the transmission power in each region S _ij is determined.

Using the Campbell theorem (Non-Patent Document 7), the moment generating function M _Iij of the interference power I _ij is expressed by the following equation.

Using Expression (3), the n-th (n is a positive integer) order cumulant κ _n (I _ij ) of the interference power I _ij is expressed by the following expression.

C _{n, ij in} Expression (4) is represented by the following expression.

E (h ⁿ ) and E (p _ij ⁿ ) in equation (5) are represented by equations (6) and (7), respectively.

_{C n} in the formula _{(5), ij} is the density and distribution of the transmission power of the transmitting station ST of the secondary user on regions _{S ij} of the divided annular sector ASR, region _{S ij} and the primary user of the antenna gain , And a statistic that depends on the assumed propagation model, and is called the n-th order cumulant of the interference power I _ij received from all the transmission stations ST of the secondary users on each region S _ij .

By obtaining the cumulant, a more general statistic can be obtained. Specifically, C _{1, ij} means the average of the interference power I _ij , and C _{2, ij} is the interference power I _ij C _{3, ij} / C _{2, ij} ^3/2 means the skewness of the interference power I _ij and C _{4, ij} / C _{2, ij} ² is the kurtosis of the interference power I _ij . means. By _obtaining C _{1, ij} , C _{2, ij} , C _{3, ij} for each interference power I _ij, the distribution of the total interference power I _S2P used thereafter can be approximated to a shifted lognormal distribution.

The total interference power I _{S2P to be} analyzed is expressed by the following equation.

Here, since {Φ _Sij } is a non-uniform Poisson point process (PPP) independent from each other, considering that {I _ij } is a random variable independent from each other, the total interference can be obtained from cumulant additivity. The power I _S2P is expressed by the following equation.

When the total interference power I _S2P is approximated as a shifted lognormal distribution (Non-Patent Documents 9 and 10) using cumulant matching (Non-Patent Document 8), the probability density function f _IS2P of the total interference power I _S2P is given by expressed.

C _SLN in the equation (10) is represented by the following equation.

In addition, μ _SLN in Expression (10) is expressed by the following expression.

Σ _SLN in Expression (10) and Expression (11) is expressed by the following expression.

  W in Formula (13) is represented by the following formula.

c _SLN , μ _SLN , σ _SLN , and W are parameters.

Further, P (I _S2P > I _th ) is expressed by the following equation.

  In the equation (15), Q (•) is a Q function and is represented by the following equation.

Note that the interference probability P (I _S2P > I _th ) with respect to the threshold value I _th is the same as the complementary cumulative distribution function of the total interference power I _S2P .

From the equations (9), (11), (12), (13), (14), the interference probability P (I _S2P > I _th ) is the transmission probability of the transmission station ST of the secondary user in each area S _ij. It can be seen that it depends on a _ij .

Next, the optimization problem for determining the transmission probability a _ij of the transmission station ST of the secondary user in each region S _ij is formulated.

  The objective function is defined by the following equation, and the optimization problem is designed so as to maximize the objective function.

F _obj (a) in Expression 17 is the average number of transmission stations ST of secondary users transmitting on ∪ _ij S _ij . Further, a constraint is imposed that the interference probability P (I _S2P > I _th ) is lower than the target value β _target . This _{constraint, f cons:} (a) when defined by the following _equation, can be expressed as _{f cons} (a) ≦ 0.

Using f _obj (a) and f _cons (a), the optimization problem can be formulated by the following equations (19) to (21).

This optimization problem is a nonlinear optimization problem with constraints, and by solving this, each region S under the constraint that the interference probability P (I _S2P > I _th ) is lower than the target value β _target. the transmission probability a _ij to maximize the mean number of the transmitting station ST of the secondary user to transmit can be determined in each region S _ij at _ij.

FIG. 6 is a flowchart for explaining a method of creating the exclusive area PER in the first embodiment. Referring to FIG. 6, when the operation for creating exclusive area PER is started, calculation means 102 of management apparatus 10 includes a plurality of two-dimensional space grids that have the receiving station PR of the primary user as the origin. The transmission power of the transmitting station ST distributed according to the non-uniform Poisson point process of the secondary user in each of the annular sector areas S _ij , the antenna directivity and the reception of the primary user at the receiving station PR of the primary user Constant affecting the antenna altitude at the station and the secondary user's transmitting station ST, fading coefficient between the primary user's receiving station PR and the secondary user's transmitting station ST, secondary user's transmitting station Using the Euclidean distance between the position of the ST and the origin and the radio wave attenuation constant, the interference power larger than the threshold received by the primary user's receiving station PR from all the transmitting stations ST transmitted by the secondary user is obtained. Multiple rings Calculation is performed as an interference probability P (I _S2P > I _th ) with respect to the receiving station of the primary user, which is a function of the transmission probability a _ij of the transmitting station ST of the secondary user in each of the sector areas S _ij (step S1). ).

Then, the calculation unit 102 outputs the calculated interference probability P (I _S2P > I _th ) to the determination unit 104.

The determination unit 104 receives the interference probability P (I _S2P > I _th ) from the calculation unit 102, and the received interference probability P (I _S2P > I _th ) is equal to or less than the target value β _target and is transmitted. The transmission probability a _ij of the secondary user's transmission station ST that maximizes the average number of user's transmission stations ST is determined in each of the plurality of annular sector regions S _ij (step S2).

Then, determination unit 104 outputs the transmission probability _{a ij} of the transmitting station ST of the secondary user in each of the plurality of annular sector area _{S ij} to create means 105.

The creation unit 105 receives the transmission probability a _ij of the secondary user's transmission station ST in each of the plurality of annular sector regions S _ij from the determination unit 104. Then, the creation unit 105 _excludes only the primary user from performing radio communication based on the transmission probability a _ij of the transmission station ST of the secondary user in each of the determined plurality of annular sector regions. A region PER is created (step S3).

More specifically, creation means 105, the area S _ij transmission probability a _ij is zero and the exclusive area, the area S _ij transmission probability a _ij is not zero as a non-exclusive region, constituting the two-dimensional spatial grid An exclusive region PER is created in the two-dimensional space grid by determining whether each of the plurality of annular sector regions S _ij is an exclusive region or a non-exclusive region.

  This completes the operation for creating the exclusive area.

  FIG. 7 is a flowchart for explaining the detailed operation of step S1 of FIG. Referring to FIG. 7, when the operation for creating exclusive area PER is started, computing means 102 sets i = 1 and j = 1 (step S11).

Then, the calculation means 102 reads the probability density function f _pi of the transmission power in the region S _ij and the position x of the secondary user's transmission station ST from the storage means 103, and reads the read secondary user's transmission station ST. The position x is substituted into the transmission power probability density function f _pij to calculate the transmission power p _ij in the region S _ij (step S12).

  Thereafter, the calculation means 102 calculates the Euclidean distance L between the position x of the transmission station ST of the secondary user and the origin O (step S13).

Then, the calculation means 102 reads the constant g _ij , fading coefficient h _x , and radio wave attenuation constant α in the region S _ij from the storage means 103, and transmits the transmission power p _ij , constant g _ij , fading coefficient h _x , Euclidean distance L, and The interference power I _ij is calculated by substituting the radio wave attenuation constant α into the equation (2) (step S14).

Subsequently, the computing means 102 calculates the n-th order cumulant κ _n (I _ij ) of the interference power I _ij using the moment generating function M _Iij (s) of the interference power I _ij according to the equations (4) to (7). Calculation is performed (step S15).

Thereafter, the computing means 102 determines whether i = N _r −1 (step S16).

When it is determined in step S16 that i = N _r −1 is not satisfied, the computing unit 102 sets i = i + 1 (step S17).

Thereafter, the series of operations returns to step S12, and steps S12 to S17 are repeatedly executed until it is determined in step S16 that i = N _r −1.

If it is determined in step S16 that i = N _r −1, the computing means 102 further determines whether or not j = N _θ −1 (step S18).

When it is determined in step S18 that j = N _θ −1 is not true, the computing means 102 sets j = j + 1 (step S19).

Thereafter, the series of operations returns to step S12, and steps S12 to S19 are repeatedly executed until it is determined in step S18 that j = N _θ −1.

Then, when it is determined in step S18 that j = N _θ −1, the computing means 102, based on the _n- th order cumulant κ _n (I _ij ), in accordance with the formulas (8) and (9), The n-th order cumulant κ _n (I _S2P ) of the total interference power I _S2P that is the interference power from all the transmission stations ST of the secondary user to the reception station PR of the primary user in the region S _ij is calculated (step S20). ).

Thereafter, the computing means 102 computes a probability density function of the total interference power I _S2P according to the equation (10) based on the _n- th order cumulant κ _n (I _S2P ), and the computed probability density function parameters c _SLN , μ _SLN , σ _SLN (Expression (11) to Expression (14)) is used to calculate the interference probability P (I _S2P > I _th ) shown in Expression (15) (Step S21).

  And a series of operation | movement transfers to step S2 of FIG.

FIG. 8 is a flowchart for explaining the detailed operation of step S2 of FIG. After step S1 in FIG. 6 (step S21 in FIG. 7), calculating means 102, according to equation (17), the average number lambda _ij transmitting stations ST transmitted by the secondary user in each of the plurality of areas _{S ij} | The addition result obtained by multiplying S _ij | by the transmission probability a _ij of the transmission station ST of the secondary user for a plurality of areas S _ij is calculated as an objective function f _obj (a) (step S22). Then, the calculation means 102 outputs the interference probability P (I _S2P > I _th ) and the objective function f _obj (a) to the determination means 104.

The determination unit 104 receives the interference probability P (I _S2P > I _th ) and the objective function f _obj (a) from the calculation unit 102. Further, the determination unit 104 holds a target value β _target of the interference probability P (I _S2P > I _th ) in advance.

Then, the determination unit 104 calculates f _cons (a) = P (I _S2P > I _th ) −β _target and sets a constraint condition _satisfying f _cons (a) ≦ 0 (step S23).

Thereafter, the determination unit 104 determines the transmission probability a _ij of the secondary user's transmission station ST that maximizes the objective function f _obj (a) under the set constraint conditions (step S24). The determined transmission probability a _ij is a transmission probability in each region S _ij and consists of “0” or “1”.

  And after step S24, a series of operation | movement transfers to step S3 of FIG.

FIG. 9 is a flowchart for explaining the detailed operation of step S3 of FIG. Referring to FIG. 9, after step S2 in FIG. 6 (step S24 in FIG. 8), creation means 105 receives transmission probability a _ij from determination means 104, and sets i = 1 and j = 1 (step S31).

Then, the creating unit 105 determines whether or not the transmission probability a _ij is “0” (step S32).

When it is determined in step S32 that the transmission probability a _ij is “0”, the creating unit 105 sets the area S _ij as an exclusive area where only the primary user can perform wireless communication (step S33). .

On the other hand, when it is determined in step S32 that the transmission probability a _ij is not “0”, the creating unit 105 sets the area S _ij as a non-exclusive area (step S34). Since the transmission probability a _ij is “0” or “1”, when it is determined that the transmission probability a _ij is not “0”, the transmission probability a _ij is “1”. Therefore, since the region S _ij can be determined not to be an exclusive region, the region S _ij is determined as a non-exclusive region.

After step S33 or step S34, the creating unit 105 determines whether i = N _r −1 (step S35).

When it is determined in step S35 that i = N _r −1 is not satisfied, the creation unit 105 sets i = i + 1 (step S36). Thereafter, the series of operations proceeds to step S32, and steps S32 to S36 are repeatedly executed until it is determined in step S35 that i = N _r −1.

If it is determined in step S35 that i = N _r −1, the creating unit 105 further determines whether or not j = N _θ −1 (step S37).

When it is determined in step S37 that j = N _θ −1 is not satisfied, the creation unit 105 sets j = j + 1 (step S38). Thereafter, the series of operations proceeds to Step S32, and Steps S32 to S38 are repeatedly executed until it is determined in Step S37 that j = N _θ −1.

If it is determined in step S37 that j = N _θ −1, the creating unit 105 creates the primary user exclusive area PER including the area S _{ij as} the exclusive area in the two-dimensional space grid. (Step S39).

  Thereafter, the series of operations proceeds to “END” in FIG.

Thus, the management apparatus 10 determines whether each of the plurality of areas S _ij is an exclusive area or a non-exclusive area according to the flowchart shown in FIG. 6 (including the flowcharts shown in FIGS. 7 to 9), to create an exclusive area PER primary user consisting the exclusive region area S _ij in the two-dimensional spatial grid.

  Therefore, it is possible to create the exclusive area PER of the primary user with a hole.

In addition, since each of the plurality of regions S _ij has an annular sector shape, the integration can be removed as shown in Expression (4), and the calculation can be simplified.

  The management apparatus 10 creates an exclusive area PER for the primary user by the method described above. Then, when there is an inquiry about whether or not communication is possible from a secondary user existing outside the created primary user exclusive area PER, the management apparatus 10 sends a notification indicating that communication is possible to the secondary user. You may make it transmit to.

The numerical evaluation of the transmission probability a _ij as the optimum solution obtained under the constraint conditions will be described. In this numerical evaluation, the following assumptions are made to explain only the constant g _ij that depends on the directivity of the primary user's antenna.

First, θ _j and R _i are set as follows.

With this assumption, all the regions S _ij have the same area. That is, | S _ij | = πR _i ² / N _θ for all i and j.

Next, it is assumed that the transmitting station ST transmitted by the secondary user on each area S _ij uses fixed power corresponding to that area. The fixed power for each region S _ij is denoted as P _ij . With this setting, f _pi for each region S _ij is expressed by Expression (24), and E (p _ij ⁿ ) is expressed by Expression (25).

Finally, let g _ij = g _j for all i. That, g _ij in each region S _ij is not dependent on the distance from the origin, depending on the angle from horizontal.

  Based on the above assumptions, two scenarios are evaluated numerically.

[Scenario 1]
In scenario 1, three types of N _θ (N _θ = 1, N _θ = 6, N _θ = 36) are evaluated. In addition, assume λ _ij = λ _const and P _ij = P _const for all i and j. That is, the transmission station ST of the secondary user are distributed according to a uniform Poisson point process of density lambda _const (PPP), to transmit at the same fixed power _{P const.}

  In scenario 1, equation (5) can be simplified as:

[Scenario 2]
In scenario 2, N _θ = 36, and either λ _ij or P _ij for each region S _ij is randomly generated in advance. When {λ _ij } (a set of λ _ij ) is randomly generated, P _ij = P _const is set for all i and j, and {P _ij } (a set of P _ij ) is randomly generated Λ _ij = λ _const for all i and j.

FIG. 10 is a diagram illustrating a set value of {g _j } at each N _θ . 10A shows a set value of {g _j } when N _θ = 1, and FIG. 10B shows a set value of {g _j } when N _θ = 6. (C) shows the set value of {g _j } when N _θ = 36, and (d) shows the reference function g (θ).

{G _j } at each N _θ is generated using the following equations (27) and (28).

In Expression (28), g (θ) is an antenna factor of a uniform linear array of N _array elements (Non-Patent Document 11), N _array = 10, the distance between elements is a half wavelength, and the phase is zero.

  Table 1 shows the evaluation specifications.

In Table 1, ^{m N} is a parameter of the Nakagami -m fading is assumed as fast fading, when ^{m N} = 1, a Rayleigh fading, when ^{m N} is infinite, so that no fast fading . Further, σ _S is σ _SLN shown in Expression (13).

FIG. 11 is a diagram illustrating values of {λ _ij } or {P _ij } generated randomly in scenario 2. In both cases where {λ _ij } is randomly generated and {P _ij } is randomly generated, {λ _ij } or {P _ij } is uniformly generated from two discrete values.

An optimization problem (Non-Patent Document 12) is implemented in Python using a modeling framework Pyomo (Non-Patent Document 13), and solved using an Interior Point Optimizer solver (Non-Patent Document 14). Nakagami-m fading and log-normal shadowing combined fading (Non-patent Document 12) are used. In this case, E (h ⁿ ) is expressed by the following equation when E (h) = 1 is considered.

In the formula (29), Γ (·) is the gamma function, _{m N} is a parameter Nakagami -m fading, sigma _{S, d B} is the parameter in dB lognormal shadowing, ξ is 10 / ln (10).

[Evaluation results]
The evaluation result of scenario 1 will be described. FIG. 12 is a diagram illustrating an optimal solution of the transmission probability a _ij at each N _θ .

In FIG. 12, (a) shows the optimal solution of the transmission probability a _ij when N _θ = 1, and (b) shows the optimal solution of the transmission probability a _ij when N _θ = 6, (C) shows the optimal solution of the transmission probability a _ij when N _θ = 36.

Further, f _obj (a ^* ) at each N _θ is shown in Table 2.

As _Nθ increases, the area of the exclusive region decreases (see FIG. 12) and f _obj (a ^* ) increases (see Table 2). That is, the number of transmitting stations ST to transmit increases with _Nθ .

Figure 13 is a diagram showing a complementary cumulative distribution function (CCDF) of the total interference power _{I S2P} at each N _theta. In FIG. 13, the vertical axis represents the complementary cumulative distribution function (CCDF), and the horizontal axis represents the total interference power I _S2P .

The complementary cumulative distribution function (CCDF) of the total interference power I _{S2P with} respect to the total interference power I _S2P is the same as the interference probability P (I _S2P > I _th ) with respect to the threshold value I _th .

In FIG. 13, each broken line is obtained from 5 × 10 ⁴ Monte Carlo simulations, and it can be seen that the simulation result agrees well with the diffraction result (solid line).

In addition, all of f _cons (a ^* ) acquired by the simulation are negative values, and it can be seen that the constraint conditions (Equations (20) and (21)) are satisfied (see Table 2).

  Next, evaluation in scenario 2 will be described.

FIG. 14 is a diagram illustrating an optimal solution of the transmission probability a _ij when {λ _ij } or {P _ij } is randomly generated.

In FIG 14, (a) is {lambda _ij} to indicate the optimal solution of the transmission probability _{a ij} in the case of randomly generated, (b), the transmission probability _{a ij} in the case of randomly generated _{{P ij}} Shows the optimal solution.

As shown in FIG. 14, a non-circular exclusive region PER with a hole is obtained both when {λ _ij } is randomly generated and when {P _ij } is randomly generated. I understand.

FIG. 15 is a diagram illustrating a complementary cumulative distribution function (CCDF) of the total interference power I _S2P when {λ _ij } or {P _ij } is randomly generated.

15, the vertical axis represents the complementary cumulative distribution function of the total interference power _{I S2P} (CCDF), the horizontal axis shows the total interference power _{I S2P.}

A curve k1 indicates a simulation result when {λ _ij } is randomly generated, a curve k2 indicates a simulation result when {P _ij } is randomly generated, and a curve k3 indicates {λ _ij }. Shows an analysis result in the case of generating randomly, and a curve k4 shows an analysis result in the case of generating {P _ij } at random.

The simulation results were obtained by 5 × 10 ⁴ Monte Carlo simulations.

Table 3 shows f _obj (a ^* ) when {λ _ij } or {P _ij } is randomly generated.

It can be seen that the simulation results agree well with the analysis results (see FIG. 15). In addition, all f _obj (a ^* ) are negative values, and it can be seen that the constraints (Equations (20) and (21)) are satisfied (see Table 3).

  As described above, in both scenarios 1 and 2, the exclusive area is created according to the flowchart shown in FIG. 6 (including the flowcharts shown in FIGS. 7 to 9), thereby creating a non-circular exclusive area with a hole. Proved to be.

  In the first embodiment, the operation of the management apparatus 10 may be executed by software. In this case, the management device 10 includes a CPU (Central Processing Unit), a ROM (Read Only Memory), and a RAM (Random Access Memory).

A program Prog_A having the flowcharts shown in FIGS. 6 to 9 is stored in the ROM. The position x of the density lambda _ij, secondary user of the transmission station ST transmitting station ST of the secondary user shown in FIG. 5, the probability density function _{f pij} of the transmission power, constant _{g ij,} radio attenuation constant α and fading The coefficient h _x is stored in the ROM in association with the area S _ij .

  The CPU reads the program Prog_A from the ROM and executes the read program Prog_A to create an exclusive area PER.

In this case, the RAM stores an intermediate calculation result in the calculation of the interference probability P (I _S2P > I _th ).

  Therefore, the program Prog_A is a program for causing the computer (CPU) to create the exclusive area PER.

  The program Prog_A may be recorded and distributed on a recording medium such as a CD and a DVD. In this case, the computer (CPU) reads and executes the program Prog_A from the recording medium, and creates the exclusive area PER. Therefore, the CD, DVD, etc., on which the program Prog_A is recorded are computer (CPU) readable recording media on which the program Prog_A is recorded.

In the above description, each of the plurality of regions S _ij constituting the two-dimensional space grid has been described as having an annular sector shape. However, in the embodiment of the present invention, the two-dimensional space grid is not limited thereto. Each of the plurality of regions S _ij constituting may have a square shape. In this case, in Equation (4), numerical calculation is performed and integration is removed.

[Embodiment 2]
In the second embodiment, for example, an unmanned aerial vehicle (UAV) is assumed as a transmission station for two users.

  The use of UAVs is increasing in various fields such as video shooting and delivery. Currently, UAV communication uses the 2.4 GHz and 5 GHz bands, which are unlicensed frequency bands, but the use of other frequency bands for higher-speed and large-capacity communication is being studied. (Non-patent document 15).

  Specifically, it has been studied to use the 5.7 GHz band currently allocated for radar communication as a main line and to use the 169 MHz band as a backup line when the main line cannot be used.

  However, in the 5.7 GHz band, frequency sharing with the radar as the primary user is necessary, and UAV communication should not interfere with the radar.

  Therefore, it is necessary to analyze the interference and design an appropriate UAV frequency channel assignment based on the analysis result.

  As means for avoiding interference with a primary user in wireless communication, there is a design of a primary user exclusive area PER (Non-patent Document 5).

  In Non-Patent Document 16, the interference power given to the primary user by the UAV is analyzed, and a hemispheric exclusive area PER is designed.

  In Non-Patent Document 17, a spatial grid is introduced in a two-dimensional space, and an exclusive area PER having a complicated shape is designed based on geographic information and antenna directivity.

  The analysis of these interference powers uses stochastic geometry that handles point processes (Non-patent Document 7).

  Therefore, in the second embodiment, for the purpose of designing an exclusive region PER having a complicated shape in a three-dimensional space, a three-dimensional space grid is introduced and stochastic geometric analysis is shown.

  FIG. 16 is a diagram illustrating an example of a system having a spatial grid in the second embodiment.

Referring to FIG. 16, the primary user's receiving station PR (one of terminals 2 and 3) is set as an origin O (represented by a white square), and cylindrical coordinates (r, θ, z) from the origin O are referred to. 3, which is composed of N _r +1 concentric circles arranged in the r direction, N _θ radial lines arranged in the θ direction, and N _z +1 lines arranged in the z direction. Assume a spatial grid.

Cylindrical coordinates (r, θ, z) are used to represent (N _θ +1) radial lines, (N _r +1) concentric circles, and N _z +1 lines.

The radial line is expressed as θ = θ _j , j = 0 _,. Here, θ ₀ = 0, θ _Nθ = 2π, and θ ₀ <... <Θ _Nθ .

The concentric circles are expressed as r = R _i , i = 0 _,. Here, R ₀ = 0 and R ₀ <... <R _Nr .

The line in the z direction is expressed as z = z _k , k = 0,..., N _z . Here, z ₀ = 0 and z ₀ <... <Z _Nz .

These radial lines, concentric circles, and z-direction lines are used to divide the space into N _r N _θ N _z regions.

Each _{region, i = 0, ···, N} r -1, j = 0, ···, N θ -1 and k = _0, ···, the _{N z -1 V ijk = {(} r, θ, z) | R _i ≦ r ≦ R _{i + 1} , θ _j ≦ θ ≦ θ _{j + 1} , z _k ≦ z ≦ z _{k + 1} }. Obviously, {V _ijk } is disjoint. The volume of the region V _ijk is expressed as | {V _ijk |.

In this way, each region V _ijk is arranged at a predetermined interval in the height direction from the origin O, a plurality of lines extending radially from the origin O, a plurality of concentric circles centered on the origin O, and a plurality of The concentric circle has a shape formed by a plurality of concentric circles.

  FIG. 17 is a configuration diagram of the management apparatus 10 shown in FIG. 1 in the second embodiment. Referring to FIG. 17, management device 10 </ b> A is the same as management device 10 except that calculation unit 102 of management device 10 shown in FIG. 4 is replaced with calculation unit 102 </ b> A.

The calculation means 102A holds in advance the three-dimensional space grid described in FIG. 16 and the area | {V _ijk | of the region V _ijk .

  The computing means 102A places one of the terminals 2 and 3 as the primary user receiving station PR at the origin O of the three-dimensional space grid.

The computing means 102A computes the density λ _ijk of the secondary user's transmission stations ST existing in each region V _ijk based on the positions of the terminals 121 to 12s. Then, the calculation unit 102A stores the calculated density λ _ijk of the secondary user's transmission station ST in the storage unit 103.

The number of secondary user transmitting stations ST existing on the region V _ijk is as follows. The density of UAV in the region V _ijk is λ _ijk, and the constant related to the laser directivity is g _ijk . Further, it is assumed that the distribution of UAVs using the main line in the region V _ijk follows a non-uniform Poisson point process (PPP) Φ _Vijk having a density function Λ _ijk (r, θ, z) of the following equation.

That is, the number of UAVs on the region V _ijk follows a Poisson distribution having an average λ _ijk | V _ijk |, and these UAVs are uniformly distributed on the region V _ijk .

Based on the information in all areas, the maximum UAV transmission probability in each area is determined. The maximum transmission probability of UAV on the region V _ijk is expressed as a _ijk (a _ijk satisfies 0 ≦ a _ijk ≦ 1).

At this time, UAVs transmitted on the region V _ijk are distributed according to non-uniform PPPΦ _Vijk of the density function a _ijk Λ _ijk (r, θ, z). Therefore, the number of UAVs transmitted on the region V _ijk follows a Poisson distribution with an average a _ijk λ _ijk | V _ijk |. The set {a _ijk } is denoted as a.

Furthermore, the calculation means 102A calculates a probability density function f _pijk of transmission power used by the secondary user's transmission station ST based on the transmission power of the terminals 121 to _12s, and stores the calculated probability density function f _pijk . Store in the means 103.

Further, the computing means 102A, by a method described later, the interference probability P with respect to the primary user receiving station PR, which is a function of the transmission probability a _ijk of the secondary user transmitting station ST in each of the plurality of regions V _ijk. (I _total > I _th ) is calculated, and the calculated interference probability P (I _total > I _th ) is output to the determining means 104.

The storage means 103 receives the density λ _ijk and the probability density function f _pijk of the secondary user's transmission station ST from the computing means 102A, and receives the density λ _ijk and the probability density function f of the secondary user's transmission station ST received. _{Store pijk} . The storage unit 103 stores a constant g _ijk in advance.

The determination unit 104 receives the interference probability P (I _total > I _th ) from the calculation unit 102A. Then, the determining means 104 minimizes the number of secondary user transmission stations ST (= UAV) whose interference probability P (I _total > I _th ) is equal to or less than the target value β _target and the main line is prohibited from being used. The transmission probability a _ijk of the secondary user's transmission station ST is determined in each of the plurality of regions V _ijk . Then, determination unit 104 outputs the transmission probability _{a ijk} transmission station ST of the secondary user in each area _{V ijk} to creation means 105.

The creation unit 105 receives the transmission probability a _ijk of the transmission station ST of the secondary user in each region V _ijk from the determination unit 104. The creation unit 105, transmission probability _{a ijk} transmission station ST secondary user and exclusive area region _{V ijk} is zero, transmission probability _{a ijk} transmission station ST secondary user is not zero region V _An exclusive area PER is created on the three-dimensional space grid with _ijk as a non-exclusive area.

FIG. 18 is a diagram showing a storage method in the storage means 103 shown in FIG. Referring to FIG. 18, the storage means 103 stores the density λ _{ijk of} the secondary user's transmission station ST, the position x of the secondary user's transmission station ST, the probability density function f _pijk of the transmission power p _ijk , and the constant g. _ijk , the radio wave attenuation constant α, and the fading coefficient h _x are stored in association with the region V _ijk .

The density λ _ijk is obtained by dividing the number of secondary user transmitting stations ST existing in the region V _{ijk by} the volume | V _ijk | of the region V _ijk by the computing unit 102A.

The position x of the transmission station ST of the secondary user is determined by cylindrical coordinates (r, θ, z). The probability density function _{f Pijk} transmission power _{p ijk} are those calculated by the calculation means 102A by using the transmission power _{p ijk} at the transmitting station ST present in each area _{V ijk.} The fading coefficient h _x corresponds to the position x of the transmission station ST of the secondary user.

A method for determining the transmission probability a _ijk of the transmission station ST of the secondary user in each of the plurality of regions V _ijk will be described.

The interference in the radar is defined as the total interference power I _total that the radar receives from the UAV using the main line exceeds a certain threshold value I _th . In this case, the radar interference probability can be expressed as P (I _total > I _th ).

The total interference power in the radar received from the UAV using the main line on a certain divided area V _ijk is calculated. When this total interference power is expressed as I _ijk , the total interference power I _ijk is expressed by the following equation.

In Equation (31), h _x is a fading coefficient (average 1) between the UAV and the radar at coordinates x∈Φ _Vijk , p _ijk is the transmission power of the UAV at coordinates x∈Φ _Vijk , and | | x || is the Euclidean distance between the coordinates xεR ² and the origin O, and α is a radio wave attenuation constant (α> 2). The transmission power p _ijk is a random variable according to the above-described probability density function f _pijk . Based on the information in all areas _{V ijk,} transmission power in each region _{V ijk} is determined.

  The Laplace transform of the total interference power in Expression (31) is calculated as follows using Campbell's theorem (Non-Patent Document 7).

Using equation _(32), n order cumulant kappa _n of _{I ijk (I ijk)} is, n = 1, 2, for ..., it can be represented by the equation (33) to (35).

Hereinafter, for the sake of simplicity, when α = 3, A _n (S) in Expression (35) can be calculated as in Expression (36) to Expression (39).

The total interference power I _{total to be} analyzed is expressed by the following equation.

Here, {Φ _Vijk } is a mutually independent non-uniform Poisson point process (PPP), so {I _ijk } is a mutually independent random variable. Therefore, from the additivity of the cumulant, the n-th order cumulant of I _total is expressed as the following formula as the sum of each cumulant.

When the I _total distribution is approximated as a lognormal distribution (Non-patent document 18) using cumulant matching (Non-patent document 8), the probability density function f _Itotal of I _total is _expressed by the equations (42) to (44). expressed.

Here, μ ₁ and σ ₁ ² are logarithmic normal distribution parameters, respectively. The interference probability P (I _total > I _th ) is expressed by the following equation. In the equations (43) and (44), κ ₁ (I _total ) ² means the square of the primary cumulant κ ₁ (I _total ).

In Expression (45), Q (•) is a Q function and is represented by Expression (16) described above. _{Incidentally, P} for _{I th (I total> I th} ) _is the same as the complementary cumulative distribution function of _{I total} (CCDF).

The threshold I _{th in} equation (45) is known, μ ₁ in equation (45) is represented by equation (43), σ _{1 in} equation (45) is represented by equation (44), Since κ ₁ (I _total ) and κ ₂ (I _total ) in equations (43) and (44) can be calculated by substituting equation (36) and equation (37) into equation (41), respectively, P ( I _total > I _th ) is a function of the transmission probability a _ijk .

Therefore, in order to request that as many UAVs as possible to use the main line, the objective function is the number of UAVs that are prohibited from using the main line, and an optimization problem is designed to minimize this objective function. To do. Next, in order to avoid interference with the radar, a constraint is imposed that P (I _total > I _th ) is below the allowable value β _target . From the above, the optimization problem is formulated as follows:

Equation (46) and Equation (47) are transmitted with the sum of (1-a _ijk ) λ _ijk | V _ijk | for all i, j, k under the constraint of Equation (47). This represents determining the probability a _ijk . That is, Expression (46) and Expression (47) are obtained by _adding the secondary user's transmission station to the average number of transmission stations (= λ _ijk | V _ijk |) transmitted by the secondary user in each of the plurality of regions V _ijk. The objective function is the addition result obtained by adding the multiplication result obtained by multiplying the non-transmission probability (= (1−a _ijk )), which is the probability of not transmitting, for a plurality of regions V _ijk , and the calculated interference probability P (I _total > I _(th ) represents that the transmission probability of the transmission station of the secondary user that minimizes the objective function is determined in each of the plurality of regions V _ijk under the constraint that the target value β _{target is} equal to or less than the target value β _target .

  Note that minimizing the number of UAVs that are prohibited from using the main line is equivalent to maximizing the number of UAVs that are allowed to use the main line.

As described above, P (I _total > I _th ) is the Q of the parameters μ ₁ and σ ₁ (see equations (43) and (44)) expressed by the first and second order cumulants of the interference power I _total. it is a function, primary cumulant and secondary cumulant of the interference power _{I total} is calculated using equation (41) indicating that the n-order cumulant of the interference power _{I total} is the sum of the cumulants. Accordingly, the exclusive region PER can be obtained by the transmission probability a _ijk while taking the entire three-dimensional space grid (see FIG. 16) into consideration.

FIG. 19 is a flowchart for explaining a method of creating an exclusive area PER in the second embodiment. Referring to FIG. 19, when the operation of creating exclusive area PER is started, computing means 102A of management apparatus 10 has a plurality of three-dimensional space grids that have the receiving station PR of the primary user as the origin. Transmission power of the transmitting station ST distributed according to the non-uniform Poisson point process of the secondary user in each of the regions V _ijk , a constant related to the antenna directivity at the receiving station PR of the primary user, and the receiving station of the primary user Using the fading coefficient between the PR and the secondary user's transmitting station ST, the Euclidean distance between the position and the origin of the transmitting station ST of the secondary user, and the radio wave attenuation constant, the receiving station PR of the primary user there but interference power larger than the threshold value received from all the transmitting stations ST transmitted by the secondary user, a function of the transmission probability a _ijk transmission station ST of the secondary user in each of the plurality of regions V _ijk Computed as interference probability _{P (I total> I th)} to the next user of the receiving station (step S1A).

Then, the calculation unit 102A outputs the calculated interference probability P (I _total > I _th ) to the determination unit 104.

The determination unit 104 receives the interference probability P (I _total > I _th ) from the calculation unit 102A, and the received interference probability P (I _total > I _th ) is equal to or less than the target value β _target and the main line is used. The transmission probability a _ijk of the secondary user's transmission station ST that minimizes the number of secondary user's transmission stations ST that are prohibited is determined in each of the plurality of regions V _ijk (step S2A).

Then, determination unit 104 outputs the transmission probability _{a ijk} transmission station ST of the secondary user in each of the plurality of regions _{V ijk} to creation means 105.

The creation unit 105 receives the transmission probability a _ijk of the transmission station ST of the secondary user in each of the plurality of regions V _ijk from the determination unit 104. Then, the creation unit 105 includes an exclusive area where only the primary user can perform wireless communication based on the transmission probability a _ijk of the transmission station ST of the secondary user in each of the determined areas V _ijk. A PER is created (step S3A).

More specifically, creation means 105, a region _{V ijk} transmission probability _{a ijk} are zero and the exclusive area, the area _{V ijk} transmission probability _{a ijk} is not zero as a non-exclusive region, constituting the three-dimensional spatial grid For each of the plurality of regions V _ijk , an exclusive region PER is created in the three-dimensional space grid by determining whether the region is an exclusive region or a non-exclusive region. This completes the operation for creating the exclusive area.

  FIG. 20 is a flowchart for explaining the detailed operation of step S1A shown in FIG.

  Referring to FIG. 20, when the operation of creating exclusive area PER is started, computing means 102A sets i = 1, j = 1, and k = 1 (step S41).

Then, the computing means 102A _{reads the} transmission power probability density function f _pijk in the region V _ijk and the position x of the secondary user's transmission station ST from the storage means 103, and the read secondary user's transmission station ST. The position x is substituted for the transmission power probability density function f _pijk to calculate the transmission power p _ijk in the region V _ijk (step S42).

  Thereafter, the calculation means 102A calculates the Euclidean distance L between the position x of the transmission station ST of the secondary user and the origin O (step S43).

Then, the computing means 102A reads the constant g _ijk , fading coefficient h _x , and radio wave attenuation constant α in the region S _ijk from the storage means 103, and transmits the transmission power p _ijk , constant g _ijk , fading coefficient h _x , Euclidean distance L and The interference power I _ijk is calculated by substituting the radio wave attenuation constant α into the equation (31) (step S44).

Subsequently, the computing unit 102A computes the n-th order cumulant κ _n (I _ijk ) of the interference power I _ijk using the Laplace transform L _ijk of the interference power I _ijk according to the equations (32) to (35) (steps). S45).

Thereafter, the calculation unit 102A determines whether i = N _r −1 (step S46).

When it is determined in step S46 that i = N _r −1 is not satisfied, the calculation unit 102A sets i = i + 1 (step S47).

Thereafter, the series of operations returns to step S42, and steps S42 to S47 are repeatedly executed until it is determined in step S46 that i = N _r −1.

If it is determined in step S46 that i = N _r −1, the computing unit 102A further determines whether j = N _θ −1 (step S48).

When it is determined in step S48 that j = N _θ −1 is not satisfied, the computing unit 102A sets j = j + 1 (step S49).

Thereafter, the series of operations returns to step S42, and steps S42 to S49 are repeatedly executed until it is determined in step S48 that j = N _θ −1.

If it is determined in step S48 that j = N _θ −1, the computing means 102A further determines whether or not k = N _z −1 (step S50).

When it is determined in step S50 that k = N _z −1 is not satisfied, the calculation unit 102A sets k = k + 1 (step S51).

Thereafter, the series of operations returns to step S42, and step S42 to step S51 are repeatedly executed until it is determined in step S50 that k = N _z −1.

If it is determined in step S50 that k = N _z −1, the computing unit 102A performs a plurality of operations according to the equations (36) to (41) based on the _n- th order cumulant κ _n (I _ijk ). The n-th order cumulant κ _n (I _total ) of the total interference power I _total that is the interference power from all the transmission stations ST of the secondary user to the reception station PR of the primary user in the region V _ijk of the region V _ijk (step) S52).

Thereafter, the calculation means 102A calculates a probability density function of the _total interference power I _total according to the equation (42) based on the _n- th order cumulant κ _n (I _total ), and parameters μ ₁ and σ of the calculated probability density function ₁ (Equation (43), Equation (44)) is used to calculate the interference probability P (I _total > I _th ) shown in Equation (45) (step S53). And a series of operation | movement transfers to step S2A of FIG.

FIG. 21 is a flowchart for explaining the detailed operation of step S2A of FIG. After step S1A in FIG. 19 (step S53 in FIG. 20), the computing means 102A, according to equation (46), calculates the average number λ _ijk | of transmission stations ST transmitted by secondary users in each of the plurality of regions V _ijk. The result obtained by multiplying S _ijk | by the probability (1-a _ijk ) of the transmission station ST of the secondary user who is prohibited from using the main line is added to a plurality of regions V _ijk as an objective function. (Step S61). Then, the calculation unit 102A outputs the interference probability P (I _total > I _th ) and the objective function to the determination unit 104.

The determination unit 104 receives the interference probability P (I _total > I _th ) and the objective function from the calculation unit 102A. Further, the determination unit 104 holds a target value β _target of the interference probability P (I _total > I _th ) in advance.

  And the determination means 104 sets the constraint condition shown in Formula (47) (step S62).

Thereafter, the determination unit 104 determines the transmission probability a _ijk of the transmission station ST of the secondary user that minimizes the objective function under the set constraint conditions (step S63). The determined transmission probability a _ijk is a transmission probability in each region V _ijk and consists of “0” or “1”. And after step S63, a series of operation | movement transfers to step S3A of FIG.

FIG. 22 is a flowchart for explaining the detailed operation of step S3A of FIG. Referring to FIG. 22, after step S2A in FIG. 19 (step S63 in FIG. 21), creation means 105 receives transmission probability a _ijk from determination means 104, and sets i = 1, j = 1, and k = 1. Set (step S71).

Then, the creating unit 105 determines whether or not the transmission probability a _ijk is “0” (step S72).

When it is determined in step S72 that the transmission probability a _ijk is “0”, the creating unit 105 sets the area V _ijk as an exclusive area where only the primary user can perform wireless communication (step S73). .

On the other hand, when it is determined in step S72 that the transmission probability a _ijk is not “0”, the creation unit 105 sets the region V _ijk as a non-exclusive region (step S74). Since the transmission probability a _ijk consists of “0” or “1”, when it is determined that the transmission probability a _ijk is not “0”, the transmission probability a _ijk is “1”. Therefore, the region V _ijk, since it can be determined that not exclusive region is obtained by the fact that the region V _ijk and non-exclusive region.

After step S73 or step S74, the creating unit 105 determines whether i = N _r −1 (step S75).

When it is determined in step S75 that i = N _r −1 is not satisfied, the creation unit 105 sets i = i + 1 (step S76). Thereafter, the series of operations proceeds to step S72, and steps S72 to S76 are repeatedly executed until it is determined in step S75 that i = N _r −1.

When it is determined in step S75 that i = N _r −1, the creating unit 105 further determines whether or not j = N _θ −1 (step S77).

When it is determined in step S77 that j = N _θ −1 is not satisfied, the creation unit 105 sets j = j + 1 (step S78). Thereafter, the series of operations proceeds to step S72, and steps S72 to S78 are repeatedly executed until it is determined in step S77 that j = N _θ −1.

If it is determined in step S77 that j = N _θ −1, the creating unit 105 further determines whether or not k = N _z −1 (step S79).

When it is determined in step S79 that k = N _z −1 is not satisfied, the creation unit 105 sets k = k + 1 (step S80). Thereafter, the series of operations proceeds to step S72, and step S72 to step S80 are repeatedly executed until it is determined in step S79 that k = N _z −1.

When it is determined in step S79 that k = N _z −1, the creation unit 105 creates the primary user exclusive area PER including the area V _{ijk as} the exclusive area in the three-dimensional space grid. (Step S81). Thereafter, the series of operations proceeds to “END” in FIG.

Thus, the management apparatus 10A determines whether each of the plurality of areas V _ijk is an exclusive area or a non-exclusive area according to the flowchart shown in FIG. 19 (including the flowcharts shown in FIGS. 20 to 22). The exclusive area PER of the primary user composed of the area V _{ijk as} the exclusive area is created in the three-dimensional space grid. Therefore, the exclusive area PER of the primary user having a complicated shape can be created.

  The management apparatus 10A creates the primary user exclusive area PER by the method described above. Then, when there is an inquiry about whether or not communication is possible from a secondary user existing outside the created primary user exclusive area PER, the management apparatus 10A sends a notification indicating that communication is possible to the secondary user. You may make it transmit to.

  Further, the secondary user may communicate using the backup line when receiving a notification indicating that communication is not possible from the management apparatus 10A.

The numerical evaluation of the transmission probability a _ijk as the optimum solution obtained under the constraint conditions will be described. Further, the radar interference probability is evaluated by Monte Carlo simulation for the designed exclusive area PER.

The boundaries are set as in Expression (48) to Expression (50) so that the accumulation | V _ijk | of the divided regions V _ijk is all constant.

Here, L is a restricted altitude, and the altitude of all UAVs is assumed to be L or less. In this case, the volume | V _ijk | of each region V _ijk is | V _ijk | = πR ₁ ² L / N _θ N _z . Next, for simplicity, it is assumed that all UAVs are transmitted with unit power, and the density of UAVs is a constant value λ for all divided regions V _ijk . As for a radar antenna gain g _ijk , as a simple model, it is assumed that a specific angular direction has a gain of 0 dB, and other directions have a gain of −30 dB. Table 4 shows the evaluation specifications.

As the fading, Nakagami m fading and logarithmic normal shadowing combined fading (Non-patent Document 19) are assumed. At this time, E (h ⁿ ) is expressed by the following equation considering E (h) = 1.

Here, Γ (·) is a gamma function, m _N is a parameter of Nakagami m fading, σ _{S, dB} is a parameter in _dB of lognormal shadowing, and ξ = 10 / ln (10). Further, the optimization problem shown in Expression (46) is implemented in Python using a modeling framework Pyomo (Non-patent Document 20), and solved using an Interior Point Optimizer (IPOPT) solver (Non-patent Document 21).

  Next, the evaluation result will be described. FIG. 23 is a diagram illustrating an optimum solution of the antenna gain and the maximum transmission probability at each altitude. FIG. 24 is a diagram illustrating a result of calculating the complementary cumulative distribution function (CCDF) of Expression (45) for the optimal solution.

In FIG. 23, (a) shows the antenna gain g _ijk in the range of altitudes from 3.5 km to 4 km, and (b) shows the optimal solution a _ijk of the maximum transmission probability in the range of altitudes from 3.5 km to 4 km. Indicates. (C) shows the antenna gain g _ijk in the altitude range of 2 km to 2.5 km, and (d) shows the optimal solution a _ijk of the maximum transmission probability in the altitude range of 2 km to 2.5 km. Further, (e) shows the antenna gain g _ijk in an altitude range of 0.5 km to 1 km, and (f) shows the optimal solution a _ijk of the maximum transmission probability in the altitude range of 0.5 km to 1 km.

In FIG. 24, the horizontal axis represents the interference power I _total received by the radar, and the vertical axis represents the complementary cumulative distribution function (CCDF) of the interference power I _total . A curve k5 indicates the analysis result, and a straight line k6 indicates the threshold value β _target .

  Referring to FIG. 23, it can be seen that the exclusive area PER is designed in a shape corresponding to the distance from the radar and the antenna pattern.

Referring to FIG. 24, it was confirmed that the interference power I _total received by the radar is smaller than the threshold value β _target .

  As shown in FIG. 23, it was found that the management apparatus 10A can design an exclusive area PER having a complicated shape.

  In the second embodiment, the operation of the management apparatus 10A may be executed by software. In this case, the management apparatus 10A includes a CPU, a ROM, and a RAM.

A program Prog_B having the flowcharts shown in FIGS. 19 to 22 is stored in the ROM. The density lambda _ijk transmission station ST of the secondary user shown in FIG. 18, secondary user position x of the transmitting station ST of the probability density function _{f Pijk} transmission power constant _{g ijk,} radio attenuation constant α and fading The coefficient h _x is stored in the ROM in association with the area V _ijk .

  The CPU reads the program Prog_B from the ROM, executes the read program Prog_B, and creates the exclusive area PER.

In this case, the RAM stores an intermediate calculation result in the calculation of the interference probability P (I _total > I _th ).

  Therefore, the program Prog_B is a program for causing the computer (CPU) to create the exclusive area PER.

  The program Prog_B may be recorded and distributed on a recording medium such as a CD and a DVD. In this case, the computer (CPU) reads and executes the program Prog_B from the recording medium, and creates the exclusive area PER. Therefore, a CD, DVD, or the like on which the program Prog_B is recorded is a computer (CPU) readable recording medium on which the program Prog_B is recorded.

  Other explanations in the second embodiment are the same as those in the first embodiment.

  In the above description, the management devices 10 and 10A have been described as being arranged in the radio station 11. However, in the embodiment of the present invention, the management devices 10 and 10A are different from the radio station 11 without being limited thereto. Or may be arranged alone.

  In the above description, the primary user is described as a licensed radio communication system. However, in the embodiment of the present invention, the primary user is not limited to this, and the interference outside the exclusive area Any wireless communication system may be used as long as the ratio of data indicating a constant value.

  According to the embodiment of the present invention, the management device 10 may have the following configuration.

(Configuration 1)
The management device includes a calculation unit, a determination unit, and a creation unit.

  The calculation means is a non-uniform Poisson point of the secondary user in each of a two-dimensional area or a plurality of areas constituting the three-dimensional area with the receiving station of the primary user having a constant ratio of interference data as the origin. Transmitting power of transmitting stations distributed according to the process, constant on antenna directivity at receiving station of primary user, fading coefficient between receiving station of primary user and transmitting station of secondary user, secondary usage Interference power greater than the threshold received by all the transmitting stations transmitted by the secondary user using the Euclidean distance between the position of the transmitting station of the user and the origin, and the radio wave attenuation constant. Is calculated as an interference probability of the primary user to the receiving station, which is a function of the transmission probability of the transmitting station of the secondary user in each of the plurality of regions.

  The determining means sets the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted, in which the calculated interference probability is equal to or less than the target value, for each of the plurality of regions. To decide on.

  The creation means creates an exclusive area where only the primary user can perform wireless communication based on the transmission probability of the transmission station of the secondary user in each of the determined areas.

(Configuration 2)
In Configuration 1, each of the plurality of regions has an annular sector shape formed by a plurality of lines extending radially from the origin and a plurality of concentric circles centered on the origin.

(Configuration 3)
In Configuration 1 or Configuration 2, the computing means includes: transmission power of the secondary user's transmission station in each of the plurality of regions; antenna directivity in the primary user's reception station; primary user's reception station; A constant that affects the antenna height at the secondary user's transmitter station, the fading coefficient between the primary user's receiver station and the secondary user's transmitter station, and the position and origin of the secondary user's transmitter station. Using the Euclidean distance and the radio wave attenuation constant, the first interference power that the secondary user's transmitting station gives to the primary user's receiving station in each of the plurality of regions is calculated, and the moment of the first interference power is calculated. Using the generating function, the n-th order cumulant (n is a positive integer) of the first interference power is calculated as a function of the transmission probability of the transmission station of the secondary user, and based on the calculated n-th order cumulant, a plurality of All secondary users in the domain The n-th order cumulant of the second interference power, which is the interference power from the transmitting station to the primary user's receiving station, is calculated, and the second interference is calculated based on the calculated n-th order cumulant of the second interference power. A probability density function of power is calculated, and an interference probability is calculated using parameters of the probability density function.

(Configuration 4)
In any one of the configurations 1 to 3, the determining unit may multiply a plurality of multiplication results obtained by multiplying an average number of transmitting stations transmitted by the secondary user in each of the plurality of regions by a transmission probability of the transmitting station of the secondary user. The result of addition for the region is used as an objective function, and the subtraction result obtained by subtracting the target value from the calculated interference probability is zero or less. By determining the transmission probability in each of the plurality of areas, the transmission probability of the secondary user's transmission station that maximizes the average number of transmission stations of the secondary user's transmission is determined.

(Configuration 5)
In Configuration 1, each of the plurality of regions is arranged with a plurality of lines extending radially from the origin, a plurality of concentric circles centered on the origin, a predetermined distance in the height direction from the origin, and a plurality of concentric circles It has a shape formed by a plurality of sets of concentric circles as one set of concentric circles.

(Configuration 6)
In the configuration 1 or the configuration 5, the calculating means includes a transmission power of a secondary user's transmission station in each of the plurality of areas, a constant related to antenna directivity in the primary user's reception station, and a primary user's reception station. Of the secondary user in each of the plurality of regions using the fading coefficient between the transmission station and the secondary user's transmission station, the Euclidean distance between the position and origin of the secondary user's transmission station, and the radio wave attenuation constant. The first interference power that the transmitting station gives to the receiving station of the primary user is calculated, and the n-th order cumulant of the first interference power (where n is a positive integer) 2 is calculated using Laplace transform of the first interference power. Calculated as a function of the transmission probability of the secondary user's transmitting station, and based on the calculated nth order cumulant, interference power from all the secondary user's transmitting stations to the primary user's receiving station in a plurality of regions The second-order key of the second interference power is Calculates the Muranto, based on the n-order cumulant of the second interference power to the operation, the probability density function of the second interference power calculated, calculates the interference probability with the parameters of the probability density function.

(Configuration 7)
In the configuration 6, the calculating means calculates the n-th order cumulant of the second interference power by calculating the sum of the second interference power from the first order cumulant to the n-th order cumulant.

(Configuration 8)
In any one of the configurations 5 to 7, the determining means sets a non-transmission probability that is a probability that the secondary user's transmitting station does not transmit to the average number of transmitting stations transmitted by the secondary user in each of the plurality of regions. The transmission result of the secondary user's transmitting station that minimizes the objective function under the constraint that the addition result obtained by multiplying the multiplication results for a plurality of areas is the objective function and the calculated interference probability is less than or equal to the target value. By determining the probability in each of the plurality of areas, the transmission probability of the secondary user's transmission station that maximizes the average number of transmission stations of the secondary user to transmit is determined.

  Further, according to the embodiment of the present invention, a program to be executed by a computer may have the following configuration.

(Configuration 9)
The program to be executed by the computer is
The computing means is a non-uniform Poisson point of the secondary user in each of a two-dimensional area or a plurality of areas constituting the three-dimensional area with the origin of the primary user's receiving station where the ratio of interference data is a constant value. Transmitting power of transmitting stations distributed according to the process, constant related to antenna directivity at receiving station of primary user, fading coefficient between receiving station of primary user and transmitting station of secondary user, secondary Using the Euclidean distance between the position of the user's transmitting station and the origin, and the radio wave attenuation constant, the primary user's receiving station is more than the threshold received from all the transmitting stations transmitted by the secondary user. A first step of calculating a large interference power as a probability of interference with a primary user's receiving station that is a function of a transmission probability of a secondary user's transmitting station in each of the plurality of regions;
The determining means sets the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted, in which the calculated interference probability is equal to or less than the target value, for each of the plurality of regions. A second step of determining in
The creation means creates an exclusive area of the primary user in which only the primary user can perform wireless communication based on the transmission probability of the transmission station of the secondary user in each of the determined areas. A program for causing a computer to execute the third step.

(Configuration 10)
In Configuration 9, each of the plurality of regions has an annular sector shape formed by a plurality of lines extending radially from the origin and a plurality of concentric circles centered on the origin.

(Configuration 11)
In Configuration 9 or Configuration 10, the computing means in the first step, the transmission power of the secondary user's transmitting station in each of the plurality of regions, the antenna directivity and the primary usage in the receiving station of the primary user Constants that affect the antenna altitude at the receiving station of the user and the transmitting station of the secondary user, fading coefficient between the receiving station of the primary user and the transmitting station of the secondary user, and the transmission of the secondary user Using the Euclidean distance between the station position and the origin and the radio wave attenuation constant, the first interference power that the secondary user's transmitting station gives to the primary user's receiving station in each of the plurality of regions is calculated, Using the moment generating function of the first interference power, the n-th order cumulant (n is a positive integer) of the first interference power is calculated as a function of the transmission probability of the transmission station of the secondary user, and the calculated n-th order Based on cumulants, The n-th order cumulant of the second interference power, which is the interference power from all the transmitting stations of the secondary user to the receiving station of the primary user in the region of, is calculated, and the n-th order of the calculated second interference power Based on the cumulant, a probability density function of the second interference power is calculated, and an interference probability is calculated using parameters of the probability density function.

(Configuration 12)
In any one of configurations 9 to 11, in the second step, the determining means sets the transmission probability of the secondary user's transmission station to the average number of transmission stations transmitted by the secondary user in each of the plurality of regions. A quadratic that maximizes the objective function under the constraint that the subtraction result obtained by subtracting the target value from the calculated interference probability is less than or equal to zero, using the addition result obtained by adding the multiplication results for a plurality of regions as the objective function. By determining the transmission probability of the user's transmission station in each of the plurality of areas, the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is determined.

(Configuration 13)
In Configuration 9, each of the plurality of regions is arranged with a plurality of lines extending radially from the origin, a plurality of concentric circles centered on the origin, and a plurality of concentric circles arranged at predetermined intervals in the height direction from the origin. It has a shape formed by a plurality of sets of concentric circles as one set of concentric circles.

(Configuration 14)
In the configuration 9 or the configuration 13, in the first step, the computing means is a constant relating to the transmission power of the secondary user's transmitting station in each of the plurality of regions, the antenna directivity in the primary user's receiving station, 1 Each of the plurality of areas is determined using a fading coefficient between the receiving station of the secondary user and the transmitting station of the secondary user, the Euclidean distance between the position and the origin of the transmitting station of the secondary user, and the radio wave attenuation constant. The first interference power given by the secondary user's transmitting station to the primary user's receiving station is calculated using the Laplace transform of the first interference power, and n (n is a positive value). (Integer) The next cumulant is calculated as a function of the transmission probability of the transmission station of the secondary user, and based on the calculated n-th order cumulant, the primary user's With interference power to the receiving station And calculating a probability density function of the second interference power based on the calculated n-order cumulant of the second interference power, and calculating a parameter of the probability density function. To calculate the interference probability.

(Configuration 15)
In the configuration 14, in the first step, the computing means computes the nth order cumulant of the second interference power by computing the sum of the second interference power from the first order cumulant to the nth order cumulant.

(Configuration 16)
In any one of Configurations 13 to 15, the determining means, in the second step, the probability that the secondary user transmitting station does not transmit the average number of transmitting stations transmitted by the secondary user in each of the plurality of regions. The secondary use that minimizes the objective function under the constraint that the calculated interference probability is less than or equal to the target value, with the addition result obtained by multiplying the multiplication results obtained by multiplying the non-transmission probabilities as the objective function. The transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is determined by obtaining the transmission probability of the transmission station of the secondary user in each of the plurality of regions.

(Configuration 17)
Furthermore, according to the embodiment of the present invention, the computer-readable recording medium on which the program is recorded is a computer-readable recording medium on which the program according to any one of Configurations 9 to 16 is recorded.

  The embodiment disclosed this time should be considered as illustrative in all points and not restrictive. The scope of the present invention is shown not by the above description of the embodiments but by the scope of claims for patent, and is intended to include meanings equivalent to the scope of claims for patent and all modifications within the scope.

  The present invention is applied to a management apparatus, a program to be executed by a computer, and a computer-readable recording medium on which the program is recorded.

  1,11 radio station, 2,3, 121 to 12s terminal, 10, 10A management device, 101 receiving means, 102, 102A calculating means, 103 storage means, 104 determining means, 105 creating means

Claims (17)

Distributed according to the non-uniform Poisson point process of the secondary user in each of a two-dimensional area or a plurality of areas constituting the three-dimensional area with the receiving station of the primary user having a constant ratio of interference data as the origin. Transmitting power of the transmitting station, constants related to antenna directivity at the receiving station of the primary user, fading coefficient between the receiving station of the primary user and the transmitting station of the secondary user, the secondary usage By using the Euclidean distance between the position of the transmitting station of the user and the origin, and the radio wave attenuation constant, the receiving station of the primary user is more than the threshold received from all the transmitting stations transmitted by the secondary user. Computing means for computing a large interference power as an interference probability to the receiving station of the primary user, which is a function of a transmission probability of the transmitting station of the secondary user in each of the plurality of regions;
The transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted is equal to or less than a target value in each of the plurality of regions. A decision means to decide;
Creating means for creating an exclusive area in which only the primary user can perform wireless communication based on the transmission probability of the transmission station of the secondary user in each of the determined areas. Management device.   2. The management device according to claim 1, wherein each of the plurality of regions has an annular sector shape formed by a plurality of lines extending radially from the origin and a plurality of concentric circles centered on the origin.   The computing means includes transmission power of a secondary user's transmitting station in each of the plurality of regions, antenna directivity at the primary user's receiving station, and the primary user's receiving station and the secondary usage. A constant that affects the antenna altitude at the transmitting station of the user, a fading coefficient between the receiving station of the primary user and the transmitting station of the secondary user, the position of the transmitting station of the secondary user and the origin Using the Euclidean distance and the radio wave attenuation constant, the first user's transmitting station in each of the plurality of regions calculates a first interference power given to the primary user's receiving station, The n-th order cumulant (n is a positive integer) of the first interference power is calculated as a function of the transmission probability of the transmission station of the secondary user using the moment generating function of the interference power of 1, and the calculated n Based on the next cumulant, The n-th order cumulant of the second interference power that is the interference power from all the transmission stations of the secondary user to the reception station of the primary user in a plurality of regions is calculated, and the calculated second interference The management according to claim 1 or 2, wherein a probability density function of the second interference power is calculated based on an n-th order cumulant of power, and the interference probability is calculated using a parameter of the probability density function. apparatus.   The determination unit adds a multiplication result obtained by multiplying an average number of transmission stations transmitted by the secondary user in each of the plurality of areas by a transmission probability of the transmission station of the secondary user for the plurality of areas. Transmission of the secondary user's transmission station that maximizes the objective function under the constraint that the addition result is an objective function and the subtraction result obtained by subtracting the target value from the calculated interference probability is zero or less The transmission probability of the transmission station of the secondary user that maximizes the average number of transmission stations of the secondary user to transmit is determined by determining a probability in each of a plurality of regions. 4. The management device according to any one of 3.   Each of the plurality of regions is arranged with a plurality of lines extending radially from the origin, a plurality of concentric circles centered on the origin, and a predetermined interval in the height direction from the origin, and the plurality of concentric circles The management device according to claim 1, wherein the management device has a shape formed by a plurality of concentric circles, each of which is a set of concentric circles.   The computing means includes a transmission power of a secondary user's transmission station in each of the plurality of regions, a constant related to antenna directivity at the primary user's reception station, the primary user's reception station and the 2 The secondary usage in each of the plurality of regions using a fading coefficient with a secondary user's transmission station, a Euclidean distance between the location of the secondary user's transmission station and the origin, and a radio wave attenuation constant. The first interference power given to the receiving station of the primary user by the first transmitter station is calculated, and n (n is a positive integer) of the first interference power using Laplace transform of the first interference power ) Calculating the next cumulant as a function of the transmission probability of the transmission station of the secondary user, and based on the calculated n-th order cumulant, from all the transmission stations of the secondary user in the plurality of regions, the primary To user's receiving station An n-th order cumulant of the second interference power which is the interference power is calculated, and a probability density function of the second interference power is calculated based on the calculated n-th order cumulant of the second interference power, and the probability density The management apparatus according to claim 1, wherein the interference probability is calculated using a parameter of a function.   The management device according to claim 6, wherein the calculation unit calculates an n-th order cumulant of the second interference power by calculating a sum of the second interference power from a first-order cumulant to an n-th order cumulant.   The determination means multiplies a multiplication result obtained by multiplying an average number of transmission stations transmitted by the secondary user in each of the plurality of areas by a non-transmission probability that is a probability that the transmission station of the secondary user does not transmit. The transmission probability of the transmission station of the secondary user that minimizes the objective function under the constraint that the addition result obtained by adding a plurality of areas is the objective function and the calculated interference probability is less than or equal to the target value. The transmission probability of the transmission station of the secondary user that maximizes the average number of the transmission stations of the secondary user to transmit is determined by determining in each of a plurality of regions. The management device according to any one of the above. The computing means is a non-uniform Poisson point of the secondary user in each of a two-dimensional area or a plurality of areas constituting the three-dimensional area with the origin of the primary user's receiving station where the ratio of interference data is a constant value. Transmission power distributed according to the process, a constant related to antenna directivity at the receiving station of the primary user, a fading coefficient between the receiving station of the primary user and the transmitting station of the secondary user, Using the Euclidean distance between the position of the transmission station of the secondary user and the origin, and the radio wave attenuation constant, the reception station of the primary user receives from all the transmission stations transmitted by the secondary user. A first step of calculating an interference power larger than a threshold value as an interference probability with respect to the receiving station of the primary user, which is a function of a transmission probability of the transmitting station of the secondary user in each of the plurality of regions. When,
The determining means determines the transmission probability of the secondary user's transmission station that maximizes the average number of secondary user's transmission stations to be transmitted when the calculated interference probability is equal to or less than a target value. A second step of determining in each of the regions;
Based on the transmission probability of the transmission station of the secondary user in each of the determined plurality of areas, the creation means can exclude the primary user that only the primary user can perform wireless communication. A program for causing a computer to execute a third step of creating an area.   10. The computer according to claim 9, wherein each of the plurality of regions has an annular sector shape formed by a plurality of lines extending radially from the origin and a plurality of concentric circles centered on the origin. Program for.   In the first step, the computing means transmits the transmission power of the secondary user's transmitting station in each of the plurality of regions, the antenna directivity of the primary user's receiving station, and the primary user's A constant that affects the antenna height at the receiving station and the secondary user's transmitting station, a fading coefficient between the primary user's receiving station and the secondary user's transmitting station, the secondary user's Using the Euclidean distance between the position of the transmitting station and the origin, and the radio wave attenuation constant, the first interference that the secondary user's transmitting station in each of the plurality of areas gives to the primary user's receiving station The power is calculated, and the n-th order cumulant (n is a positive integer) of the first interference power is used as a function of the transmission probability of the transmission station of the secondary user using the moment generating function of the first interference power. Calculated and calculated Based on the next cumulant, the n-th order cumulant of the second interference power, which is the interference power from all the transmission stations of the secondary user in the plurality of regions to the reception station of the primary user, is calculated, 10. The probability density function of the second interference power is calculated based on the n-th order cumulant of the calculated second interference power, and the interference probability is calculated using a parameter of the probability density function. Item 11. A program for causing a computer according to Item 10 to be executed.   In the second step, the determining means obtains a multiplication result obtained by multiplying an average number of transmission stations transmitted by the secondary user in each of the plurality of regions by a transmission probability of the transmission station of the secondary user. The quadratic that maximizes the objective function under a constraint condition that an addition result obtained by adding the plurality of regions is used as an objective function, and a subtraction result obtained by subtracting the target value from the calculated interference probability is zero or less. By determining the transmission probability of the user's transmission station in each of a plurality of regions, the transmission probability of the transmission station of the secondary user that maximizes the average number of transmission stations of the secondary user transmitting is determined. A program for causing a computer according to any one of claims 9 to 11 to be executed.   Each of the plurality of regions is arranged with a plurality of lines extending radially from the origin, a plurality of concentric circles centered on the origin, and a predetermined interval in the height direction from the origin, and the plurality of concentric circles A program for causing a computer to execute the program according to claim 9, having a shape formed by a plurality of sets of concentric circles.   In the first step, the computing means transmits the transmission power of a secondary user's transmitting station in each of the plurality of regions, a constant related to the antenna directivity at the receiving station of the primary user, and the primary usage. A plurality of areas using a fading coefficient between a receiver station of the user and the transmitter station of the secondary user, a Euclidean distance between the position of the transmitter station of the secondary user and the origin, and a radio wave attenuation constant The first user's transmitting station calculates the first interference power given to the primary user's receiving station by using the Laplace transform of the first interference power. An n-th order cumulant is calculated as a function of the transmission probability of the transmission station of the secondary user, and all of the secondary users in the plurality of regions are calculated based on the calculated n-order cumulant. The transmitting station The n-th order cumulant of the second interference power that is the interference power to the receiving station of the primary user is calculated, and the second interference power of the second interference power is calculated based on the calculated n-th order cumulant of the second interference power. The program for making a computer run of Claim 9 or Claim 13 which calculates a probability density function and calculates the said interference probability using the parameter of the probability density function.   The computing means computes the nth order cumulant of the second interference power by computing the sum of the second interference power from the first order cumulant to the nth order cumulant in the first step. 14. A program for causing a computer according to 14 to be executed.   In the second step, the determination means is a non-transmission probability that is a probability that the transmission station of the secondary user does not transmit the average number of transmission stations transmitted by the secondary user in each of the plurality of regions. The secondary use for minimizing the objective function under the constraint that the calculated interference probability is less than or equal to the target value, with the addition result obtained by multiplying the multiplication results obtained by multiplying the plurality of regions as the objective function Determining the transmission probability of the transmission station of the secondary user that maximizes the average number of transmission stations of the secondary user transmitting by determining the transmission probability of the transmission station of the secondary user in each of a plurality of areas; A program for causing a computer according to any one of claims 13 to 15 to be executed.   The computer-readable recording medium which recorded the program of any one of Claims 9-16.

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