CN113193900A - Network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication - Google Patents
Network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication Download PDFInfo
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Abstract
The invention provides a network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication, which comprises the steps of firstly selecting a motion model of a mobile ad hoc network, and carrying out quantitative analysis on the motion model of an unmanned aerial vehicle to obtain a probability density function when the unmanned aerial vehicle follows a RWP model; secondly, a PPM modulation mode is adopted to obtain a coverage range under a wireless ultraviolet communication mode; introducing a network connectivity approximate method expression, and performing mathematical modeling on connectivity calculation; then, implementing division integration on the basis of the established model, and calculating to obtain the network k-connectivity probability under different parameter configurations through the established model; and finally, comparing the calculation method based on the fractional integral modeling with the existing Poisson intensity approximation method, and verifying the effectiveness of the fractional integral method. The invention realizes the approximate analysis of connectivity under a polar coordinate system, reduces the division of integral intervals and simplifies the calculation process.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle network communication, and particularly relates to a network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication.
Background
Nowadays, with the wide application of unmanned aerial vehicles, especially in the military, covert communication under the battlefield environment is very important. But whether can realize reliable and stable communication between the unmanned aerial vehicle not only depends on the selection of communication mode, and whether communication link communicates in real time also influences the inside communication of unmanned aerial vehicle constantly.
The unmanned aerial vehicle can provide large capacity, long distance transmission and cover on a large scale, can extensively be used for fields such as communication, reconnaissance, supervision. However, communication between drones, especially communication between drones in a battlefield environment, has higher requirements on communication security and communication quality, and therefore, while ensuring reliable communication, the problem of network connectivity is also increasingly emphasized. Because the real-time change of the link, the network connectivity is influenced by the movement of the nodes, when the unmanned aerial vehicles in the network follow the static distribution, the network connectivity can be conveniently and quantitatively analyzed, but when the unmanned aerial vehicles in the network are dynamically distributed, the quantitative analysis of the connectivity becomes a difficult problem, so that a new research idea is provided for the calculation of the network connectivity of the unmanned aerial vehicles by providing an approximate method of the network connectivity of the ultraviolet light cooperation unmanned aerial vehicles, and a foundation is laid for the unmanned aerial vehicle networking to more efficiently and cooperatively complete tasks.
It is noted that this section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
Disclosure of Invention
The invention aims to provide a network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication, which realizes efficient cooperative task completion of unmanned aerial vehicle networking.
In order to achieve the purpose, the invention adopts the following technical scheme:
the network connectivity subsection integral calculation method for the ultraviolet light cooperation unmanned aerial vehicle communication comprises the following steps:
s1: selecting a motion model of the mobile ad hoc network, and carrying out quantitative analysis on the motion model of the unmanned aerial vehicle to obtain a probability density function when the unmanned aerial vehicle moves along the RWP model;
s2: obtaining a coverage range in a wireless ultraviolet communication mode by adopting a PPM (pulse position modulation) mode;
s3: introducing a network connectivity approximate method expression, and performing mathematical modeling on connectivity calculation;
s4: implementing division integration on the basis of the established model, and calculating to obtain the network k-connectivity probability under different parameter configurations through the established model;
s5: and comparing the calculation method based on the fractional integral modeling with the existing Poisson intensity approximation method, thereby verifying the effectiveness of the fractional integral method.
Further, the unmanned aerial vehicle motion model in step S1 follows the following rule, taking unmanned aerial vehicle i as an example:
(a) motion point from PiMoving along a zigzag line to the next point of pause Pi+1；
(b) The pause points are uniformly and randomly distributed in a convex area;
(c) before each pause point starts to move, a speed is randomly acquired from the uniform speed distribution;
(d) when the node continues to the next section and reaches the next pause point, a short thinking time exists, wherein the thinking time is independent and distributed random variables.
Further, the probability density function in step S1 is as follows:
wherein C is a fixed constant and is equal to
Further, the step S2 is specifically as follows:
in the communication process of the unmanned aerial vehicle, an ultraviolet light non-direct-view communication mode is introduced, and a PPM (pulse position modulation) mode is adopted to obtain a coverage range under a wireless ultraviolet light communication mode; wherein, coverage is with unmanned aerial vehicle as the center, and effective communication distance is the circle territory of radius, and communication radius can be expressed as:
where η is the product of the filter efficiency and the photomultiplier quantum efficiency, RbFor information modulation rate, M is PPM modulation code length, xi is path loss factor, and alpha is path loss index.
Further, the step S3 is specifically as follows:
when being discrete probability distribution to unmanned aerial vehicle, it is discrete poisson static distribution to establish n unmanned aerial vehicle in the network, and unmanned aerial vehicle i's minimum neighbor number is counted and is done: dminAnd satisfy dminAnd the probability that k is communicated in the network is equal to the probability that the minimum neighbor number of any unmanned aerial vehicle in the network is not less than k, and the following conditions are met:
when the drones are in the form of continuous probability distribution, and convert to the form of integral, equation (3) should be converted to equation (4) to adapt to the scenario of mobile ad hoc network:
wherein r is the distance from the unmanned aerial vehicle i to the center of the distribution area, f (r) is the probability density function of unmanned aerial vehicle distribution, and A is the area of the distribution area.
Further, the step S4 is specifically as follows:
let communication radius of unmanned aerial vehicle i be r0The probability of a neighboring drone existing within the coverage of drone i is denoted p (r)i,r0) The probability of no unmanned plane in the coverage range is 1-p (r)i,r0) Then, UVAiThe number of neighbor unmanned aerial vehicles in the coverage area follows binomial distribution, and is represented as Nn,k～Bin(n,p(ri,r0) ); probability of having at least k neighbor drones in the coverage area of drone i is
Substituting the formula (5) into the formula (4) to obtain the k-connectivity probability of the unmanned aerial vehicle network; wherein, p (r)i,r0) Is shown as
Wherein, S is the intersection of the unmanned aerial vehicle network distribution area and the coverage of unmanned aerial vehicle i and is represented as:
the unmanned aerial vehicle network is divided into two conditions under polar coordinates, when ri>r0When r is calculated as in the formula (6)i≤r0When f (r) integral on S is converted into fractional integral which is the probability density function on S1And S2Sum of integrals over two parts
The invention has the beneficial effects that:
(1) according to the network connectivity subsection integral calculation method for the ultraviolet light cooperation unmanned aerial vehicle communication, connectivity approximate analysis is achieved under a polar coordinate system, division of integral intervals is reduced, and the calculation process is simplified;
(2) the invention relates to a network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication, which provides a research method when the probability density of an unmanned aerial vehicle is continuous according to a research idea when the probability density of the unmanned aerial vehicle is discrete;
(3) according to the network connectivity subsection integral calculation method for the ultraviolet light cooperation unmanned aerial vehicle communication, the convergence of the connectivity approximation method based on subsection integral is faster than that of a Poisson strength approximation method in view of simulation results;
(4) according to the network connectivity subsection integral calculation method for the ultraviolet light cooperation unmanned aerial vehicle communication, the connectivity probability can be converged to 1 more quickly under the condition of the same parameter configuration based on the connectivity approximation method of subsection integral, which means that the resource configuration is saved more in the actual situation.
Drawings
Fig. 1 is a diagram of the inventive drone following the RWP model movement;
FIG. 2(a) is the fractional integral modeling (r) of the present inventioni>r0) A schematic diagram;
FIG. 2(b) is the fractional integral modeling (r) of the present inventioni≤r0) A schematic diagram;
FIG. 3(a) is a graph illustrating the variation of the network 2-connectivity probability with transmit power in accordance with the present invention;
FIG. 3(b) is a schematic diagram of the variation of the network 2-connectivity probability with information rate according to the present invention;
fig. 4 is a flow chart of the present invention.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features or characteristics may be combined in any suitable manner in one or more embodiments.
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Aiming at the high-mobility unmanned aerial vehicle network and considering the problem of safety of communication between unmanned aerial vehicles in strong electromagnetic interference environment, the importance of network connectivity to the cooperative task execution of the unmanned aerial vehicles is clarified. The unmanned aerial vehicle follows the RWP model motion rule in the designated convex area, and for convenience of analysis, the designated motion area is a circular area to obtain a probability density function of the unmanned aerial vehicle under polar coordinates; introducing a wireless ultraviolet PPM modulation mode, and calculating an ultraviolet communication range under the modulation mode; and carrying out research and derivation by taking a certain unmanned aerial vehicle as a center and a communication range as a radius, modeling connectivity calculation in a fractional integration mode, and finally comparing the result obtained by the method with the result obtained by a Poisson strength approximation method.
The method adopts the technical scheme that firstly, a motion model of the mobile ad hoc network is selected, a RWP (random waypoint) model is taken as an example, the motion model of the unmanned aerial vehicle is subjected to quantitative analysis, and a probability density function when the unmanned aerial vehicle moves along the RWP model is obtained; secondly, a PPM (pulse Position modulation) modulation mode is adopted to obtain a coverage range under a wireless ultraviolet communication mode; introducing a network connectivity approximate method expression, and performing mathematical modeling on connectivity calculation; then, implementing division integration on the basis of the established model, and calculating to obtain the network k-connectivity probability under different parameter configurations through the established model; and finally, comparing the calculation method based on fractional integral modeling with the existing Poisson intensity approximation method, and verifying the effectiveness of the proposed fractional integral method.
The method comprises the following specific implementation steps:
step 1: distribution of unmanned aerial vehicles under RWP model
First, assume that the drone follows the RWP model in a specified circular field, as shown in fig. 1. The RWP mobility model can be briefly summarized as a mobility procedure and a suspension procedure. Take UAV i as an example, UAViThe following rules were followed:
(a) motion point from PiMoving along a zigzag line to the next point of pause Pi+1；
(b) The pause points are uniformly randomly distributed in a convex area, such as a unit circle;
(c) before each pause point starts to move, a speed is randomly acquired from the uniform speed distribution;
(d) when the node continues to the next section and reaches the next pause point, a short thinking time exists, wherein the thinking time is independent and distributed random variables.
The probability density function of the RWP model in polar coordinates is expressed as:
wherein C is a fixed constant and is equal to
Step 2: communication range of unmanned aerial vehicle under PPM modulation
In the unmanned aerial vehicle communication process, in order to obtain omnidirectional coverage, introduce ultraviolet light non-direct-view (a) type communication mode, adopt PPM modulation mode, can confirm to use unmanned aerial vehicle as the centre of a circle under the circumstances that transmitted power and each parameter of system confirm, communication distance is the coverage circle region of radius, and communication radius can express as:
where η is the product of the filter efficiency and the photomultiplier quantum efficiency, RbFor information modulation rate, M is PPM modulation code length, xi is path loss factor, and alpha is path loss index.
And step 3: connectivity calculation for continuous probability distribution
When the unmanned aerial vehicles are in discrete probability distribution, it is assumed that n unmanned aerial vehicles in the network are in discrete poisson static distribution, and the minimum neighbor number of a certain unmanned aerial vehicle i is recorded as: dminAnd satisfy dminAnd the probability of k connection in the network is approximately equal to the probability that the minimum neighbor number of any unmanned aerial vehicle in the network is not less than k, and the following conditions are met:
the above formula (3) is connectivity calculation for the drone with discrete probability distribution. Then when the drones are in a continuous probability distribution, it should be converted into an integral form, and equation (3) should be converted into equation (4) to adapt to the scenario of mobile ad hoc network
Wherein r is the distance between the unmanned aerial vehicle i and the center of the distribution area, f (r) is the probability density function of the unmanned aerial vehicle distribution, A is the area of the distribution area, and the core problem is converted into P under the continuous statei(dminK) or more.
And 4, step 4: modeling based on fractional integration
As shown in fig. 2, assume that communication radius of drone i is r0The probability of a neighboring drone existing within the coverage of drone i is denoted p (r)i,r0) The probability of no unmanned plane in the coverage range is 1-p (r)i,r0) Then UVAiThe number of neighbor unmanned aerial vehicles in the coverage area follows binomial distribution, and is represented as Nn,k～Bin(n,p(ri,r0)). Probability of having at least k neighbor drones in the coverage area of drone i is
Substituting the formula (5) into the formula (4) can obtain the k-connectivity probability of the unmanned aerial vehicle network. Therefore, the solution problem of k-connected probability will be converted into p (r)i,r0) To solve the problem. p (r)i,r0) Is shown as
Wherein S is unmanned aerial vehicle network distribution area and unmanned aerial vehicleThe intersection of the coverage of machine i is represented as:
taking the example of not considering the boundary effect as an example for analysis, the unmanned aerial vehicle network is divided into two cases under the polar coordinate, namely ri>r0And ri￡r0In two cases, when ri>r0When r is calculated as in the formula (6)i￡r0When the formula (6) is converted into the formula (7) for calculation, the integral of f (r) on S should be converted into fractional integral which is the probability density function on S1And S2The sum of the integrals over the two parts.
And 5: comparison of different approximation methods
The connectivity approximation method based on fractional integral modeling proposed in step 4 is denoted as a2, the poisson strength approximation method is denoted as a1, and the radius under the PPM modulation mode in step 2 is used as the coverage.
By adopting different approximation methods and different numbers of drones, six different situations are set, as shown in fig. 3. Fig. 3(a) is the variation of the network 2-connected probability with the transmission power (Transmitted power), and fig. 3(b) is the variation of the network 2-connected probability with the information rate (Data rate), and it can be seen that, in the case that the transmission power and the number of the drones are the same, the a2 approximate method can achieve a higher connected probability than the a 1; when the information rate is the same as the number of the unmanned aerial vehicles, the connection probability under the A2 approximate method is greater than A1; therefore, from the comparison of the results in fig. 3, the effectiveness and correctness of the a2 approximation method can be clearly seen. Also in practical cases, when the same probability of connectivity needs to be achieved, the approximation method a2 based on fractional integration will require less transmission power and information rate, which saves resource allocation to some extent.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
Claims (6)
1. A network connectivity subsection integral calculation method for ultraviolet light cooperation unmanned aerial vehicle communication is characterized by comprising the following steps:
s1: selecting a motion model of the mobile ad hoc network, and carrying out quantitative analysis on the motion model of the unmanned aerial vehicle to obtain a probability density function when the unmanned aerial vehicle moves along the RWP model;
s2: obtaining a coverage range in a wireless ultraviolet communication mode by adopting a PPM (pulse position modulation) mode;
s3: introducing a network connectivity approximate method expression, and performing mathematical modeling on connectivity calculation;
s4: implementing division integration on the basis of the established model, and calculating to obtain the network k-connectivity probability under different parameter configurations through the established model;
s5: and comparing the calculation method based on the fractional integral modeling with the existing Poisson intensity approximation method, thereby verifying the effectiveness of the fractional integral method.
2. The method for fractional integral calculation of network connectivity for uv light cooperative unmanned aerial vehicle communication according to claim 1, wherein the unmanned aerial vehicle motion model in step S1 follows the following rules, for example unmanned aerial vehicle i:
(a) motion point from PiMoving along a zigzag line to the next point of pause Pi+1；
(b) The pause points are uniformly and randomly distributed in a convex area;
(c) before each pause point starts to move, a speed is randomly acquired from the uniform speed distribution;
(d) when the node continues to the next section and reaches the next pause point, a short thinking time exists, wherein the thinking time is independent and distributed random variables.
3. The method for calculating the integral of the network connectivity subsection of the UV-light cooperative unmanned aerial vehicle communication according to claim 1, wherein the probability density function in the step S1 is as follows:
wherein C is a fixed constant and is equal to
4. The method for calculating the integral of network connectivity subsection of communication of unmanned aerial vehicle cooperated with ultraviolet light according to claim 1, wherein the step S2 is as follows:
in the communication process of the unmanned aerial vehicle, an ultraviolet light non-direct-view communication mode is introduced, and a PPM (pulse position modulation) mode is adopted to obtain a coverage range under a wireless ultraviolet light communication mode; wherein, coverage is with unmanned aerial vehicle as the center, and effective communication distance is the circle territory of radius, and communication radius can be expressed as:
where η is the product of the filter efficiency and the photomultiplier quantum efficiency, RbFor information modulation rate, M is PPM modulation code length, xi is path loss factor, and alpha is path loss index.
5. The method for calculating the integral of network connectivity subsection of communication of unmanned aerial vehicle cooperated with ultraviolet light according to claim 1, wherein the step S3 is as follows:
when being discrete probability distribution to unmanned aerial vehicle, it is discrete poisson static distribution to establish n unmanned aerial vehicle in the network, and unmanned aerial vehicle i's minimum neighbor number is counted and is done: dminAnd satisfy dminAnd the probability that k is communicated in the network is equal to the probability that the minimum neighbor number of any unmanned aerial vehicle in the network is not less than k, and the following conditions are met:
when the drones are in the form of continuous probability distribution, and convert to the form of integral, equation (3) should be converted to equation (4) to adapt to the scenario of mobile ad hoc network:
wherein r is the distance from the unmanned aerial vehicle i to the center of the distribution area, f (r) is the probability density function of unmanned aerial vehicle distribution, and A is the area of the distribution area.
6. The method for calculating the integral of network connectivity subsection of UV-light cooperative UAV communication according to claim 4, wherein the step S4 is as follows:
let communication radius of unmanned aerial vehicle i be r0The probability of a neighboring drone existing within the coverage of drone i is denoted p (r)i,r0) The probability of no unmanned plane in the coverage range is 1-p (r)i,r0) Then, UVAiThe number of neighbor unmanned aerial vehicles in the coverage area follows binomial distribution, and is represented as Nn,k～Bin(n,p(ri,r0) ); probability of having at least k neighbor drones in the coverage area of drone i is
Substituting the formula (5) into the formula (4) to obtain the k-connectivity probability of the unmanned aerial vehicle network; wherein, p (r)i,r0) Is shown as
Wherein, S is the intersection of the unmanned aerial vehicle network distribution area and the coverage of unmanned aerial vehicle i and is represented as:
the unmanned aerial vehicle network is divided into two conditions under polar coordinates, when ri>r0When r is calculated as in the formula (6)i≤r0When f (r) integral on S is converted into fractional integral which is the probability density function on S1And S2Sum of integrals over two parts
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