CN103546910A - Method for calculating lower bound of transmission capacity of mine laneway wireless sensor network - Google Patents

Abstract

The invention discloses a method for calculating a lower bound of transmission capacity of a mine laneway wireless sensor network. Based on the stochastic theory, a two-dimensional cluster model and a lognormal channel model suitable for the mine laneway wireless sensor network are established, a Palm distribution mode in the stochastic geometry is further adopted, a signal interference model suitable for the mine laneway wireless sensor network is established, the Campbell theorem and the Markov inequation are adopted, and therefore the method for calculating the lower bound of the transmission capacity of the mine laneway wireless sensor network is obtained. By means of the method for calculating the lower bound of the transmission capacity of the mine laneway wireless sensor network, the mine laneway wireless sensor network can be optimized, the communication interruption rate of the mine laneway wireless sensor network can be lowered, the transmission capacity of the wireless sensor network is improved, and therefore safe production monitoring of a coal mine are guaranteed, and potential accidents are reduced. The calculation method can be popularized in other fields using the wireless sensor network, such as aviation, aerospace, environmental monitoring and modern agriculture.

Description

A kind of computational methods of mine laneway radio sensing network transmission capacity lower bound

Technical field

The present invention relates to a kind of computational methods of radio sensing network transmission capacity, particularly a kind of computational methods of applicable mine laneway radio sensing network transmission capacity lower bound.

Background technology

Radio sensing network, also be wireless sensor network (Wireless Sensor Network, be called for short WSN), it is the wireless network being formed in the mode of self-organizing and multi-hop by a large amount of static or mobile transducers, with perception collaboratively, collection, processing and transmission network, cover the information of perceived object in geographic area, and finally these information are sent to the owner of network.Compare with cable network, the feature that radio sensing network has self-healing property and survivability is strong, overlay area is large is applicable to being applied to the severe occasion of condition of work very much, even if there is serious accident, is also unlikely to paralyse completely.Therefore, radio sensing network is applied to monitoring of coal mine safety, can effectively improve the level monitoring of Safety of Coal Mine Production, reduces accident potential.But, because radio sensing network is a kind of self-organizing network, sensing node space random placement, be difficult to take the means such as centralized power control and access control, each is very easily subject to the interference of other sensing node signal to via node and sensing node link, add mine laneway rugged environment, the impact that signal transmission is easily declined, and, usually, be difficult to obtain radio sensing network transmission capacity analytic expression, also with regard to being difficult to, the radio sensing network of mine laneway be optimized.Above factor will likely cause communication disruption, reduce radio sensing network transmission capacity, affect monitoring of coal mine safety.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of computational methods of mine laneway radio sensing network transmission capacity lower bound, thereby can optimize the radio sensing network of mine laneway, reduce the communication interruption rate of mine laneway radio sensing network, improve radio sensing network transmission capacity, ensure monitoring of coal mine safety, reduce accident potential.

For solving the problems of the technologies described above, the technical solution used in the present invention is as follows:

A kind of computational methods of mine laneway radio sensing network transmission capacity lower bound.These computational methods are calculated according to following steps,

(1), theoretical based on random geometry, set up the two-dimentional clustering model and the lognormal channel model that are applicable to mine laneway radio sensing network:

Coal mine roadway radio sensing network adopts layering bunch shape radio sensing network topology, sensing node, via node and Sink node, consists of, and sensing node locus random placement also becomes Poisson distribution, via node and Sink node space position fixing part administration; Sensing node automatic data collection, a plurality of sensing nodes form one bunch, and via node is this bunch bunch head; In bunch, the data of sensing node collection are delivered to Sink node through corresponding via node, can intercom mutually and also can directly be connected with Sink node between via node; Sink node completes the processing of gas data;

Coal mine roadway radio sensing network channel adopts Lognormal shadowing model; Suppose that sensing node position is the homogeneous Poisson distribution that intensity is λ in the plane, at moment T, the sensing node location sets of attempting to communicate by letter with via node is { X _i∈ R ², i ∈ Z ₊, establishing all sensing node transmitting powers is all P _tx, sensing node and via node are at a distance of d, and the sensing node signal power that via node receives is:

in formula: K is the parameter of reflection sensing node and via node antenna performance, and α is the channel fading factor, d _refbe reference distance, Ψ is lognormal stochastic variable, and its probability density function is: $f_{\mathrm{\&Psi;}}\left(\mathrm{\&Psi;}\right)=\frac{10/\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp \{-\frac{{\left({10\log }_{10}\right)}^2\mathrm{\&Psi;}}{{2\mathrm{\&sigma;}}^2}\},$ Ψ ∈ R, push away: $E\left[\mathrm{\&Psi;}\right]=e^{{\left(\frac{\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{10}\right)}^2\frac{1}{2}{\mathrm{\&sigma;}}^2},$

e[Ψ in formula] be the mathematic expectaion of stochastic variable Ψ, E[Ψ ²] be stochastic variable Ψ ²mathematic expectaion;

(2), adopt the Palm distribution in random geometry theory, the signal interference model of the applicable mine laneway radio sensing network of foundation:

The interference characteristic of radio sensing network, mainly considers that sensing node distributes and transmission fading characteristic; Suppose Φ (λ)={ (X _i, Ψ _i), i ∈ Z ₊that spatial-intensity is the homogeneous punctuate Poisson process of λ, { X _ito launch sometime sensing node position, punctuate { Ψ _ibe i sensing node and be positioned at the shadow item between origin of coordinates place via node; Separate between punctuate, with relevant position X _ialso independent; If via node is directly connected with Sink node, proper communication sensing node and via node spacing are fixed value r _tx, the signal strength signal intensity that via node normally receives is: and the interference signal intensity that other sensing node receiving forms is:

in formula: || X _i|| be i sensing node and be positioned at origin of coordinates place via node spacing;

(3), adopt Campbell theorem and Markov inequality, obtain mine laneway radio sensing network transmission capacity lower bound:

Suppose that because interference makes the interruption rate between via node and proper communication sensing node be ε, ε ∈ (0,1), according to the definition of Gupta and Kumar, the transmission capacity c of radio sensing network (ε) is: c (ε)=λ (ε) (1-ε), in formula, λ (ε) is the space density of the sensing node of attempt proper communication; If cause that the threshold value of the wanted to interfering signal ratio SIR of communication disruption is β, if via node wanted to interfering signal ratio sir value is less than β communication and will interrupts, communication interruption rate is: $P(\mathrm{SIR}<\mathrm{\&beta;})=P(\frac{P_{\mathrm{rx}}^o}{P_{\mathrm{rx}}^{!}}<\mathrm{\&beta;})=P(\frac{P_{\mathrm{tx}}{{\mathrm{Kr}}_{\mathrm{tx}}}^{-\mathrm{\&alpha;}}{\mathrm{\&Psi;}}_o}{{\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}\left(\mathrm{\&lambda;}\right)}{P}_{\mathrm{tx}}K{\left|\right|X_i\left|\right|}^{-\mathrm{\&alpha;}}{\mathrm{\&Psi;}}_i}<\mathrm{\&beta;}),$

If note

Ψ ' _i=Ψ _i/ Ψ _o, Φ (λ) '={ (X _i, Ψ ' _i), i ∈ N}, R _i=|| X _i||, $P(\mathrm{SIR}<\mathrm{\&beta;})=P({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}\frac{{\mathrm{\&Psi;}}_i^{\&prime;}}{R_i^{\mathrm{\&alpha;}}}>\mathrm{\&gamma;}),$ Due to Ψ _iand Ψ _othe independent lognormal stochastic variable of same parameter σ, so new stochastic variable Ψ ' _i=Ψ _i/ Ψ _othat parameter is

lognormal stochastic variable; From c (ε)=λ (ε) (1-ε), transmission capacity is directly proportional to λ (ε); $\mathrm{\&lambda;}\left(\mathrm{\&epsiv;}\right)=\sup \{\mathrm{\&lambda;}:P(\mathrm{\&Sigma;}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\&GreaterEqual;\mathrm{\&gamma;})\&le;\mathrm{\&epsiv;}\};$ By Campbell theorem, stochastic variable

desired value be: $E\left({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\right)=E\left({\mathrm{\&Psi;}}_i^{\&prime;}\right)\mathrm{\&lambda;}\underset{R^2}{\&Integral;}{R}_i^{-\mathrm{\&alpha;}}\left(\mathrm{dx}\right),$ By polar coordinate transform,

in formula, while only having α > 2, integration exists, therefore: $E\left({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\right)=\frac{2\mathrm{\&pi;}}{\mathrm{\&alpha;}-2}E\left({\mathrm{\&Psi;}}_i^{\&prime;}\right)\mathrm{\&lambda;},$ By Markov inequality, can be obtained: $\mathrm{\&lambda;}\left(\mathrm{\&epsiv;}\right)\&GreaterEqual;\sup \{\mathrm{\&lambda;}:\frac{2\mathrm{\&pi;\&lambda;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}{(\mathrm{\&alpha;}-2)/\mathrm{\&gamma;}}\&le;\mathrm{\&epsiv;}\},$ Solving above-mentioned equation obtains: $\frac{2\mathrm{\&pi;\&lambda;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}{(\mathrm{\&alpha;}-2)/\mathrm{\&gamma;}}=\mathrm{\&epsiv;},$ The lower bound of trying to achieve λ (ε) is: $\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)},$ Consider $E\left[{\mathrm{\&Psi;}}^{\&prime;}\right]=e^{{\left(\frac{\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{10}\right)}^2{\mathrm{\&sigma;}}^2},$ : $\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;exp}\left[{(\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10/10)}^2\right]{\mathrm{\&sigma;}}^2},$ The lower bound of transmission capacity is: $\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)(1-\mathrm{\&epsiv;})\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;exp}\left[{(\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10/10)}^2\right]{\mathrm{\&sigma;}}^2}.$

The computational methods of above-mentioned mine laneway radio sensing network transmission capacity lower bound, in step (2), when || X _i|| < d _ref, think that via node can delete the impact of disturbing sensing node at=1 o'clock.

Beneficial effect of the present invention: compared with prior art, the present invention does not adopt classical Neyman-Scott clustering model, but based on random geometry (Stochastic Theory) theory, set up a kind of two-dimentional clustering model and lognormal channel model of applicable mine laneway radio sensing network, and then the Palm in employing random geometry distributes, set up the signal interference model of applicable mine laneway radio sensing network, and adopt Campbell theorem and Markov inequality, obtained a kind of computational methods of mine laneway radio sensing network transmission capacity lower bound.Use the method to be optimized mine laneway radio sensing network, can reduce mine laneway radio sensing network communication interruption rate, improve radio sensing network transmission capacity, thereby ensure monitoring of coal mine safety, reduce accident potential.These computational methods can be generalized to other field of employing wireless sensing network, comprise Aeronautics and Astronautics, environmental monitoring and modern agriculture etc.

Accompanying drawing explanation

Fig. 1 is layering of the present invention bunch shape radio sensing network topology diagram;

Fig. 2 is to be square type tunnel methane sensing node deployment schematic diagram;

Fig. 3 is the plane outspread drawing of Fig. 2;

Fig. 4 is mine laneway radio sensing network two dimension clustering model of the present invention;

Fig. 5 is r _tx=2 o'clock, the lower bound of transmission capacity was for being proportional to

be related to schematic diagram;

In figure, 1-sensing node, 2-via node, 3-Sink node, 4-bunch, 5-market demand center, 6-wall, top, 7-tunnel, 8-underworkings.

Below in conjunction with the drawings and specific embodiments, the present invention is further illustrated.

Embodiment

Embodiment 1.The computational methods of mine laneway radio sensing network transmission capacity lower bound:

(1), theoretical based on random geometry, set up the two-dimentional clustering model and the lognormal channel model that are applicable to mine laneway radio sensing network:

Two dimension clustering model: as shown in Figure 1, consider the feature that coal mine roadway is long and narrow, natural environment is severe, for improving coverage and the degree of communication of radio sensing network, adopt layering bunch shape radio sensing network topology comparatively suitable.Layering bunch shape radio sensing network is comprised of sensing node, via node and Sink node.Meanwhile, sensing node locus random placement, via node and Sink node space position fixing part administration, and sensing node space bit is set to Poisson distribution.Sensing node automatic data collection, a plurality of sensing nodes form one bunch, and via node is this bunch bunch head.In bunch, the data of sensing node collection are delivered to Sink node through corresponding via node, can intercom mutually, thereby can form multi-hop route between via node, also can directly be connected with Sink node, and Sink node completes the processing of gas data.Finally, gateway is sent to market demand center for various application by the data after Sink node processing through colliery integrated information network.Table 1 has provided the characteristic of each category node of mine wireless sensing network.

Table 1 gas radio sensing network node type

Node type	Energy requirement	Position arranges	Effect
				Sensing node	Limited	At random	Image data
Via node	Do not limit	Fixing	Deliver in relays
				Sink node	Do not limit	Fixing	Data processing

Usually, coal mine roadway has arch form, square type, semi-circular, ladder type etc.For simplicity, take square type tunnel is example.As shown in Figure 2, roadway longwall and top, tunnel are all deployed with methane sensing node, the plane outspread drawing that Fig. 3 is Fig. 2.Comparison diagram 2 and Fig. 3, can see that plane outspread drawing does not change this bunch and faces mutually the relation between sensing node, just be positioned at the not sensing node spacing of coplanar and increased, for example in Fig. 3, the distance between sensing node A and C is larger than the distance between sensing node A and C in Fig. 2.Therefore,, from received signal strength angle, the relation between the plane sensing node shown in research Fig. 3 is more meaningful.Therefore, can set up the radio sensing network of mine laneway shown in Fig. 4 two dimension clustering model.Due to via node and Sink node space position fixing part administration, and via node can directly be connected with Sink node, so mine laneway radio sensing network two dimension clustering model and the classical two-dimentional clustering model of Neyman-Scott are different.

Channel model: coal mine roadway is long and narrow, natural environment is severe, sensing node received signal strength can be subject to the impact of path loss, frequency selective fading and shadow loss.Path loss be one about the qualitative function really of distance between transmitter and receiver, frequency selective fading is because multipath signal causes.If sensing node adopts DS-SS technology, or FS-SS technology, can partly overcome frequency selective fading so.Shadow loss causes by fixed obstacle between transmitter and receiver by signal, and when colliery caves in, shadow loss is more obvious.Therefore, coal mine roadway radio sensing network channel adopts Lognormal shadowing model more suitable.

Consider such radio sensing network, sensing node position is the homogeneous Poisson distribution that intensity is λ in the plane.Suppose T constantly, the sensing node location sets of attempting to communicate by letter with via node is { X _i∈ R ², i ∈ Z ₊.For ease of analyzing, suppose that sensing node transmitting power is equally all P _tx.If sensing node and via node are at a distance of d, the sensing node signal power that via node receives is: $P_{\mathrm{rx}}{=P}_{\mathrm{tx}}K{\left(\frac{d_{\mathrm{ref}}}{d}\right)}^{\mathrm{\&alpha;}}\mathrm{\&Psi;}---\left(1\right)$

In formula (1), K is the parameter of reflection sensing node and via node antenna performance, and α is the channel fading factor (value 2～4 conventionally), d _refbe reference distance (its value is 1 conventionally), Ψ is lognormal stochastic variable, and its probability density function is:

$f_{\mathrm{\&Psi;}}\left(\mathrm{\&Psi;}\right)=\frac{10/\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp \{-\frac{{\left({10\mathrm{<figure-callout\; id="10"\; label="log"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">log</figure-callout>}}_{10}\mathrm{\&Psi;}\right)}^2}{{2\mathrm{\&sigma;}}^2}\},\mathrm{\&Psi;}\&Element;R_{+}---\left(2\right)$

Easily push away: $E\left[\mathrm{\&Psi;}\right]=e^{{\left(\frac{\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{10}\right)}^2\frac{1}{2}{\mathrm{\&sigma;}}^2},$ $E\left[{\mathrm{\&Psi;}}^2\right]=e^{{\left(\frac{\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{10}\right)}^{2}2{\mathrm{\&sigma;}}^2},$ E[Ψ in formula] be the mathematic expectaion of stochastic variable Ψ, E[Ψ ²] be stochastic variable Ψ ²mathematic expectaion.

(2), adopt the Palm distribution in random geometry theory, the signal interference model of the applicable mine laneway radio sensing network of foundation:

The interference characteristic of radio sensing network, mainly considers that sensing node distributes and transmission fading characteristic.This is because send and form on the sensing node space of interference signal and separates simultaneously, so, form disturb must consideration sensing node spatial distribution.Secondly, form the path loss rate that the transducing signal intensity of disturbing depends on signal transmission and transmission range.

Suppose Φ (λ)={ (X _i, Ψ _i), i ∈ Z ₊that spatial-intensity is the homogeneous punctuate Poisson process of λ, { X _ito launch sometime sensing node position, punctuate { Ψ _ibe i sensing node and be positioned at the shadow item between origin of coordinates place via node.Meanwhile, separate between punctuate, with relevant position X _ialso independent.Meanwhile, for convenience, establish via node and be directly connected with Sink node, between cluster knot point, do not have like this interference.Like this, if make proper communication sensing node and via node spacing, be fixed value r _tx, the signal strength signal intensity that via node normally receives is:

$P_{\mathrm{rx}}^o{P}_{\mathrm{tx}}K{\left(\frac{d_{\mathrm{ref}}}{r_{\mathrm{tx}}}\right)}^{\mathrm{\&alpha;}}{\mathrm{\&Psi;}}_o---\left(3\right)$

And the interference signal intensity that other sensing node receiving forms is:

$P_{\mathrm{rx}}^{!}{\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}\left(\mathrm{\&lambda;}\right)}{P}_{\mathrm{tx}}K{\left(\frac{d_{\mathrm{ref}}}{\left|\right|X_i\left|\right|}\right)}^{\mathrm{\&alpha;}}{\mathrm{\&Psi;}}_i---\left(4\right)$

In formula, || X _i|| be i sensing node and be positioned at origin of coordinates place via node spacing.Above-mentioned interference model need to be processed and work as || Xi|| < d _ref=1 o'clock, the interfering signal power that via node receives was greater than the problem of the transmitting power of sensing node.In fact, this problem does not have physical significance.In order to revise this point, when || X _i|| < d _ref, can think that via node can delete the impact of disturbing sensing node at=1 o'clock.

(3), adopt Campbell theorem and Markov inequality, obtain mine laneway radio sensing network transmission capacity lower bound:

Transmission capacity: suppose that because interference makes the interruption rate between via node and proper communication sensing node be ε, ε ∈ (0,1).According to the definition of Gupta and Kumar, the transmission capacity c of radio sensing network (ε) is:

c(ε)＝λ(ε)(1-ε)(5)

In formula, λ (ε) is the space density of the sensing node of attempt proper communication.In other words, be exactly under the constraint of given interruption rate ε, the maximum space density of the sensing node of access via node.If note causes that the threshold value of the wanted to interfering signal ratio SIR of communication disruption is β, if via node wanted to interfering signal ratio sir value is less than β, communication will be interrupted, and communication interruption rate is:

$P(\mathrm{SIR}<\mathrm{\&beta;})=P(\frac{P_{\mathrm{rx}}^o}{P_{\mathrm{rx}}^{!}}<\mathrm{\&beta;})=P(\frac{P_{\mathrm{tx}}{{\mathrm{Kr}}_{\mathrm{tx}}}^{-\mathrm{\&alpha;}}{\mathrm{\&Psi;}}_o}{{\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}\left(\mathrm{\&lambda;}\right)}{P}_{\mathrm{tx}}K{\left|\right|X_i\left|\right|}^{-\mathrm{\&alpha;}}{\mathrm{\&Psi;}}_i}<\mathrm{\&beta;})---\left(6\right)$

If note

Ψ ' _i=Ψ _i/ Ψ _o, Φ (λ) '={ (X _i, Ψ ' _i), i ∈ N}, R _i=|| X _i||, formula (6) becomes:

$P(\mathrm{SIR}<\mathrm{\&beta;})=P({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}\frac{{\mathrm{\&Psi;}}_i^{\&prime;}}{R_i^{\mathrm{\&alpha;}}}>\mathrm{\&gamma;})---\left(7\right)$

Meanwhile, due to Ψ _iand Ψ _othe independent lognormal stochastic variable of same parameter σ, so new stochastic variable Ψ ' _i=Ψ _i/ Ψ _othat parameter is

lognormal stochastic variable.

Capacity lower bound: from formula (5), transmission capacity is directly proportional to λ (ε).Therefore, asking the lower bound of transmission capacity is exactly the lower bound of asking λ (ε) in fact, is exactly using P (SIR < β) < ε as constraint, the lower bound problem of research λ (ε).

$\mathrm{\&lambda;}\left(\mathrm{\&epsiv;}\right)=\sup \{\mathrm{\&lambda;}:P(\mathrm{\&Sigma;}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\&GreaterEqual;\mathrm{\&gamma;})\&le;\mathrm{\&epsiv;}\}---\left(8\right)$

By Campbell theorem, stochastic variable

desired value be:

$E\left({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\right)=E\left({\mathrm{\&Psi;}}_i^{\&prime;}\right)\mathrm{\&lambda;}\underset{R^2}{\&Integral;}{R}_i^{-\mathrm{\&alpha;}}\left(\mathrm{dx}\right)---\left(9\right)$

By polar coordinate transform, formula (9) becomes:

In formula (10), while only having α > 2 (actual physical channel meets this and requires), integration exists.Therefore, have:

$E\left({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\right)=\frac{2\mathrm{\&pi;}}{\mathrm{\&alpha;}-2}E\left({\mathrm{\&Psi;}}_i^{\&prime;}\right)\mathrm{\&lambda;}---\left(11\right)$

By Markov inequality, can be obtained:

$\mathrm{\&lambda;}\left(\mathrm{\&epsiv;}\right)\&GreaterEqual;\sup \{\mathrm{\&lambda;}:\frac{2\mathrm{\&pi;\&lambda;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}{(\mathrm{\&alpha;}-2)/\mathrm{\&gamma;}}\&le;\mathrm{\&epsiv;}\}---\left(12\right)$

Solving above-mentioned equation obtains:

$\frac{2\mathrm{\&pi;\&lambda;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}{(\mathrm{\&alpha;}-2)/\mathrm{\&gamma;}}=\mathrm{\&epsiv;}---\left(13\right)$

Thereby the lower bound of trying to achieve λ (ε) is:

$\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}---\left(14\right)$

Consider $E\left[{\mathrm{\&Psi;}}^{\&prime;}\right]=e^{{\left(\frac{\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10}{10}\right)}^2{\mathrm{\&sigma;}}^2},$ :

$\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;exp}\left[{(\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10/10)}^2\right]{\mathrm{\&sigma;}}^2}---\left(15\right)$

By formula (15), the lower bound of transmission capacity is:

$\frac{(\mathrm{\&alpha;}-2)(1-\mathrm{\&epsiv;})\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;exp}\left[{(\mathrm{<figure-callout\; id="10"\; label="ln"\; filenames="HSA0000096582110000022.png"\; state="\{\{state\}\}">ln</figure-callout>}10/10)}^2\right]{\mathrm{\&sigma;}}^2}---\left(16\right)$

From formula (16), the lower bound of transmission capacity is for being proportional to

be inversely proportional to σ ².Fig. 5 shows: α is larger, and transmission capacity lower bound is also larger, illustrates that the decay of interference signal attenuation ratio proper communication transducing signal is also larger, thereby has reduced the impact on via node.In addition transmission capacity,

ratio is in σ ², channel shade is larger, and transmission capacity lower bound is less, illustrates that channel shade is larger than interference signal on the impact of proper communication transducing signal.

Embodiments of the present invention are not limited to above-described embodiment, within the various variations of making under the prerequisite that does not depart from aim of the present invention all belong to protection scope of the present invention.

Claims (2)

1. computational methods for mine laneway radio sensing network transmission capacity lower bound, is characterized in that: according to following steps, calculate,

(1), theoretical based on random geometry, set up the two-dimentional clustering model and the lognormal channel model that are applicable to mine laneway radio sensing network:

Coal mine roadway radio sensing network adopts layering bunch shape radio sensing network topology, sensing node, via node and Sink node, consists of, and sensing node locus random placement also becomes Poisson distribution, via node and Sink node space position fixing part administration; Sensing node automatic data collection, a plurality of sensing nodes form one bunch, and via node is this bunch bunch head; In bunch, the data of sensing node collection are delivered to Sink node through corresponding via node, can intercom mutually and also can directly be connected with Sink node between via node; Sink node completes the processing of gas data;

Coal mine roadway radio sensing network channel adopts Lognormal shadowing model; Suppose that sensing node position is the homogeneous Poisson distribution that intensity is λ in the plane, at moment T, the sensing node location sets of attempting to communicate by letter with via node is { X _i∈ R ², i ∈ Z ₊, establishing all sensing node transmitting powers is all P _tx, sensing node and via node are at a distance of d, and the sensing node signal power that via node receives is:

in formula: K is the parameter of reflection sensing node and via node antenna performance, and α is the channel fading factor, d _refbe reference distance, Ψ is lognormal stochastic variable, and its probability density function is: $f_{\mathrm{\&Psi;}}\left(\mathrm{\&Psi;}\right)=\frac{10/\ln 10}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp \{-\frac{{\left({10\log }_{10}\right)}^2\mathrm{\&Psi;}}{{2\mathrm{\&sigma;}}^2}\},$ Ψ ∈ R ₊, push away: $E\left[\mathrm{\&Psi;}\right]=e^{{\left(\frac{\ln 10}{10}\right)}^2\frac{1}{2}{\mathrm{\&sigma;}}^2},$

e[Ψ in formula] be the mathematic expectaion of stochastic variable Ψ, E[Ψ ²] be stochastic variable Ψ ²mathematic expectaion;

(2), adopt the Palm distribution in random geometry theory, the signal interference model of the applicable mine laneway radio sensing network of foundation:

The interference characteristic of radio sensing network, mainly considers that sensing node distributes and transmission fading characteristic; Suppose Φ (λ)={ (X _i, Ψ _i), i ∈ Z ₊that spatial-intensity is the homogeneous punctuate Poisson process of λ, { X _ito launch sometime sensing node position, punctuate { Ψ _ibe i sensing node and be positioned at the shadow item between origin of coordinates place via node; Separate between punctuate, with relevant position X _ialso independent; If via node is directly connected with Sink node, proper communication sensing node and via node spacing are fixed value r _tx, the signal strength signal intensity that via node normally receives

origin of coordinates place via node spacing;

(3), adopt Campbell theorem and Markov inequality, obtain mine laneway radio sensing network transmission capacity lower bound:

Suppose that because interference makes the interruption rate between via node and proper communication sensing node be ε, ε ∈ (0,1), according to the definition of Gupta and Kumar, the transmission capacity c of radio sensing network (ε) is: c (ε)=λ (ε) (1-ε), in formula, λ (ε) is the space density of the sensing node of attempt proper communication; If cause that the threshold value of the wanted to interfering signal ratio SIR of communication disruption is β, if via node wanted to interfering signal ratio sir value is less than β communication and will interrupts, communication interruption rate is:

due to Ψ _iand Ψ _othe independent lognormal stochastic variable of same parameter σ, so new stochastic variable Ψ ' _i=Ψ _i/ Ψ _othat parameter is lognormal stochastic variable;

From c (ε)=λ (ε) (1-ε), transmission capacity is directly proportional to λ (ε); $\mathrm{\&lambda;}\left(\mathrm{\&epsiv;}\right)=\sup \{\mathrm{\&lambda;}:P(\mathrm{\&Sigma;}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\&GreaterEqual;\mathrm{\&gamma;})\&le;\mathrm{\&epsiv;}\};$ By Campbell theorem, stochastic variable

desired value be: $E\left({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\right)=E\left({\mathrm{\&Psi;}}_i^{\&prime;}\right)\mathrm{\&lambda;}\underset{R^2}{\&Integral;}{R}_i^{-\mathrm{\&alpha;}}\left(\mathrm{dx}\right),$ By polar coordinate transform,

in formula, while only having α > 2, integration exists, therefore: $E\left({\mathrm{\&Sigma;}}_{i\&Element;\mathrm{\&Phi;}{\left(\mathrm{\&lambda;}\right)}^{\&prime;}}{\mathrm{\&Psi;}}_i^{\&prime;}{R}_i^{-\mathrm{\&alpha;}}\right)=\frac{2\mathrm{\&pi;}}{\mathrm{\&alpha;}-2}E\left({\mathrm{\&Psi;}}_i^{\&prime;}\right)\mathrm{\&lambda;},$ By Markov inequality, can be obtained: $\mathrm{\&lambda;}\left(\mathrm{\&epsiv;}\right)\&GreaterEqual;\sup \{\mathrm{\&lambda;}:\frac{2\mathrm{\&pi;\&lambda;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}{(\mathrm{\&alpha;}-2)/\mathrm{\&gamma;}}\&le;\mathrm{\&epsiv;}\},$ Solving above-mentioned equation obtains: $\frac{2\mathrm{\&pi;\&lambda;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)}{(\mathrm{\&alpha;}-2)/\mathrm{\&gamma;}}=\mathrm{\&epsiv;},$ The lower bound of trying to achieve λ (ε) is: $\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;E}\left({\mathrm{\&Psi;}}^{\&prime;}\right)},$ Consider $E\left[{\mathrm{\&Psi;}}^{\&prime;}\right]=e^{{\left(\frac{\ln 10}{10}\right)}^2{\mathrm{\&sigma;}}^2},$ : $\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;exp}\left[{(\ln 10/10)}^2\right]{\mathrm{\&sigma;}}^2},$ The lower bound of transmission capacity is: $\mathrm{\&lambda;}=\frac{(\mathrm{\&alpha;}-2)(1-\mathrm{\&epsiv;})\mathrm{\&epsiv;}}{2\mathrm{\&pi;\&lambda;\&gamma;exp}\left[{(\ln 10/10)}^2\right]{\mathrm{\&sigma;}}^2}.$

2. the computational methods of mine laneway radio sensing network transmission capacity lower bound according to claim 1, is characterized in that: in step (2), when || X _i|| < d _rer, think that via node can delete the impact of disturbing sensing node at=1 o'clock.

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