CN106162672B - Underwater mobile wireless sensor network Poewr control method based on non-cooperative game - Google Patents
Underwater mobile wireless sensor network Poewr control method based on non-cooperative game Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract
The invention discloses the underwater mobile wireless sensor network Poewr control methods based on non-cooperative game, include the following steps: the destination node for clearly requiring optimization: establishing the underwater mobile wireless sensor network model towards underwater complex environment, including node motion limited model and end-to-end time delay model；According to the underwater mobile wireless sensor network model of building, a non-cooperative game model is established, utility function is established；Nash equilibrium analysis is carried out to the utility function established in step 2, show that the Nash Equilibrium of utility function whether there is, thens follow the steps 4 if it exists, then follow the steps 2 if it does not exist；Judge Nash Equilibrium with the presence or absence of uniqueness, and if it exists, to then follow the steps 5, if it does not exist, then follow the steps 2；The Nash Equilibrium obtained in step 3 is solved, obtains Nash Equilibrium point.Present invention decreases single-hop time delays end to end, reduce mean power size fluctuating range caused by water flow to a certain extent.
Description
Technical field
The present invention relates to a kind of wireless sensor network Poewr control methods, are based on non-cooperative game more particularly, to one kind
Underwater mobile wireless sensor network Poewr control method.
Background technique
Underwater mobile wireless sensor network (Underwater Mobile Wireless Sensor Network,
It UMWSN) is the wireless network formed by a large amount of multifunction micro underwater sensor node with acoustic communication link self-organizing.It is logical
Often, the different depth that underwater sensor node can be deployed in monitoring waters forms three-dimensional network, collaboratively real-time monitoring, perception
With the data of measurand in acquisition underwater environment.Different from land wireless sensor network (Terrestrial Wireless
Sensor Network, TWSN), underwater environment is special and complicated, underwater mobile wireless sensor network Poewr control method and
Often there is extremely challenging for the design of related algorithm.In general, energy constraint is one of main problem of UMWSN,
Underwater sensor node is powered by common batteries to be influenced vulnerable to battery life, is consumed energy bigger than general sensor nodes, and long-term
Under water, once node is dead, recycling or energy supplement are all relatively difficult for work.Secondly, it is also UMWSN's that time delay is big and changeable
Another main problem.The aerial spread speed of electromagnetic wave is 3 × 108M/s, the spread speed of sound wave in water are about
1500m/s, the speed of the two differ 5 orders of magnitude, and every kilometer of delay about 0.67s, being unable to satisfy the higher application of real-time needs
It asks, such as the monitoring of submarine earthquake wave, mine reconnaissance application.The above problem further constrains the underwater extensive reality of UMWSN
Border application.
Although achieving certain achievement in research TWSN power control both at home and abroad, it is difficult suitable for the underwater of complexity
Three-dimensional network has ignored underwater influence of the distinctive complex environment to network.
Summary of the invention
In order to solve the above technical problems, it is an object of the invention to a kind of, the underwater mobile wireless based on non-cooperative game is passed
Sensor network power control method guarantees for features such as underwater high energy consumption, high time delays in higher Signal to Interference plus Noise Ratio and biography
While defeated success rate, transimission power and end-to-end time delay are reduced, to reduce the fluctuation width of equilibrium mean power caused by water flow
Degree.
The purpose of the present invention is what is be achieved through the following technical solutions:
Underwater mobile wireless sensor network Poewr control method based on non-cooperative game, it is characterised in that: including such as
Lower step:
1) it clearly requires the destination node of optimization: establishing the underwater mobile wireless sensor network towards underwater complex environment
Model, including node motion limited model and end-to-end time delay model；
2) according to the underwater mobile wireless sensor network model of building, a non-cooperative game model is established, establishes effect
Use function；
3) Nash equilibrium analysis is carried out to the utility function established in step 2, show that the Nash Equilibrium of utility function is
No presence thens follow the steps 4 if it exists, thens follow the steps 2 if it does not exist；
4) judge Nash Equilibrium with the presence or absence of uniqueness, and if it exists, to then follow the steps 5, if it does not exist, then follow the steps 2；
5) Nash Equilibrium obtained in step 3 is solved, obtains Nash Equilibrium point.
Specifically, solving using binary Newton iteration method to Nash Equilibrium, Nash Equilibrium point is obtained.
Specifically, the node motion limited model expression formula are as follows:
In formula (2): x', y' and z are destination node in coordinate of the t moment in X-axis, the coordinate in Y-axis and the seat on Z axis
Mark, λ1And λ2For the water velocity factor；Z is the depth distance of destination node vertical direction；K is the exchange of unit space inner curve stream
Number, c be the velocity of displacement of curvilinear flow in the Y direction；Wherein the value of x', y' and z are calculated by following formula (1) and are obtained:
In formula (1): X (t0)、Y(t0) and Z (t0) it is node in t0Coordinate of the moment in X-axis, the coordinate in Y-axis and Z axis
On coordinate；X0、Y0And Z0The initial coordinate of node；LaFor cable-length, value La=| Z0|；vxIt is node in X-direction speed
Degree, vyIt is node in Y direction speed；S is the forced area of node；The volume of liquid is discharged by node by buoyancy by V；G is
Acceleration of gravity；
The value of B (t) is calculated by following formula (3) and is obtained in formula (2):
B (t)=A+ ε cos (ω t) (3)
In formula (3): A is the mean breadth in flow field, and ε is the amplitude in flow field, and ω is the frequency that flow field is advanced.
Specifically, the end-to-end time delay model are as follows:
In formula (9): K is the number that node data packet retransmits, and L is node data packet length size, RijFor transmission rate；
DijIt (t) is the distance between t moment node i and node j, τ is maximum delay caused by multipath transmisstion, and C (T, Z, S) is sound wave
Spread speed equation can be obtained by following formula:
T is the time in formula (10), and S is the forced area of node, and Z is the depth distance of the vertical direction of node.
Compared with prior art, the beneficial effects of the present invention are: the present invention provides a kind of node more to tally with the actual situation
Mobile restricted model can guarantee that for a long time network is effectively run.Consider underwater energy consumption it is high, when the features such as extend, construct one
Non-cooperative game model regards the node in network as participant in game, objective optimisation problems is converted to and seek maximum return letter
Number problem.Signal to Interference plus Noise Ratio and transmission success rate are introduced, utility function is advanced optimized, proves that the Nash of power and rate is equal respectively
The existence that weighs and uniqueness, the approximate optimal solution of power and rate is acquired finally by binary Newton iteration method.The present invention both protected
High Signal to Interference plus Noise Ratio and high-transmission success rate have been demonstrate,proved, and has reduced single-hop mean power between whole network interior joint, to reduce
Single-hop time delay end to end, reduces mean power size fluctuating range caused by water flow to a certain extent, is underwater mobile
Wireless sensor network provides a kind of good power control.
Detailed description of the invention
Fig. 1 is the process of the underwater mobile wireless sensor network Poewr control method the present invention is based on non-cooperative game
Figure；
Fig. 2 is a kind of node motion limited model figure provided by the present invention；
Fig. 3 is sound wave multipath transmisstion schematic diagram documented by the present invention；
Fig. 4 is performance number and rate value more new technological process of the invention.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Referring to Fig.1~Fig. 3, a kind of underwater mobile wireless sensor network function based on non-cooperative game provided by the present application
Rate control method comprising following steps:
1) it clearly requires the destination node of optimization: establishing node motion limited model and end-to-end time delay model, provide one
A suitable simulated environment.
The node motion limited model as shown in Fig. 2, the application it is assumed herein that finite motion where destination node
The flow field effect of range areas is identical, i.e., water velocity vector size is identical within the scope of this；Destination node is by impulsive force, buoyancy
And anchor chain pulling force, three constitute equilibrant force, the relationship of deviation angle α and impulsive force and water flow buoyancy be represented by α=
Arctan (F/f), wherein F is impulsive force suffered by node, and f is water flow buoyancy suffered by node, initial hour offset angle
α=0 is spent, then in t=t0The position coordinates at moment are as follows:
In formula (1): X (t0)、Y(t0) and Z (t0) it is destination node in t0Coordinate of the moment in X-axis, the coordinate in Y-axis
And the coordinate on Z axis；X0、Y0And Z0For the initial coordinate of destination node；LaFor cable-length, value La=| Z0|；vxFor target
Node is in X-direction speed, vyIt is destination node in Y direction speed；S is the forced area of destination node；V is destination node
By the volume of buoyancy liquid be discharged；G is acceleration of gravity.
In addition, the application is to obtain meeting actual water flow movement situation, here, the application combination above formula (1) and three
Water flow mobility model is tieed up, show that the node motion more optimized is limited MCM model, expression formula are as follows:
B (t)=A+ ε cos (ω t) (3)
In formula (2): x', y' and z are destination node in coordinate of the t moment in X-axis, the coordinate in Y-axis and the seat on Z axis
Mark, value can be obtained by formula (1)；λ1And λ2For the water velocity factor；Z be destination node vertical direction depth distance (with
It on the basis of the water surface, to being negative under water, is positive upwards)；K is the number of unit space inner curve stream exchange, and c is curvilinear flow in the side Y
Upward velocity of displacement；
In formula (3): A is the mean breadth in flow field, and ε is the amplitude in flow field, and ω is the frequency that flow field is advanced.
In the case that the end-to-end time delay model is as shown in figure 3, have barrier under water, it is set to road surface control
Acoustic signals between the receiver at center and the transmitter being placed in water-bed monitored node sensor cannot be by direct
Distance reach, but the receiver for being set to road surface control centre be likely to be received after water-reflected or underwater reflection by
The multipath signal that destination node is sent；Here, the application assumes the water surface and the bottom is smooth, the mobility of combining target node
Influence to multipath distance, when primitive character ray is downward, the distance passed through after sound wave reflection are as follows:
Wherein, b, s are underwater reflection number and water-reflected number (0≤b-s≤1)；H is the total depth of water, θbsTo enter
Firing angle, multipath distance are also to change with the variation of time；Zi(t)、Zj(t)、Xi(t)、Xj(t)、Yi(t) and YjIt (t) is t
Moment destination node i and destination node the j coordinate on Z axis, the coordinate in X-axis and the coordinate in Y-axis respectively.As shown in figure 3,
When original acoustic wave characteristic ray is downward, in the case where b=1, s=1, reflect altogether twice, it, can be by sound wave according to principle of reflection
From node i to node j paths traversed apart from the equivalently represented direct range for after mirror image b+s times, i.e. node i to node j
Direct range.It can similarly obtain, when primitive character ray is upward (0≤s-b≤1), the distance passed through be may be expressed as:
Therefore, it is set to road surface control
End-to-end time delay model between the receiver at center processed and the transmitter being placed in water-bed monitored node sensor can be with
It is expressed by following formula:
In formula (9): K is the number that node data packet retransmits, and L is node data packet length size, RijFor transmission rate；
DijIt (t) is the distance between t moment node i and node j, τ is maximum delay caused by multipath transmisstion (for judging link-quality
One of parameter), C (T, Z, S) is the spread speed equation of sound wave, can be obtained by following formula:
T is the time in formula (10), and S is the forced area of node, and Z is the depth distance of the vertical direction of node.
In addition, the value of τ is related with the number that sound wave reflects in formula (9), be for judge link quality parameter it
One.Data are not received after receiver is in the τ time, then the link-quality between judgement and transmitter is lower, from the above it can be seen that section
The multipath transmisstion delay inequality of point i to node j can respectively indicate are as follows:
Wherein, τbsWhen downward for primitive character ray, the multipath transmisstion delay inequality of node i to node j；τsbFor original spy
When sign ray is upward, the multipath transmisstion delay inequality of node i to node j；ZiWith and ZjFor the vertical of destination node i and destination node j
The depth distance (on the basis of the water surface) in direction,WithThe multiple paths distance passed through by node i to node j,For direct range, C (T, Z, S) is velocity of sound equation.
R (t) is obtained according to formula (5), if it exists R (t) > > Zi, R (t) > > Zj, R (t) > > h, h are the total depth of water；
Then by the condition of Tyke series expansionCan proper primitive character ray it is downward when multipath
Propagation delay is poor, shown in following expression:
Can similarly obtain primitive character ray it is upward when multipath transmisstion delay inequality, shown in following expression:
2) according to the underwater mobile wireless sensor network model of building, a non-cooperative game model is established, it will be underwater
Node in wireless sensor network regards participant in game as, and objective optimisation problems are converted to and seek maximum utility function problem,
Introduce transmission success rate and Signal to Interference plus Noise Ratio, the utility function that the application is established at this are as follows:
In formula (15), pi、Ri、p-i、R-i、pijAnd viTransimission power, the transmission rate of node i respectively, in addition to node i its
Transimission power, the transmission rate of his node, the transimission power of node i to node j and the water velocity of node i present position；It is Pricing Factor,For the revenue function of the ratio between transmission rate and transimission power, RijFor transmission speed
Rate (bit/s), f (γij) it is data transmission success；For power pay off function, n is section
Point number,The signal interference of neighbouring node is increased when node power is excessive for m-th of historical power value of node i, from
And increase punishment dynamics, while considering the influence of the water velocity of node present position, when water velocity is smaller, increase is punished
It penalizes, can be adjusted according to different pattern of water flow,For the average value of preceding W performance number, for reducing
Fluctuation in gambling process；For Signal to Interference plus Noise Ratio pay off function, γtarIt is the target value of Signal to Interference plus Noise Ratio, works as node
Signal to Interference plus Noise Ratio deviate Signal to Interference plus Noise Ratio target value it is larger when, need to be by bigger punishment, to guarantee the fairness of network；For transmission rate revenue function, RthDesirable arbitrary value.
The Signal to Interference plus Noise Ratio γijIt is to be defined as receiving to one of the important indicator of transimission power evaluation in wireless network
Signal magnitude and interfering signal power size and noise power size and ratio, i.e.,
Wherein, BnFor system bandwidth (Hz), RijFor transmission rate (bit/s), A-1(rij, f) and it is acoustic signals by transmission
Distance rijAttenuation degree, NiFor signal interference.
The transmission success rate and modulation communication mode has relationship, is transmitted using the data of 4-QAM modulation communication mode
Success rate is
b1=log2M (20)
Wherein L is data package size, γijFor Signal to Interference plus Noise Ratio,For the complimentary cumulative of standard gaussian stochastic variable
Distribution function, M indicate M ary modulation mode, and the effect of formula (20) is to seek Bit Transmission Rate according to symbol system；When L is larger
When, data transmission success can indicate are as follows:
3) Nash equilibrium analysis is carried out to the utility function established in step 2, show that the Nash Equilibrium of utility function is
No presence thens follow the steps 4 if it exists, thens follow the steps 2 if it does not exist,
4) judge Nash Equilibrium with the presence or absence of uniqueness, and if it exists, to then follow the steps 5, if it does not exist, then follow the steps 2；
The application herein provided by a kind of existence of the Nash Equilibrium to the betting model and the proof side of uniqueness
Method, specifically:
1, the existence of transimission power Nash equilibrium: the single order local derviation of transmission success rate is asked to obtain utility function first
Wherein
The second order local derviation of transimission power is asked to obtain utility function
Wherein
Reasonable Pricing Factor is setFor Rij∈[Rmin,Rmax], pij∈[pmin,pmax], | vi|∈(vmin,
vmax), existSo thatPerseverance is set up, and has UijAbout pijContinuous quasiconcave function, there are extreme points, that is, deposit
In transimission power Nash equilibrium solution.
2, the existence of transmission rate Nash equilibrium: single order local derviation is asked to obtain transmission rate
Wherein
Second order local derviation is asked to obtain transmission rate
Reasonable Pricing Factor is setFor Rij∈[Rmin,Rmax], pij∈[pmin,pmax], | vi|∈(vmin,
vmax), existSo thatPerseverance is set up, and has UijAbout RijContinuous quasiconcave function, there are extreme points, that is, deposit
In transmission rate Nash equilibrium solution.
3, transimission power Nash uniqueness of equilibrium: the second-order differential local derviation of power is asked to obtain utility function
Wherein
Reasonable Pricing Factor is setFor Rij∈[Rmin,Rmax], pij∈[pmin,pmax], | vi|∈(vmin,
vmax), whenWhen,Perseverance is set up.So betting model G={ Γ, Si,Ui() } be
Equilibria of Supermodular Games, and the power Nash Equilibrium Solution of existence anduniquess.
4, transmission rate Nash uniqueness of equilibrium: by formula (28) it is found that under same constraint condition, utility function is speed
The monotonous descending function of rate, and have:
Have and only unique R*∈(Rmin,Rmax), so thatSo R*Value be it is unique, i.e.,
Nash Equilibrium meets uniqueness.
In above four proof procedures, Pricing FactorRmin、Rmax、pmin、pmaxAnd vmin、vmaxStationary phase is same,
That is initializing constraint range is identical.
5) Nash Equilibrium obtained in step 3 is solved, obtains Nash Equilibrium point, Nash equilibrium Solve problems can be with
It regards the extreme-value problem for solving binary function as, extreme value is asked to solve equation.Binary function iterative equation is established using Newton iteration method
Group enables xij=(pij Rij)T,Then Jacobi matrix is
The then iterative formula of power and rate are as follows:
Wherein, k1For iteration wheel number.
In addition, the application also further optimizes more the power and rate Nash Equilibrium point that find out according to formula (34)
Newly, as shown in figure 4, specifically: first setting Pricing FactorThe range of transmission rate, the range of transimission power, and
The range of water velocity size obtains transmission success rate f (γ under the constraint conditionij) and transmission rate RijNash Equilibrium
Existence and uniqueness, transmission success rate value and transmission rate value are solved using binary Newton iteration method, to realize transmission
The optimization of power and transmission rate, the specific steps are that:
Step 1: initial transmission power p (0), transmission rate R (0), maximum transmission power PmaxAnd peak transfer rate
Rmax, and V=1 is enabled, iteration precision ξ1And ξ2Value 10-5；
Step 2: to all node is (i ∈ Γ), the number of iterations iter=V (V=1,2,3.......), node i calculates logical
It crosses formula (16) and calculates Signal to Interference plus Noise Ratio, simultaneously convolution (33) and formula (34) update node i in V using Signal to Interference plus Noise Ratio is calculated
Power Pi(V) and rate Ri(V), if Pi(V) > Pmax、Ri(V) > Rmax, then Pi(V)=Pmax, Ri(V)=Rmax, sequentially carry out
Step 3；
Step 3: if | | pi(V),pi(V+1)||≤ξ1With | | Ri(V),Ri(V+1)||≤ξ2, obtained power Pi(V)
With rate Ri(V) it is the Nash Equilibrium power updated and rate, terminates algorithm, obtain best power and rate space set of strategies；
Otherwise, V=V+1 is enabled, gos to step 2.
The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (3)
1. the underwater mobile wireless sensor network Poewr control method based on non-cooperative game, it is characterised in that: including as follows
Step:
1) it clearly requires the destination node of optimization: establishing the underwater mobile wireless sensor network mould towards underwater complex environment
Type, including node motion limited model and end-to-end time delay model；
2) according to the underwater mobile wireless sensor network model of building, a non-cooperative game model is established, effectiveness letter is established
Number；
3) Nash equilibrium analysis is carried out to the utility function established in step 2, show whether the Nash Equilibrium of utility function is deposited
4 are being thened follow the steps if it exists, then follow the steps 2 if it does not exist；
4) judge Nash Equilibrium with the presence or absence of uniqueness, and if it exists, to then follow the steps 5, if it does not exist, then follow the steps 2；
5) Nash Equilibrium obtained in step 3 is solved, obtains Nash Equilibrium point；
The node motion limited model expression formula are as follows:
In formula (2): x', y' and z are destination node in coordinate of the t moment in X-axis, the coordinate in Y-axis and the coordinate on Z axis, λ1
And λ2For the water velocity factor；Z is the depth distance of destination node vertical direction；K is of unit space inner curve stream exchange
Number, c are the velocity of displacement of curvilinear flow in the Y direction；Wherein the value of x', y' and z are calculated by following formula (1) and are obtained:
In formula (1): X (t0)、Y(t0) and Z (t0) it is node in t0On coordinate of the moment in X-axis, the coordinate in Y-axis and Z axis
Coordinate；X0、Y0And Z0The initial coordinate of node；LaFor cable-length, value La=| Z0|；vxIt is node in X-direction speed, vy
It is node in Y direction speed；S is the forced area of node；The volume of liquid is discharged by node by buoyancy by V；G adds for gravity
Speed；
The value of B (t) is calculated by following formula (3) and is obtained in formula (2):
B (t)=A+ ε cos (ω t) (3)
In formula (3): A is the mean breadth in flow field, and ε is the amplitude in flow field, and ω is the frequency that flow field is advanced.
2. the underwater mobile wireless sensor network Poewr control method based on non-cooperative game as described in claim 1,
It is characterized in that: Nash Equilibrium being solved using binary Newton iteration method, obtain Nash Equilibrium point.
3. the underwater mobile wireless sensor network Poewr control method based on non-cooperative game as claimed in claim 1 or 2,
It is characterized by: the end-to-end time delay model are as follows:
In formula (9): K is the number that node data packet retransmits, and L is node data packet length size, RijFor transmission rate；Dij(t)
For the distance between t moment node i and node j, τ is maximum delay caused by multipath transmisstion, and C (T, Z, S) is the propagation of sound wave
Rate equation can be obtained by following formula:
T is the time in formula (10), and S is the forced area of node, and Z is the depth distance of the vertical direction of node.
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| CN107580354B (en) * | 2017-08-31 | 2020-12-22 | 大连海事大学 | Auction game theory-based underwater data transmission communication link selection method |
| CN115866735A (en) * | 2023-03-01 | 2023-03-28 | 青岛科技大学 | Cross-layer topology control method based on super-mode game underwater sensor network |
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