CN106304165A - The method for analyzing performance of the D2D honeycomb heterogeneous network based on queuing theory - Google Patents
The method for analyzing performance of the D2D honeycomb heterogeneous network based on queuing theory Download PDFInfo
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Abstract
The present invention discloses a kind of method for analyzing performance of the D2D honeycomb heterogeneous network based on queuing theory, belongs to mobile communication technology field. for the scene of the multiplexing phone user's up channel of D2D user, consider that the transmission performance of D2D is subject to the impact of the distance of phone user and D2D receiving terminal, take limited dynamic service arrival mode into consideration, the present invention proposes the analytical method of the D2D communication performance in a kind of honeycomb heterogeneous network based on queuing theory, interference region to D2D receiving terminal is divided, the probability that is fallen into interference region by phone user carries out statistical analysis, by M/G/1 queuing model, D2D user's data mode is described, utilize the transition probability of the medium data bulk to be sent in embedded Markov Chain Analysis D2D user buffering district, and then derive and obtain average queue length by steady-state distribution, average throughput, the expression formula of average delay and packet loss. finally by system emulation, correctness that can theoretical analysis and calculation, has proved the reasonability of the analytical model of setting up.
Description
Technical field
The invention belongs to mobile communication technology field, more particularly, relate to a kind of D2D honeycomb based on queuing theory differentThe method for analyzing performance of network forming network.
Background technology
Direct communication between terminals technology (Device-to-Device, D2D) in cellular system allows mobile terminal honeybeeUnder the control of nest system, use the mandate frequency range of cellular system to carry out point to point link, more high spectrum and energy efficiency can be providedCommunication mode, in communication mode or network structure, all there is great flexibility and extensibility, obtain soonThe attention of get Liao academia and industrial quarters. D2D and phone user share frequency spectrum can improve the availability of frequency spectrum, but also inevitableInterference has been introduced in ground between D2D link and cellular link, if D2D is excessive to the interference of cellular communication link, can affect former netNetwork performance; If cellular communication is excessive to the interference of D2D link, can make D2D transfer of data cutting off rate increase, D2D communication quality withoutMethod ensures.
Research for interference analysis in D2D honeycomb heterogeneous network is long-standing, and O.Tirkkonen was at IEEE in 2009VTC is upper reduces the interference to phone user by reducing D2D user to volume transmitting power, and the problem of bringing is to reduce D2DThe probability of success communication. The close-loop power control strategy that XING H. further proposes in IEEE meeting in 2010, but needExtra signaling consumption is adjusted D2D user's power progression. The centralized money that PENG T. proposes in IEEE meeting in 2009In the allocation algorithm of source, base station assigns is not produce to phone user the up channel of interference to D2D user's resource, and result isTo sacrifice the handling capacity of D2D as cost, improve phone user's systematic function. ZULHASNINE M. is in WC&P in 2011Propose to allow D2D user can multiplexingly there is the phone user's of good channel conditions frequency spectrum resource, the resource of D2D is distributed and askedTopic is described as a mixed integer nonlinear programming problem. PENG B. proposes a kind of combined optimization in IEEE meeting in 2012The algorithm of resource and power division, compared with traditional water-filling algorithm, systematic function arrived raising, but algorithm complex isHigh-leveled and difficult to realize. In addition WANG F. proposed the calculation that a kind of combined dispatching, power and resource are distributed in IEEE WCNC in 2013Method, optimizes by Stackelberg game theory solution, and the handling capacity that result shows D2D user is with the quantity of phone user in systemIncrease and improve. Above-mentioned open source literature is using phone user as investigating object, has studied the honeybee D2D interference from different aspectNest network system capacity and communication quality problem, but, guarantee the reliability no less important of D2D link, be also consider actualOne of very important factor in heterogeneous network performance.
In document D2D user being disturbed existing discussion phone user, DUONG Q. proposed based on distance in 2013From resource allocation policy, base station is D2D user's chosen distance phone user's shared channel resources far away, effectively reduces D2DUser's cutting off rate, JANIS P. has further contemplated multi-user's difference, has proposed a kind of known resource distribution of disturbingMethod, D2D user is perceived spectral environment in the time of phone user's uplink communication, and it is honeybee that base station utilizes the information that D2D user awareness arrivesNest user and D2D Resources allocation. Under above-mentioned open material Dan community and many cell scenario, propose to consider apart from informationThe resource allocation policy of road factor, thus D2D user's handling capacity improved. But the user that these documents are considered has number all the timeAccording to the duty sending, do not consider that in practical communication system, user's business is random arrival, be not always to have data etc.To be sent.
Summary of the invention
For the method for analyzing performance of existing D2D honeycomb heterogeneous network do not take into full account in system user's business be withMachine arrives, is not always to have the problems such as data etc. are to be sent, reliability requirement, low complexity algorithm practical application, and the present invention carriesGo out a kind of method for analyzing performance of the D2D honeycomb heterogeneous network based on queuing theory, up for the multiplexing phone user of D2D userThe scene of channel, considers that the transmission performance of D2D is subject to the impact of the distance of phone user and D2D receiving terminal, has taken restraint into considerationState business arrival mode, algorithm is reliable, and complexity is low, can accurate analysis systematic function.
For addressing the above problem, the technical solution adopted in the present invention is as follows:
A method for analyzing performance for D2D honeycomb heterogeneous network based on queuing theory, comprising:
Step 1: set up system model;
Under single cell scenario, N phone user takies N orthogonal channel, remembers that its set isTotalM D2D user couple, gathers for D={1, and 2 ..., M}, phone user and D2D user obey and are uniformly distributed in community, vacationIf N > is M, a pair of D2D user is a multiplexing phone user's up channel only, the multiplexing channel of the random selection of D2D user, arbitrarilyD2D receiving terminal is only subject to the interference with the phone user of its shared channel, only considers large scale decline, and path loss model can be shownBe shown P (d)=Pd-α, wherein P represents transmitting power, and P (d) is illustrated in the received power of measuring from transmitting terminal d place, and α is path lossThe factor, when reference distance is set as the near-earth reference distance of macrocellular, does not consider tranmitting frequency, antenna height, transmission environment etc.Factor is during on the affecting of path loss, and received power P (d) is directly proportional to distance. Can obtain D2D receiving terminal SINR is:
Wherein PcPhone user's transmitting power, PdThe transmitting power of D2D transmitting terminal, N0Noise power, rdRepresentLink range between D2D receiving terminal and transmitting terminal, rc,dRepresent that phone user is to the distance of sharing with it the D2D receiving terminal on trade,α is the path loss factor, and the interfering signal power that D2D receiving terminal is subject to is expressed as Pc,d|rc,d|；
Step 2: set up queuing model;
A corresponding queue of D2D transmitting terminal, D2D transmitting terminal has all configured a data buffer zone, and capacity is Lmax，It is to be transmitted that the data that arrive D2D transmitting terminal are deposited with buffering area etc., when queue length reaches LmaxTime, the follow-up packet enteringJust be dropped, the data of transmitting terminal arrive obeys the Poisson distribution that average is λ, and transmission time slot is spaced apart Δ T, supposes when eachIn gap, SINR is constant, and within the Δ T time, transfer rate is constant, and each time slot arrives the number λ Δ of the packet of buffering areaT, the service speed of queue is exactly transmission rate, relevant with its instantaneous SINR, makes eventFor at time slot tnNewly arrived dataBag and can only be at tn+1When beginning, send, in the time interval of Δ T, eventIt is λ Δ T >'s 0 that the number of times occurring is obeyed parameterPoisson distribution:
Wherein a is tnThe packet number that time slot arrives, at time slot tn, when the bit number of packet in the buffering area of D2D littleIn the time of transmittability, the packet in buffering area can all send, and newly arrived packet is queued at the end of queue and is waited for tn+1Moment opensStart and send, otherwise, in the time that the more than one time slot of data in the buffering area of D2D can transmitted bit be counted, remaining bit after sendingThe bit number that number adds newly becomes tn+1Instantaneous team leader when time slot starts, instantaneous team leader's expression formula can be written as:
In formula,Be illustrated in time slot tnTeam leader when beginning,Represent time slot tnThe transfer rate of being determined by AMC, with KbsFor unit,Be illustrated in tnThe number-of-packet that the duration of time slot sends, the length of packet is decided to be Bbits,LittleIn maximum integer;
Step 3: the derivation probability of stability;
In M/G/1 queuing system, adopt embedded Markov chain to analyze D2D node buffering area medium waiting for transmissionPacket state, to any n >=0, uses XnRepresent the number-of-packet in queue, its state space be L ∈ 0,1 ..., Lmax}，The capacity of buffering area is Lmax, this embedded Markov chain has Lmax+ 1 state, D2D node team leader's state transition diagram is as Fig. 3Shown in, wherein pijFor state transition probability, the queue length of D2D link is from time slot tnI state transitions to tn+1J stateTransition probability can be expressed as:
Under original state, in queue, the number of packet can be 0,1,2 ... Lmax, because hypothesis transmission rate is no longerStochastic variable, but the three kinds of speed being determined by AMC that affected by SINR, from time slot tnTo time slot tn+1The Δ T durationIn, under three kinds of transmission rates, team leader's state is transferred to the state transition probability p of j from iijCan be expressed as:
Step 4: system performance analysis;
Obtain according to said process after the probability of stability matrix π of system, the average queue length of D2D link is expressed as each stateThe sum of products of team leader l and this state probability of stability:
The average throughput of D2D link is expressed as:
WhereinRepresent with γkHandling capacity while sending packet;
Average delay is packet stand-by period in queue before transmission, can be obtained by little theorem:
WhereinThe average data bag number in queue,It is the effective reach that packet enters queuing system;
DefinitionFor D2D link is at Q (tnThe number-of-packet of losing when)=l, becauseWherein b is illustrated in tnThe packet number that time slot is lost, average packet loss ratio can be write as
Wherein:
Further, described step 1 also comprises:
In single macro cells, centered by a D2D receiving terminal, be divided into three annular regions, with radius r, RDivide, suppose that maximum radius is still in the coverage of macro cells, R is the maximum jamming range of grand user to D2D user,Whole SINR value is divided into 3 continuous non-overlapping intervals, according to the corresponding transfer of data speed of SINR interval selectionRate, is designated as γk, k=1,2,3, suppose γ1＜γ2＜γ3. Suppose that the probability that macrocellular user falls into each ring territory obeys evenlyDistribute, that is:
Wherein, phone user fall within three ring territories probability be p (γk)，R0It is the coverage of macro base station.
Further, the described step 3 derivation probability of stability also comprises:
WhenTime:Show in the time that team leader is less than the minimum transmission rate of time slot Δ T, no matterUnder which kind of transmission rate, in queue, all packets can all send;
WhenAndTime:Show at this moment with minimum transmitting capacity (i.e. γ1), can not realize the transfer of state, can only be with γ2And γ3Send data, and allOriginal team leader can be emptied;
WhenAndTime:With γ1When transmission, to number-of-packet beAnd with γ2And γ3When transmission, can be by all numbers in queueAll send A=j according to bag;
In like manner can obtain:
WhenAndTime:
WhenAndTime:
WhenAndTime:
WhenAndTime: pij＝0；
WhenAndTime:
WhenAndTime:
WhenAndTime:
The steady-state distribution of supposing the system be π=(π (0), π (1) ... π (Lmax)) state transition probability matrix isAccording to the normalization of probability sum, steady probability distributes and can be tried to achieve by following matrix equation group:
Wherein π also can regard the characteristic vector that the left eigenvalue of Ρ is 1 as.
Further, also comprise step 5, described step 5 comprises:
Step 5: real system simulating, verifying, Guiding Practice;
Path loss model is P (d)=Pd-α, the signal power that wherein P (d) receives for receiving terminal, d is link transmittingEnd, to the distance of receiving terminal, adopts MATLAB to carry out simulation analysis, for average queue length, average throughput, average delay peaceAll whether packet loss is differentiated proof theory and is derived and obtain a result unanimously with model's Caro method, and is adjusted correction.
Beneficial effect:
Compare in prior art, beneficial effect of the present invention is:
(1) method for analyzing performance of the present invention's difference and D2D honeycomb heterogeneous network in the past, considers in practical communication systemUser's business is random arrival, and being not always has the special circumstances to be sent such as data, has real directive significance;
(2) the present invention is directed to special application scenarios, source practical application, scene setting is careful, reasonable, more has practice to refer toLead meaning;
(3) the present invention carrys out analyzing system performance from the angle that is easy to practice, considers that the transmission performance of D2D is used by honeycombThe impact of the distance of family and D2D receiving terminal, has reduced algorithm complex, is conducive to real-time accurate analysis systematic function;
(4) the present invention, using D2D user as investigating object, analyzes phone user and disturbs lower D2D telex network performance, trueProtecting the reliability of D2D link, is also one of factor very important in the actual heterogeneous network performance of consideration;
(5) the present invention, under the assumed condition of limit Markov chain and Poisson traffic arrival, is D2D user systemSystem has built a two-dimentional markov system model that comprises channel and quene state, uses steady probability analytical systemPerformance, reliability is high;
(6) the present invention, by system emulation, has verified the correctness of theoretical analysis and calculation, has proved the analytical model of setting upReasonability, be more easy to instruct practical application;
(7) method for analyzing performance of the present invention, algorithm design is reasonable, is easy to realize.
Brief description of the drawings
Fig. 1 is system model schematic diagram of the present invention.
Fig. 2 is system interference model schematic diagram of the present invention.
Fig. 3 is the state transitions schematic diagram of D2D queue of the present invention.
Fig. 4 is D2D average queue length schematic diagram in the different arrival rate situations of the present invention.
Fig. 5 is D2D average throughput contrast schematic diagram in the different arrival rate situations of the present invention.
Fig. 6 is D2D average delay contrast schematic diagram in the different arrival rate situations of the present invention.
Fig. 7 is D2D average packet loss ratio contrast schematic diagram in the different arrival rate situations of the present invention.
Detailed description of the invention
In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, rightThe present invention is further elaborated. Should be appreciated that specific embodiment described herein is only in order to explain the present invention, andBe not used in restriction the present invention.
Embodiment mono-
Step 1: set up system model;
The present invention is directed to special application scenarios, source practical application, scene setting is careful, reasonable, more has practical adviceMeaning. As shown in Figure 1, suppose under single cell scenario, N phone user takies N orthogonal channel, remembers that its set isTotal M D2D user couple, gathers for D={1, and 2 ..., M}, phone user and D2D user are in communityAll obey and be uniformly distributed, suppose N > M, a pair of D2D user is a multiplexing phone user's up channel only, for reduction system is openedPin, D2D user is random selects multiplexing channel, and D2D receiving terminal is only subject to and the phone user's of its shared channel interference arbitrarily.Only consider large scale decline herein, path loss model can be expressed as P (d)=Pd-α, wherein P represents transmitting power, P (d) tableBe shown in the received power of measuring from transmitting terminal d place, α is the path loss factor. The near-earth that is set as macrocellular when reference distance is with reference to distanceFrom, do not consider tranmitting frequency, antenna height, the factors such as transmission environment are during on the affecting of path loss, received power P (d) and distanceFrom being directly proportional. Can obtain D2D receiving terminal SINR is:
Wherein PcPhone user's transmitting power, PdThe transmitting power of D2D transmitting terminal, N0Noise power, rdRepresentLink range between D2D receiving terminal and transmitting terminal, rc,dRepresent that phone user is to the distance of sharing with it the D2D receiving terminal on trade,α is the path loss factor, and the interfering signal power that D2D receiving terminal is subject to is expressed as Pc,d|rc,d|. The present invention is using D2D user as investigationObject, analyzes phone user and disturbs lower D2D telex network performance, guarantees the reliability of D2D link, is also considering that reality is differentOne of very important factor in structure network performance.
Step 2: set up queuing model;
The method for analyzing performance of the present invention's difference and D2D honeycomb heterogeneous network in the past, considers to use in practical communication systemThe business at family is random arrival, and being not always has the special circumstances to be sent such as data, has real directive significance.
The present invention arrives the data of D2D transmitting terminal and send the M/G/1 queuing mould that is modeled as a single queue of single serviceType. Suppose the corresponding queue of a D2D transmitting terminal, D2D transmitting terminal has all configured a data buffer zone, and capacity is Lmax, arriveIt is to be transmitted that the data that reach D2D transmitting terminal are deposited with buffering area etc., when queue length reaches LmaxTime, the follow-up packet entering is justBe dropped. The data of transmitting terminal arrive obeys the Poisson distribution that average is λ, and transmission time slot is spaced apart Δ T, supposes at each time slotInterior SINR is constant, and within the Δ T time, transfer rate is constant, and each time slot arrives the number λ Δ T of the packet of buffering area,The service speed of queue is exactly transmission rate, relevant with its instantaneous SINR. Make eventFor at time slot tnNewly arrived packetAnd can only be at tn+1When beginning, send, in the time interval of Δ T, eventIt is the pool of λ Δ T > 0 that the number of times occurring is obeyed parameterPine distributes:
Wherein a is tnThe packet number that time slot arrives.
At time slot tn, in the time that the bit number of packet in the buffering area of D2D is less than transmittability, the packet in buffering areaCan all send, newly arrived packet is queued at the end of queue and is waited for tn+1Moment starts to send, otherwise, when number in the buffering area of D2DWhile can transmitted bit number according to more than one time slot, the bit number that after sending, remaining bit number adds newly becomes tn+1Time slotInstantaneous team leader when beginning. Instantaneous team leader's expression formula can be written as:
In formula,Be illustrated in time slot tnTeam leader when beginning,Represent time slot tnThe transfer rate of being determined by AMC, with KbsFor unit,Be illustrated in tnThe number-of-packet that the duration of time slot sends, the length of packet is decided to be B bits,BeThe maximum integer being less than.
Step 3: the derivation probability of stability;
In M/G/1 queuing system, it is medium to be passed that this article adopts embedded Markov chain to analyze D2D node buffering areaDefeated packet state, to any n >=0, uses XnRepresent the number-of-packet in queue, its state space be L ∈ 0,1 ...,
Lmax, the capacity of buffering area is Lmax, this embedded Markov chain has Lmax+ 1 state, D2D node team leader's state transition diagramAs shown in Figure 3, p whereinijFor state transition probability, Fig. 3 is the state transitions schematic diagram of D2D receiving terminal queue, the team of D2D linkRow length is from time slot tnI state transitions to tn+1The transition probability of j state can be expressed as:
The present invention carrys out analyzing system performance from the angle that is easy to practice, considers that the transmission performance of D2D is subject to phone userImpact with the distance of D2D receiving terminal, has reduced algorithm complex, is conducive to real-time accurate analysis systematic function. Original stateUnder, in queue, the number of packet can be 0,1,2 ... Lmax, because hypothesis transmission rate is no longer stochastic variable, but be subject toThree kinds of speed being determined by AMC of SINR impact, from time slot tnTo time slot tn+1The Δ T duration in, three kinds send speedUnder rate, team leader's state is transferred to the state transition probability p of j from iijCan be expressed as:
Step 4: system performance analysis;
The present invention, under the assumed condition of limit Markov chain and Poisson traffic arrival, is D2D custom systemBuild a two-dimentional markov system model that comprises channel and quene state, used steady probability analytical systemCan, reliability is high. Obtain according to said process after the probability of stability matrix π of system, the average queue length of D2D link is expressed as each shapeThe team leader l of state and the sum of products of this state probability of stability:
The average throughput of D2D link is expressed as:
WhereinRepresent with γkHandling capacity while sending packet, is divided into twoThe situation of kind: when number-of-packet in queueTime, the ratio of the number-of-packet in queue is with γkThe quantity that can send is also fewTime, the number sending in the unit interval is exactly the product of the probability of stability while having l packet in team leader l and queue; Work as queueMiddle number-of-packetTime, the number sending in the unit interval is exactly the maximum capacity of transmissionWith in queue, have lThe product of probability of stability when individual packet. In the time that queue is sky, handling capacity is 0.
Average delay is packet stand-by period in queue before transmission, can be obtained by little theorem:
WhereinThe average data bag number in queue,It is the effective reach that packet enters queuing system.
DefinitionFor D2D link is at Q (tnThe number-of-packet of losing when)=l, because
Wherein b is illustrated in tnThe packet number that time slot is lost, average packet lossRate can be write as
Wherein:
Embodiment bis-
In order to carry out analyzing system performance from the angle that is easy to practice, consider the transmission performance of D2D be subject to phone user withThe impact of the distance of D2D receiving terminal, has reduced algorithm complex, is conducive to real-time accurate analysis systematic function. The present invention is in realityExecute on the basis of example one and further improve, specifically:
As shown in Figure 2, consider, in single macro cells, centered by a D2D receiving terminal, to be divided into three annularsRegion, with radius r, R divides, and supposes that maximum radius is still in the coverage of macro cells, and R is that grand user is to D2D userMaximum jamming range,, in the time that the distance of grand user and D2D receiving terminal is greater than R, grand user can neglect D2D user's interferenceSlightly. In the time that grand user falls into the nearer ring territory of distance B 2D receiving terminal, larger to the interference of D2D link, SINR is less, selectsCorresponding message transmission rate is lower. This article employing Adaptive Modulation and Coding (AMC) technology realizes the variation of transfer rate, IWhole SINR value is divided into 3 continuous non-overlapping intervals, according to the corresponding transfer of data speed of SINR interval selectionRate, is designated as γk, k=1,2,3, suppose γ1＜γ2＜γ3. Suppose that the probability that macrocellular user falls into each ring territory obeys evenlyDistribute, that is:
Wherein, phone user fall within three ring territories probability be p (γk)，R0It is the coverage of macro base station.
Embodiment tri-
The present invention, on the basis of embodiment mono-, further improves, and this is in limit Markov chain and Poisson industryUnder the assumed condition that business arrives, for D2D custom system has built a two-dimentional markov that comprises channel and quene state beSystem model, uses steady probability analyzing system performance, and reliability is high. Specifically, for solving of stable state transition probability,Comprise the following steps:
WhenTime:
Above formula shows in the time that team leader is less than the minimum transmission rate of time slot Δ T, no matter under which kind of transmission rate, in queueAll packets can all send.
WhenAndTime:
Above formula shows at this moment with minimum transmitting capacity (i.e. γ1), can not realize the transfer of state, can only be with γ2And γ3Send data, and original team leader can be emptied.
WhenAndTime:
Above formula shows with γ1When transmission, to number-of-packet beAnd with γ2And γ3When transmission,All packets in queue all can be sent to A=j.
In like manner can obtain, whenAndTime:
WhenAndTime:
WhenAndTime:
WhenAndTime: pij＝0；
WhenAndTime:
WhenAndTime:
WhenAndTime:
Thereby can obtain the transfer matrix p of D2D data queueijAs follows:
The steady-state distribution of supposing the system be π=(π (0), π (1) ... π (Lmax)) state transition probability matrix isAccording to the normalization of probability sum, steady probability distributes and can be tried to achieve by following matrix equation group:
Wherein π also can regard the characteristic vector that the left eigenvalue of Ρ is 1 as.
Embodiment tetra-
For better Guiding Practice, on the basis of four embodiment above, further improve, increase step 5, concrete.
Step 5: real system simulating, verifying, Guiding Practice;
In order to verify the accuracy of the performance parameter of deriving based on M/G/1 queuing model, this article adopts MATLAB to enterRow simulation analysis, path loss model is P (d)=Pd-α, the signal power that wherein P (d) receives for receiving terminal, d is that link is sent outPenetrate the distance of end to receiving terminal. Simulation parameter is as shown in table 1.
Table 1 simulation parameter table
Fig. 4 is in the situation of different λ, and α is respectively 3,3.5 and theoretical value and the simulation value of the average queue length of 4 o'clock, from figureCan find out, theoretical value and simulation value curve are substantially identical, and along with the growth of λ, average queue length increases, in the time that λ reaches 10, flatAll team leader is tended to be steady, and path loss factor-alpha is larger, and curve is more precipitous, reaches capacity sooner.
Fig. 5 is the graph of a relation of average throughput and transmission rate λ and fading factor α, as can be seen from Figure 5 on average handles upThe increase of amount is taking 10 as thresholding, and in the time that λ is below thresholding, average throughput amplification is obvious, when λ is in the time that thresholding is above, averageThroughput increase speed is slow; This is due to λ below thresholding time, and D2D link is in the state that supply falls short of demand, the number of buffering areaSubstantially can be transmitted at a time slot according to bag, so handling capacity is along with the increase of λ increases sharply; When λ is during higher than thresholding, chainRoad is in drug on the market state, and handling capacity is subject to the restriction of transmittability, and growth trend also just tends to be steady, and exceedes buffer pool sizePacket all can be dropped. In addition in Fig. 5 along with the increase of path loss factor-alpha, handling capacity is less, the average behavior of system presentsThe trend reducing gradually, the SINR value that D2D receives reduces, and transmission rate reduces, and causes more data bag to be trapped in buffering area,Average throughput reduces. Theoretical value and simulation value curve are substantially identical, and simulation result has confirmed theoretical correctness.
Fig. 6 is the graph of a relation of average delay and transmission rate λ and fading factor α, with average queue length and average throughput oneSample, along with the increase of arrival rate, average delay slowly increases, after λ reaches average transmission rate, fixed according to littleReason, average delay also arrives rapidly maximum held stationary, and this is because in the time that the packet number once arriving is more, teamPacket in row can not send in a time slot, because buffer pool size is limited, time delay can not continue to increase. The path loss factorLarger, transmission rate reduces, and more data bag etc. are to be sent, and average delay is longer. Theoretical value conforms to substantially with simulation value curve,Verify the correctness of theoretical derivation.
Fig. 7 is the graph of a relation of packet loss and transmission rate λ and fading factor α, and as seen from the figure, λ is larger, and buffering area is mediumPacket to be sent is more, due to finite capacity, when packet number exceedes after transmittability, just continues the packet of arrivalCan make packet loss continue to rise, and α increases, transmission rate reduces, and waits for that transmitting time extends, and packet loss is larger. Theoretical value andSimulation value curve is substantially identical, has proved theoretical correctness.
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all in essence of the present inventionAny amendment of doing within god and principle, be equal to replacement and improvement etc., within protection scope of the present invention all should be included in.
Claims (4)
1. a method for analyzing performance for the D2D honeycomb heterogeneous network based on queuing theory, is characterized in that, comprising:
Step 1: set up system model;
Under single cell scenario, N phone user takies N orthogonal channel, remembers that its set isTotal MD2D user couple, gathers for D={1, and 2 ..., M}, phone user and D2D user obey and are uniformly distributed in community, suppose N> M, a pair of D2D user is a multiplexing phone user's up channel only, random multiplexing channel, the arbitrarily D2D of selecting of D2D userReceiving terminal is only subject to the interference with the phone user of its shared channel, only considers large scale decline, and path loss model can representFor P (d)=Pd-α, wherein P represents transmitting power, P (d) is illustrated in the received power of measuring from transmitting terminal d place, α be path loss because ofSon, when reference distance is set as the near-earth reference distance of macrocellular, does not consider tranmitting frequency, antenna height, transmission environment etc. because ofElement is during on the affecting of path loss, received power P (d) with apart from being directly proportional. Can obtain D2D receiving terminal SINR is:
Wherein PcPhone user's transmitting power, PdThe transmitting power of D2D transmitting terminal, N0Noise power, rdRepresent that D2D connectsLink range between receiving end and transmitting terminal, rc,dRepresent that phone user is to the distance of sharing with it the D2D receiving terminal on trade, αShi roadDamage the factor, the interfering signal power that D2D receiving terminal is subject to is expressed as Pc,d|rc,d|；
Step 2: set up queuing model;
A corresponding queue of D2D transmitting terminal, D2D transmitting terminal has all configured a data buffer zone, and capacity is Lmax, arriveIt is to be transmitted that the data of D2D transmitting terminal are deposited with buffering area etc., when queue length reaches LmaxTime, the follow-up packet entering just byAbandon, the data of transmitting terminal arrive obeys the Poisson distribution that average is λ, and transmission time slot is spaced apart Δ T, supposes in each time slotSINR is constant, and within the Δ T time, transfer rate is constant, and each time slot arrives the number λ Δ T of the packet of buffering area, teamThe service speed of row is exactly transmission rate, relevant with its instantaneous SINR, makes eventFor at time slot tnNewly arrived packet andCan only be at tn+1When beginning, send, in the time interval of Δ T, eventIt is the Poisson of λ Δ T > 0 that the number of times occurring is obeyed parameterDistribute:
Wherein a is tnThe packet number that time slot arrives, at time slot tn, when the bit number of packet in the buffering area of D2D is less thanWhen transmittability, the packet in buffering area can all send, and newly arrived packet is queued at the end of queue and is waited for tn+1Moment startsSend, otherwise, in the time that the more than one time slot of data in the buffering area of D2D can transmitted bit be counted, remaining bit number after sendingThe bit number adding newly becomes tn+1Instantaneous team leader when time slot starts, instantaneous team leader's expression formula can be written as:
In formula,Be illustrated in time slot tnTeam leader when beginning,Represent time slot tnThe transfer rate of being determined by AMC, taking Kbs as singlePosition,Be illustrated in tnThe number-of-packet that the duration of time slot sends, the length of packet is decided to be B bits,LittleIn maximum integer;
Step 3: the derivation probability of stability;
In M/G/1 queuing system, adopt embedded Markov chain to analyze the medium data waiting for transmission of D2D node buffering areaBag state, to any n >=0, uses XnRepresent the number-of-packet in queue, its state space be L ∈ 0,1 ..., Lmax, bufferingThe capacity in district is Lmax, this embedded Markov chain has Lmax+ 1 state, D2D node team leader's state transition diagram as shown in Figure 3,Wherein pijFor state transition probability, the queue length of D2D link is from time slot tnI state transitions to tn+1The transfer of j state generalRate can be expressed as:
Under original state, in queue, the number of packet can be 0,1,2 ... Lmax, because hypothesis transmission rate is no longer randomVariable, but the three kinds of speed being determined by AMC that affected by SINR, from time slot tnTo time slot tn+1The Δ T duration in,Under three kinds of transmission rates, team leader's state is transferred to the state transition probability p of j from iijCan be expressed as:
Step 4: system performance analysis;
Obtain according to said process after the probability of stability matrix π of system, the average queue length of D2D link is expressed as the team leader of each stateThe sum of products of l and this state probability of stability:
The average throughput of D2D link is expressed as:
WhereinRepresent with γkHandling capacity while sending packet;
Average delay is packet stand-by period in queue before transmission, can be obtained by little theorem:
WhereinThe average data bag number in queue,It is the effective reach that packet enters queuing system;
DefinitionFor D2D link is at Q (tnThe number-of-packet of losing when)=l, becauseWherein b is illustrated in tnThe packet number that time slot is lost, average packet loss ratio can be write as
Wherein:
2. the method for analyzing performance of D2D honeycomb heterogeneous network according to claim 1, is characterized in that, described step 1Also comprise:
In single macro cells, centered by a D2D receiving terminal, be divided into three annular regions, with radius r, R divides,Suppose that maximum radius is still in the coverage of macro cells, R is the maximum jamming range of grand user to D2D user, by wholeIndividual SINR value is divided into 3 continuous non-overlapping intervals, according to the corresponding message transmission rate of SINR interval selection, is designated as
γk, k=1,2,3, suppose γ1＜γ2＜γ3. Suppose macrocellular user fall into each ring territory probability obey be uniformly distributed,That is:
Wherein, phone user fall within three ring territories probability be p (γk)，R0It is the coverage of macro base station.
3. the method for analyzing performance of D2D honeycomb heterogeneous network according to claim 1, is characterized in that, described step 3The derivation probability of stability also comprises:
WhenTime:Which show in the time that team leader is less than the minimum transmission rate of time slot Δ T, no matter inPlant under transmission rate, in queue, all packets can all send;
WhenAndTime:ShowAt this moment with minimum transmitting capacity (i.e. γ1), can not realize the transfer of state, can only be with γ2And γ3Send data, and can be byOriginal team leader empties;
WhenAndTime:With γ1When transmission, to number-of-packet beAnd with γ2And γ3When transmission, can be by all numbers in queueAll send A=j according to bag;
In like manner can obtain:
WhenAndTime:
WhenAndTime:
WhenAndTime:
WhenAndTime: pij＝0；
WhenAndTime:
WhenAndTime:
WhenAndTime:
The steady-state distribution of supposing the system be π=(π (0), π (1) ... π (Lmax)) state transition probability matrix isAccording to the normalization of probability sum, steady probability distributes and can be tried to achieve by following matrix equation group:
π＝πP,
Wherein π also can regard the characteristic vector that the left eigenvalue of P is 1 as.
4. the method for analyzing performance of D2D honeycomb heterogeneous network according to claim 1, is characterized in that, also comprises stepFive, described step 5 comprises:
Step 5: real system simulating, verifying, Guiding Practice;
Path loss model is P (d)=Pd-α, the signal power that wherein P (d) receives for receiving terminal, d is that link transmitting terminal arrivesThe distance of receiving terminal, adopts MATLAB to carry out simulation analysis, for average queue length, average throughput, average delay with on average loseWhether bag rate is differentiated proof theory and is derived and obtain a result unanimously with model's Caro method, and is adjusted correction.
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