On Reducing Blocking Probability in Cooperative Ad-hoc Networks

Transcription

1 On educing Blocking Pobability in Coopeative Ad-hoc Netwoks Ayda Basyouni, Walaa Hamouda ept of Electical and Compute Engineeing Concodia Univesity, Monteal, Canada {a Am Youssef Concodia Institute fo Infomation Systems Engineeing Concodia Univesity, Monteal, Canada Abstact In this pape, we popose a new channel access potocol fo tansmission ove coopeative ad-hoc netwoks The poposed potocol, which aims at minimiing the numbe of blocked nodes and consequently impoving the system thoughput, employs diectional antennas at both souce and elay stations The netwok pefomance unde the poposed settings is modelled using continues Makov chains Steady state tansmission blocking pobability and aveage netwok thoughput ae obtained by analying the Makov model Both analytical and simulation esults show the impovement in pefomance compaed to caie sense multiple access with collision avoidance potocol that employs omnidiectional antennas I INTOUCTION Mobile ad-hoc netwoks ae distibuted and infastuctueless netwoks whee mobile stations can communicate with each othe without the help of any centalied contol o access point which makes them obust to failues, easie to deploy, and moe flexible to econfigue In mobile ad-hoc netwoks, channel fading is consideed to be a seiously damaging phenomenon that can degade the oveall netwok pefomance Thoughout the liteatue, divesity techniques have been poposed to mitigate the effect of channel fading [1] Nowadays, multiple-input multiple-output (MIMO) technology has been intoduced as a means fo impoving the eliability of the eceived signal and suppoting high data ate applications []- [4] The notion of divesity is futhe expanded to include coopeative netwoks, whee the concept of use coopeation divesity is applied [5] In coopeative netwoks, a node at any given time can act as a sende, destination o elay depending on the netwok taffic and topology Neighboing stations to the tansmitte and/o eceive can act as elay nodes to tansfe the souce data to the desied destination node though an independent elay channel, ie, independent fom the soucedestination channel [6] The function of the elay node can be as simple as to amplify and fowad the eceived souce data o to decode and egeneate an estimate of this data In ad-hoc netwoks, caie sense multiple access with collision avoidance () is a commonly used channel access technique When omnidiectional antennas ae used with CSMA/C, each of the sende, eceive and elay block neighboing stations, within its tansmission ange, fom possible tansmissions This citeion esults in one of the main poblems associated with coopeative netwoks, namely inceased tansmission blocking pobability In [7] an analytical model fo evaluating the tansmission blocking pobability fo ad-hoc netwoks as a function of total numbe of nodes was developed In [8] and [9] this wok was extended to coopeative ad-hoc netwoks The divesity gain achieved in coopeative ad hoc netwoks is attained at the exta cost of wasting some wieless esouces (ie, available bandwidth) On the othe hand, the use of diectional antennas has shown to offe an effective way fo efficient bandwidth utiliation To enhance the pefomance of coopeative netwoks, we popose a new channel access potocol fo tansmission ove coopeative ad-hoc netwoks The poposed potocol, which aims at minimiing the numbe of blocked nodes employs diectional antennas at both souce and elay stations The netwok pefomance unde the poposed settings is modelled using continues Makov chains Steady state tansmission blocking pobability and aveage netwok thoughput ae obtained by analying the above Makov model Ou esults show the impovement in pefomance compaed to potocol that employs omnidiectional antennas The est of the pape is oganied as follows In the following section we descibe the poposed potocol and detemine the optimum value fo the beamwidth of the diectional antennas of the souce and elay nodes In section III, the expected value of the aveage blocked aea associated with a given numbe of tansmissions is detemined A Makov chain model fo the netwok pefomance unde the poposed setting is developed in section IV The simulation esults the validate the poposed model ae pesented in section V II POPOSE POTOCOL In coopeative systems, each time fame is divided into two slots The souce tansmits the packet to both the destination and the chosen elay in the fist slot In the second slot, the elay amplifies and fowads the eceived packet to destination When using, in ode to avoid intefeence fom othe ongoing tansmissions, the neighboing nodes of any tansmitte, elay o destination, must emain silent, ie, they ae blocked, duing the duation of the tansmission In othe wods, as shown in Fig 1, each of the souce, elay and destination blocks a full cicle with adius d max, whee d max denotes the maximum tansmission ange, which we assume to be the same fo all nodes /9/$5 9 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE "GLOBECOM" 9 poceedings

2 dmax θ S ds d max d S d S d S d S d Fig Blocked aea fo one tansmission (Poposed potocol) θ Fig 1 Blocked aea fo one tansmission in potocol A Futhe, we assume that all nodes ae also equipped with diectional antennas To evade collisions between ongoing tansmissions and newly initiated ones, a naow band channel is dedicated fo channel esevation potocol and the emaining spectum is dedicated fo data tansmission The channel esevation potocol woks as follows: The elay is chosen so that it lays within the aea coveed by the souce diectional antenna A equest to send (TS) is boadcasted by both the souce and the elay using thei omnidiectional antennas to infom all nodes, within thei tansmission ange, with thei diection of tansmission The nodes laying within the diectional beam of the souce o elay will be blocked While othe nodes within thei tansmission ange could act as a elay o souce with thei diectional antennas facing othe diections, but ae blocked fom being destinations A clea to send to send (CTS) is boadcasted by the destination using its omnidiectional antenna Consequently, the destination node blocks a full cicle with a adius of d max Fig shows the aeas blocked by both the souce and elay tansmissions whee the destination uses an omnidiectional antenna (ie, it always blocks a full cicle with adius d max ) Assume that the fixed beamwidth of the deployed diectional antenna is θ In what follows, we detemine the optimum choice fo θ that minimies the blocking aea Conside two intesected cicles, each with adius = d max, and centes C and B espectively, whee B epesents the destination, and C epesents eithe the souce o the elay When the souce (o elay) is located vey close to the destination, ie, CB, any choice fo θ = ACF 18 o would satisfy the above constaint (ie, total blocking aea is a cicle with adius d max aound the destination) In the exteme case, depicted in Fig, the souce (o elay) is located at distance d max fom the destination, ie, at the peimete of the destination s blocked cicle In this case, CB = d max Satisfying the above constaint implies that we need to have ACB =6 o, theefoe θ = ACF = 1 o C c a F Fig estiction on beamwidth (CB = ) Fig 4 epesents the case whee the souce (o elay) ae at a distance <CB<d max away fom the destination In this case, keeping θ = ACF 1 o would also satisfy the above constaints Using the above agument, it is clea that esticting the maximum beamwidth to less than o equal to 1 o optimies the blocking aea by ensuing that it is educed to one cicle with adius d max aound the destination On the othe hand, maximiing the pobability of finding a elay within the tansmission beamwidth of the souce equies that θ is maximied Thus, thoughout the est of this wok, we set θ = 1 o III AVEAGE BLOCKE AEA Let A c = πd max denote the aea of the cicle blocked due to any ongoing single tansmission It is clea that, at any point of time, nodes can be blocked due to moe than one tansmission, ie, cicles coesponding to aeas blocked by diffeent tansmissions may ovelap Assuming a elatively dense netwok, then estimating the aveage numbe of nodes involved (ie, eithe being a souce, destination, elay o blocked) in a specific numbe of tansmissions is equivalent to detemining the aveage aea blocked due to these tansmissions Let A I (l) = A 1 A denote the aea of intesection between two cicles, A 1 and A, with adius d max and centes b B /9/$5 9 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE "GLOBECOM" 9 poceedings

3 A 1 a 9 8 Total Aea=1 km M=18 c C F b B Total aea occupied A(x) Fig 4 estiction on beamwidth (CB < ) 1 Analtical Model Simulation Numbe of Tansmissions (x) sepaated by l d max Then we have A I (l) =d max cos 1 l ( ) 1 4d d max l max l (1) The pobability density function of the distance l between any two unifomly distibuted nodes within a tansmission aea of is given by [1] l ( l 4l + π), l l l p(l) = (4 1 ( l +) +(sin 1 ( l ) cos 1 ( l ))), l, Othewise To allow two tansmissions within two intesected cicles, we must have l d max, othewise the two destinations would block each othe Hence, the expected value of the aea of intesection between any two tansmissions is given by A I = d max p(l)ai (l)dl dmax 1 dmax p(l)dl = πd4 max ( d max ( d4 max ) 11d max 8d max +π d max ) Using the inclusion exclusion pinciple [11], the total aea occupied by x tansmissions is given by A(x) = x i=1 A i (A i Aj )+ i,j:1 i<j x (A i Aj Ak ) +( 1) x (A 1 A x ) i,j,k:1 i<j<k x (4) eiving the expected value fo the highe ode tems in the above equation seems an intactable poblem Howeve, as confimed by ou simulations, at modeate node density, the expected value fo A(x) can be well appoximated by consideing only the fist two tems of the above equation, ie, we have ( ) x A(x) xa c A I (5) () () Fig 5 Expected value of A(x) Fig 5 confims the quality of the above appoximation The simulations wee conducted fo M = 18 nodes and =1 km Let N(x) denote the numbe of nodes (blocked, souce, elay and destination nodes) that ae involved in x tansmissions Thus N(x) = A(x) M (6) whee M is the total numbe of nodes, is the total aea Theefoe, the aveage numbe of blocked nodes associated with x tansmissions is given by B(x) =N(x) x, (7) whee the tem x denotes the numbe of souce, elay and destination nodes Let Ω denote the maximum numbe of tansmission that can be conducted simultaneously in aea of km Then A(Ω) = Thus Ω can be appoximately estimated using (5) by setting ( ) Ω A c Ω A I =, (8) and solving fo Ω as follows Ω= (Ac+ A I ) (A c+ A I ) A I A I (9) IV MOELLING THE NUMBE OF TANSMISSIONS Thoughout ou wok, we assume that all nodes ae distibuted unifomly ove the coveed aea We also assume that the taffic is distibuted unifomly ove all nodes Packets inteaival and pocessing times ae exponentially distibuted with aival and sevice ates of λ and μ, espectively Each node is assumed to seve only one packet at a time, ie, if the node is blocked o busy, the incoming data packets ae dopped Thus ou system esembles the M/M/C/C queueing system whee customes have iid exponentially distibuted inteaival times with mean 1/λ, and iid exponentially distibuted /9/$5 9 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE "GLOBECOM" 9 poceedings

4 sevice times with mean 1/μ Assuming that the inte-aival and sevice times ae independent, then the above system can be modelled as continuous-time Makov chain The following notation will be used thoughout the est of this section: - x denotes the numbe of ongoing tansmissions at time t - λ x denotes the tansition ate fom state x to state x +1 - μ x denotes the sevice ate fom state x to state x 1 - p S (x) denotes the pobability that a souce is not blocked o used when thee is an active x tansmission - p denotes the pobability that thee is a destination available within the tansmission ange of the destination - p denotes the pobability that thee is a elay available within the tansmission ange of the destination - p denotes the pobability that both the destination and elay ae within the beamwidth of the souce to suppot this tansmission Thus λ x is given by λ x = λ (M N(x)) p S (x) p p p, (1) whee p S (x) = M N(x), (11) M p = 1, (1) p =, (1) whee denotes the aveage numbe of nodes located in the tansmission ange of the destination and is given by = Ac M (see (6)) Fom section II, θ = 1 o was shown to be optimum Thus the beamwidth of the souce coves 1 of the cicle aound the destination Theefoe, p = ( i ) 1 i i (14) The sevice ate μ x is based on the sevice ate pe existing tansmission μ and the numbe of cuent tansmissions x, hence μ x = xμ (15) The tansmission blocking pobability is defined as the pobability that a tansmission is blocked given that a packet has aived, theefoe P B (x) =1 p S (x)p p p (16) In what follows, we pesent the steady state analysis fo ou system As mentioned above, ou system esembles the M/M/C/C queuing system fo which the steady state pobability of any state x can be obtained fom the balance equations: λ π() = μπ(1) λ 1 π(1) = μπ() λ x 1 π(x 1) = xμπ(x) By solving the above system of equations we obtain x 1 (17) i= π(x) = a i π() (18) x! whee a i = λi μ and λ i is given by Eq (1) π() can be obtained by solving the nomaliation equation Ω π(j) =1 π() = j= Substituting into (18), we get π(x) = ( Ω j= x 1 i= ai x! j Ω i= ai j= j! 1 j i= ai j! ) (19) The aveage numbe of ongoing tansmissions is given by N T = π(x)x () x Let denote the data ate pe time fame One should ealie that fo each packet tansmission it takes time fames to delive the packet to destination Hence the effective data ate is given by / Theefo the total aveage thoughput of the netwok is given by TH = N T (1) The steady state blocking pobability is given by whee P B (x) is given by (16) P B = π(x)p B (x) () x V SIMULATION ESULTS In what follows we conside a total aea of 1km, tansmission ange, d max = 1km, λ=1-9, μ=1, total numbe of nodes, M=15-95, fame time of 1 sec, and data ate pe tansmission of 1Mbps Fo the pupose of compaison, we also simulated the coopeative netwok potocol in [9] which employs only omnidiectional antennas Fig 6 and Fig 7 show how ou potocol impoves the tansmission blocking pobability and thoughput elative to the potocol in [9] fo diffeent utiliation factos, ρ = λ μ The vaiation of the aveage netwok thoughput with the node density is shown in Fig 8 It is clea that fo small node density, adding moe nodes significantly inceases the netwok thoughput since it makes it easie to satisfy the conditions fo finding a pope elay Also, one can ealie that the potocol using omnidiectional antennas [9] satuates at lowe node /9/$5 9 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE "GLOBECOM" 9 poceedings

5 Tansmission blocking pobability P B λ / μ Poposed potocol (simulation) Poposed potocol (Analysis) Aveage thoughput pe netwok (Mbps) Poposed potocol (simulation) Poposed potocol (Analysis) Numbe of nodes pe km Fig 6 Tansmission blocking pobability (1 nodes pe km ) Fig 8 Aveage thoughput pe netwok (λ/μ =9) Aveage thoughput pe netwok (Mbps) thoughput ae obtained by analying the above Makov model and validated thoughout simulations It should be noted that equipping the destination node with two diectional eceive antennas (one diected at the souce and one at the elay) may povide futhe impovement in the netwok thoughput Poviding a channel access potocol that utilies this additional hadwae seems to be an inteesting futue extension fo this wok Incopoating the effect of the physical laye of the tansmission channel povides anothe useful eseach diection Poposed potocol (simulation) Poposed potocol (Analysis) λ / μ Fig 7 Aveage thoughput pe netwok (1 nodes pe km ) density as the citeion of choosing a elay in this case has less constains than the citeion used in ou potocol On the othe hand, fo lage node density, the netwok thoughput is moe influenced by its utiliation facto It is also clea that the thoughput of ou potocol satuates at a much highe value compaed to the potocol using omnidiectional antennas Both the analytical esults above, and its matched simulation esults, confim that ou poposed potocol outpefoms the potocol using omnidiectional antennas [9] VI CONCLUSION In this pape we poposed a new channel access potocol fo tansmission ove coopeative ad-hoc netwoks By utiliing diectional antennas at both the souce and elay stations, the poposed potocol impoves the tansmission blocking pobability and aveage netwok thoughput Makov chain modelling is used to model the netwok pefomance unde the poposed settings Steady state esults fo tansmission blocking pobability and aveage netwok EFEENCES [1] J G Poakis, igital Communications, 4th ed New Yok: McGaw-Hill Inc, 1 [] V Taokh, N Seshadi, and A Caldebank, Space-time codes fo high data ate wieless communication: Pefomance citeion and code constuction, IEEE Tans Infom Theoy, vol 44, pp , Mach 1998 [] G J Foschini, Layeed space-time achitectue fo wieless communication in a fading envionment when using multi-element antennas, Bell Labs Tech J, vol 1, no, pp 4159, 1996 [4] S M Alamouti, A simple tansmit divesity technique fo wieless communications, IEEE J Select Aeas Commun, vol 16, no 8, pp , Oct 1998 [5] A Sendonais, E Ekip, and B Aahang, Use coopeation divesity, pat I: Implementation aspects and pefomance analysis, IEEE Tans on Communications, vol 51, pp , Nov [6] J N Laneman, N C Tse, and G W Wonell, Coopeative divesity in wieless netwoks: efficient potocols and outage behavio, IEEE Tans on Infomation Theoy, vol 5, pp 6-8, ec 4 [7] A Futenik, A Haimovich, and S Papavassiliou, An Analytical Model fo Measuing QoS in Ad-Hoc Wieless Netwoks, IEEE Global Telecommunications Confeence (GLOBECOM ), pp 16-, ec 6 [8] A Nigaa and Blum, Tansmission blocking pobability in ad-hoc netwoks using coopeative divesity, Intenational Confeence on Wieless Netwoks, Communications and Mobile Computing, vol, pp , June 5 [9] A Nigaa, M Qin, and Blum, On the Pefomance of Wieless Ad Hoc Netwoks Using Amplify-and-Fowad Coopeative ivesity, IEEE Tans on Wieless Communications, vol 5, no 11, Nov 6 [1] LE Mille, istibution of Link istances in a Wieless Netwok, Jounal of eseach of the National Institute of Standads and Technology, vol 16, no, pp41-41, Mach-Apil 1 [11] J H van Lint and M Wilson, Couse in Combinatoics, Cambidge univesity pess, /9/$5 9 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE "GLOBECOM" 9 poceedings