Is Diversity Gai Worth the Pai: Performace Compariso Betwee Opportuistic Multi-Chael MAC ad Sigle-Chael MAC Yag Liu 1, Migya Liu 1 ad Jig Deg 2 1 Departmet of Electrical Egieerig ad Computer Sciece, Uiv. of Michiga 1301 Beal Aveue, A Arbor, MI 48105. Email: {yougliu,migya}@umich.edu 2 Departmet of Computer Sciece, Uiv. of North Carolia at Greesboro 164 Petty Bldg., Greesboro, NC 27412. Email: jig.deg@ucg.edu Abstract I this paper we aalyze the delay performace of a opportuistic multi-chael medium access cotrol scheme ad compare it to that of the correspodig sigle chael MAC scheme. I the opportuistic multi-chael MAC scheme, we assume that the pair of seder/receiver is able to evaluate the chael quality after a certai amout of chael sesig delay ad to choose the best oe for data commuicatio. We cosider three settigs: (1) a ideal sceario where o cotrol chael is eeded ad o sesig delay is icurred, (2) a more realistic scheme where users compete for access o a cotrol chael usig radom access, ad (3) a scheme similar to (2) but with a Time Divisio Multiplex (TDM) based access scheme o the cotrol chael. Our aalysis show that i terms of delay performace, the radom access overhead o the cotrol chael almost always wipe out the chael diversity gai, which is the mai motivatio behid a opportuistic multi-chael MAC. Usig a TDM based access scheme o the cotrol chael ca help remove this bottleeck, but oly whe chael sesig ca be doe sufficietly fast. I. INTRODUCTION Recet advaces i cogitive radio techologies have led to a umber of dyamic multi-chael MAC schemes (see e.g., [5], [10]) that allow radios to dyamically switch betwee chaels i search of good istataeous chael coditio. The fudametal idea is the exploitatio of multi-chael diversity: if a radio is statically assiged a fixed chael, the over time it sees the average coditio of the chael, ad obtais a average rate. I cotrast, if a radio is allowed to always pick a better chael (e.g., higher istataeous received SNR) from a set of chaels, the over time it sees a possibly much higher average rate. While ituitively appealig, i practice for such schemes to work, certai cotrol overhead becomes hard to avoid. First, a cotrol chael is typically eeded for purposes icludig reservatio (gaiig the right to use oe of the data chaels), homig (fidig a iteded destiatio ode), ad commo commuicatio (broadcastig iformatio like chael selectio, completio of trasmissios, etc.). This takes away a certai amout of available badwidth that could have bee This work is supported by NSF grat CIF-0910765 ad ARO grat W911NF-11-1-0532. used for data commuicatio. Secodly, it takes resources to determie which chael has better istataeous coditio. Successive chael sesig cosumes eergy ad time [5]. This takes away time that could have bee used for data commuicatio. The above observatio motivates us to examie whether there is ideed a advatage i usig dyamic multi-chael MAC, ad if so uder what coditios. I other words, we are iterested i uderstadig whether the diversity gai i geeral ca sufficietly compesate for the overhead metioed above. To achieve this goal, we perform the followig sequece of comparisos i terms of delay performace. We start by cosiderig a idealized opportuistic multi-chael MAC, whereby a oracle oversees chael access ad has full iformatio o the istataeous coditios of all data subchaels. It automatically assigs a arrivig user to the best chael amog those curretly available. This allows us to elimiate the eed for a cotrol chael, ad fully use the badwidth for data commuicatio: each of m data sub-chaels gets badwidth B/m. This is compared to a similar, idealized sigle-chael MAC. As expected, uder this sceario, the multi-chael MAC has a clear advatage over the sigle-chael MAC due to the chael diversity gai. We the cosider a more realistic multi-chael MAC, where users must compete for access to data sub-chaels o a cotrol chael first, ad this is doe usig RTS-CTS based radom access. Oce a user gais access it performs chael sesig before selectig a chael; it the aouces its selectio o the cotrol chael. We assume each user has two radios, with oe dedicated to the cotrol chael so that each user is able to accurately track chael usage. This is therefore a much more efficiet use of resources tha that proposed i [5]. This is compared to a commo radom access based sigle-chael MAC. Uder such a sceario, our mai fidig is that this multi-chael MAC sigificatly uder-performs the sigle-chael MAC. There are two mai reasos. Oe is that radom access o the cotrol sub-chael becomes a bottleeck as the cotrol sub-chael is typically
a very small portio of the overall badwidth. The secod reaso is the overhead i chael sesig. These observatios led us to cosider a third multi-chael MAC, similar to the secod oe but with a TDM type of access scheme o the cotrol chael. The itetio is to separate the effect of radom access from that of sesig delay. Our fidig is that while this does remove the radom access o the cotrol chael as a bottleeck, the sesig delay remais a obstacle. As a result, the multi-chael MAC oly shows a advatage whe chael sesig ca be performed much faster tha a regular RTS-CTS packet exchage. The remaider of the paper is orgaized as follows. After presetig the system model i Sectio II, we detail the three sets of comparisos i Sectios III, IV, ad V, respectively. Related work is preseted i Sectio VI ad Sectio VII cocludes the paper. II. SYSTEM MODEL AND PRELIMINARIES We assume a set of active users withi a sigle iterferece domai. The total amout of badwidth available is B. Uder a sigle-chael MAC, this whole amout is treated as a sigle chael for data trasmissio. Uder a multi-chael MAC, the amout B is divided ito a sigle cotrol chael of badwidth B c, ad m equal data sub-chaels each of badwidth B d = (B B c )/m. We will assume that these m data sub-chaels are statistically idetical. Furthermore, we assume that the dyamics of a chael is such that for a fixed size packet its trasmissio time (or service time, icludig retrasmissios) is give by a i.i.d. expoetial radom variable. This models the fact that higher received SNR leads to shorter successful trasmissio time. These are simplificatios for tractability of aalysis, but do ot affect the qualitative coclusios we draw from the aalysis. Each user is assumed to have two radio trasceivers, oe for data trasmissio, the other dedicated to moitorig activities o the cotrol chael. This is a assumptio i favor of the multi-chael MACs, as the secod radio has o utility i a sigle chael system. The itetio is so that a user has full iformatio o chael occupacy: which data sub-chaels are curretly beig used ad therefore ca avoid those whe performig chael sesig ad selectio. We assume a user always picks the best of the set of curretly available chaels as a result of chael sesig. This is agai a simplificatio ad a assumptio i favor of the multi-chael MAC. I practice a user may ot get to sese all available chaels. For a sigle data sub-chael of badwidth B d, its maximum achievable rate is give by R d = B d log(1+snr). We will assume that the aggregated sigle chael has the same SNR as a data sub-chael (e.g., by assumig that users keep the bit error rate at the same level). The trasmissio rate of the aggregated sigle chael is thus give by R = B log(1+snr) = (B c +m B d ) log(1+snr). Thus whe B c is zero, the service rate of the sigle chael is modeled as m times that of a data sub-chael. III. AN IDEAL ACCESS MODEL I a idealized sceario, a oracle has full iformatio o the data sub-chaels ad immediately assigs a arrivig packet to a available chael. There is also o eed for a cotrol chael. Uder this sceario, we cosider three schemes: the first is a sigle-chael MAC, the secod a multi-chael MAC that does ot utilize istataeous chael iformatio, ad the third a opportuistic multi-chael MAC. A. A sigle-chael MAC Uder the idealized assumptio, the dyamics of a siglechael MAC may be modeled as a M/M/1 + q queue, where the aggregate arrival process is Poisso with rate λ, the mea service rate is m µ (µ will be take as the mea service rate of a sigle data sub-chael i subsequet aalysis), ad the parameter q deotes a virtual queue size that models the fact that packets arrivig to a busy chael are forced to wait. This parameter is adjustable, ad ca easily model a fiite-queue ad o-queue situatio. Deotig by π i the steady state probability of havig i packets i such a system, ad by ρ = λ mµ the utilizatio factor, elemetary queuig aalysis suggests 1+q 1+q π i+1 = ρ π i, i = 0,1,...,q,1 = π i = ρ i π 0 ad the packet delay is give by D s = where λ = λ (1 π 1+q ). 1+q i π i, (1) λ B. Multi-chael MAC, o opportuistic access Similarly, uder this ideal sceario, we model the multichael MAC as a M/M/m/m+q queue with a aggregate arrival rate of λ ad service rate µ per server/chael. For this system the packet delay D m is give by N q = q i π m+i,d m = 1 µ + q i π m+i λ where λ = λ (1 π m+q ). Note that we have reused the same otatio π i to deote the steady state probability i this system: π i = { π 0 (mρ) i i!, i m π 0 m m ρ i m! m < i m+q. C. Multi-chael MAC, opportuistic access Uder a ideal opportuistic multi-chael MAC, a arrivig packet is immediately assiged to the best sub-chael amog all those curretly available. A packet fidig all subchaels busy will be put i a queue. We will agai model this system as a M/M/m/m+q queue. However, sice a packet is always assiged the best chael amog all those available, we ca o loger model the service rate of a sigle data sub-chael as a costat µ. Ideed the characterizatio (2) (3)
of the service rate is much more complicated: a particular sub-chael s service rate is strictly speakig a fuctio of the umber of available sub-chaels whe this sub-chael was selected. I this sese the evolutio of the system state, the umber of packets i the system, is o loger Markovia. To address this difficulty, we will adopt the followig approximatio. We will first characterize the average per subchael service rate uder such a opportuistic MAC, µ, ad the use µ as the service rate i a stadard M/M/m/m+q system. Whe there are k sub-chaels available ad the best oe is chose, the service rate of the chose sub-chael has a mea of kµ. Ad m 1 π j µ = (m j) µ m 1 π i j=0. (4) Here agai we have reused the otatioπ i to deote the steady state probability of havig i packets i this system. Note that 1 m j m whe j = 0,1,,m 1. Applyig this to Equatio (4), we have µ µ mµ, thus the opportuistic strategy clearly improves the service rate. Defie the utilizatio factor for this M/M/m/m + q model as ρ = λ m µ. Combied with the steady-state distributio of M/M/m/m + q give i (3), we ca solve µ ad the steady-state distributios simultaeously through the set of fixed poit equatios formed by (3) ad (4). Defie F( µ) = π µ m 1 j j=0 m 1 (m j). We have the followig results. Lemma 1. F( µ) πi is a o-decreasig fuctio ad cocave fuctio with respect to µ. Lemma 2. There is oly oe uique fix poit solutio to µ = F( µ). Havig obtaied µ, the rest of the delay aalysis is similar to Sectio III-B, from which packet delay D m is derived. D. Delay compariso First as m µ mµ, ad D m ad D m are derived from the same model, we have D m D m. Ituitively, for M/M/m/m + q queues, the oe with faster service rate experieces less delay. Cosider D s ad D m. Whe the traffic is light, i.e., λ is small, the delay is domiated by the service rate i which case D s D m ; whe λ gets large, as the stability regio of the sigle chael case is much less tha the multi-chael case, the delay of sigle chael grows quickly; thus it is expected that D s D m. Delay (1 time uit) 10 2 10 1 10 0 10 1 Multi chael MAC 0.2 0.4 0.6 0.8 1 1.2 Fig. 1: Delay performace compariso for idealistic model Aalytical ad simulatio results show i Fig. 1 cofirm the above comparisos. Simulatio parameters are: m = 5,q = 5 (the queue legth does ot have sigificat impact o the geeral results), packet legth L d = 1024 bits, ad the same set is used throughout the paper. These results show quite clearly the beefit of exploitig multi-chael diversity whe o other overhead is associated. IV. RANDOM ACCESS I this sectio, we tur to a more practical settig, where a cotrol sub-chael is allocated for the users to compete for access to the data sub-chaels, ad the competitio is through a RTS-CTS based radom access scheme. This settig is close to the protocol MOAR proposed i [5], but has higher chael utilizatio due to the two-radio assumptio. A. A opportuistic multi-chael MAC This prototype MAC operates i the followig steps. (1) Ay user havig packets to sed first competes o the cotrol chael for the right to access the data sub-chaels, through carrier sesig, radom backoff followed by RTS-CTS packet exchage, very much like i IEEE 802.11b. (2) After the completio of RTS-CTS exchage, the pair of users eters a sesig period, where they successively probe the set of curretly available data sub-chaels. Exactly how this is doe is left uspecified; we simply assume that certai chael sesig packets eed to be exchaged betwee the pair, ad ultimately they are able to select the sub-chael with the best curret coditio. (3) Upo this decisio the pair seds a ACK o the cotrol chael aoucig its chael selectio as well as the duratio of occupacy. This serves the purpose of lettig all other users accurately track which sub-chaels are curret busy. From this poit o the reservatio o the cotrol chael ad all available data sub-chaels is released by the pair ad other users ca resume competig for access. (4) I the meatime, the pair returs to the sub-chael of their selectio ad perform data trasmissio. Note that due to the two-radio assumptio, a user ca cotiue to moitor traffic o the cotrol chael eve as it is egaged i data trasmissio o a data sub-chael. By cotrast, uder MOAR the cotrol chael is ot released util the pair has completed data trasmissio o a sub-chael. The types of delays experieced by a user uder this MAC are as follow. (1) D 1 : time betwee a packet arrival till the completio of the curret RTS-CTS exchage (if ay). (2) D 2 : time betwee the start of competitio ad whe it successfully obtais the right to trasmit. (3) D 3 (icluded i D 2 ): time for RTS-CTS exchage o the cotrol chael ad chael sesig. (4) D 4 : time for data trasmissio. We have igored the ackowledgmet to release the cotrol chael as it s typically a much smaller packet. The derivatio of D 1 ad D 2 is essetially the same as i a o-opportuistic multi-chael system, ad will be take from [3]. I computig D 3, we eed to reserve all available chaels i order to avoid collisio. This itroduces extra waitig time. For a ready packet, we have E[D 3 ] =
E[D 3 i] π i. We assume that the sesig packets are of size L s, ad o larger tha the RTS-CTS pair, deoted as L c. Deote the ratio of the two: r cs = L s /L c, 0 < r cs 1. Also deote the ratio betwee the average rates of the cotrol chael ad a data sub-chael:r = R c /R d. We ormalize the time to trasmit oe pair of RTS/CTS o the cotrol chael to be 2 uits 1. Cosider ow E[D 3 i] i terms of the same time uit, for i = 0,1,..m 2. As there are i busy sub-chaels, E[D 3 i] = m i Ls / L c 2 = 2 m i r cs r. (5) 2 R d R c 2 I the above calculatio the umber of sesig packets (pairs) is take to be m i 2 rather tha m i as the two radios ca potetially both be used durig the sesig phase. We thus have E[D 3 j] = 0. Followig the results i [2], the average completio rate is give by Ge 2G λ =, (6) 1+(1+r r cs E[cs])Ge 2G where G is the aggregated arrival (icludig retrasmissio) o the cotrol chael i oe time uit, ad E[cs] is the expected umber of chael sesig performed: E[cs] = m 2 m i 2 π i (i time uits). Subsequetly D 2 ad D 1 are give by [3] as E[D 2 ] = E[N] E[Z], where E[N] is the expected retrasmissio time, while Z is the completio time for oe successful RTS/CTS cotetio. E[Z] = (e2g 1)(1/ζ +2)+2+E[D 3 ] 1 π m+q, (7) where 1/ζ is the average delay due to radom backoff. The delay caused by a arrival durig RTS/CTS trasmissio is E[D 1 ] = 1 λ + 1 ζ (E[D 3]+1+ 1 λ + 1 ζ )e (E[D3]+1)λ. Fially, followig the earlier model E[D 4 ] = B. Delay compariso j=0 j πj λ(1 π m+q). The delays of sigle ad multi-chael MACs uder radom access have bee calculated i [3] to be E[D sigle ] = L c R {(e2g 1)(1/ζ +2+r d )+2+1/mµ +1/λ+1/ζ [r d +1+1/λ+1/ζ]e (rd+1)λ } E[D multi ] = L c R c { (e2g 1)(1/ζ +2)+2 1 π m+q + +1/λ+1/ζ [1+1/λ+1/ζ]e λ }. For the opportuistic multi-chael MAC we have j=0 j π j λ(1 π m+q ) E[ D multi ] = L c { (e2g 1)( 1 ζ +2)+2+2rr cse[cs] + 1 R c 1 π m+q λ j=0 + j π j λ(1 π m+q ) + 1 ζ [E[D 3]+1+ 1 λ + 1 ζ ]e (E[D3]+1)λ }. 1 The actual quatity is uimportat as all other quatities will simply get scaled. Delay (sec) Multi chael MAC 10 5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Fig. 2: Delay performace compariso for radom access Defie r d = L d L c. The followig set of results compare the delay of these three systems quatitatively. Theorem 1. Whe r d gets large, E[ D multi ] E[D sigle ]. Theorem 2. Whe r d gets large, E[D multi ] E[D sigle ]. Theorem 3. For r cs close to 0, E[ D multi ] E[D sigle ]. The umerical results are show i Fig. 2. I the simulatios the cotrol packet legth is set to L c = 48 bits. We also assume that chael sesig is performed usig RTS-CTS packet exchages, i.e., r cs = 1. The overall chael data rate is 35 Mbps; the back-off parameter 1/ζ is set to 37 time uits. Similar parameters are used i Sectio V. We see from Fig. 2 as well as our aalytical results that eve though the opportuistic strategy helps improve delay performace, the radom access o the cotrol chael elimiates ay potetial gai from chael diversity. This holds eve whe the chael sesig overhead is sigificatly lowered or elimiated. V. TIME-DIVISION MULTIPLEXING (TDM) ACCESS The observatio that the radom access o the cotrol chael poses a sigificat bottleeck to the system performace motivated us to cosider a alterative access scheme o the cotrol chael. We ow cosider a TDM based access scheme o the cotrol chael while keepig other features uchaged. Agai we assume the total arrival rate o the cotrol chael is give by λ (icludig retrasmissio). Also for simplicity, we assume all users have the same arrival rate (λ/). A. TDM-based o-opportuistic multi-chael MAC We idetify two types of delays i a TDM-based multichael system: (1) D 1, time betwee the arrival of a packet ad whe it gais right to trasmit; (2) D 2, time for data trasmissio. We ormalize the time for trasmittig oe pair of cotrol packets to 2 ad i this case µ = 1 (for servig oe cotrol packet). For D 1, stadard results o TDM yield the followig delay o a sigle attempt: µ 2λ = 1 2λ. The expected umber of trasmissio times N o the cotrol chael is give by E[N] = 1/(1 π m+q ). Thus we have (1 2λ) (1 π m+q) E[D 1 ] = E[N] E[T 1 ] =. Note that the rate of completig RTS/CTS exchage o the cotrol chael is also λ. Followig earlier aalysis we have E[D 2 ] = j=0 j πj λ(1 π ad E[D m+q) multi] = Lc R c {E[D 1 ]+E[D 2 ]}.
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Delay (us) Multi chael MAC (a) r cs = 1 Delay (us),r cs = 1/3,r cs = 1/5,r cs =1/10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Arrival rate (time uit) (b) differet r cs Fig. 3: Numerical results for delay performace compariso B. TDM-based Opportuistic Multi-Chael MAC Uder a TDM-based opportuistic multi-chael MAC scheme, the pair of users first performs RTS/CTS exchage o the cotrol chael followed by chael sesig; they the aouce their decisio o the cotrol chael, all withi the same TDM time slot. They the perform data commuicatio i the selected sub-chael while other users cotiue o the cotrol chael. As before we ormalize the RTS-CTS exchage o the cotrol chael to be 2. The time till the completio of chael sesig is thus 2+2 r r cs E[cs]. We defie ad compute delay for TDM-based opportuistic multi-chael MAC the same as TDM-based multi-chael MAC i Sectio V-A, the oly differece lies i E[D 1 ]: E[D 1 ] = [1 2 (1+r r cs E[cs]) λ] (1 π m+q ). (8) C. Delay compariso Cosider first the results show i Fig. 3a, where we have set = 5. We see that the two TDM based multi-chael schemes cotiue to uder-perform their sigle-chael couterpart. The TDM scheme s advatage starts to emerge as we lower the sesig delay by usig a smaller r cs. This is show i Fig. 3b as we repeat the same experimet with eve smaller r cs. Specifically, this advatage is show at high arrival rates, whe the amout of collisio icreases uder the radom access scheme (i the sigle-chael MAC). These results show that the bottleeck i the TDM-based opportuistic multi-chael scheme lies i the iefficiecy of chael sesig. Uless the sesig overhead ca be reduced to 1/5 or less of the size of RTS-CTS trasmissio, the opportuistic multi-chael MAC scheme sigificatly uderperforms the sigle-chael MAC scheme. VI. RELATED WORKS For performace improvemet cosideratio, researchers proposed to split sigle chael ito multiple sub chaels with oe used as cotrol chael ad the others used as data chaels. Related works o split chael ca be foud i [8], [11], [13]. RTS/CTS exchages are the performed o the cotrol chael [4], [6]. I [7], a multi-chael CSMA/CD protocol was ivestigated. Marsa ad Neri cocluded that multi-chael may improve the delay performace compared to sigle chael. Xu et al. suggested the use of multiple receivers o a sigle ode [12]. With the help of improvemet o hardware implemetatio efficiecy, multiple receivers scheme becomes more practical. I [2], [3], Deg et al. preseted a queue model for aalyzig radom access multi-chael MAC scheme (without diversity gai) ad cocluded that multichael MAC scheme would ot improve either delay or throughput performace compared to sigle chael MAC. I [1], [5], [9], opportuistic chael selectio algorithms were ivestigated with system performace evaluated experimetally ad mathematically. There however lacked a geeral model for aalyzig the delay performace of these strategies. VII. CONCLUSION We aalyzed the delay performace of opportuistic multichael MAC ad their sigle-chael couterparts. Our geeral coclusio is that while there is sigificat chael diversity gai i usig the former, the overhead is also sigificat, i the form of a much slower access rate o the cotrol chael ad the cost i chael sesig. Usig a TDM based access scheme o the cotrol chael ca help remove the first bottleeck, but oly whe chael sesig ca be doe sufficietly fast. REFERENCES [1] N.B. Chag ad M. Liu. Optimal chael probig ad trasmissio schedulig for opportuistic spectrum access,. I IEEE/ACM Trasactios o Networkig,vol. 17, o. 6, pages 1805 1818, December 2009. [2] J. Deg, Y. S. Ha, ad Z. J. Haas. Aalyzig split chael medium access cotrol schemes. IEEE Tras. o Wireless Commuicatios, 5(5):967 971, May 2006. [3] J. Deg, Y. S. Ha, ad S. R. Kulkari. Ca multiple subchaels improve the delay performace of RTS/CTS-based MAC schemes? IEEE Tras. o Wireless Commuicatios, 8(4):1591 1596, April 2009. [4] Y. S. 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