1 Energy Effcency Analyss of a Multchannel Wreless Access Protocol A. Chockalngam y, Wepng u, Mchele Zorz, and Laurence B. Mlsten Department of Electrcal and Computer Engneerng, Unversty of Calforna, San Dego 9500 Glman Drve, La Jolla, CA , USA Emal: ABSTRACT When user termnals powered by a fnte battery source are used for wreless communcatons, energy constrants are lkely to nfluence the desgn/choce of meda access protocols. In ths paper, we analyze the of a multchannel wreless access protocol usng a fnte energy source n a moble rado envronment. The average number of correctly transmtted packets for a gven amount of allocated energy s used as the approprate metrc. The moble rado channel tself s characterzed by a correlated Raylegh fadng process, whose memory parameters depend on the speed of the user termnal, the data rate, and the physcs of the channel. We show that the protocol whch recovers erroneous data packets through retransmsson s more energy effcent at low channel correlatons. I. INTRODUCTION Portable user termnals for moble communcatons must rely on lmted battery energy for ther operaton. The desgn/choce of meda access protocols n such applcatons must consder judcous use of the avalable energy resources, and should explot the characterstcs of the wreless envronment towards mproved effcency. It has been recognzed that energy conservaton s a task whch should be performed at all levels of the protocol stack (and not only lmted to the search for better batteres or lowerpower crcuts), so that t should be an objectve n the desgn of a communcatons system as a whole. In , Bambos and Rulnck study the optmzaton of power control strateges to maxmze the battery lfe under QoS constrants. Energy performance of error control schemes s studed by Zorz and Rao n , and by Letter et al. n . In ths paper, we focus on analyss of access protocols n wreless networks. The ssue of energy consumpton of meda access protocols has been addressed n , and a protocol desgn followng energy conservaton prncples has been proposed n . In , t has been shown that error correlaton (naturally present n wreless channels) can be exploted to conserve energy by devsng access protocol rules that take nto account the fadng characterstcs of the wreless channel. In ths paper, based on Markov analyss and on the theory of renewal reward processes, we analyze the of a multchan- Ths work was partally supported by TRW, Artouch, the Center for Wreless Communcatons at the Unversty of Calforna, San Dego, the MICRO Program of the State of Calforna, and the Focused Research Intatve on Wreless Multmeda Networks, grant DAA H y A. Chockalngam s presently wth Qualcomm, Inc., 6455 Lusk Boulevard, San Dego, CA E-mal: nel wreless access protocol n a moble rado envronment. In multchannel systems, there are several ndependent, orthogonal channels, and a user can transmt on any of these channels based on a sutable access protocol ,. We use a stochastc model for jontly trackng the evoluton of the protocol and the avalable energy. By consderng a dscretetme process whch tracks the protocol evoluton by means of a state machne, t s possble to defne a set of metrcs assocated wth the state transtons. We evaluate the of the protocol by approprately defnng the metrcs and by studyng the correspondng reward earned throughout the evoluton of the process. II. ENERGY EFFICIENCY In order to evaluate the energy performance of access protocols under dfferent fadng scenaros usng a unfed metrc, we defne the of a protocol, whch was ntroduced n , as total amount of data delvered U = : (1) total energy consumed We assume here that the protocol evoluton can be tracked by means of a Markov chan wth fnte state space. By approprately defnng metrcs on the transtons of ths chan, renewal reward analyss allows to compute and energy performance ,. Let P j be the transton probablty from state to state j, and let be the steady-state probablty of the chan beng n state 2. It s possble to defne varous sem-markov processes n whch ths Markov chan s embedded . In general, consder two reward functons, R (1) and R (2), where R (1) j ; R(2) j are quanttes assocated wth transton j, and let R (1) ( ); R (2) ( ) be the cumulatve values of those functons,.e., the total reward earned through the system evoluton n the tme nterval [0; ]. From renewal theory , we have the followng fundamental result: R (2) ( ) = 2 j2 R (1) ( ) lm!1 2 j2 P j R (1) j ; (2) P j R (2) j whch can be easly computed for a number of cases of nterest. For example, let S j, C j and D j be the average number of fully receved packets, amount of consumed energy, and tme delay assocated wth transton j, respectvely. Then, f R (2) = D, evaluaton of (2) for R (1) = S and R (1) = C gves
2 no new data falure completed DATA_T FAILURE new header IDLE/HEADER N--j-k data falure data completed new header new header falure/ all channels busy old header DATA_T SUCCESS j old header BACKLOGGED k data old header falure Fg. 1. Moble state transton dagram (n Markov fadng) the average and energy consumpton, respectvely (ergodcty of all processes nvolved wll be assumed throughout). On the other hand, the choce R (1) = S and R (2) = C yelds the of the protocol. Therefore, once the Markov chan for the protocol evoluton has been found, all the relevant performance metrcs can be easly computed from the above. III. MULTICHANNEL PROTOCOL PERFORMANCE In ths secton, we present the analyss of a multchannel wreless access protocol, whch can be vewed as a hybrd protocol employng the slotted ALOHA and reservaton concepts, based on the -delay analyss for the same multchannel wreless access protocol . M equal-capacty, orthogonal, traffc channels are shared by N moble users (N M) on the uplnk (moble-to-base staton lnk). A header packet s sent on a contenton bass frst, followng whch data packets are sent on a reservaton bass. By ths approach, packet losses due to collsons are restrcted to occur only among header packet transmssons. Refer to  for a detaled descrpton of the protocol, the system model, and the fadng channel model. The moble state transton dagram s shown n Fgure 1. A new s assumed to arrve at each moble wth probablty n each slot (Bernoull arrval process). The moble accepts a newly arrvng for transmsson only when t has no to send, and does not generate new s when t already has a to send. The length of the data segment of each,, measured n nteger number of packets, s assumed to follow a geometrc dstrbuton wth parameter g d. Each moble, n any gven slot, can be n any one of four states, namely, dle/header tx state, data tx state, data tx falure state, and backlogged state (see Fgure 1). Note that the data transmt state s dvded nto and falure substates n order to account for the one slot channel memory (defned by a frst-order Markov chan wth parameters p and q n ). In the dle/header tx state, the moble remans dle wth probablty 1? or generates a new wth probablty. In the latter case, t randomly chooses an dle uplnk channel (f avalable), and transmts the header packet n the uplnk slot. If the header packet transmsson s ful, then the moble moves from the dle/header tx state to ether data tx state or data tx falure state. In the data transmt state, the moble transmts the data packets contnuously untl all the packets n the are sent, and then moves back to the dle/header tx state. Durng the transmsson of data packets, the moble moves from data tx state to ether data tx state or data tx falure state, wth probablty p and 1? p, respectvely. Smlarly, from data tx falure state, the moble moves to data tx state and data tx falure state wth probablty 1? q and q, respectvely. The moble moves from the dle/header tx state to a backlogged state f all the uplnk channels are found busy upon arrval of a. Smlarly, f the header packet s lost due to collson or bad channel condtons, the moble moves from the dle/header tx state to the backlogged state. In the backlogged state, the moble rechecks the status of the uplnk channels after a random number of slots. The rescheduled transmsson attempt delay s assumed to be geometrcally dstrbuted wth parameter g r. If a moble n the backlogged state fals to transmt ts header packet fully, t stays n ths state untl ts header packet transmsson s ful, after whch t moves to ether data tx state or data tx falure state. A. Throughput Let x t be the number of mobles n the data tx falure state, y t be the number of mobles n the data tx state, and z t be the number of mobles n the backlogged state at the begnnng of slot t. The three dmensonal random process fx t ; y t ; z t g can be modeled as a fnte state Markov chan. Based on the condtonal probablty that n mobles smultaneously transmt header packets and c s of those packets are fully receved at the base staton, the one step transton probablty, P 1j 1k 1; 2j 2k 2, that the system moves from (x t = 1 ; y t = j 1 ; z t = k 1 ) at tme slot t to (x t+1 = 2 ; y t+1 = j 2 ; z t+l = k 2 ) at tme slot t+1 s gven by Eq. (5) n . Let P = (P 1j 1k 1; 2j 2k 2 ) be the probablty transton matrx and let = f 1j 1k 1 g, 0 1 M, 0 j 1 M? 1, 0 k 1 N? 1? j 1, denote the steady-state probablty vector. The vector can be calculated by solvng the lnear equatons = P and usng the unty conservaton relatonshp. The number of ful data packets n a slot s equal to the number of users n the data tx state, so that the average number of es per slot s gven by EfS d g = M M? 1 1=0 j 1=0 N? 1?j 1 k 1=0 j 1 1j 1k 1 : (3) The average per channel, defned as the average number of packets (excludng the header packets) fully receved per slot per channel, s then gven by B. Delay c = EfS dg M : (4) As derved n , the average delay experenced by a s gven by EfDg = 1 + Efg ; (5)
3 where Efg s the average number of users whch ether are n the transmsson mode or are backlogged,.e., Efg = M M? 1 N? 1?j 1 1=0 j 1=0 and = (N? Efg). C. Energy Effcency k 1=0 ( 1 + j 1 + k 1 ) 1j 1k 1 ; (6) Let the system be n state ( 1 ; j 1 ; k 1 ) n a gven slot (.e., 1 users experence data falure, j 1 users experence data, k 1 users are backlogged and N? 1? j 1? k 1 users are dle). Users n the data transmsson state (both ful and unful) wll transmt one packet wth probablty one n that slot. If 1 + j 1 < M (.e., not all channels are occuped), users n the backlogged state wll each attempt transmsson wth probablty g r, and dle users wll each attempt transmsson wth probablty, so that the average number of packet transmssons n the slot s gven by 1 + j 1 + k 1 g r + (N? 1? j 1? k 1 ). On the other hand, f 1 +j 1 = M (.e., all channels are busy), backlogged and dle users wll not attempt transmsson and the number of transmssons wll be equal to M. From the above expressons for the probablty dstrbuton of the Markov chan, t s then possble to compute the average number of transmtted packets n a slot (whoch s defned to be the average energy consumpton) as " = M?1 M? 1?1 N? 1?j 1 1 =0 j 1 =0 k 1 =0 +(N? 1? j 1? k 1)] + [ 1 + j 1 + k 1g r 1 +j 1 =M M 1 j 1 0: (7) The of the scheme, defned as the average number of ful transmssons per unt energy, can be computed as U = EfS dg ; (8) " where the energy unt s assumed to be equal to one packet transmsson. IV. RETRANSMISSION OF ERRONEOUS DATA PACKETS In the multchannel protocol analyzed above, packets whch get corrupted durng the data segment transmsson are lost and the recovery of such errors s left to the hgher layer protocols. A classc way of recoverng errors n packet transmsson s through retransmsson. Instead of gnorng the packet errors, a data packet s retransmtted f t s receved n error. In the local wreless envronment under consderaton, where the feedback s assumed to be practcally nstantaneous, a data packet n error can be retransmtted n the mmedately followng slot. In ths case, the base staton would need to send a non-bnary feedback (busy/dle/retransmt) n order to avod a collson among retransmsson packets from a moble wth header packets from other mobles. Thus, wth the persst-untl- retransmsson strategy, the expressons for the expected value of the effectve length of the and the one step transton probablty need to be modfed as gven n Secton V of  d, F=5 db d, F=10 db corr, F=5 db corr, F=10 db 0.4 Fg. 2. Energy effcency vs. for..d. fadng and correlated Raylegh fadng wth fdt = 0:02, for varyng. Dfferent ponts correspond to dfferent. M = 3; N = 15; F = 5 and 10 db. No retransmsson. No capture. V. RESULTS AND DISCUSSION Numercal results are obtaned from the analyss presented above for M = 3, N = 15, g d = 0:1, g r = 0:1, and a normalzed Doppler bandwdth of f D T = 0:02, where f D s the maxmum Doppler shft and T s the packet duraton. At a carrer frequency of 900 MHz and a packet duraton of 10 ms, the f D T value of 0.02 represents slow fadng (.e., hgh correlaton n fadng) correspondng to the user movng at a speed of 2.5 km/h. The values of the fadng margn 1, F, consdered are 5 and 10 db, and no capture s assumed (plots showng the effect of capture are not presented here due to lack of space, even though the analyss presented here would make that calculaton possble). We also found good agreement between analytcal and smulaton results. Average per-channel, average delay, and are computed usng (4), (5), and (8), respectvely. The performance n..d. fadng s also plotted for comparson. Fgure 2 shows the vs. (dfferent ponts on the curve correspond to dfferent values of the peruser arrval rate, ). It can be seen that the relatonshp between the two performance metrcs mples a trade-off, snce any ncrease results n a loss n. Note that n ths case, when the traffc load s ncreased, s ncreased (as shown n ), but the number of transmssons per slot also ncreases, and the latter effect s seen to always be more sgnfcant than the former. From Fgure 2, t s also seen that the correlated fadng case performs better than the..d. fadng case, as the latter curve always les below the former. Ths had been observed for n , and s seen here to be true for as well (n fact, the mprovement n nduced by error correlaton s even more sgnfcant than that n ). Smlar behavor s exhbted by the /delay trade-off (see Fgure 3). 1 The fadng margn s the maxmum tolerable attenuaton whch stll guarantees good recepton qualty.
4 80 average delay d, F=5 db d, F=10 db corr, F=5 db corr, F=10 db rtx, F=5 db rtx, F=10 db no rtx, F=5 db no rtx, F=10 db Fg. 3. Average delay vs. for..d. fadng and correlated Raylegh fadng wth fdt = 0:02, for varyng. Dfferent ponts correspond to dfferent. M = 3; N = 15; F = 5 and 10 db. No retransmsson. No capture. Fg. 5. Energy effcency vs. for varyng fdt and = 1. Dfferent ponts correspond to dfferent fdt. M = 3; N = 15; F = 5 and 10 db. Protocols wth and wthout retransmsson. No capture rtx, F=5 db rtx, F=10 db no rtx, F=5 db no rtx, F=10 db Fg. 4. Energy effcency vs. fdt for = 1. M = 3; N = 15; F = 5 and 10 db. Protocols wth and wthout retransmsson. No capture. As the performance metrcs depend on the channel correlaton, t s of nterest to study n more detal ths dependence. Fgure 4 shows the vs. the normalzed Doppler bandwdth, f D T, for = 1. Two cases are consdered n ths fgure, namely the protocol wth retransmsson and wthout retransmsson. It s seen that n the case of the protocol wth retransmsson the s actually ndependent of the channel correlaton. Ths s consstent wth the results reported n  and wth the fact that at the consdered value of the average number of packet transmssons per slot s close to 1 and only weakly dependent on f D T. On the other hand, when retransmsson s not used, s no longer ndependent of f D T. In fdt partcular, n hghly correlated channels (small f D T ), the protocol wthout retransmsson s more energy effcent than the protocol wth retransmsson. On the other hand, when the channel correlaton s very low (large f D T ), the protocol wth retransmsson s more energy effcent than the protocol wthout retransmsson. Ths performance varaton over f D T suggests that t s possble to devse more effcent versons of the protocol that could explot the memory n the channel fadng process for better energy performance. For example, f the base staton detects a data packet error from a moble, t can smply ask the moble to termnate ts on-gong data transmsson and release the channel. Such a scheme s expected to gve good results n the presence of sgnfcant channel burstness (.e., slow fadng), as t avods nsstng on transmsson n slots whch are lkely to be n error, and lets other mobles (whose channel condtons mght be good) access and use the channel. On the other hand, the above strategy could be wasteful n fast fadng condtons where packet errors could occur ndependently from slot to slot. In such fast fadng condtons, error recovery by retransmsson would be preferred. The relatonshp between and as the channel correlaton changes s llustrated n Fgure 5, whch shows the vs. the average for varous values of f D T and for = 1. The energy consumpton s always ndependent of f D T, snce n our model users attemptng transmsson of a header packet experence steady-state channel condtons. Ths accounts for the lnear relatonshp between and (gven by dvded by the constant energy consumpton), whch reduces to a sngle pont for the case n whch retransmsson s used ( s also ndependent of f D T n ths case). Fnally, a comparson between the multchannel and sngle channel cases s provded n Fgure 6, whch shows results for N = 1; M = 5 and for N = 3; M = 15 (the number of users per channel s kept fxed for a far comparson). It can be seen that the
5 d, N=3, M=15 corr, N=3, M=15 d, N=1, M=5 corr, N=1, M=5 0.4 Fg. 6. Energy effcency vs. for..d. fadng and correlated Raylegh fadng wth fdt = 0:02, for varyng. Dfferent ponts correspond to dfferent. M = 3; N = 15 and M = 1; N = 5 compared. F = 10 db. No retransmsson. No capture. multchannel case yelds slghtly better n most cases, as one would expect due to statstcal multplexng. Also, sgnfcantly better s acheved n the multchannel case, whch s to be ascrbed to the decreased collson rate. In fact, n the absence of capture, for a sngle channel a header can only occur when a sngle user attempts transmsson (.e., f two or more users smultaneously attempt, the probablty of header s zero), whereas n the multchannel case there s always a postve (although possbly small) probablty that a user succeeds. The fact that n the multchannel case users choose channels at random when tryng to gan access also accounts for the performance crossover at hgh arrval rates. In fact, n ths case, f, for example, three users attempt transmsson and there are three dle channels, there s no guarantee that no collson wll occur, as more than one user may end up choosng the same channel, resultng n collsons on some channels and n some other channels beng dle. VI. CONCLUSIONS We analyzed the effect of packet error burstness caused by the correlaton n the multpath fadng process on the delay and performance of a multchannel wreless access protocol. The packet error burstness was modeled usng a frst-order Markov chan whose parameters were defned as a functon of the normalzed Doppler bandwdth and the fadng margn. Followng Markov analyss and renewal reward analyss, expressons for the average per channel, average transfer delay and were derved. Numercal and smulaton results showed that the correlated fadng model resulted n better performance than the..d. fadng model. A smple persst-untl- retransmsson strategy to recover erroneous data packets was also analyzed. It was shown that the protocol wthout retransmsson benefted from hghly correlated fadng. It was observed that the multchannel protocol wthout retransmsson performed better on slow fadng channels (e.g., pedestran user speeds) than the protocol wth retransmsson. However, the protocol wth retransmsson performed better n fast fadng channels (e.g., vehcular user speeds). The gans n are paralleled by even more sgnfcant gans n terms of. We recognze that, n networks comprsng battery-powered devces, maxmzng alone may not be the prmary concern. The results shown, as well as others whch can be obtaned from the analyss presented, can help the desgner tune the protocol parameters to trade-off for. REFERENCES  N. Bambos and J. M. Rulnck, Moble power management for wreless communcaton networks, Wreless Networks, vol. 3, pp. 3 14,  M. Zorz and R. R. Rao, Energy constraned error control for wreless channels, IEEE Personal Communcatons, pp , December  P. L. Letter, C. Fragoul and M. B. Srvastava, Low power error control for wreless lnks, n Proc. Mobcom 97, Budapest (Hungary), pp , September  J-C. Chen, K. M. Svalngam, P. Agrawal and S. Kshore, A comparson of MAC protocols for wreless local networks based on battery power consumpton, n Proc. IEEE INFOCOM 98, San Francsco, CA, pp , Aprl  K. M. Svalngam, M. B. Srvastava, P. Agrawal, and J-C. Chen, Low-power access protocols based on schedulng for wreless and moble ATM networks, Proc. IEEE ICUPC 97, pp , San Dego, October  A. Chockalngam and M. Zorz, Energy consumpton performance of a class of access protocols for moble data networks, n Proc. IEEE VTC 98, Ottawa, June Also, to appear n IEEE Trans. Commun.  W. u, A. Chockalngam, and L. B. Mlsten Throughput-delay analyss of a multchannel packet CDMA scheme n a fadng envronment, Proc. IEEE ICUPC 97, vol. 1, pp , San Dego, October,  W. u, A. Chockalngam, and L. B. Mlsten, Performance Analyss of a Multchannel Wreless Access Protocol n the Presence of Bursty Packet Losses n Proc. IEEE MILCOM 98, Bedford, MA, October  W. C. Jakes, Jr., Mcrowave moble communcatons, New York: John Wley & Sons,  R. A. Howard, Dynamc probablstc systems, John Wley & Sons,  S. H. Ross, Stochastc processes, John Wley & Sons, 1983.