FEEDBACK enables wireless links with high data rates

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. XX, MONTH 0 Link Adapaion wih Posiion/Moion Informaion in Vehicle-o-Vehicle Neworks Rober C. Daniels, Member, IEEE, and Rober W. Heah, Jr. Fellow, IEEE Absrac Wireless communicaion neworks use link adapaion o selec physical layer parameers ha opimize he ransmission sraegy as a funcion of he wireless channel realizaion. In he vehicle-o-vehicle VV) neworks considered in his leer, he shor coherence ime of he wireless channel makes link adapaion based on he impulse response challenging. Consequenly, link adapaion in VV wireless neworks may insead exploi he large-scale characerisics of he wireless channel i.e. pah loss) since hey evolve slowly and enable less frequen feedback. Large-scale channel informaion may be capured hrough channel or posiion/moion measuremens. We show, hrough he definiion of new large-scale coherence expressions, ha channel measuremens render large-scale coherence as a funcion of ime-change while he posiion/moion measuremens render coherence as a funcion of velociy-change. This leer is concluded wih highway simulaions of modeled and measured channels o demonsrae he advanage of posiion/moion informaion for feedback reducion in VV link adapaion. Index Terms I. INTRODUCTION FEEDBACK enables wireless links wih high daa raes hrough link adapaion. Wihou link adapaion, ransmiers mus consider he wors case channel qualiy o provide reliable communicaion. In his leer we sudy link adapaion for wireless communicaion beween wo auomobiles also called vehicle-o-vehicle VV) wireless communicaion). Because he ransmier and receiver are ypically moving a high speeeds in poenially opposie direcions, mulipah changes very rapidly, especially a higher frequencies. VV communicaion is also inermien since links appear and disappear very quickly. Therefore, i is criical ha he maximum amoun of informaion is ransferred when a link is acive. Clearly, link adapaion is imporan for fuure VV neworks ha will carry imporan driver safey and raffic informaion []. I may no be feasible, however, o provide complee channel feedback for link adapaion in VV wireless links. Channel measuremens of VV links have shown ha he coherence ime is someimes less han msec due o he high mobiliy of vehicles in highway scenarios [], []. The proocol delay of feedback beween vehicles may exceed his coherence ime. For example, he immediae feedback exchange in IEEE Manuscrip received January, 0; revised Augus, 0; acceped November 7, 0. The associae edior coordinaing he review of his leer and approving i for publicaion was Dr. G. Song. The auhors are wih he Wireless Neworking & Communicaions Group in Dep. of Elec. & Comp. Eng. a he Universiy of Texas a Ausin, Universiy Saion C080, Ausin, TX , fax: rober.daniels@uexas.edu, rheah@ece.uexas.edu). R. C. Daniels is also wih Kuma Signals, LLC, Ausin, TX. Work funded by Army Research Laboraory Conrac W9F Digial Objec Idenifier 0.09/TWC /08$.00 c 0 IEEE 80.n provides a bes 0..0 msec of feedback delay []. Moreover, low-laency, high-rae feedback proocols yield large overhead, which reduces link adapaion uiliy. To enable link adapaion for wireless communicaions over channels wih a shor coherence ime, several have proposed proocols ha exploi large-scale channel informaion, i.e., pah loss [] [6]. For link adapaion wih pah loss, he receiver may feed back one of wo measuremens: ) received signal srengh ) posiion/moion informaion [7]. Posiion/moion informaion is made available by GPS or similar localizaion echnologies which have become pervasive in vehicular environmens [8], [9]. For ) he ransmier mus complee a windowed average of received signal srengh o esimae pah loss. In ) he ransmier firs predics he communicaion disance based on he curren ransmier posiion and he expeced receiver posiion given posiion/moion feedback. The ransmier compues pah loss afer disance predicion hrough, for example, he log-disance model or inverse wireless fingerprining [0], []. This leer sudies he preference of feeding back ) or) o enable link adapaion in VV links. We propose a new meric o measure he consisency of pah loss: large-scale coherence. We use his meric o propose expressions of large-scale coherence ime and large-scale coherence velociy in logdisance pah loss models. Large-scale coherence ime quanifies he freshness of he pah loss esimae a he ransmier hrough feedback wih ) while large-scale coherence velociy quanifies he freshness of he derived pah loss esimae a he ransmier hrough feedback wih ). Inuiively, assuming ha vehicle posiion rajecory beween feedback periods is compleely characerized by s and nd order informaion vehicle velociy and acceleraion), wih ) we canno infer he locaion of vehicles beween feedback periods so we canno infer he variaion of pah loss beween feedback periods. To deermine he inerval of feedback, we simply find he ime ha he channel becomes large-scale incoheren as a funcion of vehicle posiion, velociy, and acceleraion. In ), wihou acceleraion, we can indefiniely deermine pah loss wih one feedback exchange. Hence, large-scale channel incoherence is fundamenally ied o he coherence of vehicle velociy, or acceleraion. Using hese new expressions we will show ha, hrough simulaion sudies of VV highway communicaions, posiion/moion feedback requires less overhead han link adapaion wih received power measuremens. Assumpions: This work assumes ha each pah loss or posiion/moion feedback exchange requires he same ime allocaion on he nework. Therefore, he rae of feedback will deermine wheher link adapaion wih ) or) incurs more

2 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. XX, MONTH 0 overhead. While our simulaions include accurae pah loss measuremens, our proposed coherence expressions assume simplisic pah loss models. These simple models help us o develop inuiion in he radeoff beween link adapaion wih posiion and moion informaion. Our resuls also assume ha pah loss and posiion informaion can be resolved exacly, which will no be he case for eiher in pracice. Relaxaion of hese assumpions will be reaed as fuure work. II. LARGE-SCALE CHANNEL COHERENCE Consider single-anenna, frequency-fla channels where realizaion h) C is decomposed ino small- and large-scale effecs such ha h) α)β) where [0, ) is he relaive ime arbirarily saring a 0), α) 0, ] is he imevarying large-scale channel componen due o pah loss, and β) is due o small-scale effecs resuling from ime-varying mulipah saisically β) could represen Rayleigh fading, for example). A. Channel Coherence Definiions The minimum feedback rae for link adapaion is ypically deermined by he coherence ime of he channel []. Calculaion of channel coherence hrough he correlaion coefficien of he impulse response is no relevan here, however, since we consider link adapaion based on pah loss. Definiion. Using 0 as our iniial ime reference and >, we propose α ) α ) <ηor α ) α ) > ) η implies ha α ) is large-scale incoheren a ime wih respec o α ) for η 0, ]. Our definiion of large-scale channel coherence was inspired by observing adapive modulaion and coding AMC). Typically, he differen AMC sraegies are separaed approximaely) by he same difference in average SNR on a logarihmic scale. For example, using he AMC sysem in [], he average SNR gap is around db 0 log 0 η) η 0.. Therefore our definiion allows us o relae large-scale channel incoherence wih a change in ransmission sraegy. Moreover, ) allows us o fairly and accuraely characerize large-scale channel coherence using boh pah loss measuremens and posiion/moion measuremens in he nex wo subsecions. B. Vehicle-o-Vehicle Large-Scale Channel Coherence Consider a VV wireless link beween wo vehicles which boh lie in -dimensional Euclidean space o model a general propagaion environmen. The posiion and moion velociy) of he firs vehicle as a funcion of ime are represened as p) [p ),p ),p )] T and m) [m ),m ),m )] T, respecively, where each are defined in R. Similarly, he posiion and moion of he second vehicle are defined by q) and n). We assume pah loss may be defined in erms of posiion and ime, i.e. α) is deerminisic if p) and q) are known. Consider ha posiion and moion informaion are measured and known a ime.for >, assuming ha higher order saisics of posiion acceleraion and above) vary oo quickly o measure accuraely, we esimae/predic he posiion informaion a wih only velociy, i.e. ˆp, ) p )+ )m ) ˆq, ) is defined similarly). We also define he prediced disance hrough velociy informaion, ˆd, ) ˆp, ) ˆq, ). The accuracy of he prediced pah loss a hrough ˆd, ) depends on variaion of m) and n) over [, ]. Thus, we have wo measures of large-scale coherence: wih pah loss measuremens largescale coherence ime) and wih posiion/moion measuremens large-scale coherence velociy). To bound he change in m) and n) over he inerval [, ] and deermine large-scale coherence in erms of velociy change, we assume linear acceleraion for boh vehicles. We define δ m ) n )) m ) n ))) / ) as he relaive acceleraion beween he firs and second vehicle. Assuming δ compleely characerizes he change in velociy over [, ], he iner-vehicle disance a is defined d,, δ) p ) q )+ ) δ )+m ) n ) ). The large-scale coherence ime of he channel can now be defined in erms of he relaive acceleraion τ c, δ,η) min { : α )/α,, δ) μη)} ), ) where α,, δ) is he pah loss mapped from d,, δ) and he erm μη) η if α,, δ) >α ) and μη) /η oherwise. Similarly, he large-scale coherence velociy region of he channel can be defined in erms of he inerval [, ], ν c,,η) {δ :ˆα, )/α,, δ) μη)} R ) given ˆα, ) is he pah loss mapped from ˆd, ). Here, μη) η if ˆα, ) < α,, δ) and μη) /η oherwise. Therefore, large-scale coherence velociy is he se of relaive acceleraion hresholds ha, when me, cause he prediced pah loss a hrough posiion/moion informaion, ˆα, ), o become large-scale incoheren. C. VV Large-Scale Coherence in Log-Disance Model For a deeper insigh ino he definiion of large-scale coherence ime and large-scale coherence velociy in VV neworks, le us consider he log-disance pah loss model wih pah loss exponen n and pah loss reference measuremen value γ 0 a reference disance d 0. [0]. Wih his model α) γ 0 d 0 /d)) n where d) p) q) is he disance beween he firs and second vehicle. By redefining he numeraor in erms of he velociies and acceleraion, he pah loss measuremen a ime resuls in large-scale channel incoherence a if μη) d,, δ)/d )) n ) b + b + b + b + b 0 0 ) for ), b 0 μη) /n ) d ), b k m k ) n k ))p k ) q k )), b k δ kp k )

3 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. XX, MONTH 0 Node Node p0) 0 q0) posiion Fig.. Illusraion of nework opology. Two vehicles approaching each oher where he x-axis represens he posiion of each vehicle. A node acceleraes a δ m/s unil when he vehicle sops acceleraion. q k )) + m k ) n k )), b k δ km k ) n k )), and b k δ k /. The large-scale coherence ime is he minimum non-negaive roo of his quaric polynomial. Similarly, large-scale incoherence hrough posiion/moion informaion occurs a when μη) d,, δ)/ ˆd n, )) 6) δ + a μη) n a 7) δ μη) n ) a 8) by Cauchy-Schwarz where a p ) q ) + m ) n ))). We can also define an upper bound on each relaive acceleraion componen by seing he oher componens equal o zero and solving he quadraic equaion in 8). Thus, for a [a,a,a ] T, he inequaliy { } ak δ k max + μη) /n ), a k μη) /n ) 9) provides an upper bound on each componen of he coherence velociy. Hence, in he general -dimensional propagaion scenario we canno complee a simple large-scale coherence velociy expression due o he degrees of freedom available in he acceleraion componens. We can, however, place lower and upper bounds on he acceleraion values. Noice ha as n pah loss exponen increases indefiniely), he upper bound limi per dimension is a k. I can also be shown in ) ha as n, b 0 0 τ c, δ,η) 0. Hence, he larger he pah loss exponen, he more aracive posiion informaion becomes for esimaing pah loss. In -dimensional spaces, such as he sysem in he sequel, he expressions for large-scale coherence ime and large-scale coherence velociy simplify dramaically. III. HIGHWAY STUDY OF VV LINK ADAPTATION To demonsrae he pracical significance of he large-scale coherence expressions in Secion II, we consider he highway VV nework opology. We show simplified large-scale coherence expressions due o he posiion dimensionaliy reducion. Feedback rae radeoffs are simulaed for pracical operaing condiions o demonsrae ha posiion/moion informaion availabiliy ofen resuls in less feedback exchanges. A. Large-Scale Coherence Expressions in -D We now proceed wih he compuaion of large-scale coherence ime for he VV nework opology in Fig.. We consider he scenario where wo vehicles are raveling on a line and he pah loss beween hem is modeled by he Friis free space propagaion formula n, d 0, γ 0 λ/π) wih operaing wavelengh λ meers in he log-disance pah loss model). We only consider a single acceleraing vehicle node acceleraion δ, node acceleraion 0), since relaive acceleraion deermines large-scale coherence velociy. For dimension, ) simplifies o q ) p )+n ) m )) δ μη) 0) q ) p ) τ c,δ,η) m ) n ) ± δ m ) n )) δ κ ) μη) d ) ) δ where κ if he sign inside he absolue value of he numeraor and denominaor in 0) mach, oherwise κ. If he signs do no mach, his means ha node and node cross pahs, i.e. he crossover poin is in he inerval, ) such ha heir direcion relaive o each oher has changed. We can similarly simplify large-scale coherence velociy. Equaion 6) simplifies o q ) p )+n ) m )) δ μη) ) q ) p )+n ) m )) ν c,,η) κ ) μ η) q ) p )+ n ) m ))) ) where κ is defined he same manner as before. We now have simple expressions ha characerize he large-scale coherence ime and he large-scale coherence velociy in -dimensional space. B. Large-Scale Coherence Simulaions in -D The -dimensional VV link wih free space pah loss simplifies a very ineresing pracical scenario: highway communicaion as shown in Fig.. Reflecive pahs for example ground reflecions) are assumed o conribue primarily o mulipah and no pah loss []. Since we are adaping based on pah loss hey are no considered here. Moreover, adding complexiy o he channel model will lead o racabiliy issues, limiing he resuling sysem design inuiion. We use ) and ) o define he large-scale coherence ime and large-scale coherence velociy. The large-scale coherence boundary, where he large-scale coherence ime equals he large-scale coherence velociy, can be solved by evaluaing he quadraic equaions produced by ν c,τ c,δ,η)+,η) and τ c,ν c,,η),η) in erms of δ, and,, respecively. Examine he following highway scenario wih maximum link disance of km in free space: m) m/s mph) for [0, ], n) 0 m/s 6 mph) for [0, ), p0) 0, q0) 000, and η 0.. Figs. and show he large-scale coherence ime and large-scale coherence velociy conours, respecively. Fig. demonsraes ha largescale coherence ime is much larger han radiional coherence ime for he highway scenario. Figs. and lend considerable insigh ino he radeoff beween he feedback of pah loss informaion and he feedback of posiion/moion informaion. For any realizaion of and δ we can find wheher feedback

4 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. XX, MONTH 0 sec) Conour Boundary δ m/sec ) sec) a) Conour plo of τ c Fig.. The numbers on each line represen he values for each large-scale coherence velociy conour in m/s. The vehicle crossover poin for each realizaion of, is shown wih he fine doed line. For ime reference, he maximize acceleraion olerable o mainain large-scale channel coherence a is found on he conour ha inersecs, ). The conour boundary shows he inersecion of δ and ν c,,η) where δ is seleced such ha τ c, δ,η). Hence, values o he righ of he conour boundary show scenarios where posiion/moion informaion resuls in less feedback overhead han pah loss informaion. highway scenario is favorable when compared o he overhead incurred for he feedback of pah loss informaion. Mos imporanly, near he crossover poin, where he pah loss changes very rapidly, posiion/moion informaion is preferred for all realizable acceleraion scenarios δ m/sec ) b) Close up view of τ c conour plo Fig.. The numbers on each line in Fig. a) and Fig. b) represen he values for each large-scale coherence ime conour in seconds. The ime reference is only considered in he inerval [0,.] since. is he crossover ime under no acceleraion. We can see ha near he crossover poin he coherence ime decreases rapidly. This is a consequence of free space pah loss which is inversely proporional o vehicular disance squared. The dashed line represens he conour boundary. The region o he righ of he conour boundary represens scenarios where pah loss informaion resuls in less feedback overhead whereas he region o he lef of he conour boundary shows where posiion/moion informaion is preferred. of posiion/moion informaion is advised by observing he black doed line conour boundary). In Fig., realizaions of δ, o he lef of he conour boundary show acceleraion values and he associaed ime reference ) ha resul in less feedback overhead wih posiion/moion informaion han pah loss informaion. Similarly, in Fig., conour poins o he righ of he black doed line represens node acceleraion ha resuls in link adapaion wih less feedback overhead for posiion/moion informaion. Pracically speaking, in ypical driving scenarios, he maximum acceleraion is somewhere beween m/s. Highperformance vehicles achieve a maximum of around 8 m/s in racing condiions. Consequenly, for mos conceivable VV nework scenarios, he overhead incurred for feedback of posiion informaion o accomplish link adapaion in he C. Simulaion wih Highway Pah Loss Measuremens The -D coherence models and simulaions are imporan for insigh ino channel dynamics in he conex of posiion and moion informaion, however, hey are insufficien for creaing link adapaion algorihms in pracice due o he presence of refleced pahs, shadows pah blockages), and amospheric absorpion. For final validaion of posiion and moion informaion, link adapaion simulaions are compleed wih highway pah loss measuremens a. GHz as repored in []. These measuremens repor pah loss capured over 0 seconds on a highway in Sweden) beween wo vehicles raveling in opposie direcions a a relaive speed of 80 km/hr includes vehicle crossover), as recreaed in Figure. We model link adapaion in IEEE 80.p by assigning each ransmission one of he eigh modulaion and coding schemes ha provide 6- Mbps in 0 MHz specrum allocaions. We use he sensiiviy requiremens defined in he sandard Table 7- of []) o deermine if communicaion is successful which means ha he ransmier will selec he highes rae ha mees he sensiiviy requiremens). We will assume ha one node is designaed as he ransmier and he oher as he receiver wih pah loss given by []. The baseline link adapaion algorihm wih aperiodic feedback does no have posiion or moion informaion so i mus send back channel informaion whenever he channel becomes incoheren wih respec o he las feedback exchange. Aperiodic feedback is opimisic since raffic may be bursy, resuling in sale pah loss informaion a he receiver. This moivaes

5 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. XX, MONTH 0 may provide conrolled nonzero ouage for aperiodic and hybrid feedback sraegies. Resuls show ha posiion and moion informaion can subsanially reduce feedback wihou compromising daa rae excep when η close o due o inaccuracy of log-disance pah loss models in pracice). Noe ha acceleraion informaion is no needed o complee his sudy nor is previous knowledge of he ideal pah loss coefficien n was used for resuls in Table I and empirically we observed ha varying his parameer beween and did no significanly impac performance). Fig.. Pah loss reference curve) reproduced from [] for VV highway channel measuremens a. GHz. Pah loss depiced unil vehicle crossover for opposing vehicles raveling a a relaive velociy of 80 km/hr. The various forms of feedback allow he ransmier o mainain esimaes of he pah loss. The ransmier-prediced pah loss esimaes shown here hrough various feedback sraegies assume η 0.. Feedback Sraegy η 9 η 0.6 η 0.00 Aperiodic 7/.7 7/. /. Periodic 80/.8 /. 0/. Hybrid 7/6.0 8/. /.7 TABLE I x/y - x FEEDBACK EXCHANGES REQUIRED BY FEEDBACK STRATEGY, RESULTING IN AVERAGE RATE OF y MBPS IN IEEE 80.P LINK ADAPTATION SIMULATION WITH MEASURED PATH LOSS ON A HIGHWAY IN SWEDEN AT. GHZ FIRST 7. SECONDS SIMULATED, IMMEDIATELY BEFORE VEHICLE CROSSOVER) []. RESULTS ARE SHOWN IN TERMS OF THE THE LARGE-SCALE COHERENCE METRIC,, DB) WITH THE CONSTRAINT OF ZERO EMPIRICAL OUTAGE. link adapaion wih periodic feedback which is pessimisic since i sends back pah loss informaion a regular inervals regardless of how much pah loss esimaes have changed. To incorporae posiion and moion informaion, we canno use sraighforward feedback due o model and measuremen inconsisencies. Our soluion is a hybrid feedback proocol which sends back posiion, moion, and pah loss informaion. The pah loss informaion is required o re-iniialize he logdisance pah loss model for each feedback exchange. Feedback exchanges only occur during large-scale incoherency. To preven sale pah loss exchanges as in aperiodic feedback) we piggyback ransmier pah loss informaion wih he firs daa packe afer each feedback exchange. Table I shows ha, even in he presence of log-disance model inaccuracy, posiion and moion informaion can be leveraged o subsanially reduce feedback in VV largescale link adapaion wihou compromising performance. The ransmi power is se a 0 dbm o ensure ha all modes 6- Mbps in 0 MHz channels) are required for opimal rae adapaion. To provide zero ouage we add an η penaly facor o he pah loss esimae a he ransmier, which is used o selec he mode. Sraegically decreasing his penaly IV. CONCLUSION In his leer we considered he use of posiion/moion informaion in VV neworks. To his end we defined coherence as a funcion of ime and velociy change in pah loss models. Simulaions demonsrae he value of posiion/moion informaion o reduce feedback overhead. ACKNOWLEDGEMENTS The auhors would like o hank Seven W. Peers for valuable discussions ha led o his work as well as he anonymous reviewers who encouraged enhancemen of he simulaion resuls. REFERENCES [] D. Maolak, Channel modeling for vehicle-o-vehicle communicaions, IEEE Commun. Mag., vol. 6, no., pp. 76 8, May 008. [] A. Paier e al., Descripion of vehicle-o-vehicle and vehicle-oinfrasrucure radio channel measuremens a. GHz, in COST 00, 6h Managemen Commiee Meeing, Lille, France, Oc [] IEEE sandard for informaion echnology - par : Wireless LAN medium access conrol and physical layer specificaions, IEEE Sd , 007. [] J. Gozalvez and J. Dunlop, On he dynamics of link adapaion updaing periods for packe swiched sysems, Wireless Personal Commun., vol., no., pp. 7, 00. [] S. J. Lee, Trade-off beween frequency diversiy gain and frequencyselecive scheduling gain in OFDMA sysems wih spaial diversiy, IEEE Commun. Le., vol., no. 6, pp , June 007. [6] H. Touheed, A. Quddus, and R. 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