Medium access control for 60 GHz outdoor mesh networks with highly directional links

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1 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE INFOCOM 29 poceedings. Medium access contol fo 6 GHz outdoo mesh netwoks with highly diectional links R. Mudumbai, S. Singh and U. Madhow Dept. of Electical and Compute Engineeing Univesity of Califonia, Santa Babaa, C 936 [aghu,sumit,madhow]@ece.ucsb.edu bstact We investigate an achitectue fo multi-gigabit outdoo mesh netwoks opeating in the unlicensed 6 GHz millimete (mm) wave band. In this band, the use of naow beams is essential fo attaining the equied link anges in ode to ovecome the highe path loss at mm wave caie fequencies. Howeve, highly diectional links make standad MC methods fo intefeence management, such as caie sense multiple access, which ely on neighboing nodes heaing each othe, become inapplicable. In this pape, we study the extent to which we can educe, o even dispense with, intefeence management, by exploiting the eduction in intefeence due to the naow beamwidths and the oxygen absoption chaacteistic of the 6 GHz band. We povide a pobabilistic analysis of the intefeence incued due to uncoodinated tansmissions, and show that, fo the paametes consideed, the links in the netwok can be thought of as pseudo-wied. That is, intefeence can essentially be ignoed in MC design, and the challenge is to schedule half-duplex tansmissions in the face of the deafness esulting fom highly diectional links. We povide peliminay simulation esults to validate ou appoach. I. INTRODUCTION Recent pogess in RFIC design in the mm-wave band has spued significant ecent inteest in 6 GHz netwoks fo indoo multimedia applications, including standadization effots within the IEEE c (WPN) and 82. (WLN) task goups. Howeve, use of the 6 GHz band is also vey attactive fo outdoo mesh netwoks with multigigabit links at elatively shot anges (of the ode of metes). Such mm wave mesh netwoks can seve as a high-speed backhaul needed fo boadband connectivity whee thee is limited wied o optical infastuctue. In this pape, we take the fist steps towads defining an achitectue fo such outdoo mm wave netwoks, accounting fo the unique chaacteistics of mm wave communication. The fundamental distinguishing featue of the 6 GHz band elative to, say, the 2.4 GHz WiFi band, is the ode of magnitude diffeence in wavelength. The fee space popagation loss of electomagnetic waves scales as λ 2, and (fixing the antenna apetues at each end), the diectivity scales as λ whee λ is 2 the caie wavelength. Thus, the oveall path-loss vaies as λ ; 2 This wok was suppoted by the National Science Foundation unde gants CNS-52335, ECS and CNS-83254, by the Office fo Naval Reseach unde gant N , and by the Institute fo Collaboative Biotechnologies unde gant DD9-3-D-4 fom the US my Reseach Office. this coesponds to a net gain of 28 db in going fom 2.4 GHz to 6 GHz. This is fotunate: given the RF powe constaints of low-cost silicon implementations, employing highly diective antennas at both tansmitte and eceive is essential fo the ange/ate combinations we wish to achieve. The small wavelength in the mm-wave band allows the design of nodes with a compact fom facto (compaable to a WiFi access point) that can achieve diectivities of aound 25 dbi quite easily. The use of electonic beamsteeing with highly diectional links opens up a numbe of questions in netwok design, and we focus on the most fundamental of these in this pape: medium access contol (MC). If neighbos can no longe hea each othe, potocols such as CSM/C, o vaiants theeof designed fo the mildly diectional links possible at lowe caie fequencies, simply do not wok. t the same time, the highly diectional tansmissions lead to vastly educed intefeence between neaby tansmissions, which aises the inteesting possibility that high level of intefeence management povided by conventional MC potocols may not be needed fo netwoks in the mm-wave band. In this pape, we use a statistical analysis of intefeence to show that, fo the antenna diectivities of inteest to us, even uncoodinated tansmission fo diffeent tansmit-eceive pais leads to small collision pobabilities. This motivates a pseudowied abstaction to seve as a fist ode appoximation of mm-wave wieless links, and povide insights to guide MC design. Unde this abstaction, tansmissions on diffeent links do not intefee with each othe. Howeve, unlike a tuly wied node, mm-wave netwok nodes have a half-duplex constaint, i.e. they can only send o eceive at a given time. This allows MC designes to concentate on developing lightweight potocols whose pupose is to schedule in a deaf netwok, subject to half-duplex constaints. Related Wok. Diectional netwoking fo cellula, boadband, and WiFi-based multihop wieless netwoks opeating ove lowe fequency bands has been extensively studied in pevious wok [] [3]. In [4], [5], it was shown that diectional tansmission impoves the connectivity of ad-hoc netwoks by establishing long-ange links even without using smat beamsteeing (i.e. using andomly diected beams). Most of the diectional netwoking poposals fo multihop wieless netwoks employ a sepaate omni-diectional mode fo potocol opeation in ode to avoid the coodination issues that aise /9/$ IEEE 287

2 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE INFOCOM 29 poceedings. fom being fully diectional (such as neighbo discovey and deafness). This dual-mode opeation is not appopiate fo the mm wave mesh netwoks, whee vey high diectionality is equied simply to achieve a eliable high data ate link. Futhemoe, the diectivity achievable at the lowe fequency bands is much smalle, so that the focus of MC design in pevious wok on diectional netwoking is still on intefeence management. To the best of ou knowledge, the pesent pape is the fist to conside mm wave mesh netwoks, and show quantitatively that the vey high antenna diectivities lead to vey low levels of intefeence even with uncoodinated tansmissions. II. NETWORK MODEL Fo ou intefeence analysis, we conside a Poisson distibution of nodes ove a lage aea with a density ρ s.if we now andomly select a subset of N T nodes as tansmittes, the distibution of tansmittes on the aea of inteest is also Poisson, with density ρ = ρ s p t whee p t is the pobability that the selected node is tansmitting. Fo a lage deployment aea, wehaveρ NT. We assume that all the nodes have aleady completed a netwok discovey pocedue, and thus know how to stee thei antennas to each of thei neighbos. We also assume that each node can communicate with at most one othe node at any given time slot. In othe wods, we do not ely on advanced physical laye capabilities such as spatial multiplexing o multi-use detection. If multiple neighbos ae tansmitting to the same eceive, at most one of them can be successfully decoded by the eceive. ll othe tansmissions in the netwok act as intefeence fo the eceive. The amount of intefeence depends on the location of the intefee elative to the eceive, and the adiation pattens of the antennas at the eceive and the intefee. We assume that a tansmission is successfully decoded by the eceive if the total signal to intefeence and noise atio (SINR) is above a given theshold, say β =5dB (which allows fo uncoded QPSK modulation at a BER of < 9 ). Othewise, a collision occus and the tansmission is lost. The standad Fiis tansmission equation gives the eceived powe as a function of ange as α P R () =P T G R G T () 4π whee P T is the tansmitted powe, G R, G T ae the gains of the eceive and tansmit antennas espectively, λ is the wavelength, and α is the attenuation facto due to absoption in the medium. Fo a mm wave link at 6 GHz, λ =5mm and α can be as high as 5 db/km. Since lowe absoption ates leads to moe intefeence, we use the consevative value of α =db/km in ou numeical esults. Conside the link budget fo a 2 Gbps Line of Sight (LoS) link at a ange of R = m, which povides a baseline fo the est of the pape. ssuming QPSK signaling, a desied SNR of 5 db, oxygen absoption loss of db/km, and mw tansmit powe, we need antenna gains of about 24 dbi at both tansmitte and eceive in ode to povide a db link magin.. Diectional ntenna Model Diectional antennas ae chaacteized by thei patten functions that measue the powe gain G(φ, θ) ove the spheical azimuthal and elevation angle coodinates φ, θ. We assume that all nodes ae on the same hoizontal plane, and do not conside vaiation in beam patten ove the elevation angle θ, and wok with the nomalized 2-dimensional patten g(φ) G(φ, ) G max whee G max = max G(φ, ) (2) φ The azimuthal beamwidth of the antenna is then given by Δφ = π φ= π g(φ)dφ (3) One idealization that poves to be vey useful fo ou intefeence analysis is that of a sectoized flat-top diectional antenna, which has unit gain within its beamwidth and zeo gain outside. Moe pecisely, {, φ Δφ g(φ) = 2, (4), othewise While the flat-top antenna is an useful idealization, pactical diectional antenna gains have a moe complex dependence on the azimuth angle. Fo instance, sidelobes in the gain function could cause significant intefeence even in diections fa fom the antenna boesight. While exact computation of the gain functions of pactical mm-wave antenna aays can be messy (because aay elements usually ae diectional themselves), we can obtain useful models with some simplifying assumptions. In paticula, we obtain the following gain function fo an N element linea aay in which each individual flat-top element has beamwidth Δφ : sin( N 2 π sin φ) Δφ N, φ g(φ) ={ sin( 2 π sin φ) 2,, othewise ideal "flat top" antenna linea aay with 2 flat top elements Fig.. Gain patten fo a flat-top antenna and a linea aay of flat-top elements. Fig. shows the beam pattens fo a naow beam flat-top antenna and a 2-element linea aay of boad-beam flat-top elements. The beamwidth in both cases (as defined as in (3)) is the same, 2. III. INTERFERENCE NLYSIS We now investigate the validity of a pseudo-wied model fo the links in a mm wave mesh netwok, by analyzing the pobability of packet failue fo uncoodinated tansmissions. Conside the tansmitte-eceive pai shown in Fig. 2; without 33 (5) 2872

3 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE INFOCOM 29 poceedings. loss of geneality, assume that the eceive is located at the oigin and is communicating with the tansmitte located along the X-axis, at a distance less than o equal to the efeence link distance R while undegoing intefeence fom othe concuent tansmissions. The othe N T intefeing tansmittes ae andomly placed ove the aea, and ae tansmitting to eceives located at andomly chosen oientations. Fig. 2. Tansmitte Intefee φ2 φ Receive intended eceive fo intefee The geomety of intefeence with diectional antennas. In thei well-known wok on wieless netwok capacity [6], Gupta et al intoduce two diffeent models of intefeence. In the potocol model, a packet loss occus if and only if thee is some intefeing node whose signal at the eceive exceeds a given theshold. In the physical model, a packet loss occus when the total intefeence fom all nodes exceeds a given theshold. The models ae summaized as follows: { ( P maxk P k β P ), (potocol model) P(collision) P ( N T k= P k β P ), (physical model) whee P k is the powe at the eceive of the signal fom the k th intefee. Since k P k max k P k, it follows that the P(collision) fo the physical model is lowe-bounded by the coesponding value fo the potocol model. We fist deive an expession fo the collision pobability unde the potocol model fo the flat-top antenna, and extend the deivation to moe geneal diectional antennas, and then to the physical model. Ou deivation is simila to the analysis of localization eo in [7].. Potocol model with ideal flat-top antennas Fo the ideal flat-top antenna, only intefees located within the boesight of the eceive can cause a collision. Futhe, a tansmitting node within this secto causes intefeence only if the eceive is within its boesight, which has pobability q = Δφ (since the potentially intefeing tansmitte is sending to a andomly chosen eceive). Let R i be the intefeence ange i.e. the maximum distance an intefee can be fom the eceive and still cause a collision. Using (), the signal and intefeence powes ae evaluated as: P R P = P T G 2 αr max (6) 4πR P intef = P T G 2 αr i max (7) 4πR i whee we used G T = G R = G max fo the antenna gains assuming that the intefee and the eceive ae within each othe s boesights. We set P R = P : when the tansmitte and eceive ae steeed towads each othe, this is the signal powe designed fo at the efeence distance R. Using the collision condition P intef β P, we can ewite (7) as: Ri 2 R 2 e α(ri R) = β (8) which detemines R i as a function of the SINR theshold β. The numbe of potentially intefeing tansmittes is theefoe a Poisson andom vaiable with mean ρ i, whee i = 2 ΔφR2 i. The pobability of any of these actually causing a collision is q, so that the numbe of intefees N i causing a collision is also Poisson, with mean qμ i. The pobability of a collision is theefoe given by P(collision) P(N i > ) = e qμi (9) = e (Δφ)2 4π ρr2 i e βρr 2 c, whee c (Δφ)2 4π e α(ri R) () Fo a beamwidth of Δφ =, β =5dB and ρr 2 = (coesponding to oughly πρr 2 3 tansmitting nodes within communication ange of each eceive), () gives an estimate of P(collision) 3.7%, which suggests that acceptable MC pefomance may be possible with minimal coodination fo intefeence management. B. Potocol model with geneal diectional antennas We now genealize () to a geneal diectional antenna. We fist compute the pobability of collision due to a single intefee at a fixed location at a distance, and angle φ elative to the eceive as shown in Fig. 2. The angle φ 2 epesents the diection of the intefee s beam elative to the eceive. We model φ, φ 2 as independent and unifomly distibuted ove ( π, π], given the andom oientation of the intefeing tansmitte and its beam elative to the desied eceive. Signal powe is still given by (6), and the intefeence powe is: P intef = P T G 2 α maxg(φ )g(φ 2 ) () 4π whee we used G R = G max g(φ ) and G T = G max g(φ 2 ). Using (6), we can ewite () as ( R α( R P intef = P g(φ )g(φ 2 ) ) (2) Theefoe the pobability p c (, φ ) that this intefee would cause a collision is p c (, φ ) P ( P intef β P ) ( =P g(φ )g(φ 2 ) ( ) ) 2e α( R ) β R = π ( g(φ )g(φ 2 ) ( ) α( R ) dφ 2 (3) β R π whee (.) is the indicato function that takes the value when its agument is tue, and othewise. 2873

4 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE INFOCOM 29 poceedings. Conside now an intefee placed at andom within a lage aea. Then the pobability of collision ˆp c can be obtained by aveaging (3) ove all possible positions of the intefee: ˆp c = p c (, φ ) d dφ = βr2 whee we set ˆ β (,φ ) ˆ,φ ( ) p c βrˆ, φ ˆdˆ dφ (4) R, i.e. ˆ is the distance of the intefee nomalized to the efeence link distance R and intefeence theshold β. Using (3) in (4), we get ˆp c = βr2 ˆ,φ π φ 2= π ( )) (g(φ )g(φ 2 ) ˆ 2 e βˆ αr dφ 2 ˆdˆ dφ (5) We now let the aea become infinitely lage and cove the whole plane. Fom (2), g(φ ) and g(φ 2 ) ae uppe-bounded by. We theefoe only need to conside ˆ e αr 2 in (5), because the agument of the indicato function (.) in (5) is always false outside this ange. Then we have C. Physical Model In the potocol model, only nodes located within a bounded distance fom the eceive ae capable of causing a collision. On the othe hand, fo the physical model, intefeing signals fom a lage numbe of fa-away tansmittes could, in pinciple, sum up at a desied eceive to cause packet failue. It tuns out that taditional uppe bound techniques such as Chenoff and Makov-type bounds do not wok well when chaacteizing sum intefeence ove a lage aea. We theefoe use a hybid appoach, using an analytical Makov uppe bound to chaacteize the effect of fa-away intefees, and chaacteizing the sum intefeence fom intefees within a bounded egion though Monte-Calo simulations. Let k be the distance of the k th intefee fom the eceive. We wite the total intefeence powe as the sum of two contibutions P nea and P fa, defined as: P nea P k, and P fa P k (9) {k: k R th } {k: k >R th } whee R th is a suitable lage distance, say R th = 4R. Then we have P(collision) = P ( P nea + P fa β P ) P ( P fa β ΔP ) +P ( P nea β (P ΔP ) ) c ˆp c = βr 2, whee (6) αr c e 2 π ( )) (g(φ )g(φ 2 ) ˆ 2 e βˆ αr ˆ= φ,φ 2= π dφ 2 ˆdˆ dφ (7) We now conside N T =ρ intefees placed andomly in the aea. Each intefee has a collision pobability ˆp c with the eceive given by (6). collision occus if at least one of these intefees cause a collision, and its pobability is given by P(collision) = ( ˆp c ) NT ( = lim βr 2 c = e βρr2 c (8) Since (8) has an identical fom to (), the collision pobability depends on the antenna patten only though c. Thus, fo the potocol model, we can estict attention to an equivalent flat-top model whose beamwidth can be calculated fom () and (6) as Δφ eq 4π c e α 2 (Ri R). Fo instance, a linea 24-element linea aay of flat-top antennas of secto size 2 and half-wavelength spacing has an equivalent flat-top beamwidth of about 5 fo α =db/km. Fig. 3 shows the equivalent flat-top beamwidths fo linea aays of diffeent numbes of flat-top elements and half-wavelength spacing; as seen fom the figue, the flat-top beamwidth is numeically close to the algebaic beamwidth given by (3) and does not vay much with the SINR theshold β. ) ρ E[P fa] ΔP/β +P( P nea β (P ΔP ) ) (2) whee we used the Makov Inequality to bound the fist tem in (2). The expectation in the fist tem is eadily evaluated as: E[P fa ] ρ π ˆ=R th φ,φ 2= π = (Δφ)2 P (ρr)e 2 αr (Δφ)2 P g(φ )g(φ 2 ) R2 2 e α( R) =R th P (ρr) 2 e α(r R th) αr th e α d dφ dφ 2 d (2) D. pseudo-wied abstaction Figs. 4 and 5 show the collision pobabilities fo ideal flattop aays and fo linea aays with ρr 2 =and α = db/km and beamwidth= and diffeent values of the SINR theshold β. The pobabilities wee computed analytically fom (8) and also fom (2) whee the second tem in (2) was evaluated by the use of Monte-Calo simulations and the fist tem fom (2) with R th =4R and ΔP = P 3 db. We obseve that when the desied SINR β inceases beyond about 5 db, the pobability of collision appoaches %. Howeve, fo the paametes coesponding to the efeence link budget descibed in Section II, the collision pobabilities ae vey small (less than 4%). Futhemoe, in this highly diectional egime, the pobability of collision unde the physical model does not appeciably diffe fom the potocol 2874

5 This full text pape was pee eviewed at the diection of IEEE Communications Society subject matte expets fo publication in the IEEE INFOCOM 29 poceedings. equivalent "flat top" beamwidth (degees) ggegate netwok thoughput (Mbps) azimuthal beamwidth (degees) β= db β=5 db β=2 db Fig. 3. Flat-top beamwidth P(collision) Slotted loha (p etx =.).5..5 analytical potocol model Monte Calo potocol model Monte Calo physical model SINR theshold β (db) Flat-top an- Fig. 4. tenna Pe-flow ate (Mbps) Fig. 6. ggegate netwok thoughput vesus pe-flow ate. F(thoughput) P(collision) Monte Calo potocol model Monte Calo physical model analytical potocol model SINR theshold β (db) Fig nodes 5 nodes Pe flow thoughput (Mbps) Linea aay. Fig. 7. Pe-flow thoughput empiical CDF vesus node density. model. This indicates that we may not need to woy about fa-away intefees o the details of antenna beam pattens (using the notion of the equivalent flat-top beamwidth). We conclude that the MC designe can use the following pseudo-wied abstaction: as a stating point: () Half-duplex constaint. Each node can eithe tansmit o eceive at any given time but not both. (2) No intefeence. Tansmissions between two distinct pai of nodes ae unlikely to intefee with each othe, and can be lagely ignoed in MC design. IV. MC SIMULTIONS To veify the pseudowied abstaction, we simulate a naive slotted loha potocol (pio studies on slotted loha with diectional communication include [8] [], but ou goal is to examine the elative effects of intefeence and deafness on pefomance). We note that fa bette pefomance can be obtained using moe sophisticated MC designs; this is a topic of ongoing eseach to be epoted in late publications. Simulation set-up: We conside andom netwok topologies with 25 o 5 nodes spead ove a 5m x5m flat teain. Evey node initiates one constant bit ate (CBR) flow to each of its neighbos. Wheneve a node has a new packet to tansmit, it beamfoms towads the diection of the intended eceive and tansmits the packet in the next slot. If the node does not eceive an CK, it attempts to etansmit the packet with a pobability p etx ove the next slots. node etuns to the unbacklogged state afte evey successful packet tansmission. We conside a sectoized antenna design with each secto coveed by an aay of high-gain hon elements (e.g., a linea aay of fou hon elements of diectivity 8dBi each achieves the total diectivity of 24dBi, with the hoizontal secto-span of 2 degees.) We use the QualNet Netwok Simulato [], modifying the QualNet PHY and ntenna modules to model popagation in the mm-wave band and ou link budget design. Fig. 6 shows (fo 25 nodes) the aggegate netwok thoughput vesus netwok load, with p etx =.. The thoughput is significantly highe than with omnidiectional loha. Fig. 7 plots the empiical cumulative distibution function of the pe-flow thoughput fo slotted loha fo an input pe-flow ate of 3Mbps fo 25 and 5 node andom topologies ove a fixed teain. Clealy, naive loha does not achieve anywhee nea fai esouce allocation among flows. The aveage thoughput pe flow deceases with node density: having moe neighbos makes tansmit-eceive coodination moe difficult, and inceases intefeence. Howeve, packet losses due to failed coodination ae an ode of magnitude highe than those due to intefeence: the factions of failed eceptions elative to the total eceived packets because of intefeence and failed coodination ae 2.2% and 35.7%, espectively, fo 25 nodes, and 5.6% and 47.2% fo 5 nodes. V. CONCLUSIONS We have pointed out how the unique physical laye chaacteistics of mm wave links impact MC design. Ou intefeence analysis famewok enables a quantitative evaluation of when we can model highly diective links as pseudo-wied. Fo the diectivities typical of mm wave nodes with compact fom factos, the pseudo-wied model is indeed appopiate, which motivates a adically diffeent appoach to MC design. Rathe than focusing on intefeence management as in conventional MC design, we must now devise scheduling mechanisms that addess deafness. REFERENCES [] R. R. Choudhuy, X. Yang, R. Ramanathan, and N. H. Vaidya, On designing mac potocols fo wieless netwoks using diectional antennas, IEEE Tans. Mob. Comput., vol. 5, no. 5, pp , 26. [2] R. Ramanathan, J. Redi, C. Santivanez, D. Wiggins, and S. Polit, d hoc netwoking with diectional antennas: a complete system solution, IEEE J. Sel. eas Commun., vol. 23, no. 3, pp , Mach 25. [3] T. Koakis, G. Jakllai, and L. Tassiulas, Cd-mac: potocol fo full exploitation of diectional antennas in ad hoc wieless netwoks, IEEE Tans. Mob. Comput., vol. 7, no. 2, pp , Feb. 28. [4] C. Bettstette, C. Hatmann, and C. Mose, How does andomized beamfoming impove the connectivity of ad hoc netwoks? 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