Preprint,January27,2015. 1 All-to-all Broadcast for Vehicular Networks Based on Coded Slotted ALOHA Mikhail Ivanov, Fredrik Bra¨nnstro¨m, Alexandre Graell i Amat, and Petar Popovski§ Department of Signals and Systems, Chalmers University of Technology, Gothenburg, Sweden §Department of Electronic Systems, Aalborg University, Aalborg, Denmark {mikhail.ivanov, fredrik.brannstrom, alexandre.graell}@chalmers.se, [email protected] 5 1 Abstract—We propose an uncoordinated all-to-all broadcast and there are hard deadlines for accessing the channel. In 0 protocol for periodic messages in vehicular networks based on such scenarios, CSMA-CA fails to provide a reliable channel 2 coded slotted ALOHA (CSA). Unlike classical CSA, each user access. Furthermore, the high user mobility prohibits the use acts as both transmitter and receiver in a half-duplex mode. As n of acknowledgements in VANETs, and thereby methods for in CSA, each user transmits its packet several times. The half- a duplexmodegivesrisetoaninterestingdesigntrade-off:themore mitigating the hidden terminal problem. J the user repeats its packet, the higher the probability that this The other uncoordinated MAC protocols used for VCs can 6 packet is decoded by other users, but the lower the probability be roughly divided into two classes: i) the ones based on 2 for this user to decode packets from others. We compare the CSMA-CA, that try to improve its performance by adjust- proposedprotocolwithcarriersensemultipleaccesswithcollision ] ing the load by means of power control [4] or transmis- avoidance, currently adopted as a multiple access protocol for T vehicularnetworks. Theresultsshow that theproposedprotocol sion rate control [5]. However, they retain the drawbacks of I . greatlyincreasesthenumberofusersinthenetworkthatreliably the original CSMA-CA. ii) The second class includes self- s communicate with each other. We also provide analytical tools organizing protocols predominantly based on time division c to predict the performance of the proposed protocol. [ multiple access (TDMA), which are advantageous for over- loaded networks [6], but cannot guarantee high reliability. 2 These self-organizing algorithms require a learning phase, v I. INTRODUCTION 9 whichincreasesthechannelaccessdelay;moreover,transmis- Reliable vehicular communications (VCs) is presently one 8 sion errors during this phase render such protocols unusable. 3 of the most challenging problems of communication engi- Recently, a novel uncoordinated MAC protocol, called 3 neering. Its deployment will enable numerous applications, codedslottedALOHA(CSA),hasbeenproposedforaunicast 0 such as intelligent transportation systems and autonomous . scenario [7], [8]. It uses the idea of the original slotted 1 driving,aswellasimprovetrafficsafety.VCsentailsanumber ALOHA[9]togetherwithsuccessiveinterferencecancellation 0 of challenges, such as high mobility networks with rapidly (SIC). The contending users introduce redundancy by encod- 5 changingtopologiesandalargenumberofusers,poorchannel 1 ingtheirmessagesintomultiplepackets,whicharetransmitted quality, and strict reliability and delay requirements. These : toabasestation(BS)inrandomlychosenslots.TheBSbuffers v challenges require new ideas and design at the physical layer thereceivedsignal,decodesthepacketsfromtheslotswithno Xi (PHY) and the medium access control (MAC) layer. collision and attempts to reconstruct the packets in collision ThecurrentstatusofVCsissummarizedinthestandard[1] r exploiting the introduced redundancy. The main difference a and is usually referredto as 802.11p.The PHY and the MAC between CSMA-CA and CSA it that the formertries to avoid layer in 802.11p are based on the Wi-Fi protocol that works collisions, whereas the latter tries to exploit them. well for low mobility networks. In the context of VCs, the In this paper, we propose a novel MAC protocol for all- PHY is mainly criticized for not being able to cope with to-all broadcast in VANETs based on CSA, called all-to- time-varyingchannels[2].802.11pusescarriersensemultiple all broadcast CSA (B-CSA). We consider a scenario where access with collision avoidance (CSMA-CA) as the MAC users in the network periodically broadcast messages to the protocol. It does not require any coordination and is shown neighboring users. Each user is equipped with a half-duplex to work well for networks with a small number of users, transceiver, so that a user cannot receive packets in the slots large amounts of information to be transmitted at each user, it uses for transmission1, which is the main difference of the and no delay constraints. Under these conditions, CSMA- proposed protocol with respect to the classical unicast CSA. CA can provide large throughputs [3]. In vehicular ad hoc This is modeled as a packet erasure channel and it affects networks (VANETs), however, the number of users is large, the design and the performance analysis of CSA. Using the the amount of information to be transmitted is rather small, analytical tools from [10], we analyze the packet loss rate This research was supported by the Swedish Research Council, Sweden, (PLR)performanceoftheproposedB-CSA.Analyticalresults under Grant No.2011-5950, inpart bythe Ericsson’s Research Foundation, show good agreement with simulation results for low to Sweden,underGrantNo.556016-0680,inpartbyChalmersAntennaSystems ExcellenceCenterintheproject‘AntennaSystemsforV2XCommunication’, andinpartbytheDanishCouncilforIndependentResearchwithintheSapere 1If full-duplex communication is possible, the analysis of the all-to-all AudeResearch Leaderprogram,GrantNo.11-105159. broadcast scenarioisidentical tothatoftheunicast scenario. Preprint,January27,2015. 2 TABLE I: The PHY parameters. The values in the upper part are taken from [1]; the values in the lower part are derived. Parameter Variable Value Units Datarate rdata 6 Mbps PHYpreamble tpream 40 µs A CSMAslotduration tcsma 13 µs AIFStime taifs 58 µs Frameduration tframe 100 ms Fig. 1: Networkmodel.Rectanglesrepresentusers.Thecircleshows Guardinterval tguard 5 µs thetransmissionrangeofuserA.Theusersmarkedwithgray Packet size dpack 200 400 byte are neighbors of user A. Packet duration tpack 312 576 µs Slotduration tslot 317 581 µs Numberofslots n 315 172 A 1 s er 2 s mediumchannelloads.Theresultsarefurtherusedtooptimize u .. m.−1 theparametersofB-CSA.Finally,weshowthatB-CSAgreatly outperforms CSMA-CA for medium to high channel loads. 1 2 3 4 5 6 ... n slots II. SYSTEMMODEL Fig. 2: Users’ transmissions in B-CSA system within one frame. There are two types of packets in VCs, namely decen- Rectangles represent transmittedpackets. Graylinesindicate tralized environmental notification messages (DENMs) and the time slots in which user A cannot receive. cooperativeawareness messages (CAMs). DENM packets are sent if requested by a higher-layer application, e.g., in case of an emergency. On the other hand, CAM packets are sent achievedbymeansof,e.g.,GlobalPositioningSystem (GPS), periodically every t seconds. In this paper, we consider which provides an absolute time reference for all users. frame transmission of CAM packets. We assume that all packets Thetransmissionphaseoftheproposedprotocolisidentical havedurationt ,whichdependsonthepacketsize d (in to that of classical CSA [7], and is briefly described in the pack pack bytes), transmission rate r , and duration of the preamble following. Every user maps its message to a PHY packet and data added to every packet t , i.e., t = t +d /r . thenrepeatsitl times (l is a randomnumberchosenbased on pream pack pream pack data The parameters in this paper are taken from the PHY in [1] a predefined distribution) in randomly and uniformly chosen and are given in Table I. slotswithinoneframe,asshowninFig.2.Suchauseriscalled We consider a VANET where users are arbitrarily dis- adegree-luser.Everypacketcontainspointerstoitscopies,so tributed on a 2-dimensional plane as shown in Fig. 1. Every that, once a packet is successfully decoded, full information userhasacirculartransmissionrange,e.g.,thecircleinFig.1 about the location of the copies is available. It is possible shows the transmission range of user A. All users within to analyze B-CSA under idealized assumptions on the PHY this transmission range receive packets sent by user A. The presented in the following without specifying it explicitly2. transmission range may vary across users, hence, the set of Unlike classical CSA, where a BS is the intended recipient usersfromwhichuser A receivespackets,denotedbyU, may ofthemessages,everyuserinB-CSAactsasaBS,i.e.,auser be differentfromthe set of userswithin user A’s transmission buffersthereceivedsignalwheneveritisnottransmitting.The range . Without loss of generality, we assume that U consists received signal buffered by user A in slot i is ofm−1users.TheusersinU arecalledtheneighborsofuser A. As an example, the neighbors of user A are marked with yi = hi,jaj, (1) gray in Fig. 1. We assume that U remains unchanged during jX∈Ui t . In this paper, we focus on the performance of a single frame where a is a packet of the jth user in U, h is the channel user (user A in Fig. 1), also referred to as the receiver. From j i,j coefficient, and U ⊂ U is the set of user A’s neighbors that the network perspective, the performance of B-CSA depends i transmit in the ith slot. The ith slot is called a singleton slot only on the users in U. The rest of the users are ignored as if it contains only one packet. If it contains more packets, we user A cannot receive packets from them. say that a collision occurs in the ith slot. First, user A decodes the packets in singleton slots and A. All-to-all Broadcast Coded Slotted ALOHA obtainsthelocationoftheircopies.Usingdata-aidedmethods, the channel coefficients corresponding to the copies are then We assume that time is divided into frames of duration estimated. After subtracting the interference caused by the t . Every user transmits one packet during each frame. frame identifiedcopies, decodingproceedsuntilno furthersingleton Frames are divided into n = ⌊t /t ⌋ slots each, where frame slot slots are found. t =t +t and t is a guard interval that accounts slot pack guard guard for the propagation delay and timing inaccuracy. We assume 2We use the PHY from [1] mainly to capture timing parameters of the that users are both frame and slot synchronized. This can be system. Preprint,January27,2015. 3 The performanceof the system greatly dependson the dis- especially if k is large. This also suggests that depending on tributionthatusersusetochoosethedegreel.Thedistribution the chosen degree, user A has different decoding capabilities. is expressed in the form of a polynomial, Ontheotherhand,asshownin[10],usersofdifferentdegrees have different protection, namely the higher the degree, the q λ(x)= λxl, (2) better the protection. We call this property double unequal l Xl=0 errorprotection(DUEP).Therationalebehindthispropertyis thatthechanceofausertoberesolvedbyotherusersincreases where λ is the probability of choosing degree l and q is the l if the user transmits more, but at the same time the chance to maximum degree. resolve other users decreases. The performance parameters are defined as follows. The channelloadg =m/nshowshow“busy”themediumaround user A is. The average number of users that are not success- B. Stopping Sets fully decoded by user A, termed unresolved users, is denoted Inthispaper,wefocusonthereceivingaspectofDUEP,i.e., byw¯. Asreliabilityisoneofthemostimportantrequirements we characterize different decoding capabilities. The average in VCs, we focusontheaveragePLR, p¯=w¯/(m−1),which PLR for a degree-k receiver can be defined as istheprobabilityofausertobeunresolved,i.e.,theprobability that its message is not successfully decoded by user A. q 1 p¯(k) = w¯(k), (4) m−1 d III. PERFORMANCE ANALYSIS Xd=0 ThetypicalperformanceofCSAexhibitsathresholdbehav- where w¯(k) is the average number of unresolved induced d ior, i.e., all users are successfully resolved if the channelload degree-dusers as observedby a degree-k receiver. For d=0, isbelowacertainthresholdvaluewhenn→∞.Thethreshold w¯(k) = (m−1)λ(k). For other degrees, we show how w¯(k) 0 0 d dependsonlyonthedegreedistributionandisusuallyobtained can be approximated in the following. Since user A chooses via density evolution [7]. In VANETs, however, n is rather its degree at random according to λ(x), the average PLR p¯ small (see Table I), which causes an error floor in the PLR can then be found by averaging (4) over the original degree performance. distribution, i.e., For transmission over a packet erasure channel, it was q shown in [10] that the error floor can be accurately predicted p¯= λkp¯(k). (5) based on an induced distribution observedby the receiver. As kX=0 mentionedearlier,inB-CSA,ausercannotreceiveintheslots The only error source in the considered model is the so- it uses for transmission. This can be modeled by means of a called stopping sets. A stopping set is a set of users that packeterasurechannel.Therefore,theperformanceof B-CSA cannot be resolved due to an unfortunate choice of slots for can be analyzed using the framework in [10]. In this section, transmission. For instance, if two degree-2 users transmit in we briefly outline the analysis presented in [10] and adapt it the same two slots they cannotbe resolvedby any other user. to account for the broadcast scenario. We denote a stopping set by S and describe it by a vector v(S)=[v (S),v (S),...,v (S)],wherev (S)isthenumber 0 1 q d A. Induced Distribution of degree-d users in the stopping set S and v (S) = 0. For 0 the example above, v(S)=[0,0,2,0,...,0]. Assuming that user A chooses degree k, a degree-l user is The probabilities of stopping sets can be accurately pre- perceived by user A as a degree-d user if the degree-l user dicted using the induced distribution in (3) and the induced transmits in l−d slots that user A uses for its transmission. FromuserA’spointofview,thesel−dslotscanbeconsidered frame length n(k) = n − k as follows. We denote the erased, which occurswith probability n−k k / n . Given probability of a stopping set S to occur by ρ(k)(S). It can d l−d l be approximated as [10] the constraint 0 ≤ l −d ≤ k, the di(cid:0)stribu(cid:1)t(cid:0)ion (cid:1)pe(cid:0)rce(cid:1)ived by userA, whichwe callthe k-induceddistribution,λ(k)(x), can ρ(k)(S)≈α(k)(S)β(k)(S), (6) be written similarly to (2), where whereβ(k)(S)istheprobabilityofthestoppingsetS tooccur min{q,k+d} n−k k λd(k) = (cid:0) d (cid:1)n(cid:0)l−d(cid:1)λl (3) calculatedundertheassumptionthatU consistsofvd(S)users Xl=d l of degree d, d = 1,...,q. There are, however, more users in (cid:0) (cid:1) U andthisisaccountedforbythecoefficientα(k)(S), defined is the fraction of users of degree d as observed by user A if as the number of combinations to choose v (S) users out of it chooses degree k. d It is easy to show that for any finite k, λ(k) = λ ∀k,l all degree-d users in U for d=1,...,q. α(k)(S) is [10] l l when n → ∞, i.e., λ(k)(x) = λ(x) if the number of slots is q λ(k) vd(S) large enough and q is finite. In this case, density evolution α(k)(S)=kv(S)k ! m−1 (cid:16) d (cid:17) . (7) can be used to predict the performance of B-CSA in the 1 (cid:18)kv(S)k (cid:19) v (S)! 1 dY=0 d waterfallregionbasedontheoriginaldegreedistributionλ(x). However,whenthenumberofslotsissmall,thedifferencebe- β(k)(S) is not known in general and needs to be found for tween the originaland the induced distributionsis significant, each stopping set individually based on λ(k)(x) and n(k). Preprint,January27,2015. 4 10−2 IV. CARRIER SENSEMULTIPLEACCESS Comparing B-CSA with CSMA-CA for the network de- scribed in Section I is not straightforwardfor severalreasons. First, time is not structured in slots in CSMA-CA and new 10−3 definitions of channel load and PLR are therefore needed. This also hinders modeling users’ mobility. Second, the be- R havior of each user in a CSMA-CA system depends on the L P behavior of its neighbors, whereas users in B-CSA act inde- k = 8 pendently.Thus, to estimate the performanceof an individual 10−4 average ubseermiondealedC.STMhAir-dC,Athesypsetermfo,rmthaenceentoifreCnSeMtwAo-rCkAnefeodrsthtoe k = 3 network in Fig. 1 is affected by the hidden terminal problem since acknowledgements are not used in VANETs. Hence, a proper modeling requires specification of: sensing threshold, 10−5 path loss, transmitted power, decoding model with signal-to- 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 g[user/slot] interference-plus-noise,and actualnetworkgeometry.Instead, Fig. 3: PLR performance of B-CSA for λ(x) = 0.86x3 +0.14x8 we introduce a simplified system model which represents the and n = 172. The solid lines show simulation results and best-case scenarioin termsofthe performanceof CSMA-CA. thedashed linesshow analytical approximations (4) and (5). It is easy to implement and compare with B-CSA. We consider a network with m users indexed by j = 1,...,m, where every user is within all other users’ trans- LetAbethesetofallpossiblestoppingsets.Usingaunion mission range, i.e., no collision occurs due to the hidden bound argument, w¯(k) can be upperboundedas terminal problem. This makes the considered system model d favorable for CSMA-CA compared to the system model w¯(k) ≤ v (S)ρ(k)(S)≈ v (S)α(k)(S)β(k)(S). (8) in Section II. The set of users is denoted by V. Time is d d d SX∈A SX∈A denoted by t. At the beginning of contention (t = 0), every user chooses a real random number τ ∈ [0, t ), which j frame Identifyingallstoppingsetsandcalculatingthecorresponding represents the time when the jth user attempts to transmit β(k)(S) in a systematic way is notstraightforwardin general. its first packet invoking the CSMA-CA procedure from [6, In practice, distributions with large fractions of degree-2 and Fig. 2(a)]. The contention window size c is chosen from the degree-3 users are most commonly used since they provide set {2u−1:u is an interger}, t is the sensing period, and aifs a large threshold [7]. By running extensive simulations for t is the duration of a backoff slot [6]. The values of these csma such distributions, we determined in [10] the set A8 of eight parametersarespecifiedin[1](seeTableIforthevaluesused stopping sets with their β(k)(S) given in [10, eq. (14) with n in simulations). At time instant τ +(i−1)t , the jth user j frame replaced by n(k)] that contribute the most to the error floor. attemptstotransmitits ithpacket.Ifbythistimethe (i−1)th Substituting (8) with the stoppingsets in A8 into (4) gives an packet has not been transmitted, the packet is dropped. Each approximation of the average PLR for a degree-k receiver. packet is transmitted at most once. The channel load is defined as the ratio of the number of users m and t (expressed in slots) to match the definition frame C. Numerical Results of the channel load for B-CSA, i.e., g = m/(t /t ) = frame slot m/n. The PLR for user j is defined as We use the analytical error floor approximation (5) to optimize the degree distribution for B-CSA with finite frame E e length.Weconstrainthedistributiontoonlyhavedegreestwo, τ1,...,τm(cid:26) ii∈6=Vj i(cid:27) p = P , (9) j three, and eightto reducethe search space. Such distributions m−1 have been shown to have good performance both in terms where e ∈ {0,1,2} is the number of dropped and collided i of error floor and threshold [7]. The distribution is optimized packets of the ith user over the time interval [t , t +t ) 0 0 frame for the channel load g = 0.5 by performing a grid search. and E {·} stands for the expectationover a random variable x The obtained distributions are λ(x) = 0.86x3 +0.14x8 for x. For estimating the performance,we introducea time offset n=172 and λ(x)=0.87x3+0.13x8 for n=315. t in order to remove the transient in the beginning of con- 0 The analytical error floor predictions in (4) and (5) are tention.As theperformancedoesnotdependonthe particular shownwithdashedlinesinFig.3forλ(x)=0.86x3+0.14x8 user, without loss of generality, we choose user j at random. and n = 172. Simulation results are shown with solid lines. InFig.4,weshowtheperformanceofCSMA-CAfordiffer- It can be seen from the figure that the higher the degree of ent values of the contention window size. We set t =2t 0 frame thereceiver,theworse theperformance.The analyticalresults for simulations. Largervalues of c reduce the probabilityof a show good agreement with the simulation results for low to collision but increase the time required to access the channel: mediumchannelloads.InSectionIV-Awe also showthatthe for values of c≤2047 (u≤11), lost packets are only caused accuracy improves when n increases. by collisions, whereas for c = 8191 (u = 13), the PLR is Preprint,January27,2015. 5 100 100 n=172 n=315 10−1 10−1 u = 13 10−2 4 10−2 = R u R L L CSMA-CA B-CSA P P 10−3 10−3 = 9 = 11 u u 10−4 10−4 10−5 10−5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 g[user/slot] g[user/slot] Fig. 4: PLR performance of CSMA-CA for 400 byte packets (n= Fig. 5: PLRcomparisonofoptimizedCSMA-CAandB-CSAfordif- 172) and different values of c=2u−1 . ferentframelengths.Thesolidandthedash-dottedlinesshow theperformanceofB-CSAandCSMA-CA,respectively.The dashedlinesshowtheanalyticalPLRapproximation(5).Red and blue lines correspond to n = 172 and n = 315 slots, predominantly defined by dropped packets. It can be seen respectively. from Fig. 4 that the value c = 2047 (u = 11) provides good performancefortheentirerangeofchannelloads.Foru=10 andu=12(notshowninthefigure),thePLRperformanceis V. CONCLUSIONS AND FUTUREWORK slightly worse than that of u=11. We remark that the order The proposed protocolcan provide an uncoordinatedMAC of the curves remains the same for shorter packets. c=2047 all-to-all broadcast with predictable delay and high reliability (u=11) is thus used later on for both packetsizes in Table I at large channel loads, which makes it highly appealing when comparing CSMA-CA with B-CSA. for VCs. The proposedB-CSA is a cross-layer protocolsince the actual PHY greatly affects SIC performance.Therefore, a A. B-CSA vs CSMA Comparison more realistic PHY needs to be considered. One of the main The PLR performance of the two protocols is shown challenges we foresee here is the channel estimation needed in Fig. 5 for n = 172 and n = 315. The solid and the dash- forSIC.Amongotherinterestingresearchdirections,wepoint dotted lines show simulation results for B-CSA and CSMA- outtheunequalerrorprotectionpropertyofB-CSAwhichcan CA, respectively. The dashed lines show the PLR approxi- bepotentiallyutilizedtoprovidedifferentprioritiestopackets. mation (5). The first observation is that the performance of CSMA-CA degradeswhenn increases.Thiscan be explained REFERENCES bythefactthatthesensingoverheadgrowswithrespecttothe [1] IEEEStd.802.11-2012,“Part11:WirelessLANmediumaccesscontrol packet length when the packet length decreases. On the other (MAC)andphysicallayer(PHY)specifications,”Tech.Rep.,Mar.2012. hand, the performance of B-CSA improves when n grows [2] T. Zemen, L. Bernado´, N. Czink, and A. F. 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