Preprint, August 5, 2018. 1 All-to-all Broacast for Vehicular Networks Base on Coe Slotte ALOHA Mikhail Ivanov, Frerik Brännström, Alexanre Graell i Amat, an Petar Popovski Department of Signals an Systems, Chalmers University of Technology, Gothenburg, Sween Department of Electronic Systems, Aalborg University, Aalborg, Denmark {mikhail.ivanov, frerik.brannstrom, alexanre.graell}@chalmers.se, petarp@es.aau.k arxiv:1501.03389v2 [cs.it] 26 Jan 2015 Abstract We propose an uncoorinate all-to-all broacast protocol for perioic messages in vehicular networks base on coe slotte ALOHA (CSA). Unlike classical CSA, each user acts as both transmitter an receiver in a half-uplex moe. As in CSA, each user transmits its packet several times. The halfuplex moe gives rise to an interesting esign trae-off: the more the user repeats its packet, the higher the probability that this packet is ecoe by other users, but the lower the probability for this user to ecoe packets from others. We compare the propose protocol with carrier sense multiple access with collision avoiance, currently aopte as a multiple access protocol for vehicular networks. The results show that the propose protocol greatly increases the number of users in the network that reliably communicate with each other. We also provie analytical tools to preict the performance of the propose protocol. I. INTRODUCTION Reliable vehicular communications (VCs) is presently one of the most challenging problems of communication engineering. Its eployment will enable numerous applications, such as intelligent transportation systems an autonomous riving, as well as improve traffic safety. VCs entails a number of challenges, such as high mobility networks with rapily changing topologies an a large number of users, poor channel quality, an strict reliability an elay requirements. These challenges require new ieas an esign at the physical layer (PHY) an the meium access control (MAC) layer. The current status of VCs is summarize in the stanar [1] an is usually referre to as 802.11p. The PHY an the MAC layer in 802.11p are base on the Wi-Fi protocol that works well for low mobility networks. In the context of VCs, the PHY is mainly criticize for not being able to cope with time-varying channels [2]. 802.11p uses carrier sense multiple access with collision avoiance (CSMA-CA) as the MAC protocol. It oes not require any coorination an is shown to work well for networks with a small number of users, large amounts of information to be transmitte at each user, an no elay constraints. Uner these conitions, CSMA- CA can provie large throughputs [3]. In vehicular a hoc networks (VANETs), however, the number of users is large, the amount of information to be transmitte is rather small, This research was supporte by the Sweish Research Council, Sween, uner Grant No. 2011-5950, in part by the Ericsson s Research Founation, Sween, uner Grant No. 556016-0680, in part by Chalmers Antenna Systems Excellence Center in the project Antenna Systems for V2X Communication, an in part by the Danish Council for Inepenent Research within the Sapere Aue Research Leaer program, Grant No. 11-105159. an there are har ealines for accessing the channel. In such scenarios, CSMA-CA fails to provie a reliable channel access. Furthermore, the high user mobility prohibits the use of acknowlegements in VANETs, an thereby methos for mitigating the hien terminal problem. The other uncoorinate MAC protocols use for VCs can be roughly ivie into two classes: i) the ones base on CSMA-CA, that try to improve its performance by ajusting the loa by means of power control [4] or transmission rate control [5]. However, they retain the rawbacks of the original CSMA-CA. ii) The secon class inclues selforganizing protocols preominantly base on time ivision multiple access (TDMA), which are avantageous for overloae networks [6], but cannot guarantee high reliability. These self-organizing algorithms require a learning phase, which increases the channel access elay; moreover, transmission errors uring this phase rener such protocols unusable. Recently, a novel uncoorinate MAC protocol, calle coe slotte ALOHA (CSA), has been propose for a unicast scenario [7], [8]. It uses the iea of the original slotte ALOHA [9] together with successive interference cancellation (SIC). The contening users introuce reunancy by encoing their messages into multiple packets, which are transmitte to a base station (BS) in ranomly chosen slots. The BS buffers the receive signal, ecoes the packets from the slots with no collision an attempts to reconstruct the packets in collision exploiting the introuce reunancy. The main ifference between CSMA-CA an CSA it that the former tries to avoi collisions, whereas the latter tries to exploit them. In this paper, we propose a novel MAC protocol for allto-all broacast in VANETs base on CSA, calle all-toall broacast CSA (B-CSA). We consier a scenario where users in the network perioically broacast messages to the neighboring users. Each user is equippe with a half-uplex transceiver, so that a user cannot receive packets in the slots it uses for transmission 1, which is the main ifference of the propose protocol with respect to the classical unicast CSA. This is moele as a packet erasure channel an it affects the esign an the performance analysis of CSA. Using the analytical tools from [10], we analyze the packet loss rate (PLR) performance of the propose B-CSA. Analytical results show goo agreement with simulation results for low to 1 If full-uplex communication is possible, the analysis of the all-to-all broacast scenario is ientical to that of the unicast scenario.
Preprint, August 5, 2018. 2 TABLE I: The PHY parameters. The values in the upper part are taken from [1]; the values in the lower part are erive. Parameter Variable Value Units Data rate r ata 6 Mbps PHY preamble t pream 40 µs CSMA slot uration t csma 13 µs AIFS time t aifs 58 µs Frame uration t frame 100 ms Guar interval t guar 5 µs Packet size pack 200 400 byte Packet uration t pack 312 576 µs Slot uration t slot 317 581 µs Number of slots n 315 172 meium channel loas. The results are further use to optimize the parameters of B-CSA. Finally, we show that B-CSA greatly outperforms CSMA-CA for meium to high channel loas. II. SYSTEM MODEL There are two types of packets in VCs, namely ecentralize environmental notification messages (DENMs) an cooperative awareness messages (CAMs). DENM packets are sent if requeste by a higher-layer application, e.g., in case of an emergency. On the other han, CAM packets are sent perioically every t frame secons. In this paper, we consier transmission of CAM packets. We assume that all packets have uration t pack, which epens on the packet size pack (in bytes), transmission rate r ata, an uration of the preamble ae to every packet t pream, i.e., t pack = t pream + pack /r ata. The parameters in this paper are taken from the PHY in [1] an are given in Table I. We consier a VANET where users are arbitrarily istribute on a 2-imensional plane as shown in Fig. 1. Every user has a circular transmission range, e.g., the circle in Fig. 1 shows the transmission range of user A. All users within this transmission range receive packets sent by user A. The transmission range may vary across users, hence, the set of users from which user A receives packets, enote by U, may be ifferent from the set of users within user A s transmission range. Without loss of generality, we assume that U consists of m 1 users. The users in U are calle the neighbors of user A. As an example, the neighbors of user A are marke with gray in Fig. 1. We assume that U remains unchange uring t frame. In this paper, we focus on the performance of a single user (user A in Fig. 1), also referre to as the receiver. From the network perspective, the performance of B-CSA epens only on the users in U. The rest of the users are ignore as user A cannot receive packets from them. A. All-to-all Broacast Coe Slotte ALOHA We assume that time is ivie into frames of uration t frame. Every user transmits one packet uring each frame. Frames are ivie into n = t frame /t slot slots each, where t slot = t pack +t guar an t guar is a guar interval that accounts for the propagation elay an timing inaccuracy. We assume that users are both frame an slot synchronize. This can be A Fig. 1: Network moel. Rectangles represent users. The circle shows the transmission range of user A. The users marke with gray are neighbors of user A. users A 1 2... m 1 1 2 3 4 5 6... n slots Fig. 2: Users transmissions in B-CSA system within one frame. Rectangles represent transmitte packets. Gray lines inicate the time slots in which user A cannot receive. achieve by means of, e.g., Global Positioning System (GPS), which provies an absolute time reference for all users. The transmission phase of the propose protocol is ientical to that of classical CSA [7], an is briefly escribe in the following. Every user maps its message to a PHY packet an then repeats it l times (l is a ranom number chosen base on a preefine istribution) in ranomly an uniformly chosen slots within one frame, as shown in Fig. 2. Such a user is calle a egree-l user. Every packet contains pointers to its copies, so that, once a packet is successfully ecoe, full information about the location of the copies is available. It is possible to analyze B-CSA uner iealize assumptions on the PHY presente in the following without specifying it explicitly 2. Unlike classical CSA, where a BS is the intene recipient of the messages, every user in B-CSA acts as a BS, i.e., a user buffers the receive signal whenever it is not transmitting. The receive signal buffere by user A in slot i is y i = j U i h i,j a j, (1) where a j is a packet of the jth user in U, h i,j is the channel coefficient, an U i U is the set of user A s neighbors that transmit in the ith slot. The ith slot is calle a singleton slot if it contains only one packet. If it contains more packets, we say that a collision occurs in the ith slot. First, user A ecoes the packets in singleton slots an obtains the location of their copies. Using ata-aie methos, the channel coefficients corresponing to the copies are then estimate. After subtracting the interference cause by the ientifie copies, ecoing procees until no further singleton slots are foun. 2 We use the PHY from [1] mainly to capture timing parameters of the system.
Preprint, August 5, 2018. 3 The performance of the system greatly epens on the istribution that users use to choose the egree l. The istribution is expresse in the form of a polynomial, q λ(x) = λ l x l, (2) l=0 where λ l is the probability of choosing egree l an q is the maximum egree. The performance parameters are efine as follows. The channel loa g = m/n shows how busy the meium aroun user A is. The average number of users that are not successfully ecoe by user A, terme unresolve users, is enote by w. As reliability is one of the most important requirements in VCs, we focus on the average PLR, p = w/(m 1), which is the probability of a user to be unresolve, i.e., the probability that its message is not successfully ecoe by user A. III. PERFORMANCE ANALYSIS The typical performance of CSA exhibits a threshol behavior, i.e., all users are successfully resolve if the channel loa is below a certain threshol value whenn. The threshol epens only on the egree istribution an is usually obtaine via ensity evolution [7]. In VANETs, however, n is rather small (see Table I), which causes an error floor in the PLR performance. For transmission over a packet erasure channel, it was shown in [10] that the error floor can be accurately preicte base on an inuce istribution observe by the receiver. As mentione earlier, in B-CSA, a user cannot receive in the slots it uses for transmission. This can be moele by means of a packet erasure channel. Therefore, the performance of B-CSA can be analyze using the framework in [10]. In this section, we briefly outline the analysis presente in [10] an aapt it to account for the broacast scenario. A. Inuce Distribution Assuming that user A chooses egree k, a egree-l user is perceive by user A as a egree- user if the egree-l user transmits in l slots that user A uses for its transmission. From user A s point of view, these l slots can be consiere erase, which occurs with probability ( )( n k k ( l ) / n l). Given the constraint 0 l k, the istribution perceive by user A, which we call the k-inuce istribution, λ (k) (x), can be written similarly to (2), where min{q,k+} λ (k) = l= ( n k )( k ) l ( n l) λ l (3) is the fraction of users of egree as observe by user A if it chooses egree k. It is easy to show that for any finite k, λ (k) l = λ l k,l when n, i.e., λ (k) (x) = λ(x) if the number of slots is large enough an q is finite. In this case, ensity evolution can be use to preict the performance of B-CSA in the waterfall region base on the original egree istributionλ(x). However, when the number of slots is small, the ifference between the original an the inuce istributions is significant, especially if k is large. This also suggests that epening on the chosen egree, user A has ifferent ecoing capabilities. On the other han, as shown in [10], users of ifferent egrees have ifferent protection, namely the higher the egree, the better the protection. We call this property ouble unequal error protection (DUEP). The rationale behin this property is that the chance of a user to be resolve by other users increases if the user transmits more, but at the same time the chance to resolve other users ecreases. B. Stopping Sets In this paper, we focus on the receiving aspect of DUEP, i.e., we characterize ifferent ecoing capabilities. The average PLR for a egree-k receiver can be efine as p (k) = 1 m 1 q =0 w (k), (4) where w (k) is the average number of unresolve inuce egree- users as observe by a egree-k receiver. For = 0, w (k) 0 = (m 1)λ (k) 0. For other egrees, we show how w(k) can be approximate in the following. Since user A chooses its egree at ranom accoring to λ(x), the average PLR p can then be foun by averaging (4) over the original egree istribution, i.e., q p = λ k p (k). (5) k=0 The only error source in the consiere moel is the socalle stopping sets. A stopping set is a set of users that cannot be resolve ue to an unfortunate choice of slots for transmission. For instance, if two egree-2 users transmit in the same two slots they cannot be resolve by any other user. We enote a stopping set by S an escribe it by a vector v(s) = [v 0 (S),v 1 (S),...,v q (S)], where v (S) is the number of egree- users in the stopping set S an v 0 (S) = 0. For the example above, v(s) = [0,0,2,0,...,0]. The probabilities of stopping sets can be accurately preicte using the inuce istribution in (3) an the inuce frame length n (k) = n k as follows. We enote the probability of a stopping set S to occur by ρ (k) (S). It can be approximate as [10] ρ (k) (S) α (k) (S)β (k) (S), (6) where β (k) (S) is the probability of the stopping set S to occur calculate uner the assumption that U consists of v (S) users of egree, = 1,...,q. There are, however, more users in U an this is accounte for by the coefficient α (k) (S), efine as the number of combinations to choose v (S) users out of all egree- users in U for = 1,...,q. α (k) (S) is [10] ( ( ) q m 1 α (k) (S) = v(s) 1! v(s) 1 =0 λ (k) ) v (S) v (S)!. (7) β (k) (S) is not known in general an nees to be foun for each stopping set iniviually base on λ (k) (x) an n (k).
Preprint, August 5, 2018. 4 PLR 10 2 10 3 10 4 10 5 k = 8 average k = 3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 g [user/slot] Fig. 3: PLR performance of B-CSA for λ(x) = 0.86x 3 + 0.14x 8 an n = 172. The soli lines show simulation results an the ashe lines show analytical approximations (4) an (5). Let A be the set of all possible stopping sets. Using a union boun argument, w (k) can be upperboune as w (k) v (S)ρ (k) (S) (S)α S A S Av (k) (S)β (k) (S). (8) Ientifying all stopping sets an calculating the corresponing β (k) (S) in a systematic way is not straightforwar in general. In practice, istributions with large fractions of egree-2 an egree-3 users are most commonly use since they provie a large threshol [7]. By running extensive simulations for such istributions, we etermine in [10] the set A 8 of eight stopping sets with their β (k) (S) given in [10, eq. (14) with n replace by n (k) ] that contribute the most to the error floor. Substituting (8) with the stopping sets in A 8 into (4) gives an approximation of the average PLR for a egree-k receiver. C. Numerical Results We use the analytical error floor approximation (5) to optimize the egree istribution for B-CSA with finite frame length. We constrain the istribution to only have egrees two, three, an eight to reuce the search space. Such istributions have been shown to have goo performance both in terms of error floor an threshol [7]. The istribution is optimize for the channel loa g = 0.5 by performing a gri search. The obtaine istributions are λ(x) = 0.86x 3 + 0.14x 8 for n = 172 an λ(x) = 0.87x 3 +0.13x 8 for n = 315. The analytical error floor preictions in (4) an (5) are shown with ashe lines in Fig. 3 for λ(x) = 0.86x 3 +0.14x 8 an n = 172. Simulation results are shown with soli lines. It can be seen from the figure that the higher the egree of the receiver, the worse the performance. The analytical results show goo agreement with the simulation results for low to meium channel loas. In Section IV-A we also show that the accuracy improves when n increases. IV. CARRIER SENSE MULTIPLE ACCESS Comparing B-CSA with CSMA-CA for the network escribe in Section I is not straightforwar for several reasons. First, time is not structure in slots in CSMA-CA an new efinitions of channel loa an PLR are therefore neee. This also hiners moeling users mobility. Secon, the behavior of each user in a CSMA-CA system epens on the behavior of its neighbors, whereas users in B-CSA act inepenently. Thus, to estimate the performance of an iniviual user in a CSMA-CA system, the entire network nees to be moele. Thir, the performance of CSMA-CA for the network in Fig. 1 is affecte by the hien terminal problem since acknowlegements are not use in VANETs. Hence, a proper moeling requires specification of: sensing threshol, path loss, transmitte power, ecoing moel with signal-tointerference-plus-noise, an actual network geometry. Instea, we introuce a simplifie system moel which represents the best-case scenario in terms of the performance of CSMA-CA. It is easy to implement an compare with B-CSA. We consier a network with m users inexe by j = 1,...,m, where every user is within all other users transmission range, i.e., no collision occurs ue to the hien terminal problem. This makes the consiere system moel favorable for CSMA-CA compare to the system moel in Section II. The set of users is enote by V. Time is enote by t. At the beginning of contention (t = 0), every user chooses a real ranom number τ j [0, t frame ), which represents the time when the jth user attempts to transmit its first packet invoking the CSMA-CA proceure from [6, Fig. 2(a)]. The contention winow size c is chosen from the set {2 u 1 : u is an interger}, t aifs is the sensing perio, an t csma is the uration of a backoff slot [6]. The values of these parameters are specifie in [1] (see Table I for the values use in simulations). At time instant τ j +(i 1)t frame, the jth user attempts to transmit its ith packet. If by this time the (i 1)th packet has not been transmitte, the packet is roppe. Each packet is transmitte at most once. The channel loa is efine as the ratio of the number of users m an t frame (expresse in slots) to match the efinition of the channel loa for B-CSA, i.e., g = m/(t frame /t slot ) = m/n. The PLR for user j is efine as { } E τ1,...,τ m i V e i i j p j =, (9) m 1 where e i {0,1,2} is the number of roppe an collie packets of the ith user over the time interval [t 0, t 0 +t frame ) an E x { } stans for the expectation over a ranom variable x. For estimating the performance, we introuce a time offset t 0 in orer to remove the transient in the beginning of contention. As the performance oes not epen on the particular user, without loss of generality, we choose user j at ranom. In Fig. 4, we show the performance of CSMA-CA for ifferent values of the contention winow size. We set t 0 = 2t frame for simulations. Larger values of c reuce the probability of a collision but increase the time require to access the channel: for values of c 2047 (u 11), lost packets are only cause by collisions, whereas for c = 8191 (u = 13), the PLR is
Preprint, August 5, 2018. 5 10 0 10 1 u = 13 10 0 10 1 n = 172 n = 315 PLR 10 2 u = 4 PLR 10 2 CSMA-CA B-CSA 10 3 u = 9 u = 11 10 3 10 4 10 4 10 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 g [user/slot] Fig. 4: PLR performance of CSMA-CA for 400 byte packets (n = 172) an ifferent values of c = 2 u 1. preominantly efine by roppe packets. It can be seen from Fig. 4 that the value c = 2047 (u = 11) provies goo performance for the entire range of channel loas. For u = 10 an u = 12 (not shown in the figure), the PLR performance is slightly worse than that of u = 11. We remark that the orer of the curves remains the same for shorter packets. c = 2047 (u = 11) is thus use later on for both packet sizes in Table I when comparing CSMA-CA with B-CSA. A. B-CSA vs CSMA Comparison The PLR performance of the two protocols is shown in Fig. 5 for n = 172 an n = 315. The soli an the ashotte lines show simulation results for B-CSA an CSMA- CA, respectively. The ashe lines show the PLR approximation (5). The first observation is that the performance of CSMA-CA egraes when n increases. This can be explaine by the fact that the sensing overhea grows with respect to the packet length when the packet length ecreases. On the other han, the performance of B-CSA improves when n grows large, asymptotically approaching the threshol (equal to 0.87 for the consiere istributions) performance preicte by ensity evolution. This gives an extra egree of freeom when esigning a B-CSA system, as increasing the banwith will ecrease the packet uration an, hence, increase the number of slots. We also remark that the accuracy of the analytical PLR approximation in (5) improves when n increases. It can be seen from Fig. 5 that B-CSA significantly outperforms CSMA-CA for meium to high channel loas. For example, B-CSA achieves a PLR of 10 3 at channel loas g = 0.68 an g = 0.73 forn = 172 an n = 315, respectively. CSMA-CA achieves the same reliability at g = 0.4 an g = 0.35 for n = 172 an n = 315, respectively, i.e., B-CSA can support approximately twice as many users as CSMA-CA for this reliability. For heavily loae networks (g > 0.74), CSMA-CA shows better performance. However, in this case both protocols provie a poor reliability (PLR of aroun 0.1), which is unacceptable in VANETs. 10 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 g [user/slot] Fig. 5: PLR comparison of optimize CSMA-CA an B-CSA for ifferent frame lengths. The soli an the ash-otte lines show the performance of B-CSA an CSMA-CA, respectively. The ashe lines show the analytical PLR approximation (5). Re an blue lines correspon to n = 172 an n = 315 slots, respectively. V. CONCLUSIONS AND FUTURE WORK The propose protocol can provie an uncoorinate MAC all-to-all broacast with preictable elay an high reliability at large channel loas, which makes it highly appealing for VCs. The propose B-CSA is a cross-layer protocol since the actual PHY greatly affects SIC performance. Therefore, a more realistic PHY nees to be consiere. One of the main challenges we foresee here is the channel estimation neee for SIC. Among other interesting research irections, we point out the unequal error protection property of B-CSA which can be potentially utilize to provie ifferent priorities to packets. REFERENCES [1] IEEE St. 802.11-2012, Part 11: Wireless LAN meium access control (MAC) an physical layer (PHY) specifications, Tech. Rep., Mar. 2012. [2] T. Zemen, L. Bernaó, N. Czink, an A. F. Molisch, Iterative timevariant channel estimation for 802.11p using generalize iscrete prolate spheroial sequences, IEEE Trans. Veh. Tech., vol. 61, no. 3, pp. 1222 1233, Mar. 2012. [3] G. Bianchi, Performance analysis of the IEEE 802.11 istribute coorination function, IEEE J. Sel. Areas Commun., vol. 18, no. 3, pp. 535 547, Mar. 2000. [4] M. Torrent-Moreno, J. Mittag, P. Santi, an H. Hartenstaein, Vehicleto-vehicle communication: Fair transmit power control for safety-critical information, IEEE Trans. Veh. Tech., vol. 58, no. 7, pp. 3684 3703, Sep. 2009. [5] C.-L. Huang, Y. Pourmohammai, R. Sengupta, an H. Krishnan, Intervehicle transmission rate control for cooperative active safety system, IEEE Trans. Intell. Transp. Syst., vol. 12, no. 3, pp. 645 658, Sep. 2011. [6] K. Bilstrup, E. Uhlemann, E. Ström, an U. Bilstrup, On the ability of the 802.11p MAC metho an STDMA to support real-time vehicle-tovehicle communication, EURASIP Journal on Wireless Commun. an Networking, vol. 2009, pp. 1 13, Apr. 2009. [7] G. Liva, Graph-base analysis an optimization of contention resolution iversity slotte ALOHA, IEEE Trans. Commun., vol. 59, no. 2, pp. 477 487, Feb. 2011. [8] C. Stefanovic an P. Popovski, ALOHA ranom access that operates as a rateless coe, IEEE Trans. Commun., vol. 61, no. 11, pp. 4653 4662, Nov. 2013.
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