All-to-all Broadcast for Vehicular Networks Based on Coded Slotted ALOHA

0.13 MB·English

by  Mikhail Ivanov

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. Molisch, “Iterative time-
large,asymptoticallyapproachingthethreshold(equalto 0.87 variantchannelestimationfor802.11pusinggeneralizeddiscreteprolate
spheroidalsequences,”IEEETrans.Veh.Tech.,vol.61,no.3,pp.1222–
for the considered distributions) performance predicted by
1233,Mar.2012.
densityevolution.Thisgivesanextradegreeoffreedomwhen [3] G. Bianchi, “Performance analysis of the IEEE 802.11 distributed
designing a B-CSA system, as increasing the bandwidth will coordination function,” IEEE J. Sel. Areas Commun., vol. 18, no. 3,
pp.535–547, Mar.2000.
decrease the packet duration and, hence, increase the number
[4] M.Torrent-Moreno, J.Mittag, P.Santi, and H.Hartenstaein, “Vehicle-
of slots. We also remark that the accuracy of the analytical to-vehiclecommunication:Fairtransmitpowercontrolforsafety-critical
PLR approximation in (5) improves when n increases. information,”IEEETrans.Veh.Tech.,vol.58,no.7,pp.3684–3703,Sep.
2009.
It can be seen from Fig. 5 that B-CSA significantly out-
[5] C.-L. Huang, Y. Pourmohammadi, R. Sengupta, and H. Krishnan,
performs CSMA-CA for medium to high channel loads. For “Intervehicle transmission rate control for cooperative active safety
example, B-CSA achieves a PLR of 10−3 at channel loads system,”IEEETrans.Intell. Transp.Syst.,vol.12,no.3,pp.645–658,
Sep.2011.
g =0.68andg =0.73forn=172andn=315,respectively.
[6] K.Bilstrup,E.Uhlemann,E.Stro¨m,andU.Bilstrup,“Ontheabilityof
CSMA-CA achieves the same reliability at g = 0.4 and the802.11pMACmethodandSTDMAtosupportreal-timevehicle-to-
g =0.35 for n=172 and n=315, respectively, i.e., B-CSA vehicle communication,” EURASIPJournal on Wireless Commun. and
Networking, vol.2009,pp.1–13,Apr.2009.
cansupportapproximatelytwice asmanyusersasCSMA-CA
[7] G.Liva,“Graph-basedanalysisandoptimizationofcontentionresolution
for this reliability. For heavily loaded networks (g > 0.74), diversity slotted ALOHA,” IEEE Trans. Commun., vol. 59, no. 2, pp.
CSMA-CA shows better performance. However, in this case 477–487,Feb.2011.
[8] C.StefanovicandP.Popovski,“ALOHArandomaccessthatoperatesas
both protocolsprovidea poor reliability (PLR of around0.1),
aratelesscode,”IEEETrans.Commun.,vol.61,no.11,pp.4653–4662,
which is unacceptable in VANETs. Nov.2013.
Preprint,January27,2015. 6
[9] L. G. Roberts, “ALOHA packet system with and without slot and
capture,” SIGCOMMComput. Commun.Rev.,vol.5,no.2,pp.28–42,
Apr.1975.
[10] M. Ivanov, F. Bra¨nnstro¨m, A. Graell i Amat, and P. Popovski,
“Error floor analysis of coded slotted ALOHA over packet erasure
channels,” to appear in IEEE Commun. Lett. [Online]. Available:
http://arxiv.org/pdf/1412.2888v1.pdf