contention resolution diversity slotted aloha (crdsa): an

1408 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 4, APRIL 2007

Contention Resolution Diversity Slotted ALOHA(CRDSA): An Enhanced Random Access Scheme

for Satellite Access Packet NetworksEnrico Casini, Riccardo De Gaudenzi, Senior Member, IEEE, and Oscar del Rio Herrero

Abstract— In this paper a new multiple access scheme dubbedContention Resolution Diversity Slotted Aloha (CRDSA) is intro-duced and its performance and implementation are thoroughlyanalyzed. The scheme combines diversity transmission of databursts with efficient interference cancellation techniques. It isshown that CRDSA largely outperforms the classical SlottedAloha (SA) technique in terms of throughput under equal packetloss ratio conditions (e.g. 17-fold improvement at Packet LossRatio = 2 · 10−2). CRDSA allows to boost the performance ofrandom access (RA) channels in the return link of interactivesatellite networks, making RA very efficient and providinglow latency for the transmission of small size sparse packets.Implementation-wise it is shown that the CRDSA techniquecan be easily integrated in systems equipped with digital burstdemodulators.

Index Terms— Access control, interference suppression, mul-tiaccess communication, satellite communication, time divisionmultiaccess.

I. INTRODUCTION

DESPITE having been proposed more than 30 years ago,Slotted Aloha (SA) [1], [2] and its slightly enhanced

version named Diversity Slotted Aloha (DSA) [3] are todaywidely used in satellite networks for initial terminal access orshort packet transmissions over a shared medium. The currentsatellite standards for interactive satellite broadband networkslike the Digital Video Broadcasting (DVB) Return Channel viaSatellite (DVB-RCS) [4] and the Telecommunication IndustryAssociation (TIA) IP over Satellite (IPoS) [5] provide thecapability to transmit small packets through a SA Random Ac-cess (RA) contention channel. In particular, the IPoS standardexploits the DSA protocol to enhance the RA channel capabil-ities. The satellite standards also include a capacity reservationmechanism, Demand Assignment Multiple Access (DAMA)[6], for longer packets transmission or for terminals offering amedium to high level of traffic aggregation. However, DAMAresponse time can be too long for the transmission of shortbursts, which is frequent in consumer type of terminals [7].The family of Carrier Sense Multiple Access (CSMA) [8]protocols cannot be used for satellite networks because their

Manuscript received July 10, 2005; revised December 5, 2005, April 30,2006, and August 3, 2006; accepted August 10, 2006. The associate editorcoordinating the review of this paper and approving it for publication was V.Leung. This work was supported by the European Space Agency.

The authors are with the European Space Agency, European Spaceand Technology Center, ESTEC, Keplerlaan 1, 2200 AG, Noordwjik, TheNetherlands (e-mail: [email protected]; [email protected];[email protected]).

Digital Object Identifier 10.1109/TWC.2007.05528.

large propagation latency (250 ms for a geostationary satellite)prevents the exploitation of the carrier sensing mechanism.

Moving towards consumer type of interactive satellite ter-minals (ST), the amount of traffic aggregation at the ST willlargely decrease and consequently the RA channel utilizationpotential will increase. In fact, although SA represents today awell established Random Access technique for TDMA satellitenetworks doubling the maximum throughput compared to thepure Aloha protocol [9], its utilization is typically limitedto initial login, capacity request or Medium Access Control(MAC) signalling packets. This is because in practice SAworks with very moderate normalized average loading (e.g. 2-5%) to ensure acceptable packets transmission delay and lossprobability [10]. DSA provides better delay and throughputperformance than SA under very moderate loading condi-tions by transmitting twice the same packet in a differentTDMA slot, or a different frequency and time slot in caseof Multi-Frequency TDMA (MF-TDMA) [3]. However, thethroughput difference between Aloha and Slotted Aloha orDiversity Slotted Aloha is limited and quite poor in absoluteterms. Another possible improvement of SA is the so calledSelective Reject Aloha (SRE) protocol [11], [12]. Its mainclaimed advantage lies in the SRE capability to achievethroughput performance similar to the SA without the needfor STs network synchronization. SRE exploits message sub-packetization jointly with selective reject ARQ retransmissionfor partial packet overlaps occurring in practice avoiding theneed for network synchronization. This advantage is howevermitigated by the need for extra overhead in the packets.It is therefore pivotal to enhance the satellite RA channelperformance in terms of throughput and delay with minimumimpact on the existing satellite standards, currently based onMF-TDMA access scheme. The novel Contention ResolutionDiversity Slotted Aloha (CRDSA) scheme described in thepresent paper represents an improved version of the wellknown SA and DSA schemes. Similarly to DSA, the CRDSAprotocol generates two replicas of the same burst (in thefollowing we will call burst the physical layer packet) atrandom time within a frame instead of only once as in SA.While the driver for DSA is to slightly enhance the SAperformance by increasing the probability of packet successfultransmission at the expense of increased RA load, CRDSA inaddition is designed in a way to resolve most of the DSApacket contentions. Burst collisions are cleared up througha simple yet effective iterative Interference Cancellation (IC)

1536-1276/07$25.00 c© 2007 IEEE

CASINI et al.: CONTENTION RESOLUTION DIVERSITY SLOTTED ALOHA (CRDSA) 1409

approach that uses frame composition information from thereplica bursts. The main CRDSA advantages lie in the im-proved packet loss ratio and reduced packet delivery delayperformance versus channel load jointly with a much higheroperational throughput compared to SA and DSA.

II. SYSTEM ASSUMPTIONS

As stated in Section I, we consider here the return linkof a satellite access network (i.e. link from satellite terminalto the gateway). Although the CRDSA application is notrestricted to satellite networks, it appears to be the mostnatural application of this scheme. For simplicity we assumea bent-pipe satellite payload in which users are connectedthrough the satellite to one gateway providing ground networkaccess. Findings reported in the following sections can alsobe applied to the case of regenerative systems. In this case,the inbound link demodulator will be located on-board thesatellite. The various STs will share satellite inbound resourcesaccording to the selected access scheme. Conventional Multi-Frequency TDMA (MF-TDMA) will be considered, althoughfor simplicity the following analysis will be focused on onesingle carrier. STs once registered in the network will keepTDMA slot synchronization through procedures such as theone described in [13] or in [5] with a slot timing random errorthat we assumed bounded by τmax = NRA

guardTs, where Ts isthe TDMA symbol duration, NRA

guard represents the TDMA slotguard expressed in symbols and Rs = 1/Ts is the ST baudrate. STs transmitted power can be optionally controlled by apower control mechanism based on a closed loop algorithm.

III. PROPOSED RANDOM ACCESS SCHEME

The proposed TDMA frame structure for the RA schemeis shown in Fig. 1. Each RA frame is composed of MRA

slots.A terminal can transmit at most one MAC packet per RAframe. In fact, the terminal will physically send two copiesof the same MAC packet (also called "twins" bursts) withexactly the same preamble and payload information bits intwo randomly selected slots within the same RA frame (seeFig. 1). The payload shall also contain signalling informationconcerning the slot position of the corresponding twin burstwithin the frame. Each burst signalling information points toits twin location and vice versa. It is known that sendingthe same packet twice slightly improves the probability oftransmission success (i.e. no collision) for small MAC loads[3]. The CRDSA scheme key novelty is that the recoveredinformation from a successful packet is exploited to cancelthe interference that its twin may generate on another TDMAslot. This approach is iterated to recover most of the framepackets that were initially lost due to collision(s). In theexample provided in Fig. 1, packet 2 cannot be initiallyrecovered as both twins have suffered a collision in slot 1and slot 4 of the frame. However, one copy of packet 3 (inslot 5) has been successfully recovered and its informationcan be used to cancel the interference caused by packet 3in slot 4. Then packet 2 can be recovered in slot 4, afterremoving the interference generated by packet 3. Removingpacket 2 in slot 1 allows to recover packet 1 so that alsopacket 6 can be decoded in slot M. This heuristic explanation

PK 2 PK 3 PK 4

PK 1

PK 2

PK 1

PK 4

RA frame (TF seconds)

Nslot.TS

M slots perRA frame

PK 5 PK 5

PK 6

PK 6

PK 3

Fig. 1. TDMA frame structure for the Random Access channel.

clearly shows the pivotal role of IC jointly with DSA andtwin location signalling for effective interference resolutionin CRDSA. In the following sections, the CRDSA processingwill be generalized, detailed and formalized.

A. RA Channel Description

As described in the previous section, each RA frame iscomposed by a fixed amount of slots MRA

slots. Each TDMAslot of duration NRA

slot symbols can allocate one RA burstcomposed of NRA

pre acquisition preamble symbols, followed byNRA

pay payload symbols. The guard-time is required in practiceto compensate for the incoming TDMA burst timing errors.We will assume that NRA

guard guard symbols are allocated inthe slot so that NRA

slot = NRAguard + NRA

pre + NRApay . The RA

frame duration in symbols then corresponds to NRAframe =

NRAslot MRA

slots and TF = NRAframe Ts. Let us now describe the

signals characterizing the RA channel behavior. We refer toa generic RA frame, thus for notation simplicity we drop thedependency on the frame index. We also represent discretesignals samples at symbol distance and we assume for notationsimplicity without loss of generality that relative STs burstdelays are occurring in integer multiples of the symbol perioditself. Let’s now consider the generic discrete burst signalsamples array s[i, n] generated by ST # i in slot # n. s[i, n]is composed by a preamble sub-array spre[i], a payload sub-array spay[i, n] and an empty guard time sub-array sguard sothat:

s[i, n] =√

PTx[i]

NRAslot︷︸︸︷

[spre[i], spay[i, n], sguard], (1)

spre[i] =[c1[i], c2[i] . . . cNRA

pre[i]

], (2)

sguard =

NRAguard︷︸︸︷

[0, 0, . . .0] (3)

spay[i, n] =1√2

[dp,1[i, n] + jdq,1[i, n] . . .

. . . dp,NRApay

[i, n] + jdq,NRApay

[i, n]]

(4)

where cl[i] is the l-th symbol of the preamble binary (±1)BPSK modulated sequence (in the more general case thepreamble can also be QPSK modulated) and dp,l[i, n] anddq,l[i, n] are the l-th in-phase and quadrature binary (±1)payload symbols, respectively. The payload dependency on theslot n is due to the twin burst signalling information relation tothe current burst location. Assuming that the delay, amplitudeand phase of the received signal at the gateway remainsconstant over a TDMA slot, the received signal samples can


be written as:

r[n] =NST∑i=1

δ[i, n]L[i, n]s[i, n]z−D[i,n]

· exp {j (φ[i, n] + Δω[i, n] t[n])} + w[n] (5)

where NST represents the total number of registered STs,δ[i, n] is 1 if the i-th terminal is active in slot # n and0 otherwise, L[i, n] < 1 represents the signal attenuation,0 ≤ D[i, n] ≤ NRA

guard is the differential TDMA ST slot delayin symbols, z−D[i,n] is the delay operator shifting towards theright the array s[i, n] by D[i, n] positions (symbols), φ[i, n]and Δω[i, n] represent the carrier phase and frequency offsetrespectively, t[n] is the time corresponding to the start ofslot n and w[n] is a complex array of NRA

slot elements eachrepresenting a circular symmetric white Gaussian noise withvariance σ2

w. We also define the received preamble for user #i in slot # n as the following sub-array derived from r[n]:

rpre[n, i] =[rD[i,n]+1, rD[i,n]+2, . . . rD[i,n]+NRA

pre

]. (6)

In a similar way we introduce the received burst payload sub-array as:

rpay[n, i] =[rD[i,n]+NRA

pre +1, rD[i,n]+NRApre +2, . . .

. . . rD[i,n]+NRApre +NRA

pay

]. (7)

For our analysis we will assume that the power of the STburst received in slot # n from user # i is given by PRx[i, n] =L2[i, n]PTx[i]. PRx[i, n] is modelled by a lognormal r.v. whichis characterized by a mean power PRx[i] and lognormallydistributed with standard deviation in dB σPRx[i]. We alsodefine the received burst signal amplitude at the gateway asARx[i, n] =

√PRx[i, n] = L[i, n]

√PTx[i]. The lognormal

received power distribution well approximates the combinedeffects of the time variant atmospheric propagation, open looppower control errors (if applicable), ST EIRP and satellitereceive antenna gain variations. The number of packets presentin slot # n corresponds to N [n] =

∑NSTi=1 δ[i, n].

B. Burst Preamble Issues

As we have seen in Section III, compared to knownsolutions the performance boost of the CRDSA protocol isachieved thanks to the implementation on the gateway burstdemodulator of a contention resolution capability. In fact, ifone of the twin bursts transmitted in the frame is successfullydecoded, the information about the replica burst location al-lows resolving the possible generated collisions by exploitinginterference cancellation (IC) techniques. IC techniques havebeen largely investigated for Code Division Multiple Access(CDMA) [14] but, at the authors knowledge, have never beenproposed in a TDMA SA context. One of the main issues inapplying IC techniques to TDMA SA is related to the needfor accurate channel estimation for the burst where collision(s)occur. In fact, collisions in a (satellite) TDMA multiple accesschannel are typically destructive. This is particularly true insatellite networks whereby the near-far effect is typically verylimited.

Contention resolution is achieved in CRDSA by meansof IC which requires good channel estimation for collidingburst(s) removal. As detailed in Section III-C, while carrierfrequency, amplitude and timing estimation for IC can bederived from the twin "clean" burst, carrier phase has to beestimated on the slot where collision(s) occurs. This is becausethe phase in practical broadband systems is time variant alsofrom slot to slot. This key problem has been solved hereby exploiting the burst preamble which is now individually"signed" by a pseudo-random binary sequence spre randomlyselected among the available code family by each active STfor each burst in each frame. Both frame replicas (twins) ofthe same burst use the same preamble code. This approachdoes not require a centralized preamble code assignment thusallowing to maintain the random access nature of the proposedscheme. In this way the preamble can be used for carrier phaseestimation also in case of multiple collisions which normallyare destructive for channel estimation and payload decoding.The preamble "signature" sequence is randomly selected outof a set belonging to a known family of size SPR. The familyof signature sequences of length NRA

pre shall provide goodauto and cross-correlation properties and having a family sizecomparable to the preamble length i.e. SPR � NRA

pre . Due tothe TDMA slots random timing offset, cross-correlation withcolliding bursts will also involve the first symbols of the pay-load. It is important to note that despite using a pseudo-randomsequence, the proposed CRDSA scheme significantly differsfrom a code-time two-dimensional Aloha scheme (e.g. SpreadAloha). CRDSA is basically a TDMA access scheme thatuses the information from the successfully decoded packetsto cancel the interference their replicas may generate on otherslots. We are able to cancel the interference because we knowthe data symbols of the interference from the successfullydecoded packets. In CRDSA, a pseudo-random sequence hasbeen applied only to the preamble (and not the payload datafield) for the solely purpose of deriving the carrier phase infor-mation of the un-clean burst. In a code-time two-dimensionalAloha scheme such as Spread Aloha, packets are sent onlyonce (no replicas are sent) and a spreading code is appliedover the whole packet (preamble and payload) with a certainspreading factor. It is important to observe that as the preamblesequences are randomly selected by the ST modulator froma finite family of SPR codes, there is a non zero probabilityof reusing the same preamble sequence within the same slotfrom one or more STs simultaneously transmitting a burst.However, due to the good off-peak autocorrelation propertyof the preamble sequence, the event will be catastrophic onlywhen the two ST bursts reusing the same preamble sequenceare arriving with an absolute differential delay of less than1 symbol. Assuming that the differential delay among STsis uniformly distributed between [0, Dmax] the probabilityof preamble collision in slot n can be computed as1 (seeAppendix I):

Ppre−coll(G) =G·MRA

slots−1∑i=1

Pint(i| G)

1In Section V-B it is shown that the preamble collision probability istypically lower than MAC packet loss ratio.


·⎡⎣ i∑

j=1

(i

j

)· pj · (1 − p)i−j

⎤⎦

=G·MRA

slots−1∑i=1

Pint(i| G) · [1 − (1 − p)i]

(8)

where G is the normalized MAC load measured in packetsper slot, G ·MRA

slots is the MAC load measured in packets perRA frame (assumed to be an integer), p is the probability thatthe same sequence and differential delay of the useful burstare chosen by an interfering burst (i.e. p = 1/ [SPR · Dmax])and Pint(i| G) is the probability that i interfering packets arepresent in the same slot n (see Appendix II). The normal-ized MAC load G does not take into account the replicas;this normalization has been chosen in order to facilitatecomparison with other access schemes (e.g. SA). Insteadthe physical channel load takes into account the CRDSAphysical layer burst replicas, therefore a normalized MACload G=0.5 corresponds to a physical channel load of 1 inCRDSA. It is remarked that for CRDSA, (G · MRA

slots) alsorepresents the maximum number of physical packets that canbe present over one slot as both copies of the same MACpacket cannot be sent over the same slot. It is important toobserve that with the proposed CRDSA scheme, the gatewayTDMA demodulator is used in a "conventional" manner i.e.it successfully operates when there is a clean burst. In thissituation the TDMA demodulator is capable to recover thetiming and carrier frequency offset due to the offset caused bySTs relative synchronization errors. The key differences is thatfor the same RA frame the burst demodulator is used Nmax

iter

times due to the proposed successive cancellation algorithmsthat allows to increase the throughput. This iterative burstdemodulator exploitation is made possible by the fact thatthe input frame complex signal samples are initially stored toallow for successive burst "cleaning". This process is describedin the following section.

C. Interference Cancellation Algorithm

As stated in Section IV-B, the CRDSA burst demodulatorwill store in memory the baseband samples corresponding toa full RA frame duration in order to perform an iterativedecoding process. The CRDSA demodulator iteration counteris set initially to Niter = 1. At each iteration, the demodulatorwill perform the following steps:1. Demodulation and decoding of clean bursts: By cleanbursts we mean those bursts for which the signal, noise andinterference level allow to achieve preamble recognition andpayload decoding (e.g. packet 3 in slot 5 in Fig. 1).(a) In this step the gateway burst demodulator shall search inparallel for each slot of the full frame for all the SPR possibleburst preambles. This can be efficiently achieved by imple-menting a bank of preamble sequence acquisition units similarto the one used in CDMA packet networks [15]. Typicallythe preamble time search region is limited to the guard timeperiod around the nominal preamble location in each frameslot. Once the presence of one or more preamble sequences arerecognized in the slot by the multi preamble searcher, the burstdemodulator will estimate, as for a conventional one, the burst

channel parameters (clock timing, carrier frequency and phase)and attempt to decode the payload content. If the preambleis detected and the burst payload Code Redundancy Check(CRC) verification is successfully passed, then the recoveredburst is declared as "clean". At this point the operation ofa conventional burst (D)SA demodulator will terminate. Weassume that there are Nrecov(Niter) bursts recovered at thecurrent iteration.(b) When a burst is successfully decoded it can be fullyregenerated at complex baseband level by re-encoding andmodulating the decoded useful bits multiplexed with thecurrent burst slot location signalling bits. In the twin burstregeneration the slot nr where the "replica" of the burst wastransmitted (e.g. packet 3 in slot 4 in Fig. 1) is derived fromthe burst payload signaling information bits. Furthermore,the acquisition preamble binary signature sequence and itstiming are extracted from the burst demodulator preamble codecorrelator and timing estimation unit respectively.(c) The twin burst signalling information is protected by thesame FEC of the useful payload bits thus it is correctlyrecovered when the CRC check is positive. Detected cleanburst(s) twin(s) location within the frame is stored and usedfor next step jointly with their amplitude and clock informationderived from the clean burst detection. The phase informationextracted from the clean burst cannot be used for the twin burstbeing the carrier phase typically uncorrelated from burst-to-burst because of the local oscillator instabilities.2. Contention Resolution Algorithms: Following the previousstep, the CRDSA demodulator will now process the slotswhere the replica burst of the "clean" bursts were transmittedand which have not been already detected in the previousstep (i.e. step 1-(a)) of the current iteration (e.g. packet 3in slot 4 in Fig. 1). So the demodulator will now operate onthe slots where collision(s) occurred (i.e. whereby more thanone burst were simultaneously transmitted and destructivelyinteracting). The CRDSA algorithm aims at post-processingthe stored frame samples to resolve contention in some of theslots where collisions occurred.

Let us assume that in the current frame and it-eration Niter, the set of bursts identified by indexq = [q1, q2, . . . qNrecov(Niter)]

2 corresponding to STs i =[i1, i2, . . . iNrecov(Niter)] have been successfully decoded inslots n = [n1, n2, . . . nNrecov(Niter)]. We also assume that thereplicas of bursts q are located (according to clean packetsignaling information) in slots nr = [nr

1, nr2, . . . n

rNrecov(Niter)

]belonging to the same frame.(a) We assume that the successfully detected clean burstsq from STs i in slots n provides an accurate estimate ofthe signal amplitude ARx[ik, nk], k = 1, 2, . . .Nrecov(Niter)and of the angular carrier frequency offset Δω[ik, nk], k =1, 2, . . .Nrecov(Niter). The carrier phase between two succes-sive bursts sent from the same ST is typically uncorrelatedmainly because of the fast phase noise components of the ST.Received burst frequency, timing and amplitude coming fromthe same ST can instead be assumed almost constant withina frame thus Δω[ik, nr

k] � Δω[ik, nk], A[ik, nrk] � A[ik, nk]

2As described in the previous paragraph the set q contains only those cleanbursts for which their replicas have not been detected yet at iteration Niter.


and τ [ik, nrk] � τ [ik, nk] for k = 1, 2, . . .Nrecov(Niter). For

notation simplicity in the following the carrier frequency offsetwill be dropped.(b) The amplitude information of the replica burst slotnr

k, k = 1, 2, . . .Nrecov(Niter) can be accurately esti-mated from the twin "clean" burst which has been suc-cessfully detected in slot nk as: A[ik, nr

k] � A[ik, nk] �1

NRApay

∣∣∣rpay[ik, nk] · {s∗pay[ik, nk]}T

∣∣∣, where the complex array

spay[ik, nk] represents the estimated payload transmitted sym-bols as derived by re-encoding at the CRDSA demodulator thedecoded bits, the operator T indicates array transposition and∗ the complex conjugate. Having assumed a correct decodingof the payload encoded bits it follows that spay[ik, nk] =spay[ik, nk].(c) For each replica burst slot nr

k, k = 1, 2, . . .Nrecov(Niter),the carrier phase information corresponding to this slot foruser ik can be derived by correlating the stored slot nr

k

soft samples rpre[ik, nrk] with the user ik preamble se-

quence spre[ik] of length NRApre symbols as: φ[ik, nr

k] �arg

{rpre[ik, nr

k] · {s∗pre[ik]}T

}where we assumed that the

burst timing offset error is negligible. This timing estimatecan be based on the successfully detected packet from user ikdetected in slot nk.(d) Colliding burst from user ik in slot nr

k can now be removedby IC (e.g. in Fig. 1 packet 3 can be removed from slot 4):

r[nrk, Niter + 1] � r[nr

k, Niter] − A[ik, nk]

· exp[j(φ[ik, nr

k] + Δω[ik, nk] t[nrk]

)]· [spre[ik], spay[ik, nk]

](9)

(e) Increase the iteration counter as: Niter = Niter + 1.(f) Having introduced the CRDSA demodulator maximumnumber of iterations Nmax

iter , if Niter = Nmaxiter then stop, else

go to step 1-(a).

D. Analytic CRDSA Throughput Upper Bound Derivation

In this section, a bound for the throughput of the CRDSAaccess scheme is derived. All the subsequent results are ex-pressed as a function of the normalized MAC load G measuredin packets per slot. It should be recalled that the CRDSA andDSA physical layer load is double compared to SA because ofthe twin burst transmission. The following assumptions havebeen made for the derivation: a) The probability of preamblecollision is assumed to be negligible (this hypothesis willbe validated in Section V-B); b) The MAC load per frame,measured in packets per frame (G · MRA

slots), is assumed to bean integer; c) The demodulator can perform a maximum ofNmax

iter iterations.The throughput T at the iteration Niter for a load G

measured in packets/slot, can be computed as: T (Niter| G) =G Ppd(Niter| G), where Ppd(Niter| G) = P { packet success-fully decoded at iteration Niter | load =G}. The probabilityPpd can be derived as:

Ppd(Niter| G) = 1 − [(1 − PA

pd(Niter| G))

· (1 − PB

pd(Niter| G))]

= 1 −[(

1 − PApd(Niter| G)

)2]

(10)

where PApd and PB

pd correspond respectively to the probabilitythat the twins A and B of the same packet are successfullydecoded. By symmetry, the two probabilities are equal i.e.,PA

pd = PBpd. An upper bound for the probability PA

pd can berecursively derived as follows:

PApd(Niter| G) ≤ PA

al (G) +G·MRA

slots−1∑i=1

Pint(i|G)

· [PBpd(Niter − 1| G)

]i(11)

where PAal (G) represents the probability that the packet is

alone in the slot (or "clean" i.e. no other interfering burstis arriving in the same slot) and Pint(i|G) represents theprobability that the useful burst is colliding with i interferingbursts on the same slot, PB

pd represents the probability that thereplicas of the interfering packets are successfully decoded andG ·MRA

slots − 1 represents the maximum number of interferingpackets that can be present in one slot. By recalling thatPA

pd = PBpd we get the following recursive equation:

PApd(Niter| G) ≤ PA

al (G) +G·MRA

slots−1∑i=1

Pint(i|G)

· [PApd(Niter − 1| G)

]i(12)

with an initial value of PApd(0) = 0. The derivation of Pint and

PAal is provided in Appendix II. The first iteration corresponds

to the case of no interference cancellation and yields the sameperformance of DSA [3]. The second iteration correspondsto one interference cancellation iteration and so forth untilNmax

iter iterations are accomplished. Equation (12) represents anupper bound as the probability of occurrence of the so called"loops" has not been considered. A loop can occur when, in therecursive process of decoding a packet, we find an interferingpacket which is either a replica of the packet of interest ora replica of any of the previously found interfering packets.In these situations a loop (or deadlock) occurs thus makingthe recursive contention resolution process impossible. Forexample, in the frame shown in Fig. 1, a loop occurs betweenpackets 4 and 5, i.e. to recover packet 4 in slot MRA

slots−1, weneed to cancel the interference from packet 5, but to cancel theinterference from packet 5 we need the information from itstwin copy which is in slot MRA

slots−3. Unfortunately, packet 5in that slot has an interfering packet which is the twin copy ofpacket 4, so a loop occurs between them and they cannot be berecovered. The situations whereby occurrence of loops takesplace can be very diverse (e.g. different number of packets canbe involved in the loop) and thus cannot be easily modelled inthe analytical model. Therefore, the current analytical modelrepresents an upper bound for the performance of CRDSA.In Section V the tightness of the analytical throughput upperbound for the region of interest will be demonstrated.

IV. IMPLEMENTATION CONSIDERATIONS

The definition of the location signalling information insidethe MAC packets will be specific to each satellite air interfacestandard. In general, a field of one byte (i.e. a RA frame ofup to 256 slots) would be sufficient. In the case of trafficbursts containing one or more ATM cells the overhead shall


be ≤ 1.8% and for the case of a traffic bursts containing oneor more MPEG2 cells the overhead shall be ≤ 0.5%. Unusedexisting fields could also be redefined for this purpose yielding0% overhead. When transmitting very short bursts (e.g. 14-Byte long bursts such as SYNC bursts in the case of a DVB-RCS system), the overhead due to the replica pointer maybecome non-negligible (e.g. 1Byte/14Byte, which is about 7%overhead).

In the following, a possible way to apply CRDSA fora DVB-RCS type of system is shortly discussed. First, forlogging into the system the current Slotted Aloha modeproposed by the standard is used. Once the ST has been loggedinto the satellite network and the ST timing error has beenreduced within the acceptable boundaries trough standard STsynchronization procedures, the random access channel canoperate in CRDSA mode. RA shall be selected to transmitsmall size or infrequent packets while DA shall be selectedwhen the ST buffer exceeds a certain threshold.

A short functional description of the modulator and de-modulator operations is presented in Fig. 2. Functions notpresent in a standard (D)SA burst modulator/demodulator willbe indicated in italic in the text and in the block diagram.

A. CRDSA Modulator Operation

The CRDSA modulator depicted in the upper part of Fig. 2represents a simple variant of a classical MF-TDMA burstmodulator. In fact, incoming information packets are firstbuffered and then segmented into fixed size MAC packets.MAC packets are then encoded, modulated and located intotwo random slots (ni and nr

i ) of a generic frame at acertain carrier frequency ω[ik] according to the ST bursttime plan (TBTP) that is broadcasted to all STs throughthe satellite downlink signalling channel [4]. It should beremarked that for a given number of useful payload bits,the overall CRDSA ST burst duration is more than doubledcompared to a conventional burst modulator because of thetransmission of the twin burst within the same frame plusthe small twin location signalling overhead. For each framethe mapping of the ST RA twin bursts onto the TBTP israndomly generated and signaled in the burst payload fieldreserved bits (twin burst signalling information generator andmultiplexer). The burst accommodates a preamble composedof a pseudo-random (e.g. Gold) sequence followed by thecomplex payload symbols. As detailed in Section III-B, thepreamble pseudo-random sequence is the same for the twinbursts and it is randomly selected by the ST among the SPR

available preamble sequences. This is a key difference withrespect to conventional (D)SA whereby the same preamblesequence is used by all STs. The payload symbols are theresults of the coding and modulation of the useful informationbits and twin location signalling information.

B. CRDSA Demodulator Operation

The CRDSA demodulator is depicted in the lower part ofFig. 2. The local oscillator converts the input (MF-TDMA)signal coming from the RF front-end to a low IF frequency.The ADC then converts the low-IF input analogue signal in

digital samples for further processing. The digital demulti-plexer is able to separate the multi-carrier MF-TDMA inputsignal in different individual carriers. The frame basebanddigital complex samples corresponding to the different MF-TDMA carriers separated by the digital demultiplexer are thenstored in a digital memory encompassing at least 2 times thefull RA frame duration. In this way once a full frame is storedthe iterative CRDSA burst processing can be performed athigher speed while next frame’s samples are being collectedin the remaining available memory. The overall demodulationprocessing delay is therefore bounded to less than one frame.The frame digital samples stored are read in a sequentialorder corresponding to the individual MF-TDMA slots. Foreach slot of the frame the multiple preamble searcher looksin parallel for the possible SPR preambles presence in orderto detect the presence and the start time of the bursts. Theburst demodulator performs an initial burst carrier frequencyand phase estimation based on the preamble. The same unitalso extracts the symbol timing and performs symbol matchedfiltering to deliver the burst I-Q baseband samples at symbolrate. Typically, a more accurate phase estimation is performedby processing the payload symbols to enhance the initialpreamble-based phase estimate. The payload Forward ErrorCorrecting (FEC) decoder extracts the burst payload usefulinformation bits as well as the information about the locationof the "twin" burst within the frame. The useful and signallingbits are then separated by a demultiplexer. The estimatedburst information bits coming out from the FEC decoder aftermultiplexing with the current burst slot location signallingbits are re-encoded by the payload FEC encoding block toprovide the twin burst coded bits information to the replicaburst generation. The encoded payload bits together with theinformation provided by the preamble searcher, the payloadburst channel estimate (frequency, amplitude, clock) and thetwin preamble phase estimator are used by the twin burstregeneration unit to produce the replica burst in the rightslot location. The twin burst interference cancellation unititeratively removes possible burst collisions to allow DSAperformance boost through the contention resolution process.

V. NUMERICAL RESULTS

A CRDSA system simulator has been developed wherea number of independent traffic generators are generatingtraffic bursts and driving the TDMA CRDSA modulator. Eachmodulator burst carrier phase is a r.v. uniformly distributedover [0, 2π) and constant over the burst. All modulators areaffected by independent amplitude fluctuations with program-mable statistics and adding up after a delay correspondingto the ST to gateway propagation delay (about 250 ms forthe GEO satellite considered in the following). When notstated otherwise, the ST transmitted power lognormal r.v. isassumed to have a mean and standard deviation of 0 dB.Complex AWGN noise samples addition follows. The noisyTDMA signals are then entering the CRDSA demodulator forfurther processing. To properly assess the CRDSA schemeperformance, the channel estimation for the useful "clean"burst demodulator is considered ideal. In all simulations, aRA frame size of 100 slots has been assumed. Longer RAframes do not provide any further significant performance


PAYLOAD FECCODING &

MODULATOR

BASEBANDSRRC

FILTERS

TRAFFICPACKETS

QUEUE

BURSTMUX

CARRIERLOCAL

OSCILLATOR

MACPACKET

SEGMENT

TWIN BURSTSIGNALLINGINFORMAT

GENERATION

VARIABLEPREAMBLE

GENERATION

TWINS BURST MODULATOR CONTROLLER

BUFFER MUX

ADC FRAME SAMPLESMEMORY

DIGITALDEMUX

CARRIERLOCAL

OSCILLATOR

BURST DEMODULATOR CONTROLLER

P/SCONVER

TER

BURSTDEMODULATOR

FECDECODER

MULTIPREAMBLESEARCHER

TWINPREAMBLE

PHASEESTIMATOR

TWINBURST

REGENERATION

FECENCODING

TWINBURST

INTERFERENCECANCELLATION

PROCESSOR

PAYLOAD CHANNELESTIMATE

USEFUL PAYLOADBITS

DEMUX

TWIN SLOTSIGNALLING BITS

CURRENT SLOTSIGNALLING BITS

TWIN BURST PHASE ESTIMATE

TWIN BURST PREAMBLESEQUENCE

MULTIPLE ACCESS CHANNEL

AWGN

Fig. 2. CRDSA modem functional block diagram. In dark grey the new blocks compared to a conventional TDMA burst demodulator. In light grey themodified ones.

improvement. A MAC packet corresponds to 1 ATM cell.For the simulations in Section V-A, Poisson and Web Clienttraffic sources have been used. These models are consideredrepresentative of the return link traffic generated from smallterminals with low level of traffic aggregation. The Web Clienttraffic source has been derived from [16], but assuming anexponential packet length distribution with a mean of 40 bytes.The performances achieved are so similar between both trafficsources that no distinction has been made between them in theresults obtained. For the simulations in Sections V-B and V-C,Poisson traffic sources have been assumed.

A. Results Assuming Ideal Channel Estimation for Interfer-ence Cancellation

Performance results from Figs. 3 and 4 have been obtainedin the following way. For all studied random access schemes(SA, DSA and CRDSA), we have assumed an open looptransmission scheme. Therefore, no congestion control or re-transmission mechanisms have been applied, and packets aresent by the transmitters as they arrive after a randomizedtime. This is the reason why after a certain system loading,all the schemes saturate and performance (throughput) startsto collapse (i.e. too many collisions occur on the channel).


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Normalized Load [G]

Thro

ughp

ut

Simulated CRDSAAnalytical CRDSASimulated Slotted−Aloha

Niter=1

Niter=2

Niter=3

Niter=6

Niter=16

Fig. 3. Simulated (circles) and analytical (dotted line) results for the CRDSAthroughput (ideal channel estimation for IC) versus the normalized channelloading for Niter = 1, 2, 3, 6, 16. Slotted Aloha (SA) (continuous line)and Diversity Slotted Aloha Niter = 1 performance is also reported forcomparison.

The randomization time corresponds to one frame (i.e. aslot is chosen randomly within one frame). The performanceparameter used in Fig. 3 is throughput (measured in usefulpackets received per slot) vs. load (measured in useful packetstransmitted per slot). One slot can carry one data packet,that corresponds to one ATM cell in our simulations, for allschemes. In Fig. 3, the throughput of the CRDSA protocolhas been first simulated versus the normalized MAC load fora variable number of maximum iterations in the contention res-olution process (Nmax

iter = 1, 2, 3, 6, 16) and initially underthe assumption of perfect channel estimation for IC. Computersimulation results are compared in Fig. 3 to the analyticalthroughput upper bound calculation reported in Section III-D. As expected, for the reasons explained in Section III-D,simulation results are slightly below the bound in particular fornormalized loads close to the maximum throughput and whenthe number of iterations is large. This corresponds to situationswhen "loops" occurrence probability is non negligible. Itis interesting to observe that there is a diminishing returnadvantage increasing the number of CRDSA demodulatoriterations Nmax

iter . The choice of Nmaxiter = 10 appears to achieve

most of the CRDSA recursive algorithm potential gain. Theresults obtained for SA in our simulations correspond to thosereported in [2]. To remark that while standard SA reaches itsthroughput peak of 0.36 for a normalized MAC load G = 1,CRDSA achieves a peak throughput of about 0.52 for anormalized MAC load of 0.65. In addition, CRDSA achievesa linear throughout (with almost no packet losses) up to anormalized channel load of 0.4, while SA achieves a similarbehavior only up to 0.1 load.

Let us now define the MAC packet loss ratio as:PLRMAC(G) = 1 − T (G)

G being G the normalized load andT the normalized MAC throughput. Fig. 4 reports the MACpacket loss ratio (PLRMAC) for the SA, DSA and CRDSAcases. In this figure we can see that in open loop conditions(i.e. no re-transmissions applied to any scheme), CRDSA hasa much lower PLR on all loads, therefore it is a much more

10−3 10−2 10−1 10010−4

10−3

10−2

10−1

100

Pac

ket L

oss

Rat

io P

LR

Normalized load [G]

CRDSASADSA

o o o

X X X

T T T

Fig. 4. MAC Packet Loss Ratio for CRDSA (continuous line), DSA(dashed) and SA (dashed dot) with ideal CRDSA channel estimation forIC. Different markers (O,X,T) correspond respectively to PLRMAC =2 · 10−2, 10−2, 10−3 for each random access technique.

reliable RA scheme that SA and DSA. The results show thatthe CRDSA channel can be loaded 50 times more that theSA channel if we want to achieve a PLRMAC = 10−3, 26times more to achieve PLRMAC = 10−2, and 17 times moreif we want to achieve a PLRMAC = 2 · 10−2. Alternatively,we could say that for a given load G = 0.35, the SA losses(PLRSA

MAC(0.35) = 0.3) are 15 times higher that the CRDSAlosses (PLRCRDSA

MAC (0.35) = 2 · 10−2).In Fig. 5, a re-transmission scheme has been introduced to

the CRDSA technique for those packets experiencing colli-sions and that cannot be recovered by means of interferencecancellation techniques at the gateway. It is expected that thelosses around the nominal operational point in CRDSA willbe very low (e.g. below 0.02). As a consequence, the volumeof retransmitted packets on the channel is also expectedto be very modest without affecting the average channelload. In order to increase the probability of success for theretransmitted packets and considering the low volume of thosepackets on the channel, a double retransmission mechanism issuggested for satellite applications, i.e. retransmitted packetsare sent twice on two different RA frames. This solution willapproximately provide the performance loss of a two-packetretransmission mechanisms and the delay performance of onepacket retransmission for the retransmitted packets. Numericalresults corresponding to this retransmission mechanism arepresented in Fig. 5. The packet loss ratio is significantlyimproved with a double retransmission mechanism (by morethan 3 orders of magnitude at G = 0.35 load and more than2 orders of magnitude at G = 0.4). The average delay isrelatively not affected as the amount of re-transmitted packetsrepresents a small percentage of the total transmitted trafficon the channel (see delay PDF distribution in Fig. 6).

B. Results on Burst Preamble Destructive Collision Probabil-ity

In Fig. 7, the estimation of the analytical formula for theprobability of preamble collision Equation (8) is comparedwith the results of the simulation. This exercise has been done


0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.4610−6

10−5

10−4

10−3

10−2

10−1

Normalised Load

Pac

ket L

oss

Rat

io

2 re−TX1 re−TX0 re−TX

Fig. 5. Simulated CRDSA packet loss ratio with double, single and nore-transmissions.

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.02

0.04

0.06

0.08

0.1

0.12

Delay (s)

Delay PDF at 0.4 normalized load

Fig. 6. Simulated CRDSA delay PDF distribution for normalized load G =0.4 with a double retransmission mechanism.

assuming a set of Gold sequence of length SPR = 31 andDmax = 5. As we can see, for a load G = 0.4, Ppre−coll =5 · 10−3. This probability is one order of magnitude lowerthan the PLRMAC for the same load, thus it is considered tobe acceptable. The probability of preamble collision be couldhalved by using twice the number of codes (i.e. SPR = 63)as shown on the same Fig. 7.

C. Results Assuming Non-Ideal Channel Estimation for Inter-ference Cancellation

Next experiment takes into account the non ideal channelestimation effects in solving the channel contentions in theCRDSA burst demodulator. For this simulation the presenceof a burst guard time of NRA

guard = 5 symbols, a preamble oflength NRA

pre = 31 symbols and a payload of NRApay = 424 sym-

bols (corresponding to 1 ATM cell with a convolutional code

0 0.2 0.4 0.6 0.8 10

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Pro

babi

lity

of p

ream

ble

colli

sion

[Ppr

e−co

ll]

Normalized load [G]

analytical SPR=31analytical SPR=63simulated results

Fig. 7. Analytic and simulation results for preamble collision probability forSPR = 31, 63 , Dmax = 5 and Es/N0 = 6 dB.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Normalized load [G]

Thro

ughp

ut

ideal ch. est.SNR = 5 dBSNR = 6 dBSNR = 8 dB

SNR = 8 dB

SNR = 5 dB

SNR = 6 dB

Fig. 8. Simulated ideal channel estimation (continuous line) and real channelestimation for IC (dashed dot line) results for the CRDSA throughput versusthe normalized channel loading for Niter = 10 and Es/N0 = 5, 6, 8 dB.

rate r = 1/2 [1338, 1718] and QPSK modulation3) have beenchosen. For each burst and its duplicate in case of CRSDA, theBPSK preamble sequences are randomly extracted out of theSPR Gold sequences available. For deciding if the packet iscorrectly received we look if the decoder has correctly decodedthe payload burst data. The performance of the chosen code ona AWGN channel are such that BER=10−5 is achieved whenEs/N0 = 4.2 dB. Channel estimation for IC is performedaccording to the algorithms described in Section III-C andwe recall that the carrier phase is randomly generated foreach burst of the frame even if the bursts are coming fromthe same ST. The simulated throughput results versus thenormalized load for various Es/N0 values and Niter = 10are reported in Fig. 8 and compared to the case of CRDSAwith ideal channel estimation. It is apparent that the imperfect

3We assume that this physical layer configuration represents a worst-casefor the channel estimation in the burst demodulator. The preamble length of31 symbols is also a worst-case for channel estimation as for this coding rateand modulation scheme typically a longer preamble (≥ 48) is required toprovide acceptable burst synchronization performance.


−0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

12

14

PD

F

phase estimation error [rad]

amplitude estimation

Fig. 9. Simulated CRDSA preamble amplitude and carrier phase estimationerror for Niter = 10, Es/N0 = 6 dB, G=0.4 and NRA

guard = 5.

channel estimation is causing a slight performance degradationwhich is more noticeable (about 5 %) for normalized loadin excess of 0.45 which are not used in practice. For arealistic operational normalized load G = 0.35 correspondingto PLRMAC = 0.02, the impact of the imperfect channelestimation on the throughput is negligible4.

To better understand the causes of degradation it is usefulto analyze the key channel parameter estimation errors. Fig. 9shows the preamble-based carrier phase estimator PDF usedfor cancelling the colliding burst when Es/N0 = 6 dB andG = 0.4. For this reason the PDF of the carrier phase esti-mation error is evaluated on the preamble of bursts that haveexperienced at least one collision. The estimator phase erroris a combination of several factors such as the AWGN noiseand the colliding bursts preamble cross-correlation effect. Thecross-correlation impact increases with the amount of packetsN [n] present in slot n. It is also interesting to observe theestimated amplitude error distribution. Following Section III-C step 2, amplitude estimation takes place on the whole burstpayload using the FEC-based regenerated channel symbols.Thus it is expected the amplitude estimation is accurate andvery close to a data-aided amplitude estimator. This intuitionis confirmed by the simulation results of Fig. 9. Compared tothe phase estimator operating on a shorter preamble sequenceof length NRA

pre = 31 symbols, the amplitude estimator isfurther advantaged by the fact that it operates on "clean" burstso in the absence of collisions. It is apparent that the maincontributor to the contention resolution channel estimationerror is the carrier phase5.

To better understand the capability of the proposed CRDSAcontention resolution demodulator processing it is interesting

4Simulation runs indicated that even simulating realistic time variant overthe burst ST phase noise process according to the DVB-RCS mask [13], noappreciable impact on the CRDSA performance are experienced for Rs ≥128 Kbaud.

5It can be shown that the equivalent signal to interference ratio causedby the carrier phase of the burst to be removed can be approximated bySIR � 1/σ2

Δφ, Δφ being the burst phase estimate error. This contribution

is normally negligible compared to the AWGN impairment when no phasenoise is present.

to observe the scatter diagram of the baseband signal in theabsence of AWGN (Es/N0 = ∞) for a specific slot of theTDMA frame when multiple collisions occur for Nmax

iter = 1(see Fig. 10(a)) and for Nmax

iter = 10 (see Fig. 10(b)). Theremarkable cleaning of the baseband QPSK signal scatterdiagram thanks to the recursive IC approach is apparent.

The impact of imperfect power control or ST power unbal-ance on the CRDSA protocol performance is shown in Fig. 11for Es/N0 = 6 dB. In the simulations it is assumed that the STpower is lognormally distributed with 0 dB mean and standarddeviation σPrx = 1, 2, 3 dB. We observe that the presenceof other STs received power unbalance at the gateway burstdemodulator results in a modest degradation of throughputperformance that is more evident in the maximum throughputregion, G ∈ [0.5−0.8]. Nevertheless, for the nominal operatingregion, G ≤ 0.4, the loss with respect to the ideal case isalmost negligible when σPrx ≤ 2 dB.

VI. CONCLUSION

In this paper the so-called Contention Resolution Diver-sity Slotted Aloha (CRDSA) scheme has been introducedand in depth analyzed. It is shown that CRDSA providesa major boost in performance compared to known randomaccess (RA) techniques currently used by TDMA satellitesystems such as SA and DSA. By simple modification ofthe modulator MAC scheme, CRDSA allows to achieve a17 and 4.5 fold throughput increase compared to SA andDSA respectively for a MAC packet loss ratio of 2 %.Higher gains are achieved at lower MAC PLR (e.g. 50-fold atPLR=10−3). An upper bound for the CRDSA throughput hasbeen derived and successfully compared to simulation results.Channel estimation for interference cancellation is obtained byexploiting the burst preamble which is now "signed" by se-quences belonging to a family of quasi-orthogonal sequences.Simulation results showed that for realistic preamble lengthsused in today TDMA systems, the channel estimation errorimpact is negligible for realistic operating conditions. Alsothe probability of preamble collision was analytically derivedand results compared to simulation findings. It is shown thatthis major performance enhancement over known techniquescan be achieved with a minor overhead increase. It is demon-strated that the CRDSA contention scheme can be practicallyoperated at normalized loads of up to 0.4, thus allowing thetransmission of small/medium sized bursty packets withoutallocating resources as often done in today satellite broadbandnetworks. The impact of received power errors among STs wasfound to be fully acceptable. A possible packet retransmissionmechanism for lost packets has been also described makingthe random access channel highly reliable (PLR = 10−4)with little impact on the overall channel performance in termsof throughput and delay.

APPENDIX IPROBABILITY OF PREAMBLE COLLISION DERIVATION

The probability of preamble collision is the probability thata packet suffers from the collision with other packets thathave the same preamble sequence and the same time delay.Considering i packets interfering with the reference packet,


−4 −3 −2 −1 0 1 2 3 4−4

−3

−2

−1

0

1

2

3

4

real

imag

Scatter diagram received Symbols, Niter=1

(a) Niter = 1

−1 −0.5 0 0.5 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

real

imag

Scatter diagram received Symbols, Niter=10

(b) Niter = 10

Fig. 10. Simulated CRDSA demodulator scatter diagram for Es/N0 = ∞ dB and G = 0.4 with real channel estimation for IC.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Normalized load [G]

Thro

ughp

ut

σPwr = 1 dB

σPwr = 2 dB

σPwr = 3 dB

Ideal Power Control

Fig. 11. Simulated ideal channel estimation (continuous line) and realchannel estimation (dashed dot line) results for the CRDSA throughput versusthe normalized channel loading for Niter = 10 and various STs power errorstandard deviations.

the probability that j of them choose the same code and thesame differential delay value is P(j out of i) =

(ij

) · pj · (1 −p)i−j where p = 1/(SPR ·Dmax). Hence, considering that theprobability of having i interfering packets in the same slot nis Pint(i| G) (see Appendix II), the probability of collision iseasily calculated as:

Ppre−coll(G) =G·MRA

slots−1∑i=1

Pint(i| G)

·⎡⎣ i∑

j=1

(i

j

)· pj · (1 − p)i−j

⎤⎦

=G·MRA

slots−1∑i=1

Pint(i| G) · [1 − (1 − p)i](13)

where G is the load measured in packets per slot and G·MRAslots

is the number of packets per RA frame and it is assumed tobe an integer number.

APPENDIX IIPROBABILITY THAT i BURSTS ARE COLLIDING

We need to derive the probabilities Pint(i| G) and PAal

defined in Sections III-B and III-D. First, we derive theprobability that the packet pk (represented by the two replicaspA

k and pBk ) is present on a given slot Sn from the set of

MRAslots slots available in one frame. It should be recalled that

each packet is transmitted twice on a given frame but neverover the same slot. Thus the probability can be computed asfollows:

P {pk ∈ Sn} = P{pA

k ∈ Sn

}+ P

{pA

k /∈ Sn

}·P {

pBk ∈ Sn

}=

2MRA

slots

(14)

assuming that slots are selected randomly with uniform dis-tribution and never selected twice the same slot. Then, theprobability that i interfering packets are present on a givenslot Sn can be derived as a binomial where i packets arepresent in slot Sn and the remaining G ·MRA

slots−1− i packetsare not present in slot Sn:

Pint(i| G) =(

G · MRAslots − 1i

)[P {pk ∈ Sn}]i

· [1 − P {pk ∈ Sn}]G·MRAslots−1−i (15)

Finally the probability that the copy A of a packet pk is aloneon a given slot Sn is equivalent to having zero interferingpackets in slot Sn:

PAal (G) = Pint(0| G) = [1 − P {pk ∈ Sn}]G·MRA

slots−1. (16)

REFERENCES

[1] L. G. Roberts, “ALOHA packet systems with and without slots andcapture,” ARPANET System Note 8 (NIC11290), June 1972.

[2] N. Abramson, “The throughput of packet broadcasting channels,” IEEETrans. Commun., vol. 25, pp. 117–128, Jan. 1977.

[3] G. L. Choudhury and S. S. Rappaport, “Diversity ALOHA - A randomaccess scheme for satellite communications,” IEEE Trans. Commun.,vol. 31, pp. 450–457, Mar. 1983.

[4] Digital Video Broadcasting (DVB); Interaction Channel for SatelliteDistribution Systems, European Telecommunication Standardisation In-stitute (ETSI) EN 301 790 V1.4.1 (2005-09).


[5] IP Over Satellite, Telecommunication Industry Association TIA-1008,Oct. 2003.

[6] T. Le-Ngoc and J. I. Mohammed, “Combined free/demand assignmentmultiple access (CFDAMA) protocols for packet satellite communica-tions; Universal personal communications,” in Proc. 2nd InternationalConf. Pers. Commun., Oct. 1993, vol. 2, pp. 824–828.

[7] O. del Rio Herrero, G. Foti, and G. Gallinaro, “Spread-spectrumtechniques for the provision of packet access on the reverse link ofnext-generation broadband multimedia satellite systems,” IEEE J. Select.Areas Commun., vol. 22, no. 3, pp. 574–583, Apr. 2004.

[8] S. S. Lam, “A carrier sense multiple access protocol for local networks,”Computer Networks, vol. 4, pp. 21–32, Feb. 1980.

[9] N. Abramson, “The ALOHA system - Another alternative for computercommunications,” in Proc. AFIPS Conf., Nov. 1970, vol. 37, pp. 281–285.

[10] D. Raychaudhuri and K. Joseph, "Channel access protocols for Ku-bandVSAT networks: A comparative evaluation,” IEEE Commun. Mag., vol.26, no. 5, pp. 34–44, May 1998.

[11] D. Raychaudhuri, “ALOHA with multipacket messages and ARQ-typeretransmission protocols-throughput analysis,” IEEE Trans. Commun.,vol. 32, no. 2, pp. 148–154, Feb. 1984.

[12] D. Raychaudhuri, “Stability, throughput, and delay of asysnchronousselective reject ALOHA,” IEEE Trans. Commun., vol. 35, no. 7, pp.767–772, July 1987.

[13] Digital Video Broadcasting (DVB); Interaction Channel for SatelliteDistribution Systems; Guidelines for the use of EN 301 790, EuropeanTelecommunication Standardisation Institute (ETSI) TR 101 790 V1.2.1(2003-01).

[14] P. Patel and J. Holtzman, “Analysis of a simple successive interferencecancellation scheme in a DS/CDMA system,” IEEE J. Select. AreasCommun., vol. 12 , no. 5, pp. 796–807, June 1994.

[15] R. De Gaudenzi, F. Giannetti, and M. Luise, “Signal recognition andsignature code acquisition in CDMA receivers for mobile communica-tions,” IEEE Trans. Veh. Technol., vol. 47, no. 1, pp. 196–208, Feb.1998.

[16] Universal Mobile Telecommunications System (UMTS); Selection Pro-cedures for the Choice of Radio Transmission Technologies of theUMTS, European Telecommunication Standardisation Institute (ETSI)TR 101 112 V3.2.0 (1998-04)

Enrico Casini was born in Figline Valdarno, Italy,on March 13th 1976. He received the Laura Degree(summa cum Laude) from the University of Flo-rence, Florence, Italy in 2002. In 2001 he joined theESA’s Research and Technology Center (ESTEC),Noordwijk, The Netherlands. During 2001-2003 hewas a trainee investigating advanced synchronisationtechniques for space communications and interfer-ence mitigation techniques. Since 2003 is workingfor the RF Payload and System Division as com-munication system engineer. His research interests

include the characterization of non-linear satellite channel, advanced modemdesign, physical layer system simulation and the analysis of the satellitepayloads.

Riccardo De Gaudenzi (M’89-SM’97) was bornin Italy in 1960. He received his Doctor Engineerdegree (cum Laude) in electronic engineering fromthe University of Pisa, Italy in 1985 and the PhDfrom the Technical University of Delft, The Nether-lands in 1999. From 1986 to 1988 he was withthe European Space Agency (ESA), Stations andCommunications Engineering Department, Darm-stadt (Germany) where he was involved in satellitetelecommunication ground systems design and test-ing. In particular, he followed the development of

two new ESA’s satellite tracking systems. In 1988, he joined ESA’s Researchand Technology Centre (ESTEC), Noordwijk, The Netherlands where in2000 he has been appointed head of the Communication Systems Sectionand since 2005 he is Head of the RF Payload and Systems Division. Thedivision is responsible for the definition and development of advanced satellitesystem, subsystems and technologies for telecommunications, navigation andearth observation applications. In 1996 he spent one year with QualcommInc., San Diego USA, in the Globalstar LEO project system group underan ESA fellowship. His current interest is mainly related with efficientdigital modulation and access techniques for fixed and mobile satelliteservices, synchronization topics, adaptive interference mitigation techniquesand communication systems simulation techniques. From 2001 to 2005 hehas been serving as Associate Editor for CDMA and Synchronization forthe IEEE TRANSACTIONS ON COMMUNICATIONS. He is co-recipient of theVTS Jack Neubauer Best System Paper Award from the IEEE VehicularTechnology Society.

Oscar del Rio Herrero was born in Barcelona,Spain, in 1971. He received the B.E. degree inTelecommunications and the M.E. degree in Elec-tronics from the University Ramon Llull, Barcelona,Spain, in 1992 and 1994, respectively. He re-ceived a post-graduate degree in Space Science andTechnology with emphasis in Satellite Communica-tions from the Space Studies Institute of Catalonia(IEEC), Barcelona, Spain, in 1995. He joined ESA’sResearch and Technology Center (ESTEC), Noord-wijk, The Netherlands, in 1996. In 1996 and 1997

he worked as a Radio-navigation System Engineer in the preparation of theGalileo programme. Since 1998, he has worked as a Communications SystemsEngineer in the Electrical Systems Department. His current research interestsinclude high-performance on-board processors, packet access and resourcemanagement schemes and IP inter-working for future broadband satellitesystems.

contention resolution diversity slotted aloha (crdsa): an

Documents