Asynchronous Contention Resolution Diversity ALOHA: Making CRDSA Truly Asynchronous

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 11, NOVEMBER 2014 6193

Asynchronous Contention Resolution DiversityALOHA: Making CRDSA Truly Asynchronous

Riccardo De Gaudenzi, Oscar del Río Herrero, Guray Acar, and Eloi Garrido Barrabés

Abstract—Following the introduction of contention resolutiondiversity slotted ALOHA (CRDSA), a number of variants of thescheme have been proposed in literature. A major drawback ofthese slotted random access (RA) schemes is related to the needto keep slot synchronization among all transmitters. The volumeof signaling generated to maintain transmitters’ slot synchroniza-tion is impractical for large networks. In this paper, we describein detail asynchronous contention resolution diversity ALOHA(ACRDA), which represents the evolution of the CRDSA RAscheme. ACRDA provides better throughput performance withreduced demodulator complexity and lower transmission latencythan its predecessor while allowing truly asynchronous access tothe shared medium. The performance of the ACRDA protocolis evaluated via mathematical analysis and computer simulationsand is compared with that of CRDSA.

Index Terms—Satellite communication, SCADA systems, multi-access communication, time division multiple access, interferencesuppression.

I. INTRODUCTION

THERE is a growing interest to enhance the performanceof random access protocols suitable to support low-

cost interactive satellite and terrestrial terminals for the fixedbroadband consumer market and mobile applications, includ-ing machine-to-machine (M2M) communications. ContentionResolution Diversity Slotted ALOHA (CRDSA) [1]–[3] hasshown how the Slotted ALOHA (SA) [4] and Diversity SlottedALOHA (DSA) [5] throughput can be significantly increasedby a relatively simple extension of the DSA concept togetherwith iterative interference cancellation at the demodulator. The2nd generation Digital Video Broadcasting Return Channelby Satellite (DVB-RCS2) standard [6] optionally supportsCRDSA on the return link for both data and signaling traffic.

Reference [7] provides a comprehensive analytical frame-work able to assess the performance of a number of slottedaccess techniques from the more conventional SA and DSA tothe more elaborated CRDSA in the presence of arbitrary trafficand power distribution and taking into account effective codingand modulation schemes adopted at physical layer. In particular,in [3] and in [7] it is shown that the CRDSA performance can

Manuscript received November 7, 2013; revised March 22, 2014 andJune 16, 2014; accepted June 24, 2014. Date of publication July 2, 2014; date ofcurrent version November 7, 2014. The associate editor coordinating the reviewof this paper and approving it for publication was L. Cai.

R. De Gaudenzi, O. del Río Herrero, and G. Acar are with the EuropeanSpace Agency, 2200 AG Noordwijk, The Netherlands (e-mail: [email protected]; [email protected]; [email protected]).

E. Garrido Barrabés is with the Delft University of Technology (TUD), 2628CN Delft, The Netherlands (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TWC.2014.2334620

be enhanced by using more than two replicas so as to reducethe probability of the so-called “loop” phenomenon.1 Liva in[8] extended the concept of CRDSA to encompass an irregularrepetition scheme which is dubbed Irregular Repetition SlottedALOHA (IRSA). The author has been exploiting the bipartitegraphs theory, which is typically used in the design and analysisof forward error correcting schemes, in order to design theoptimized IRSA irregular graph and packet repetition scheme.CRDSA represents a special case of IRSA in which all thepacket replicas have the same mass probability thus leadingto a regular graph. Although IRSA exhibits some maximumthroughput increase compared to the two-replicas CRDSA, itsperformance at the Packet Loss Ratio (PLR) of 10−3 or lowerappears less attractive when compared to CRDSA with 3–4replicas results reported in [3]. The Coded Slotted ALOHA(CSA) [9] scheme represents a further generalization of theIRSA scheme. CSA is encoding rather than repeating thepackets like in CRDSA and IRSA and splitting them as packetsegments in the frame slot. For each transmission the code to beused is randomly selected from a p re-defined co de-book anda probability mass function like in IRSA. Other CRDSA-likeschemes have been recently proposed and are shortly reviewedin the following. The first one is the Multi-Slots Coded ALOHA(MuSCA) RA scheme was introduced by Bui et al. [10]. UnlikeCRDSA, but similarly to CSA, the different slots randomlyassigned to a single user in a given frame are not containingthe same payload information. Instead, the coded symbolsembedding Forward Error Correction (FEC) redundancy arespread a cross two or more bursts in the frame slots. In theMuSCA scheme the signaling bits are not included in the packetpayload but are independently coded from the payload. Resultsreported in [10] show a sizeable improvement in throughputcompared to CRDSA and IRSA schemes. With the MuSCAscheme a lower coding rate than the CRDSA one is achieved atthe expenses of additional complexity and signaling overhead.A further enhancement of the MuSCA scheme is reported in[11] where, similarly to CSA, an irregular degree distributionof the MuSCA coding rates is applied to the different packets.In this way the throughput performances compared to MuSCAare further enhanced. Other slotted RA schemes exploitingiterative cancellation have been proposed for application in thedomain of Radio-frequency identification (RFID). In [12] theslot selection in each frame is not random as in conventional SAbut rather based on a deterministic pseudo-random function ofthe message payload. This allows to perform cancellation of the

1A loop phenomenon occurs when all replicas of a set of packets are inunrecoverable collision with one or more replicas (see Section III).

1536-1276 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

6194 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 11, NOVEMBER 2014

received message from previous frames transmission attemptsthus improving the system throughput. In [13] the previousconcept of inter-frame interference cancellation is coupled withconvolutional encoding allowing inter-frame soft combiningof multiple transmission attempts a cross different frames toincrease the probability of correct message decoding. In partic-ular, to reduce memory occupancy, it is proposed to only storethe log-likelihood ratios instead of complex samples by usingsoft combining algorithms instead of interference cancellation.

Another approach to enhance the performance ofpacket-based Spread-Spectrum ALOHA (SSA) RA adoptingpacket-oriented window memory-based iterative interferencecancellation dubbed Enhanced Spread-Spectrum ALOHA(E-SSA) is described in detail and analyzed by analyticaland simulations means in [14], [15]. The analysis reported in[14] takes into account arbitrary traffic arrival processes andpower distribution as well as the real coding and modulationadopted. E-SSA outperforms CRDSA for two main reasons:a) the avoidance of packet replicas transmission thanks tothe direct-sequence spreading sequence “isolation” mitigatingthe other packets’ collision impact; b) the higher trafficaggregation achieved by using spreading techniques [16] thatlargely reduces the fluctuations in the number of receivedpackets for a given Poisson traffic load. Moreover, E-SSA (asSSA) has another major advantage over SA/DSA/CRDSAi.e. its truly asynchronous RA nature eliminates the need tomaintain accurate slot synchronization among all transmittersunlike the case in SA/DSA/CRDSA. The need for transmittersynchronization is a major drawback for large networks as thesignaling overhead scales up with the number of transmittersindependently from their traffic activity factor. The capacityof asynchronous collision channel without feedback wasinvestigated by Massey in his seminal paper together withprotocols sequences for achieving the capacity boundaries[17]. In this work the capacity region for RA with no slotsynchronization was derived. The capacity of asynchronousRA for infinite number of users was found to be identicalto the one of SA. This information theory result encouragesthe search for efficient non slotted RA schemes not usingspread-spectrum techniques.

A first contribution in relaxing the synchronization accuracyfor slotted RA has been provided by Kissling in [18], whichproposed a new RA scheme dubbed Contention ResolutionALOHA (CRA). CRA removes the notion of slots inside theCRDSA or IRSA frames allowing the replica packet(s) fromindividual transmitters to be sent with a random delay (andpossibly different duration) within the frame boundaries. CRArepresents an interesting evolution of the original CRDSAscheme, although it still requires the transmitter to remainsynchronized at frame level. It should be remarked that theanalysis reported in [18] compares CRA with that of a sub-optimal CRDSA configuration. If the results in [7] for CRDSAwith coding rate 1/3 and three-replicas are compared with theCRA 3 replica case in [18], it is apparent that CRDSA out-performs CRA. Another relevant RA scheme recently proposedis the Enhanced Contention Resolution ALOHA (ECRA) [19].It represents an extension of the frame-based CRA protocoldescribed above. The initial demodulation steps are identical to

the CRA ones. The enhancement consists in making a furtherattempt to decode those packets that were detected but notsuccessfully decoded due to the collision(s). The idea is tocombine symbols from different packet replica(s) to generate anew packet with higher signal-to-noise ratio than the individualreplicas and to attempt its decoding. If decoding is successfulthe original replicas will be cancelled and a new frame decodingpass begins. With two replicas, ECRA performance were shownto be superior to CRA but inferior to CRDSA for QPSK withFEC code rate 1/4. ECRA was shown to outperform CRDSAfor code rate 1/2.

The ACRDA scheme described in this paper introducesa novel approach to achieve high-performance, truly-asynchronous RA without the need to use spread spectrumtechniques. ACRDA reduces the gap between the CRDSA andE-SSA RA schemes for systems that do not adopt spread-spectrum techniques and it performs better than CRDSA.While ACRDA demodulator design will be shown to possessseveral similarities with that of E-SSA, the feature of exploitingpacket replicas and associated location signaling typical ofCRDSA is preserved, which boosts packet collision resolutionprobability. The reason for basing ACRDA on the CRDSAtype of processing instead of IRSA or MuSCA is related toits simplicity and robustness of implementation (includingsignaling) and good performance at PLR ≤ 10−3 which is ofpractical interest.

Section II describes in detail the ACRDA concept empha-sizing the differences with respect to CRDSA and CRA. Ananalytical model for estimating the ACRDA performance isderived in Section III. Section IV presents analytical and simu-lation results comparing ACRDA and CRDSA performance interms of throughput, packet loss ratio, and transmission latency.Section V presents the conclusions of the paper.

II. ACRDA CONCEPT DESCRIPTION

In slotted RA, for a given receiver, the boundaries of timeslots and slots frames are defined in reference to the timelineat the given receiver. Slot synchronization mechanisms areadopted to control each transmitter slot timing, so that burstsarrive at the receiver within the boundaries of the intendedslot. In ACRDA, slot and frame boundaries are not definedglobally in reference to the timeline at the centralized gatewaydemodulator. Instead, the boundaries of slots and frames arelocal to the transmitter and completely asynchronous amongtransmitters. The term Virtual Frame (VF) is used in the restof the paper to specifically refer to this concept of frame ofslots that is only local to each transmitter. In ACRDA, forall transmitters, each VF is composed of a number of slotsNslots and each slot has a duration Tslot with an overall frameduration Tframe = Nslots · Tslot. In the following we assumethat one slot corresponds to a burst length. In general theslot duration could actually take any other value includingfractions of the burst length. Fig. 1(a) depicts packets at theslotted CRDSA demodulator. Frame and slot boundaries aredefined reference to the receiver timeline. Hence, all packetsarrive within slot boundaries, and all packets that are copiesof each other arrive in the same CRDSA frame. This allows

DE GAUDENZI et al.: ASYNCHRONOUS CONTENTION RESOLUTION DIVERSITY ALOHA 6195

Fig. 1. Frame composition in: a) conventional CRDSA slotted RA;b) ACRDA asynchronous RA. The second packet index in the parenthesisindicate the packet replica identifier. (a) CRDSA frame. (b) ACRDA frame.

a frame-based memory processing at the demodulator side asframes’ contents are totally decorrelated. Instead, Fig. 1(b)shows the notion of ACRDA VFs and associated slots whosedefinition is local to each transmitter. Different transmittersare not time synchronized, and hence, the time offset betweenVF(i), VF(i− 1), VF(i+ 1) is arbitrary. In a given transmitterthe VFs will start with a random time offset, which is typicallyspecified by the random access congestion control mechanism,as shown in Fig. 1(b). In the ideal case the slot (Tslot) andframe (Tframe) durations are the same for the all transmitters inthe shared medium. In case of mobile applications the Dopplereffect may have an appreciable impact in terms of incomingpackets clock frequency offset. In this situation the VFs willhave slightly different duration. However, the localization pro-cess of the replica packets within each VF will remain accurateas the gateway burst demodulator will extract for each VF itsown clock reference. The ACRDA RA scheme can easily beincorporated in a conventional Multi-Frequency Time DivisionMultiple Access (MF-TDMA) system by reserving a numberof frequency slots for ACRDA usage in a semi-static fashion.Standard MF-TDMA can still be operated in the remainingfrequency slots. When more frequency slots are available forRA the ACRDA scheme can also be used in multi-frequencyfashion placing VFs also on different frequency slots randomlyselected.

A. ACRDA Modulator

1) Baseline: The ACRDA modulator functional block di-agram is similar to the CRDSA one described in detail in[4, Fig. 2, p. 1414]. The ACRDA modulator operation can besummarized as follows:

1) The incoming information is buffered and organized inpackets of fixed size;

2) The locations of the Nrep packet replicas within the VFslots are randomly selected among the possible Nslots

each having duration Tslot. In case the randomly gener-ated replica locations are overlapping a new set of randomlocations is produced;

3) The current i-th packet is coded together with the replicapacket location(s) slot offset(s) information relative tothe start of the current packet time within the VF withduration Tframe. The replicas signaling location occupiesa given number of bits in a known location in the packetpayload;

4) The start time τi of the current VF i is defined at thetransmitter side once the physical layer packet is ready tobe transmitted. No network-wide timing synchronizationis required for controlling τi thus the access is trulyasynchronous;

5) The coded and modulated packets with ancillary replicalocation signaling information are then transmitted in therandomly selected slots of the VF. If required, the associ-ated packet replica(s) power level can be randomized ona frame-by-frame basis to further enhance the ACRDAthroughput. In general, the same randomized power levelis applied to all the packet replicas present in the VF.However, depending on the system design, it may be moreconvenient to exploit different realizations of the powerrandomization for the packet replica(s) contained in theVF (See Section IV).

6) A packet preamble containing a known sequence com-mon to all transmitters is then appended at the beginningof the packet to allow packet acquisition and channelestimation by the central demodulator.

It is remarked that only the third and fourth steps above aredifferent from the CRDSA modulator processing [1] wherebythe start of frame at the satellite transponder (or gatewaydemodulator) interface input is common to all network trans-mitters and the signaled packet replica(s) location (slot number)is absolute and not relative to the current packet replica as inACRDA. The VF is generated at the terminal side when a newpacket is ready for transmission. In case the new packet arrivedduring the current packet VF duration, the VF will be generatedafter the last replica of the current VF.

2) Variant: A slightly modified version of ACRDA can beobtained by “forcing” the location of the first packet replicainto the first slot of the VF while randomizing the locationsof the remaining replicas in the rest of the VF slots. As we willsee in Section IV, the main advantage of this ACRDA variantresides in the transmission delay reduction since, compared tothe baseline, there is no waiting time for the first packet replicatransmission. However, this ACRDA variant advantage maybe less significant when congestion control schemes that runon top of the Media Access Control (MAC) layer, as in anypractical RA system, generate delays that are much longer thanthe ACRDA VF duration. The variant approach works fine if theVF start time is random, which is the case when packet arrivalinstants are random. If this is not the case, VF start time ran-domization is needed (see below). Congestion control policiesfor RA over satellite typically delay the transmission of the nextpackets by a randomly distributed interval (e.g. following anexponential distribution). The congestion control algorithm canbe applied when collision occurs or depending on the current


Fig. 2. ACRDA demodulator functional block diagram. In yellow (light gray) the slightly modified blocks compared to a CRDSA, in green the heavilymodified ones.

gateway MAC load estimation to avoid congestion instabilities.There are applications such as tele-voting whereby the con-gestion control countermeasures have to be implemented bydefault as the traffic by nature is very concentrated in time anddiffers from Poisson type of distribution. In summary, in themajority of systems, congestion control kicks-in when the MACload approaches a critical level potentially impacting the systemstability, thus the ACRDA variant will provide a delay reductionfor non-critical MAC loads (see Section IV for further details).In addition, we intend to operate our system at very low PLR(e.g. PLR < 10−4). Therefore, the need for retransmissionswill be very modest. However, depending on the system andservice characteristics, the inclusion of an ARQ mechanismcould be justified [20], [21]. Following the discussion above, inthe following we will report the results for both the ACRDAbaseline and variant. In order to facilitate comparison withother RA schemes, no congestion control and retransmissionmechanism will be included in this study.

B. ACRDA Demodulator

ACRDA demodulator operation is considerably differentfrom that of CRDSA due to the asynchronous nature ofACRDA VFs. Nonetheless, the proposed ACRDA demodulatorarchitecture shows some similarities with both the E-SSA [14],[15] and the CRDSA ones [2] (see Fig. 2). On one hand, thesame E-SSA window-based memory processing is adopted tohandle the asynchronously arriving packet replicas (see Fig. 3).On the other hand, the replica packet(s) cancellation schemeis borrowed from the CRDSA demodulator processing. From ahardware implementation perspective, the ACRDA demodula-tor can be viewed quite comparable to that of CRDSA. It shouldbe noted that the ACRDA demodulator description in thissection is valid for both the baseline ACRDA and its variant.

The ACRDA demodulator operation can be summarized asfollows:

1) The signal is downconverted, filtered and sampled atbaseband. The sampling rate shall at least satisfy theNyquist criterion with some oversampling to account forthe radio frequency front-end excess bandwidth;

2) For the sliding window index s = 1, 2, 3 . . .a) As shown in Fig. 3, the incoming baseband signal

samples are stored in a memory spanning W VFs2

i.e. from tleading = (s− 1)ΔWTframe to tlagging =[(s− 1)ΔW +W ]Tframe. This means that once theprocess of a specific window is completed the newwindow is made of new signal samples spanning atime interval of ΔWTframe where ΔW is the windowshift in fractions of the VF duration. The windowmemory will be shifted towards the right in time byΔWTframes so that “oldest” samples spanning theleftmost part of the memory will be removed. Theemptied rightmost part of the memory will be thenfilled with the new incoming complex samples.

b) For Niter = 1, . . . Nmaxiter :

i) The common packet preamble is searched through-out the window memory using a correlator matchedto the preamble sequence.3

2The window span W in general may be a non-integer multiple of the VFduration although typically W = 3 VFs is assumed.

3The preamble sizing is following conventional techniques used for burstyMF-TDMA demodulators. The only ACRDA preamble design difference isthat it shall be sized to operate at the lowest SNIR at which the payload is ableto decode the packet. This minimum SNIR is typically derived by simulationencompassing the AWGN and the colliding packets interference. Shorteningthe preamble may reduce the overhead at the expenses of some performancedegradation. This represents a system specific design trade-off that is out ofscope for the paper. Some examples of practical preamble sizing valid forCRDSA but also applicable to ACRDA can be found in [22].


Fig. 3. ACRDA demodulator window-based block diagram: in dashed black line current window, in red dashed line the shifted window.

ii) Every time a preamble presence is detected, packetdetection is attempted using the preamble-basedchannel estimation. Similarly to E-SSA demodula-tor, packet detection can exploit power unbalancestarting with the strongest in power preambles iden-tified while scanning the memory.

iii) When the packet payload Cyclic Redundancy Check(CRC) is successfully decoded the packet is de-clared detected and then payload and signaling bitsare re-encoded and modulated to locally regeneratethe packet modulated symbols.

iv) A refined symbol-by-symbol channel estimation(complex phasor) for the decoded packet is per-formed based on the full packet content i.e. pream-ble plus data payload symbols (for more detailson the algorithm used refer to the CRDSA onesreported in [2] and [8] which are also applicable tothe ACRDA case).

v) The modulated symbol samples from the locally re-generated packet corresponding to the i-th detectedpacket are subtracted from the demodulator windowmemory to cancel this i-th packet.

vi) The physical layer packet replica(s) of the i-thdetected packet are regenerated by re-encodingand modulating the payload data and the associ-ated signaling bits. In performing this operationthe replica location signaling embedded in thepacket payload has to be modified compared tothe detected packet i as the relative location ofthe replicas is different for each replica packetreconstructed.

vii) The channel estimation (complex phasor) of thei-th detected packet replicas is obtained by corre-lating the demodulator window memory samplesat the replicas packet location with the regenerated

packet replicas.4 For more details on the algorithmadopted refer to the CRDSA ones reported in [2] and[8] which are also applicable to the ACRDA case.The replica(s) packet location can be easily derivedusing the start of the i-th decoded packet time ref-erence and shifting (with relative sign) in memoryby an integer amount of Tslot periods according tothe signaling information contained in the decodedpacket.

viii) The i-th replica packets are cancelled subtractingfrom memory the regenerated versions as describedabove at the locations identified by the i-th packetreplica location signaling.

ix) Due to the window time steps implemented in pointa) above, it is possible that a correctly detectedpacket points to a future replica location that is notwithin the current span of the sliding window. In thiscase, the demodulator shall store the location of thisreplica and packet information (location signalingand packet content). When, after a number of win-dow shifts, the replica location is finally within thespan of the sliding window, the subject stored packetcan be re-encoded, modulated, and subtracted fromthe memory.

The ACRDA gateway demodulator memory size in bits canbe simply computed as:

Λ = 2NbitsTframeWνBw, (1)

where Nbits is the number of quantization bits in the demodula-tor Analogue to Digital Converter (ADC), ν is the oversampling

4To be remarked that in general the amplitude and phase of each replica willbe different even if it is generated from the same transmitter. This is becausethe channel is typically time variant.


factor and Bw the overall signal bandwidth. It is easy to seethat in practice the memory occupancy is modest also whenconsidering the extra memory required to store the edge packetspayload bits and their location as required to implement theoption described above in ix).

C. ACRDA Versus CRDSA

The key features of the ACRDA scheme are multi-fold. Morespecifically:

1) ACRDA access is truly asynchronous, exactly like theSSA and E-SSA type of random access. ACRDA canoperate in a truly asynchronous mode with no needfor direct-sequence spread-spectrum as for SSA andE-SSA to allow contention resolution. Similar toCRDSA, ACRDA resolves packet collisions by means oftime and/or power/carrier frequency5 diversity. Althoughtime is still slotted within VFs, this concept is only localto each transmitter. ACRDA VF concept allows for trulyasynchronous access while keeping replica signaling andmodulator processing very close to CRDSA. Globally,ACRDA does not necessitate slot timing synchronizationamong transmitters. This significantly reduces systemcomplexity, signaling traffic, and modulator complexitythus enhancing network scalability.

2) ACRDA replica signaling overhead is similar to that ofCRDSA. Each ACRDA packet replica contains informa-tion about the locations of other replicas with respectto the current replica location and expressed as integernumber of slots. The proposed approach is quite simple:all VFs are composed of a known and fixed number ofslots and associated duration. When the packet is gener-ated at the transmitter side the randomly generated slotlocation of the replicas is known. Each packet containslow-overhead information about their location in terms ofrelative slots shift compared to current packet. The gate-way demodulator accurately recovers the packet symbolclock timing as well as the packet start time identified bythe preamble. With the knowledge of how many symbolsare contained in the slot the packet replica(s) locationscan be easily reconstructed.

3) ACRDA can operate with a lower number of replicasper packet than CRDSA for the same or lower loopprobabilities. The loop phenomenon basically refers tothe situation where a number of packets cannot be de-coded because all of their replicas are in unresolvablecollision with one or more replicas of other packets.As shown in [7] the loop probability rapidly decreaseswith the number of replicas, which explains why forCRDSA the best performances were obtained for 3 oreven 4 replicas despite the associated increase of physicallayer packets fed into the channel. Instead, for ACRDA,the asynchronous nature of the incoming packets at the

5By frequency diversity we mean a slight frequency offset affecting theincoming packets. The frequency diversity is particularly useful for the pream-ble detection as, thanks to their different frequency offset, it will allow todecorrelate the possible colliding packets sharing a common preamble.

gateway demodulator greatly mitigates the probability ofloops. This explains why, as shown in Section IV, thebest performances are now obtained with only 2 replicas.Note that the reduction in the required number of repli-cas is beneficial for the demodulator complexity whichalmost linearly grows with the number of replicas (seeSect. B.3.2 of [22]). At the same time ACRDA requiresa signal samples memory size that is W times (with Wtypically equal to 3) larger than CRDSA. However, mem-ory size is not considered as critical as the signal process-ing complexity. In addition, reduced number of replicasresults in lower energy consumption at transmitters.

The key advantages explained in the 3 points above are alsoaccompanied by ACRDA throughput and delay performancethat is better than CRDSA. Exhaustive simulations reportedin Section IV show that ACRDA can achieve throughput per-formance that is superior to CRDSA and a delay performancethat is decidedly better than that of CRDSA. At first glance,one could expect that ACRDA may exhibit longer accessdelays than CRDSA because of the window presence in thedemodulator, which introduces the decoding delay. However,this disadvantage is more than counterbalanced by the factthat the VF can start as soon as the packet is ready to betransmitted thanks to the RA asynchronous nature. In addition,in the ACRDA variant the first packet replica can be sent at thebeginning of the VF thus further reducing the latency. Instead,in CRDSA, all packet transmissions have to wait for the start ofnext CRDSA frame.

III. ACRDA ANALYTICAL PERFORMANCE DERIVATION

To derive the ACRDA analytical performance we need first toderive the probability mass function for the number of packetscolliding with the desired one. Considering a time window ofplus or minus a packet duration around the arrival time of thestart of the desired packet p, as described in Fig. 4 of [14],we observe that the total number kt of packets colliding withthe desired one can be represented by the sum of two randomvariables (rvs) ka and kb. Thus:

kt = kb + ka, (2)

where kb and ka represent respectively the number of collidingpackets that arrive before and after the start of the desired packetp. Assuming that packets are generated according to a Poissondistribution, kb and ka are two Poisson rvs with intensity λp =GGpNrep, while kt is a Poisson rv with intensity:

λt = 2λp = 2GGpNrep, (3)

where G is the average medium access (MAC) channel usefultraffic load expressed in information bits/symbol, Gp representsthe processing gain defined as Gp = Rs/Rb = 1/(r log2 M)where Rs is the channel baud rate, Rb is information bit rate, ris the FEC scheme coding rate, M is the modulation cardinalityand Nrep represents the number of replicas transmitted for eachpacket. Therefore, λp represents the average number of packet


Fig. 4. Example of loop event in ACRDA.

arrivals during one packet duration and λt = 2λp correspondsto the average number of packet arrivals over the ±1 packetwindow. The Poisson rv probability mass function is given bythe following equation:

fK(k;λt) =λkt exp(−λt)

k!. (4)

As it is apparent from (3), the average MAC traffic load G is anet input load which does not include the effect of replicas andthe physical layer spectral efficiency which is instead accountedin the physical layer packet traffic intensity λt. It is also recalledthat, following [1], the relation between the RA throughput Texpressed in bits/symbol, the average MAC load G and thepacket loss ratio PLR is given by:

T (G) = G [1− PLR(G)] . (5)

As shown in Fig. 4 the interference is generated by asyn-chronously arriving packets that might only partially overlapthe desired packet. In the general case, this will generate a time-varying interference component that is a function of the numberof interfering packets at each time instant. For the purpose ofthis analytical modeling, we will focus on the average interfer-ence generated over the desired packet. An empirically derivedcorrective factor (see β parameter below) will be introduced inthe analytical interference model to compensate for the smalldifference in performance of the Forward Error Correction(FEC) scheme in the presence of a time-varying interferenceover the physical layer code block.6 Assuming k equal-power7

packet arrivals interfering with the desired packet, as shown in(4), the resulting interference to noise Power Spectral Density(PSD) ratio can be approximated as the sum of k uniformrandom variables distributed from 0 to χi (0 meaning nooverlap and χi full overlap with the desired packet). χi is theinterference to noise PSD ratio χi = I0/N0 of the interferingpacket and can be derived as χi = ω/Gp, where ω = Eb/N0

is the energy per bit to noise power spectral density and Gp

the processing gain. The sum of the k uniformly distributed rvsresults in an Irwin-Hall distribution [23], [24] with mean μχ =

6The interference variability over the FEC block is due to the asynchronousnature of the ACRDA colliding packets.

7The assumption of equal packet power is required to keep the analyticalevaluation within reasonable complexity boundaries. The main objective of thefollowing approximate analysis is to provide some justification to the simulatedACRDA performance enhancement in particular for the 2 replicas case.

Fig. 5. Comparison between the interferer(s) Irwin-Hall analytical and simu-lated power PDF for the number of interfering packet Ninterf = 1, 2, 3, 4.

(k/2) · (ω/Gp), variance σ2χ = (k/12) · (ω/Gp)

2 and the fol-lowing probability density function (PDF):

fΞ(χ; k) =1

2(k − 1)!· Gp

ω

k∑n=0

(−1)n(k

n

)

·[χ · Gp

ω− n

]k−1

sign

{χ · Gp

ω− n

}, (6)

where the operator sign{·} denotes the sign function.Fig. 5 shows the PDFs for the mean interference that we

have measured within each packet duration in the simulationsassuming a Poisson packet arrival process, and it comparesit with the corresponding Irwin-Hall PDF. Note that Fig. 5shows conditional PDFs; the condition being the number ofoverlapping packet arrivals (i.e. k = Ninterf = 1, 2, 3, 4) duringthe reception of the desired packet. In regards to the replicasof the desired and interfering packets, two situations can occur.In the general case the different replicas of the desired packetwill have uncorrelated interfering packets as shown in Fig. 1(b).But in the worst case, the location of the replicas of the inter-fering packets will be correlated with the desired packet, i.e.they will have the same Tslots offset as shown in Fig. 4. In thesesituations a loop occurs in the recursive interference cancelation


process, as the replicas of the interferer packets collide withthe replicas of the desired packet, and the benefits of thespatial diversity are mitigated. It is important to characterizethe probability of occurrence of these loops in ACRDA, as theywill be driving the PLR performance of the scheme in a similarway as for CRDSA [8]. The probability of occurrence of theseloops will be driven by the RA virtual frame size (Nslots), thenumber of replicas transmitted for each packet (Nrep) and theload on the channel (G). In ACRDA, due to the asynchronousnature of the access scheme, the VFs from different users willin general partially overlap, where the perfect alignment of VFsis the exception as opposed to CRDSA where all frames fromall users are perfectly aligned in time (see Fig. 1(a)). Thus, itis expected that in ACRDA the probability of loops will belower than in CRDSA and its evaluation is the subject of thepresent model. To simplify our analysis we will consider theACRDA modulator variant described in Section II, where we“force” the location of the first packet into the first slot of theVF while randomizing the locations of the remaining replicasin the rest of the VF slots (see Fig. 4). This assumption willnot limit the applicability of the model, as we have proven bysimulations that the PLR performances of both the baselineand the variant are equivalent. The probability that the firstreplica of t packets arrive and collide with the first replica ofthe desired packet follows a Poisson distribution with intensityλl = 2GGp. Assuming that the first replica of t packets arecolliding with the first replica of the desired packet we nowderive the probabilities PT

loop(l) to have l loops with l integerand 0 ≤ l ≤ t. PT

loop(0) corresponds to the probability that noneof the t interfering packets has a loop with the desired packet(i.e. no loops). The number of different combinations thatoccur when the remaining Nrep − 1 replicas are transmitted inthe remaining Nslots − 1 of the VF can be simply computedas Nc =

(Nslots−1Nrep−1

)being

(nk

)= (n!/k!(n− k)!) the binomial

operator. Therefore, the probability that an interfering packetselects the same combination of slots in the VF than the desiredpacket for the remaining Nrep − 1 replicas is p = 1/Nc. Itshall be noted that, given a reference number of slots per VF,the probability p decreases exponentially as we increase thenumber of replicas Nrep. For example, when Nslots = 100,p = 1.0 · 10−2 for Nrep = 2 and p = 2.1 · 10−4 for Nrep = 3.Given t interfering packets and the probability p that the samecombination of slots is selected, the probability PT

loop(l) to havel loops can be simply derived as a binomial distribution:

PTloop(l; t, p) =

(t

l

)· pl · (1− p)t−l. (7)

Therefore, the general probability to have l loops regardless ofthe number of collisions can be derived as follows:

Ploop(l;G,Nrep, Nslots) =

∞∑t=0

PTloop(l; t, p) · fK(t;λl). (8)

We have considered in our model the simplest and the mostfrequently occurring form of loops which take place when twoor more independent transmitters have overlapping VFs andtransmit all their replicas with the same randomized replicas

pattern (see example in Fig. 4). In practice, more complexloops may occur when all replicas of a set of packets arein unrecoverable collision(s) with one or more replicas. Themore general case of loops has not been considered in thisassessment, as their probability of occurrence is at least oneorder of magnitude lower compared to the simpler loop casestudied. It can be proven through probabilistic analysis that theprobability of loop occurrence decreases exponentially as weincrease the number of packets involved in the loop, in a similarway as it decreases when we increase the number of replicassent for each packet, as previously described.

We now derive the ACRDA analytical performance by usingthe random access analytical framework presented in [7] forslotted systems, and extended here to the asynchronous case.We limit our analysis to the case of equal-power packets.We derive an approximation of the PLR because, as notedpreviously, not all type of loops will be taken into account inthis assessment. The general expression for the ACRDA packetloss ratio can be derived as follows:

PLR(G,Nrep, Nslots)

�[PLRNiter(G,Nrep)

]NrepPloop(0;G,Nrep, Nslots)

+∞∑l=1

[PLRloop(l)]Nrep Ploop(l;G,Nrep, Nslots), (9)

where Ploop(l) represents the probability to have l loops and hasbeen previously derived in (8), PLRNiter is the PLR expressionwhen no loops are present at Niter interference cancellation andPLRloop(l) is the PLR expression when l loops are present.We shall use the generalized random access model withoutinterference cancellation ([8, Sec. II]) for the assessment ofPLRloop(l) and the generalized random access model withinterference cancellation ([8, Sec. IV]) for the assessment ofthe PLRNiter , but adapted to the asynchronous scenario.

1) Derivation of PLRloop(l): The probability of loss of thedesired packet in the presence of l loops is approximated by:

PLRloop(l) �∞∫0

Γ

[10 log10

(ω

1 + βχ

)]· fΞ(χ; l) · dχ,

(10)

where fΞ(χ; l) is the PDF for the interference to noise PSDratio χ = I0/N0 when there are l colliding packets and has beendefined in (6). The noise power spectral density N0 is constant,but the interference power spectral density I0 is a randomvariable as it is the result of the sum of l colliding packetsover the desired packet each with a random time offset value.As explained before, the empirically derived corrective factorβ = 0.9 is multiplying the χ factor to compensate for the smalldifference in performance of the FEC scheme in the presenceof a time-varying interference over the FEC block duration.There are two effects to be considered: a) The turbo FEC hasa block interleaver which partly randomizes the non-uniformityof SNIR a cross the FEC block; b) The residual SNIR variationin the FEC block may cause some slight difference in the FERdepending on where the interfering packets are located. We


have been experimentally investigating this effect and notedthat when the SNIR is below the FEC threshold over a sizeablepart of the FEC frame, the simulated packet detection fails evenif the average SNIR over the FEC frame is above the detectionthreshold. It is known that an ideal FEC with coding rate rin a binary erasure channel can correct up to 1− r channelerasures. Practical FEC codes are able to cope with fewererasures than the ideal case and this we believe explains theslight discrepancy observed. Γ(x) is a polynomial interpolationof the coded modulation Packet Error Rate (PER) curve for agiven channel code as a function of the argument x = Eb/N0

in dB [7]. In this model (10) we have assumed the multipleaccess interference (MAI) to behave as additive white Gaussiannoise (AWGN). In general, the approximation is loose when wehave few colliding packets. Although this approximation cannotbe rigorously justified, the accuracy of this approach has beeninvestigated in Appendix B from [7].

2) Derivation of PLRNiter(G,Nrep): ACRDA implementsan iterative interference cancellation process within a slidingdecoding window. Therefore, once the window has been pro-cessed as described in Section II-B, some interfering packetsto the desired packet will have been recovered due to theInterference Cancellation (IC) process a cross the decodingwindow. We introduce here an iterative model for the PLRwhere Niter represents the window processing iteration numberand we consider that the IC process takes place at the end ofeach window processing iteration. It follows that:

PLRNiter(G,Nrep) =

∞∑k=0

PK,Niter

loss (k) · fK(k;λt), (11)

where PK,Niter

loss (k) is the probability for loss of the desiredpacket when there are k colliding packets at IC iteration Niter

and fK(k;λ) is the probability mass function for the packetarrivals as defined in (4).

Considering that the detection of the different replicas of agiven packet are independent of each other (i.e. no loops cantake place), then all replicas of the interfering packets to thedesired packet present in other locations of the window willfollow the same PLRNiter(G,Nrep) as for the desired packetgenerated by (11). As a result, after each window processingiteration, some of the k interfering packets to the desiredpacket may be cancelled because one of their Nrep − 1 replicashas been successfully decoded. The cancellation of interferingpackets due to successful detection of one of their replicasat each window processing iteration is accounted for in thefollowing expression:

PK,Niter

loss (k) =

k∑r=0

PRloss(r) · fR(r; k, q),

q =[PLRNiter−1(G,Nrep)

]Nrep−1, (12)

where PRloss(r) is the probability of loss when there are still

r residual interfering packets over the desired packet at ICiteration Niter, and fR is a Binomial distribution where thenumber of trials is k and the probability of success q is derivedfrom the PLR of the previous IC iteration given by (11). It shall

be noted that we have introduced here a recursive equation totake into account the iterative IC process within the windowand PLRNiter shall be initialized to 1 when Niter = 0. Theprobability of loss of the desired packet in the presence of rcolliding packets can be calculated in a similar way as it hasbeen done in (10) as:

PRloss(r) =

∞∫0

Γ

[10 log10

(ω

1 + β · χ

)]· fΞ(χ; r) · dχ.

(13)

IV. NUMERICAL RESULTS

Let us now analyze the ACRDA performance comparedto the CRDSA RA scheme whose analytical and simulationperformance results have been extensively reported in [7]. Acomprehensive ACRDA simulator has been developed follow-ing the RA scheme modulator and demodulator descriptionreported in Section II. All packets arrivals and associated VFare asynchronous with random delays. Packet arrival process isassumed to have a Poisson distribution. In general, the receivedpacket power levels are assumed to be distributed accordingto a lognormal distribution with mean μ = 0 and standarddeviation σ both expressed in dB. The simulation model isaccurate as real physical layer packets representative of thecoding and modulation scheme selected are generated. Aninfinite number of traffic sources are assumed to be generatinga Poisson-distributed aggregate packet traffic. In each symbolduration, the simulator generates a Poisson-distributed numberof packet arrival instances. To reduce the simulation time, thepackets relative time offset granularity is assumed to be ininteger multiples of the symbol duration. The carrier phaseis uniformly distributed in (0, 2π) while following [7] thereceived packet amplitude is typically distributed according toa lognormal distribution. AWGN is added at the input of theACRDA demodulator. The ACRDA demodulator architectureclosely follows the scheme described in Section II and theblock diagram of Fig. 3. The only simplification is relatedto the assumption of ideal estimation for the packet carrierfrequency, phase and amplitude. This assumption is justifiedby the fact that past CRDSA work has shown that there is nopractical impact of channel estimation errors on the CRDSA de-modulator performance [2], [8]. When comparing ACRDA andCRDSA performances, unless stated otherwise, it is assumedthat both ACRDA VF and CRDSA frames are composed of 100slots (i.e. Nslots = 100) each containing 100 bit informationbits. The 3GPP rate r = 1/3 FEC is assumed jointly withQPSK modulation. The energy per symbol to noise PowerSpectral Density ratio Es/N0 in the absence of packet powerfluctuations (i.e. μ = σ = 0 dB) is assumed to be 10 dB. Forthe ACRDA detector, unless stated otherwise, a window sizeof W = 3 VFs and a window shift of ΔW = 0.15 VFs areassumed. At each window shift, the ACRDA detector runs amaximum of Nmax

iter = 15 interference cancellation iterations.In Fig. 6 the analytical (see Section III) and simulated

throughput and PLR performance of ACRDA is comparedto that of CRDSA for the case of Nrep = 2. The superior


Fig. 6. Simulation and analytical CRDSA and ACRDA performance forNrep = 2, Nslots = 100 (simulations), QPSK modulation, 3GPP FEC r =1/3, packet block size 100 bits, Es/N0 = 10 dB in the presence of lognormalpackets power unbalance with μ = 0 dB, standard deviation σ = 0 dB andPoisson traffic, window size of W = 3 frames and a window step ΔW =0.15. (a) Throughput. (b) PLR.

performance of ACRDA compared to CRSDA in case of twopacket replicas is evident in particular in the low PLR region.As explained in Appendix D of [7], the loop probability is themain reason for the observed 2 replicas CRDSA reduced slopePLR characteristic. The asynchronous nature of the ACRDAreduces the probability of occurrence for destructive loops. Asa consequence, for ACRDA with 2 replicas the PLR floor isalmost two orders of magnitude lower than CRDSA. We canconclude that if the target PLR is 10−4 or higher, for ACRDAthere is no need for increasing the number of replicas to 3 as forCRDSA. The fact that PLR simulation results in the [0, 1] bits/symbol G region are slightly higher than the analytical findingsis related to the fact that we limit the analysis to the mostbasic and frequent form of loop. Thus the theoretical loopanalysis represents a lower bound for the PLR (see AppendixD in [7]). The theoretical and simulated ACRDA and CRDSAthroughput and PLR performance with 3 replicas is reported in

Fig. 7. Simulation and analytical CRDSA and ACRDA performance forNrep = 3, Nslots = 100 and Nslots = 1000 (simulations), QPSK modula-tion, 3GPP FEC r = 1/3, packet block size 100 bits, Es/N0 = 10 dB inthe presence of lognormal packets power unbalance with μ = 0 dB, standarddeviation σ = 0 dB and Poisson traffic, window size of W = 3 frames and awindow step ΔW = 0.15. (a) Throughput. (b) PLR.

Fig. 7. It is remarked the good matching between simulationand analytical results when the simulated number of frameslots is 1000. Instead when Nslots = 100 the simulation resultsare slightly worse. This can be explained by the fact thatthe analytical framework developed in [7] assumes an infinitenumber of slots/frame. In this case the loop event probabilityis very low for CRDSA too. Thus for the 3 replicas case,CRDSA has essentially the same PLR performance and slopeas ACRDA for Nslots = 1000 and slightly worse for the morepractical case Nslots = 100. This confirms the conjecture thatthe asynchronous interference nature in ACRDA and CRA hasno impact on the RA throughput. However when comparing inFig. 8 the best simulated performance of CRDSA with Nrep =3, Nslots = 100 to that of ACRDA (simulated only) withNrep = 2 with a lognormal packet power distribution with σ =3 dB, it is apparent that for a target PLR = 10−4, ACRDA hasa 35% better throughout than CRDSA. The ACRDA superior


Fig. 8. Simulation of CRDSA and ACRDA with Nrep = 2, 3 performancefor Nslots = 100, QPSK modulation, 3GPP FEC r = 1/3, packet blocksize 100 bits, Es/N0 = 10 dB in the presence of lognormal packets powerunbalance with μ = 0 dB, standard deviation σ = 0, 3 dB and Poisson traffic,window size of W = 3 frames and a window step ΔW = 0.15. The red dia-monds correspond to the case of independent lognormal power (IP) allocationfor each replica packet. (a) Throughput. (b) PLR.

performance is obtained while operating in a truly asyn-chronous access mode instead of the slotted CRDSA mode.Furthermore, as discussed before, the fact that the numberof ACRDA replicas can be reduced to 2 is reducing the de-modulator complexity by an approximate 33% factor. Giventhe positive impact of incoming packets power unbalance onperformance, one can think of artificially using different real-izations of the packet power randomization process for eachreplica transmitted by the same transmitter. In this way furtherdiversity is created among the replica packets in addition tothe location within the VF. This has the beneficial effect ofremoving the PLR floor for lognormal packet power distribu-tion investigated in [7] as Fig. 8 (dotted/diamonds line) testi-fies. Some investigation about the performance impact of thegateway ACRDA demodulator window memory size has been

Fig. 9. Simulation of ACRDA performance for Nrep = 2, Nslots = 100,QPSK modulation, 3GPP FEC r = 1/3, packet block size 100 bits, Es/N0 =10 dB in the presence of lognormal packets power unbalance with μ = 0 dB,standard deviation σ = 0 dB and Poisson traffic, window size of W = 1, 2, 3frames and a window step ΔW = 0.15. (a) Throughput. (b) PLR.

performed in Fig. 9. As already found for E-SSA, a window sizeW of three frames seems to be the optimum choice [14]. As it isseen in Fig. 9, reducing the ACRDA demodulator window sizeW to 2 VFs reduces by about 10% the throughput performanceat PLR = 10−4 while for W = 1 frame the performance lossbecomes unacceptably large. A window size 2 < W ≤ 3 istherefore recommended. Another system parameter impactingthe access latency is the number of slots per frame. Simulationshave been performed for a VF composed by 64 slots and resultscompared to 100 slots. As anticipated, the reduction of thenumber of slots/frame slightly increases the loop occurrenceprobability, as also explained analytically in [7]. This explainsthe observed increase in the PLR floor around 10−4 when usinga 64 slots VF.

The rest of this section discusses the delay performance ofboth ACRDA and CRDSA. We have considered ACRDA with2-replicas configuration and CRDSA with 3-replicas configu-ration with Nslots = 100 for both ACRDA VF and CRDSA


Fig. 10. Simulation of ACRDA (Nrep = 2, virtual frame starts with the first replica) and CRDSA (Nrep = 3) delay statistics for Nslots = 100, QPSKmodulation, 3GPP FEC r = 1/3, packet block size 100 bits, Es/N0 = 10 dB in the presence of lognormal packets power unbalance with μ = 0 dB, standarddeviation a) [left plot] σ = 0 dB, b) [right plot] σ = 3 dB and Poisson traffic, ACRDA window size of W = 3 frames and a window step ΔW = 0.15.

frame. In the simulator the delay is measured packet-by-packetas the time interval from the moment a packet is placedin the transmitter input buffer to the moment the packet issuccessfully decoded at the receiver minus the propagationdelay of the satellite link. As such, the delay results do notcontain the delay that may be induced by a congestion controlmechanism that may run before the transmitter output. In orderto present a fair and clear comparison between ACRDA andCRDSA, the delay results are expressed as normalized to theframe length, and they exclude the signal propagation delaybetween the transmitter and the receiver. Note that, unless statedotherwise, the delay results are presented corresponding tothe normalized MAC loads at which the PLR is less than orequal to 10−3. Between the ACRDA baseline and its variantexplained in this paper, Fig. 10 shows results for the variantthat dictates first replica transmission at the beginning of theVF. Fig. 11, however, shows results for both ACRDA baselineand its variant. Fig. 10(a) (left handside plot) shows the CRDSAand ACRDA percentiles of the transmission delay for equally-powered packets and for various average MAC channel loadsG. It clearly appears that for the 90% percentile the ACRDAdelay is reduced by a factor of 2.8 for G = 0.9 bits/symbol upto more than a factor of 10 for G = 0.3 bits/symbol. In case oflognormal packet power distribution with σ = 3 dB the delaysimulation results are reported in Fig. 10(b) (right handsideplot); it is apparent that the ACRDA delay reduction w.r.t.

Fig. 11. Simulation of ACRDA delay statistics for Nrep = 2, Nslots = 100,QPSK modulation, 3GPP FEC r = 1/3, packet block size 100 bits, Es/N0 =10 dB equal power packets (μ = 0 dB, standard deviation σ = 0 dB) andPoisson traffic, ACRDA window size of W = 3 frames and a window stepΔW = 0.15.

CRDSA is comparable to the case σ = 0 shown in Fig. 10(a).Fig. 11 shows delay percentiles for both ACRDA baseline andits variant with lognormal packet power distribution σ = 0 dB.At 90% percentile delay for G = 0.9 bits/symbol the baseline


ACRDA delay is reduced by a factor of 2 compared to CRDSA.The ACRDA variant (with first packet replica located at thebeginning of the VF) will have instead a delay reduction factorof 2.8. For G = 0.3 bits/symbol the ACRDA baseline delayreduction factor compared to CRDSA is limited to 1.9 (w.r.t. afactor of 10 in the ACRDA variant). Looking at the MAC accessdelay performance of ACRDA, the variant scheme is definitelythe preferable option. However, as discussed in Section II, thelatency performance should, in general, be analyzed also con-sidering congestion control algorithms and the type of traffic tobe supported, which may be of non-Poisson nature.

V. CONCLUSION

A novel RA scheme dubbed Asynchronous Contention Res-olution Diversity ALOHA (ACRDA) has been described to-gether with its key features and implementation aspects. Witha similar signaling overhead and modulator complexity com-pared to CRDSA, ACRDA achieves slightly better throughputperformance than CRDSA while operating in a truly asyn-chronous mode. This improved performance is achieved witha sizeable reduction in the demodulator complexity since onlytwo replicas are necessary. The transmission latency of theproposed scheme is also considerably improved with respectto CRDSA with a delay reduction ranging from a factor 2 to 9depending on the ACRDA scheme adopted and the MAC load.Compared to more conventional Slotted ALOHA or ALOHA,ACRDA’s throughput is about three orders of magnitudes betterallowing to achieve efficiency well in excess of 1 bits/symbolover a pure RA channel in the presence of Poisson traffic.The proposed ACRDA scheme proposed and analyzed in thispaper may benefit from techniques recently proposed which canfurther enhance its performance. The exploitation in ACRDA oftechniques such as soft combining of packet replicas proposedin [13] or the combining of the best replica packets chunks togenerate a better packet of interest as suggested in [19] or theCoded Slotted ALOHA soft combining scheme [9] representpotential area of future investigation. Similarly one can con-sider the technique proposed in [12], [13] to pseudo-randomizethe slot positions as a function of the transmitted data to removethe replica signaling overhead. This is particularly interestingin case small packets have to be transmitted. Finally the useof the bipartite graph-based framework introduced by Liva[8] for slotted ALOHA may be potentially extended to theasynchronous ACRDA case.

ACKNOWLEDGMENT

The authors would like to thank Dr. Pantelis-DanielArapoglou for his support to the work reported in this paper.The authors are also thankful for the constructive commentsand suggestions provided by the Editor and the anonymousreviewers which allowed to improve the quality of the paper.

REFERENCES

[1] E. Casini, R. De Gaudenzi, and O. del Río Herrero, “Contention Reso-lution Diversity Slotted ALOHA (CRDSA): An enhanced random accessscheme for satellite access packet networks,” IEEE Trans. Wireless Com-mun., vol. 6, no. 4, pp. 1408–1419, Apr. 2007.

[2] E. Casini, R. De Gaudenzi, O. del Río Herrero, D. Delaruelle, andJ. P. Choffray, “Method of packet mode digital communication over atransmission channel shared by a plurality of users,” U.S. Patent 8 094 672B2, Jan. 10, 2012.

[3] O. del Río Herrero and R. De Gaudenzi, “A high-performance MACprotocol for consumer broadband satellite systems,” in Proc. 27th AIAAInt. Commun. Satell. Syst. Conf., Edinburgh, U.K., Jun. 1–4, 2009,pp. 512–512.

[4] N. Abramson, “The ALOHA system—Another alternative for computercommunication,” in Proc. AFIPS Fall Joint Comput. Conf., 1970, vol. 37,pp. 281–285.

[5] G. L. Choudhury and S. S. Rappaport, “Diversity ALOHA—A randomaccess scheme for satellite communications,” IEEE Trans. Commun.,vol. COM-31, no. 3, pp. 450–457, Mar. 1983.

[6] Digital Video Broadcasting (DVB); Second Generation DVB InteractiveSatellite System; Part 2: Lower Layers for Satellite Standard, ETSI ENStd. 301 545-2 V1.1.1, Jan. 2012.

[7] O. del Río Herrero and R. De Gaudenzi, “Generalized analytical frame-work for the performance assessment of slotted random access proto-cols,” IEEE Trans. Wireless Commun., vol. 13, no. 2, pp. 809–821,Feb. 2014.

[8] G. Liva, “Graph-based analysis and optimization of contention resolutiondiversity slotted ALOHA,” IEEE Trans. Commun., vol. 59, no. 2, pp. 477–487, Feb. 2011.

[9] E. Paolini, G. Liva, and M. Chiani, “High throughput random access viacodes on graphs: Coded slotted ALOHA,” in Proc. IEEE ICC, Kyoto,Japan, Jun. 5–9, 2011, pp. 1–6.

[10] H.-C. Bui, J. Lacan, and M.-L. Boucheret, “An enhanced multiple randomaccess scheme for satellite communications,” in Proc. WTS, Apr. 18–20,2012, pp. 1–6.

[11] H.-C. Bui, J. Lacan, and M.-L. Boucheret, “Multi-slot coded ALOHAwith irregular degree distribution,” in Proc. IEEE 1st AESS ESTEL, Rome,Italy, Oct. 2012, pp. 1–6.

[12] F. Ricciato and P. Castiglione, “Pseudo-random Aloha for enhancedcollision-recovery in RFID,” IEEE Commun. Lett., vol. 17, no. 3, pp. 608–611, Mar. 2013.

[13] P. Castiglione, F. Ricciato, and P. Popovski, “Pseudo-random ALOHA forinter-frame soft combining in RFID systems,” in Proc. 18th Int. Conf.Digit. Signal Process., 2013, pp. 1–6.

[14] O. del Río Herrero and R. De Gaudenzi, “High efficiency satellite multipleaccess scheme for machine-to-machine communications,” IEEE Trans.Aerosp. Electron. Syst., vol. 48, no. 4, pp. 2961–2989, Oct. 2012.

[15] O. del Río Herrero and R. De Gaudenzi, “Methods, apparatuses andsystem for asynchronous spread-spectrum communication,” U.S. Patent7 990 874 B2, Aug. 2, 2011.

[16] O. del Río Herrero, R. De Gaudenzi, and J. L. Pijoan Vidal, “Designguidelines for advanced random access protocols,” in Proc. 30th AIAAInt. Commun. Satell. Syst. Conf., Ottawa, ON, Canada, Sep. 24–27, 2012,pp. 1–15.

[17] J. Massey and P. Mathys, “The collision channel without feedback,” IEEETrans. Inf. Theory, vol. IT-31, no. 2, pp. 192–204, Mar. 1985.

[18] C. Kissling, “Performance enhancements for asynchronous random accessprotocols over satellite,” in Proc. IEEE ICC, Kyoto, Japan, Jun. 5–9, 2011,pp. 1–6.

[19] F. Clazzer and C. Kissling, “Enhanced contention resolution ALOHA—ECRA,” in Proc. 9th Int. ITG Conf. SCC, Munich, Germany, Jan. 2013,pp. 1–6.

[20] O. del Río Herrero, E. Casini, and R. De Gaudenzi, “Contention Res-olution Diversity Slotted Aloha Plus Demand Assignment (CRDSA-DA): An enhanced MAC protocol for satellite access packet networks,”in Proc. 23rd AIAA Int. Commun. Satell. Syst. Conf., Rome, Italy,Sep. 25–28, 2005. [CD-ROM].

[21] Satellite Earth Stations and Systems; Air Interface for S-band MobileInteractive Multimedia (S-MIM); Part 5: Protocol Specifications, LinkLayer, ETSI TS Std. 102 721-5 v1.1.1, Dec. 2011.

[22] Digital Video Broadcasting (DVB); Second Generation DVB InteractiveSatellite System (DVB-RCS2); Guidelines for Implementation and Use ofLLS: DVB Document A162, EN Std. 301 545-2, Feb. 2013.

[23] J. O. Irwin, “On the frequency distribution of the means of samples from apopulation having any law of frequency with finite moments, with specialreference to Pearson’s type II,” Biometrika, vol. 19, no. 3/4, pp. 225–239,Dec. 1927.

[24] P. Hall, “The distribution of means for samples of size n drawn from apopulation in which the variate takes values between 0 and 1, all suchvalues being equally probable,” Biometrika, vol. 19, no. 3/4, pp. 240–245,Dec. 1927.


Riccardo De Gaudenzi was born in Italy, in 1960.He received the Doctor of Engineer (cum laude)degree in electronic engineering from the Universityof Pisa, Pisa, Italy, in 1985 and the Ph.D. degreefrom the Technical University of Delft, Delft, TheNetherlands, in 1999. From 1986 to 1988, he waswith the Department of Stations and Communica-tions Engineering, European Space Agency (ESA),Darmstadt, Germany, where he was involved in satel-lite telemetry, tracking and control (TT&C) groundsystems design and testing. In 1988, he joined ESA’s

Research and Technology Centre (ESTEC), Noordwijk, The Netherlands,where he has been the Head of the Radio Frequency Systems, Payload andTechnology Division since 2005. The division is responsible for supportingthe definition and development of advanced satellite systems, subsystems, andrelated technologies for telecommunications, navigation, and earth observationapplications. He has been responsible for a large number of research anddevelopment activities for TT&C and telecom and navigation applications. In1996, he spent one year with Qualcomm Inc., San Diego, CA, USA, withthe Globalstar LEO Project System Group under an ESA fellowship. Hiscurrent interests mainly include efficient digital modulation and multiple accesstechniques for fixed and mobile satellite services, synchronization topics, adap-tive interference mitigation techniques, and communication systems simulationtechniques. He actively contributed to the development and demonstration ofthe ETSI S-UMTS Family A, S-MIM, DVB-S2, DVB-S2X, DVB-RCS2, andDVB-SH standards. From 2001 to 2005, he has been serving as an AssociateEditor for CDMA and Synchronization for the IEEE TRANSACTIONS ON

COMMUNICATIONS. He is currently an Associate Editor for the JOURNAL

OF COMMUNICATIONS AND NETWORKS. He was the corecipient of the 2003and 2008 Jack Neubauer Memorial Award Best Paper from the IEEE VehicularTechnology Society.

Oscar del Río 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, and a Post-graduate degree in space science and technologywith emphasis in satellite communications from theInstitute for Space Studies of Catalonia (IEEC),Barcelona, Spain, in 1995. In 1996, he joined the Re-search and Technology Center (ESTEC), EuropeanSpace Agency (ESA), Noordwijk, The Netherlands,

where he worked as a Radio Navigation System Engineer in the preparationof the Galileo Program in 1996 and 1997 and as a Communications SystemsEngineer with the Department of Electrical Systems from 1998 to 2009. Since2010, he has been working for the Iris Project in ESA’s TelecommunicationDirectorate, aiming at the development of a new satellite-based air–groundcommunication system for air traffic management. His research interests in-clude packet access, resource management schemes, and Internet Protocolinterworking for future broadband satellite systems.

Guray Acar was born in Antakya, Turkey, in 1974.He received the B.Sc. degree in electrical and elec-tronics engineering from the Middle East TechnicalUniversity, Ankara, Turkey, in 1996 and the M.Sc.degree in communications and signal processing andthe Ph.D. degree in broadband satellite networkingfrom the Imperial College of London, London, U.K.,in 1997 and 2001, respectively. In 2010, he joinedthe Research and Technology Center (ESTEC),European Space Agency (ESA), Noordwijk, TheNetherlands, after having worked with the Centre

for Communication Systems Research, University of Surrey, Surrey, U.K.,from 2005.

His research and development interests include packet-level network simu-lations, medium-access control, radio resource management, mobility manage-ment, and higher layer protocol adaptations in satellite networks.

Eloi Garrido Barrabés was born in Barcelona,Spain, in 1990. He received the B.Sc. degree in elec-tronic systems engineering in telecommunicationsfrom the University Ramon Llull, Barcelona, Spain,in 2013. He is currently working toward the M.Sc.degree in embedded systems at Delft Universityof Technology (TUD), Delft, The Netherlands. In2012, he joined the Research and Technology Cen-ter (ESTEC), European Space Agency, Noordwijk,The Netherlands, as a Stagiaire. He worked on thecommunication protocol named ACRDA described

in this paper and presented it as final project degree in Barcelona.

Documents

Asynchronous Contention Resolution Diversity ALOHA: Making CRDSA Truly Asynchronous