Asynchronous Contention Resolution Diversity ... - Semantic Scholar

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2014.2334620, IEEE Transactions on Wireless Communications 1

Asynchronous Contention Resolution Diversity ALOHA: Making CRDSA Truly Asynchronous Riccardo De Gaudenzi, Oscar del R´ıo Herrero, Guray Acar, Eloi Garrido Barrab´es European Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands e-mail: {Riccardo.De.Gaudenzi}{Oscar.del.Rio.Herrero}{Guray.Acar}@esa.int, {[email protected]}

Abstract—Following the introduction of Contention Resolution Diversity Slotted ALOHA (CRDSA), a number of variants of the scheme have been proposed in the literature. A major drawback of these slotted Random Access (RA) schemes is related to the need to keep slot synchronization among all transmitters. The volume of signalling generated to maintain transmitters’ slot synchronization is impractical for large networks. In this paper, we describe in detail Asynchronous Contention Resolution Diversity ALOHA (ACRDA), which represents the evolution of the CRDSA RA scheme. ACRDA provides better throughput performance with reduced demodulator complexity and lower transmission latency than its predecessor while allowing truly asynchronous access to the shared medium. The performance of the ACRDA protocol is evaluated via mathematical analysis and computer simulations and is compared to that of CRDSA.

Keywords: Satellite communication, SCADA systems, Multiaccess communication, Time division multiple access, Interference suppression. I. I NTRODUCTION There is a growing interest to enhance the performance of random access protocols suitable to support low-cost interactive satellite and terrestrial terminals for the fixed broadband consumer market and mobile applications, including machineto-machine (M2M) communications. Contention Resolution Diversity Slotted ALOHA (CRDSA) [4], [5], [6] has shown how the Slotted ALOHA (SA) [1] and Diversity Slotted ALOHA (DSA) [2] throughput can be significantly increased by a relatively simple extension of the DSA concept together with iterative interference cancellation at the demodulator. The 2nd generation Digital Video Broadcasting Return Channel by Satellite (DVB-RCS2) standard [7] optionally supports CRDSA on the return link for both data and signalling traffic. Reference [8] provides a comprehensive analytical framework able to assess the performance of a number of slotted access techniques from the more conventional SA and DSA to the more elaborated CRDSA in the presence of arbitrary traffic and power distribution and taking into account effective coding and modulation schemes adopted at physical layer. In particular, in [6] and in [8] it is shown that the CRDSA performance can be enhanced by using more than two replicas so as to reduce the probability of the so-called ”loop” phenomenon1 . Liva in [9] extended the concept of CRDSA to encompass an irregular repetition scheme which is dubbed Irregular Repetition Slotted ALOHA (IRSA). The author has been exploiting the bipartite graphs theory, which is typically 1 A loop phenomenon occurs when all replicas of a set of packets are in unrecoverable collision with one or more replicas (see Sect. III).

used in the design and analysis of forward error correcting schemes, in order to design the optimized IRSA irregular graph and packet repetition scheme. CRDSA represents a special case of IRSA in which all the packet replicas have the same mass probability thus leading to a regular graph. Although IRSA exhibits some maximum throughput increase compared to the two-replicas CRDSA, its performance at the Packet Loss Ratio (PLR) of 10−3 or lower appears less attractive when compared to CRDSA with 3-4 replicas results reported in [6]. The Coded Slotted ALOHA (CSA) [10] scheme represents a further generalization of the IRSA scheme. CSA is encoding rather than repeating the packets like in CRDSA and IRSA and splitting them as packet segments in the frame slot. For each transmission the code to be used is randomly selected from a pre-defined code-book and a probability mass function like in IRSA. Other CRDSA-like schemes have been recently proposed and are shortly reviewed in the following. The first one is the Multi-Slots Coded ALOHA (MuSCA) RA scheme was introduced by Bui et al [11]. Unlike CRDSA, but similarly to CSA, the different slots randomly assigned to a single user in a given frame are not containing the same payload information. Instead, the coded symbols embedding Forward Error Correction (FEC) redundancy are spread across two or more bursts in the frame slots. In the MuSCA scheme the signalling bits are not included in the packet payload but are independently coded from the payload. Results reported in [11] show a sizeable improvement in throughput compared to CRDSA and IRSA schemes. With the MuSCA scheme a lower coding rate than the CRDSA one is achieved at the expenses of additional complexity and signalling overhead. A further enhancement of the MuSCA scheme is reported in [12] where, similarly to CSA, an irregular degree distribution of the MuSCA coding rates is applied to the different packets. In this way the throughput performances compared to MuSCA are further enhanced. Other slotted RA schemes exploiting iterative cancellation have been proposed for application in the domain of Radio-frequency identification (RFID). In [13] the slot selection in each frame is not random as in conventional SA but rather based on a deterministic pseudo-random function of the message payload. This allows to perform cancellation of the received message from previous frames transmission attempts thus improving the system throughput. In [14] the previous concept of inter-frame interference cancellation is coupled with convolutional encoding allowing inter-frame soft combining of multiple transmission attempts across different frames to increase the probability of correct message decoding. In particular, to reduce memory occupancy, it is proposed to

1536-1276 (c) 2013 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.


only store the log-likelihood ratios instead of complex samples by using soft combining algorithms instead of interference cancellation. Another approach to enhance the performance of packetbased Spread-Spectrum ALOHA (SSA) RA adopting packetoriented window memory-based iterative interference cancellation dubbed Enhanced Spread-Spectrum ALOHA (E-SSA) is described in detail and analyzed by analytical and simulations means in [15], [16]. The analysis reported in [15] takes into account arbitrary traffic arrival processes and power distribution as well as the real coding and modulation adopted. E-SSA outperforms CRDSA for two main reasons: a) the avoidance of packet replicas transmission thanks to the direct-sequence spreading sequence ”isolation” mitigating the other packets’ collision impact; b) the higher traffic aggregation achieved by using spreading techniques [17] that largely reduces the fluctuations in the number of received packets for a given Poisson traffic load. Moreover, E-SSA (as SSA) has another major advantage over SA/DSA/CRDSA i.e. its truly asynchronous RA nature eliminates the need to maintain accurate slot synchronization among all transmitters unlike the case in SA/DSA/CRDSA. The need for transmitter synchronization is a major drawback for large networks as the signalling overhead scales up with the number of transmitters independently from their traffic activity factor. The capacity of asynchronous collision channel without feedback was investigated by Massey in his seminal paper together with protocols sequences for achieving the capacity boundaries [18]. In this work the capacity region for RA with no slot synchronization was derived. The capacity of asynchronous RA for infinite number of users was found to be identical to the one of SA. This information theory result encourages the search for efficient non slotted RA schemes not using spread-spectrum techniques. A first contribution in relaxing the synchronization accuracy for slotted RA has been provided by Kissling in [19], which proposed a new RA scheme dubbed Contention Resolution ALOHA (CRA). CRA removes the notion of slots inside the CRDSA or IRSA frames allowing the replica packet(s) from individual transmitters to be sent with a random delay (and possibly different duration) within the frame boundaries. CRA represents an interesting evolution of the original CRDSA scheme, although it still requires the transmitter to remain synchronized at frame level. It should be remarked that the analysis reported in [19] compares CRA with that of a suboptimal CRDSA configuration. If the results in [8] for CRDSA with coding rate 1/3 and three-replicas are compared with the CRA 3 replica case in [19], it is apparent that CRDSA outperforms CRA. Another relevant RA scheme recently proposed is the Enhanced Contention Resolution ALOHA (ECRA) [20]. It represents an extension of the frame-based CRA protocol described above. The initial demodulation steps are identical to the CRA ones. The enhancement consists in making a further attempt to decode those packets that were detected but not successfully decoded due to the collision(s). The idea is to combine symbols from different packet replica(s) to generate a new packet with higher signal-to-noise ratio than the individual replicas and to attempt its decoding. If decoding is successful the original replicas will be cancelled and a

new frame decoding pass begins. With two replicas, ECRA performance were shown to be superior to CRA but inferior to CRDSA for QPSK with FEC code rate 1/4. ECRA was shown to outperform CRDSA for code rate 1/2. The ACRDA scheme described in this paper introduces a novel approach to achieve high-performance, trulyasynchronous RA without the need to use spread spectrum techniques. ACRDA reduces the gap between the CRDSA and E-SSA RA schemes for systems that do not adopt spreadspectrum techniques and it performs better than CRDSA. While ACRDA demodulator design will be shown to possess several similarities with that of E-SSA, the feature of exploiting packet replicas and associated location signalling typical of CRDSA is preserved, which boosts packet collision resolution probability. The reason for basing ACRDA on the CRDSA type of processing instead of IRSA or MuSCA is related to its simplicity and robustness of implementation (including signalling) and good performance at PLR ≤ 10−3 which is of practical interest. Section II describes in detail the ACRDA concept emphasizing the differences with respect to CRDSA and CRA. An analytical model for estimating the ACRDA performance is derived in Section III. Section IV presents analytical and simulation results comparing ACRDA and CRDSA performance in terms of throughput, packet loss ratio, and transmission latency. Section V presents the conclusions of the paper. II. ACRDA C ONCEPT D ESCRIPTION In slotted RA, for a given receiver, the boundaries of time slots and slots frames are defined in reference to the timeline at the given receiver. Slot synchronization mechanisms are adopted to control each transmitter slot timing, so that bursts arrive at the receiver within the boundaries of the intended slot. In ACRDA, slot and frame boundaries are not defined globally in reference to the timeline at the centralized gateway demodulator. Instead, the boundaries of slots and frames are local to the transmitter and completely asynchronous among transmitters. The term Virtual Frame (VF) is used in the rest of the paper to specifically refer to this concept of frame of slots that is only local to each transmitter. In ACRDA, for all transmitters, each VF is composed of a number of slots Nslots and each slot has a duration Tslot with an overall frame duration Tframe = Nslots · Tslot . In the following we assume that one slot corresponds to a burst length. In general the slot duration could actually take any other value including fractions of the burst length. Figure 1-a depicts packets at the slotted CRDSA demodulator. Frame and slot boundaries are defined reference to the receiver timeline. Hence, all packets arrive within slot boundaries, and all packets that are copies of each other arrive in the same CRDSA frame. This allows a frame-based memory processing at the demodulator side as frames’ contents are totally decorrelated. Instead, Fig. 1-b) shows the notion of ACRDA VFs and associated slots whose definition is local to each transmitter. Different transmitters are not time synchronized, and hence, the time offset between VF(i), VF(i − 1), VF(i + 1) is arbitrary. In a given transmitter the VFs will start with a random time offset, which is typically



specified by the random access congestion control mechanism, as shown in Fig. 1-b. In the ideal case the slot (Tslot ) and frame (Tframe ) durations are the same for the all transmitters in the shared medium. In case of mobile applications the Doppler effect may have an appreciable impact in terms of incoming packets clock frequency offset. In this situation the VFs will have slightly different duration. However, the localization process of the replica packets within each VF will remain accurate as the gateway burst demodulator will extract for each VF its own clock reference. The ACRDA RA scheme can easily be incorporated in a conventional Multi-Frequency Time Division Multiple Access (MF-TDMA) system by reserving a number of frequency slots for ACRDA usage in a semi-static fashion. Standard MF-TDMA can still be operated in the remaining frequency slots. When more frequency slots are available for RA the ACRDA scheme can also be used in multi-frequency fashion placing VFs also on different frequency slots randomly selected. A. ACRDA Modulator 1) Baseline: The ACRDA modulator functional block diagram is similar to the CRDSA one described in detail in Fig. 2, p. 1414 of [4]. The ACRDA modulator operation can be summarized as follows: 1) The incoming information is buffered and organized in packets of fixed size; 2) The locations of the Nrep packet replicas within the VF slots are randomly selected among the possible Nslots each having duration Tslot . In case the randomly generated replica locations are overlapping a new set of random locations is produced; 3) The current i-th packet is coded together with the replica packet location(s) slot offset(s) information relative to the start of the current packet time within the VF with duration Tframe . The replicas signalling location occupies a given number of bits in a known location in the packet payload; 4) The start time τi of the current VF i is defined at the transmitter side once the physical layer packet is ready to be transmitted. No network-wide timing synchronization is required for controlling τi thus the access is truly asynchronous; 5) The coded and modulated packets with ancillary replica location signalling information are then transmitted in the randomly selected slots of the VF. If required, the associated packet replica(s) power level can be randomized on a frame-by-frame basis to further enhance the ACRDA throughput. In general, the same randomized power level is applied to all the packet replicas present in the VF. However, depending on the system design, it may be more convenient to exploit different realizations of the power randomization for the packet replica(s) contained in the VF (See Sect. IV). 6) A packet preamble containing a known sequence common to all transmitters is then appended at the beginning of the packet to allow packet acquisition and channel estimation by the central demodulator.

It is remarked that only the third and fourth steps above are different from the CRDSA modulator processing [4] whereby the start of frame at the satellite transponder (or gateway demodulator) interface input is common to all network transmitters and the signalled packet replica(s) location (slot number) is absolute and not relative to the current packet replica as in ACRDA. The VF is generated at the terminal side when a new packet is ready for transmission. In case the new packet arrived during the current packet VF duration, the VF will be generated after the last replica of the current VF. 2) Variant: A slightly modified version of ACRDA can be obtained by ”forcing” the location of the first packet replica into the first slot of the VF while randomizing the locations of the remaining replicas in the rest of the VF slots. As we will see in Sect. IV, the main advantage of this ACRDA variant resides in the transmission delay reduction since, compared to the baseline, there is no waiting time for the first packet replica transmission. However, this ACRDA variant advantage may be less significant when congestion control schemes that run on top of the Media Access Control (MAC) layer, as in any practical RA system, generate delays that are much longer than the ACRDA VF duration. The variant approach works fine if the VF start time is random, which is the case when packet arrival instants are random. If this is not the case, VF start time randomization is needed (see below). Congestion control policies for RA over satellite typically delay the transmission of the next packets by a randomly distributed interval (e.g. following an exponential distribution). The congestion control algorithm can be applied when collision occurs or depending on the current gateway MAC load estimation to avoid congestion instabilities. There are applications such as tele-voting whereby the congestion control countermeasures have to be implemented by default as the traffic by nature is very concentrated in time and differs from Poisson type of distribution. In summary, in the majority of systems, congestion control kicks-in when the MAC load approaches a critical level potentially impacting the system stability, thus the ACRDA variant will provide a delay reduction for non-critical MAC loads (see Sect. 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 retransmissions will be very modest. However, depending on the system and service characteristics, the inclusion of an ARQ mechanism could be justified [21], [22]. Following the discussion above, in the following we will report the results for both the ACRDA baseline and variant. In order to facilitate comparison with other RA schemes, no congestion control and retransmission mechanism will be included in this study. B. ACRDA Demodulator ACRDA demodulator operation is considerably different from that of CRDSA due to the asynchronous nature of ACRDA VFs. Nonetheless, the proposed ACRDA demodulator architecture shows some similarities with both the ESSA [15], [16] and the CRDSA ones [5] (see Fig. 2). On one hand, the same E-SSA window-based memory processing is adopted to handle the asynchronously arriving packet replicas



(see Fig. 3). On the other hand, the replica packet(s) cancellation scheme is borrowed from the CRDSA demodulator processing. From a hardware implementation perspective, the ACRDA demodulator can be viewed quite comparable to that of CRDSA. It should be noted that the ACRDA demodulator description in this section is valid for both the baseline ACRDA and its variant. The ACRDA demodulator operation can be summarized as follows: 1) The signal is downconverted, filtered and sampled at baseband. The sampling rate shall at least satisfy the Nyquist criterion with some oversampling to account for the 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)∆W Tframe to tlagging = [(s − 1)∆W + W ]Tframe . This means that once the process of a specific window is completed the new window is made of new signal samples spanning a time interval of ∆W Tframe where ∆W is the window shift in fractions of the VF duration. The window memory will be shifted towards the right in time by ∆W Tframes so that ”oldest” samples spanning the leftmost part of the memory will be removed. The emptied rightmost part of the memory will be then filled with the new incoming complex samples. max b) For Niter = 1, · · · Niter : i) The common packet preamble is searched throughout the window memory using a correlator matched to the preamble sequence3 . ii) Every time a preamble presence is detected, packet detection is attempted using the preamble-based channel estimation. Similarly to E-SSA demodulator, packet detection can can exploit power unbalance starting with the strongest in power preambles identified while scanning the memory. iii) When the packet payload Cyclic Redundancy Check (CRC) is successfully decoded the packet is declared detected and then payload and signalling bits are re-encoded and modulated to locally regenerate the packet modulated symbols. iv) A refined symbol-by-symbol channel estimation (complex phasor) for the decoded packet is performed based on the full packet content i.e. preamble plus data payload symbols (for 2 The window span W in general may be a non-integer multiple of the VF duration although typically W = 3 VFs is assumed. 3 The preamble sizing is following conventional techniques used for bursty MF-TDMA demodulators. The only ACRDA preamble design difference is that it shall be sized to operate at the lowest SNIR at which the payload is able to decode the packet. This minimum SNIR is typically derived by simulation encompassing the AWGN and the colliding packets interference. Shortening the preamble may reduce the overhead at the expenses of some performance degradation. This represents a system specific design trade-off that is out of scope for the paper. Some examples of practical preamble sizing valid for CRDSA but also applicable to ACRDA can be found in [23].

more details on the algorithm used refer to the CRDSA ones reported in [5] and [9] which are also applicable to the ACRDA case). v) The modulated symbol samples from the locally regenerated packet corresponding to the i-th detected packet are subtracted from the demodulator window memory to cancel this ith packet. vi) The physical layer packet replica(s) of the i-th detected packet are regenerated by reencoding and modulating the payload data and the associated signalling bits. In performing this operation the replica location signalling embedded in the packet payload has to be modified compared to the detected packet i as the relative location of the replicas is different for each replica packet reconstructed. vii) The channel estimation (complex phasor) of the i-th detected packet replicas is obtained by correlating the demodulator window memory samples at the replicas packet location with the regenerated packet replicas4 . For more details on the algorithm adopt refer to the CRDSA ones reported in [5] and [9] which are also applicable to the ACRDA case. The replica(s) packet location can be easily derived using the start of the i-th decoded packet time reference and shifting (with relative sign) in memory by an integer amount of Tslot periods according to the signalling information contained in the decoded packet. viii) The i-th replica packets are cancelled subtracting from memory the regenerated versions as described above at the locations identified by the i-th packet replica location signalling. ix) Due to the window time steps implemented in point a) above, it is possible that a correctly detected packet points to a future replica location that is not within the current span of the sliding window. In this case, the demodulator shall store the location of this replica and packet information (location signaling and packet content). When, after a number of window shifts, the replica location is finally within the span of the sliding window, the subject stored packet can be re-encoded, modulated, and subtracted from the memory. The ACRDA gateway demodulator memory size in bits can be simply computed as: Λ = 2Nbits Tframe W νBw ,

(1)

where Nbits is the number of quantization bits in the demodulator Analogue to Digital Converter (ADC), ν is the oversampling factor and Bw the overall signal bandwidth. It is 4 To be remarked that in general the amplitude and phase of each replica will be different even if it is generated from the same transmitter. This is because the channel is typically time variant.



easy to see that in practice the memory occupancy is modest also when considering the extra memory required to store the edge packets payload bits and their location as required to implement the option described above in ix). C. ACRDA versus CRDSA The key features of the ACRDA scheme are multi-fold. More specifically: 1) ACRDA access is truly asynchronous, exactly like the SSA and E-SSA type of random access. ACRDA can operate in a truly asynchronous mode with no need for directsequence spread-spectrum as for SSA and E-SSA to allow contention resolution. Similar to CRDSA, ACRDA resolves packet collisions by means of time and/or power/carrier frequency5 diversity. Although time is still slotted within VFs, this concept is only local to each transmitter. ACRDA VF concept allows for truly asynchronous access while keeping replica signalling and modulator processing very close to CRDSA. Globally, ACRDA does not necessitate slot timing synchronization among transmitters. This significantly reduces system complexity, signalling traffic, and modulator complexity thus enhancing network scalability. 2) ACRDA replica signalling overhead is similar to that of CRDSA. Each ACRDA packet replica contains information about the locations of other replicas with respect to the current replica location and expressed as integer number of slots. The proposed approach is quite simple: all VFs are composed of a known and fixed number of slots and associated duration. When the packet is generated at the transmitter side the randomly generated slot location of the replicas is known. Each packet contains low-overhead information about their location in terms of relative slots shift compared to current packet. The gateway demodulator accurately recovers the packet symbol clock timing as well as the packet start time identified by the preamble. With the knowledge of how many symbols are contained in the slot the packet replica(s) locations can be easily reconstructed. 3) ACRDA can operate with a lower number of replicas per packet than CRDSA for the same or lower loop probabilities. The loop phenomenon basically refers to the situation where a number of packets cannot be decoded because all of their replicas are in unresolvable collision with one or more replicas of other packets. As shown in [8] the loop probability rapidly decreases with the number of replicas, which explains why for CRDSA the best performances were obtained for 3 or even 4 replicas despite the associated increase of physical layer packets fed into the channel. Instead, for ACRDA, the asynchronous nature of the incoming packets at the gateway demodulator greatly mitigates the probability of loops. This explains why, as shown in Sect. IV, the best performances are now obtained with only 2 replicas. Note that the reduction in the required number of replicas is beneficial for the demodulator complexity which almost linearly grows with the 5 By frequency diversity we mean a slight frequency offset affecting the incoming packets. The frequency diversity is particularly useful for the preamble detection as, thanks to their different frequency offset, it will allow to decorrelate the possible colliding packets sharing a common preamble.

number of replicas (see Sect. B.3.2 of [23]). At the same time ACRDA requires a signal samples memory size that is W times (with W typically equal to 3) larger than CRDSA. However, memory size is not considered as critical as the signal processing complexity. In addition, reduced number of replicas results in lower energy consumption at transmitters. The key advantages explained in the 3 points above are also accompanied by ACRDA throughput and delay performance that is better than CRDSA. Exhaustive simulations reported in Sect. IV show that ACRDA can achieve throughput performance that is superior to CRDSA and a delay performance that is decidedly better than that of CRDSA. At first glance, one could expect that ACRDA may exhibit longer access delays than CRDSA because of the window presence in the demodulator, which introduces the decoding delay. However, this disadvantage is more than counterbalanced by the fact that the VF can start as soon as the packet is ready to be transmitted thanks to the RA asynchronous nature. In addition, in the ACRDA variant the first packet replica can be sent at the beginning of the VF thus further reducing the latency. Instead, in CRDSA, all packet transmissions have to wait for the start of next CRDSA frame. III. ACRDA A NALYTICAL P ERFORMANCE D ERIVATION To derive the ACRDA analytical performance we need first to derive the probability mass function for the number of packets colliding with the desired one. Considering a time window of plus or minus a packet duration around the arrival time of the start of the desired packet p, as described in Fig. 4 of [15], we observe that the total number kt of packets colliding with the desired one can be represented by the sum of two random variables (rvs) ka and kb . Thus: kt = kb + ka ,

(2)

where kb and ka represent respectively the number of colliding packets that arrive before and after the start of the desired packet p. Assuming that packets are generated according to a Poisson distribution, kb and ka are two Poisson rvs with intensity λp = GGp Nrep , while kt is a Poisson rv with intensity: λt = 2λp = 2GGp Nrep , (3) where G is the average medium access (MAC) channel useful traffic load expressed in information bits/symbol, Gp represents the processing gain defined as Gp = Rs /Rb = 1/(r log2 M ) where Rs is the channel baud rate, Rb is information bit rate, r is the FEC scheme coding rate, M is the modulation cardinality and Nrep represents the number of replicas transmitted for each packet. Therefore, λp represents the average number of packet arrivals during one packet duration and λt = 2λp corresponds to the average number of packet arrivals over the ±1 packet window. The Poisson rv probability mass function is given by the following equation: λkt exp(−λt ) . (4) k! As it is apparent from (3), the average MAC traffic load G is a net input load which does not include the effect of replicas fK (k; λt ) =



and the physical layer spectral efficiency which is instead accounted in the physical layer packet traffic intensity λt . It is also recalled that, following [4], the relation between the RA throughput T expressed in bits/symbol, the average MAC load G and the packet loss ratio P LR is given by: T (G) = G[1 − P LR(G)].

(5)

As shown in Fig. 4 the interference is generated by asynchronously arriving packets that might only partially overlap the desired packet. In the general case, this will generate a time-varying interference component that is a function of the number of interfering packets at each time instant. For the purpose of this analytical modelling, we will focus on the average interference generated over the desired packet. An empirically derived corrective factor (see β parameter below) will be introduced in the analytical interference model to compensate for the small difference in performance of the Forward Error Correction (FEC) scheme in the presence of a time-varying interference over the physical layer code block6 . 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 uniform random variables distributed from 0 to χi (0 meaning no overlap and χi full overlap with the desired packet). χi is the interference to noise PSD ratio χi = I0 /N0 of the interfering packet 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 rvs results in an Irwin-Hall distribution k · ( Gωp )2 [24], [25] with mean µχ = k2 · Gωp , variance σχ2 = 12 and the following probability density function (PDF): k Gp X 1 n k fΞ (χ; k) = · (−1) n 2(k − 1)! ω n=0 k−1 Gp Gp · χ· −n sign χ · − n , (6) ω ω 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 simulations assuming a Poisson packet arrival process, and it compares it with the corresponding Irwin-Hall PDF. Note that Fig. 5 shows conditional PDFs; the condition being the number of overlapping packet arrivals (i.e. k = Ninterf = 1, 2, 3, 4) during the reception of the desired packet. In regards to the replicas of the desired and interfering packets, two situations can occur. In the general case the different replicas of the desired packet will have uncorrelated interfering packets as shown in Fig. 1-b. But in the worst case, the location of the replicas of the interfering packets will be correlated with the desired packet, i.e. they will have the same Tslots offset 6 The interference variability over the FEC block is due to the asynchronous nature of the ACRDA colliding packets. 7 The assumption of equal packet power is required to keep the analytical evaluation within reasonable complexity boundaries. The main objective of the following approximate analysis is to provide some justification to the simulated ACRDA performance enhancement in particular for the 2 replicas case.

as shown in Fig. 4. In these situations a loop occurs in the recursive interference cancelation process, as the replicas of the interferer packets collide with the replicas of the desired packet, and the benefits of the spatial diversity are mitigated. It is important to characterize the probability of occurrence of these loops in ACRDA, as they will be driving the PLR performance of the scheme in a similar way as for CRDSA [8]. The probability of occurrence of these loops will be driven by the RA virtual frame size (Nslots ), the number of replicas transmitted for each packet (Nrep ) and the load on the channel (G). In ACRDA, due to the asynchronous nature of the access scheme, the VFs from different users will in general partially overlap, where the perfect alignment of VFs is the exception as opposed to CRDSA where all frames from all users are perfectly aligned in time (see Fig. 1-a). Thus, it is expected that in ACRDA the probability of loops will be lower than in CRDSA and its evaluation is the subject of the present model. To simplify our analysis we will consider the ACRDA modulator variant described in Sect. II, where we ”force” the location of the first packet into the first slot of the VF while randomizing the locations of the remaining replicas in the rest of the VF slots (see Fig. 4). This assumption will not limit the applicability of the model, as we have proven by simulations that the PLR performances of both the baseline and the variant are equivalent. The probability that the first replica of t packets arrive and collide with the first replica of the desired packet follows a Poisson distribution with intensity λl = 2GGp . Assuming that the first replica of t packets are colliding with the first replica of the desired packet we now derive T the probabilities Ploop (l) to have l loops with l integer and T 0 ≤ l ≤ t. Ploop (0) corresponds to the probability that none of the t interfering packets has a loop with the desired packet (i.e. no loops). The number of different combinations that occur when the remaining Nrep − 1 replicas are transmitted in the remaining Nslots be simply computed as − 1 of nthe VF can −1 n! the binomial operator. Nc = NNslots being = k!(n−k)! −1 k rep Therefore, the probability that an interfering packet selects the same combination of slots in the VF than the desired packet for the remaining Nrep − 1 replicas is p = 1/Nc . It shall be noted that, given a reference number of slots per VF, the probability p decreases exponentially as we increase the number 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 same combination of T slots is selected, the probability Ploop (l) to have l loops can be simply derived as a binomial distribution: t T Ploop (l; t, p) = · pl · (1 − p)t−l . (7) l Therefore, the general probability to have l loops regardless of the number of collisions can be derived as follows: ∞ X T Ploop (l; G, Nrep , Nslots ) = Ploop (l; t, p) · fK (t; λl ). (8) t=0

We have considered in our model the simplest and the most frequently occurring form of loops which take place when two or more independent transmitters have overlapping VFs and transmit all their replicas with the same randomized replicas



pattern (see example in Fig. 4). In practice, more complex loops may occur when all replicas of a set of packets are in unrecoverable collision(s) with one or more replicas. The more general case of loops has not been considered in this assessment, as their probability of occurrence is at least one order of magnitude lower compared to the simpler loop case studied. It can be proven through probabilistic analysis that the probability of loop occurrence decreases exponentially as we increase the number of packets involved in the loop, in a similar way as it decreases when we increase the number of replicas sent for each packet, as previously described. We now derive the ACRDA analytical performance by using the random access analytical framework presented in [8] for slotted 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 noted previously, not all type of loops will be taken into account in this assessment. The general expression for the ACRDA packet loss ratio can be derived as follows: Nrep P LR(G, Nrep , Nslots ) ' P LRNiter (G, Nrep ) · +

Ploop (0; G, Nrep , Nslots ) ∞ X N [P LRloop (l)] rep

·

Ploop (l; G, Nrep , Nslots ), (9)

l=1

where Ploop (l) represents the probability to have l loops and has been previously derived in (8), P LRNiter is the PLR expression when no loops are present at Niter interference cancellation and P LRloop (l) is the PLR expression when l loops are present. We shall use the generalized random access model without interference cancellation (Sec. II in [8]) for the assessment of P LRloop (l) and the generalized random access model with interference cancellation (Sec. IV in [8]) for the assessment of the P LRNiter , but adapted to the asynchronous scenario. 1) Derivation of P LRloop (l): The probability of loss of the desired packet in the presence of l loops is approximated by: Z ∞ ω · fΞ (χ; l) · dχ, P LRloop (l) ' Γ 10 log10 1 + βχ 0 (10) where fΞ (χ; l) is the PDF for the interference to noise PSD ratio χ = I0 /N0 when there are l colliding packets and has been defined in (6). The noise power spectral density N0 is constant, but the interference power spectral density I0 is a random variable as it is the result of the sum of l colliding packets over the desired packet each with a random time offset value. As explained before, the empirically derived corrective factor β = 0.9 is multiplying the χ factor to compensate for the small difference in performance of the FEC scheme in the presence of a time-varying interference over the FEC block duration. There are two effects to be considered: a) The turbo FEC has a block interleaver which partly randomizes the nonuniformity of SNIR across the FEC block; b) The residual SNIR variation in the FEC block may cause some slight difference in the FER depending on where the interfering

packets are located. We have been experimentally investigating this effect and noted that when the SNIR is below the FEC threshold over a sizeable part of the FEC frame, the simulated packet detection fails even if the average SNIR over the FEC frame is above the detection threshold. It is known that an ideal FEC with coding rate r in a binary erasure channel can correct up to 1 − r channel erasures. Practical FEC codes are able to cope with fewer erasures than the ideal case and this we believe explains the slight discrepancy observed. Γ(x) is a polynomial interpolation of the coded modulation Packet Error Rate (PER) curve for a given channel code as a function of the argument x = Eb /N0 in dB [8]. In this model (10) we have assumed the multiple access interference (MAI) to behave as additive white Gaussian noise (AWGN). In general, the approximation is loose when we have few colliding packets. Although this approximation cannot be rigorously justified, the accuracy of this approach has been investigated in Appendix B from [8]. 2) Derivation of P LRNiter (G, Nrep ): ACRDA implements an iterative interference cancellation process within a sliding decoding window. Therefore, once the window has been processed as described in Sect. II-B, some interfering packets to the desired packet will have been recovered due to the Interference Cancellation (IC) process across the decoding window. We introduce here an iterative model for the P LR where Niter represents the window processing iteration number and we consider that the IC process takes place at the end of each window processing iteration. It follows that: P LRNiter (G, Nrep ) =

∞ X

K,Niter Ploss (k) · fK (k; λt ),

(11)

k=0 K,Niter where Ploss (k) is the probability for loss of the desired packet when there are k colliding packets at IC iteration Niter and fK (k; λ) is the probability mass function for the packet arrivals as defined in (4). Considering that the detection of the different replicas of a given packet are independent of each other (i.e. no loops can take place), then all replicas of the interfering packets to the desired packet present in other locations of the window will follow the same P LRNiter (G, Nrep ) as for the desired packet generated by (11). As a result, after each window processing iteration, some of the k interfering packets to the desired packet may be cancelled because one of their Nrep −1 replicas has been successfully decoded. The cancellation of interfering packets due to successful detection of one of their replicas at each window processing iteration is accounted for in the following expression: K,Niter Ploss (k)

=

k X

R Ploss (r) · fR (r; k, q),

(12)

r=0

q

=

Nrep −1 P LRNiter −1 (G, Nrep ) ,

R where Ploss (r) is the probability of loss when there are still r residual interfering packets over the desired packet at IC iteration Niter , and fR is a Binomial distribution where the number of trials is k and the probability of success q is derived from the PLR of the previous IC iteration given by (11). It shall



be noted that we have introduced here a recursive equation to take into account the iterative IC process within the window and P LRNiter shall be initialized to 1 when Niter = 0. The probability of loss of the desired packet in the presence of r colliding packets can be calculated in a similar way as it has been done in (10) as: Z ∞ ω R · fΞ (χ; r) · dχ. Ploss (r) = Γ 10 log10 1+β·χ 0 (13) IV. N UMERICAL R ESULTS Let us now analyze the ACRDA performance compared to the CRDSA RA scheme whose analytical and simulation performance results have been extensively reported in [8]. A comprehensive ACRDA simulator has been developed following the RA scheme modulator and demodulator description reported in Sect. II. All packets arrivals and associated VF are asynchronous with random delays. Packet arrival process is assumed to have a Poisson distribution. In general, the received packet power levels are assumed to be distributed according to a lognormal distribution with mean µ = 0 and standard deviation σ both expressed in dB. The simulation model is accurate as real physical layer packets representative of the coding and modulation scheme selected are generated. An infinite number of traffic sources are assumed to be generating a Poisson-distributed aggregate packet traffic. In each symbol duration, the simulator generates a Poisson-distributed number of packet arrival instances. To reduce the simulation time, the packets relative time offset granularity is assumed to be in integer multiples of the symbol duration. The carrier phase is uniformly distributed in (0, 2π) while following [8] the received packet amplitude is typically distributed according to a lognormal distribution. AWGN is added at the input of the ACRDA demodulator. The ACRDA demodulator architecture closely follows the scheme described in Sect. II and the block diagram of Fig. 3. The only simplification is related to the assumption of ideal estimation for the packet carrier frequency, phase and amplitude. This assumption is justified by the fact that past CRDSA work has shown that there is no practical impact of channel estimation errors on the CRDSA demodulator performance [5], [9]. When comparing ACRDA and CRDSA performances, unless stated otherwise, it is assumed that both ACRDA VF and CRDSA frames are composed of 100 slots (i.e. Nslots = 100) each containing 100 bit information bits. The 3GPP rate r = 1/3 FEC is assumed jointly with QPSK modulation. The energy per symbol to noise Power Spectral Density ratio Es /N0 in the absence of packet power fluctuations (i.e. µ = σ = 0 dB) is assumed to be 10 dB. For the ACRDA detector, unless stated otherwise, a window size of W = 3 VFs and a window shift of ∆W = 0.15 VFs are assumed. At each window shift, the ACRDA detector runs max a maximum of Niter = 15 interference cancellation iterations. In Fig. 6 the analytical (see Sect. III) and simulated throughput and PLR performance of ACRDA is compared to that of CRDSA for the case of Nrep = 2. The superior performance of ACRDA compared to CRSDA in case of two packet replicas is evident in particular in the low PLR region.

As explained in Appendix D of [8], the loop probability is the main reason for the observed 2 replicas CRDSA reduced slope PLR characteristic. The asynchronous nature of the ACRDA reduces the probability of occurrence for destructive loops. As a consequence, for ACRDA with 2 replicas the PLR floor is almost two orders of magnitude lower than CRDSA. We can conclude that if the target PLR is 10−4 or higher, for ACRDA there is no need for increasing the number of replicas to 3 as for CRDSA. The fact that PLR simulation results in the [0, 1] bits/symbol G region are slightly higher than the analytical findings is related to the fact that we limit the analysis to the most basic and frequent form of loop. Thus the theoretical loop analysis represents a lower bound for the PLR (see Appendix D in [8]). The theoretical and simulated ACRDA and CRDSA throughput and PLR performance with 3 replicas is reported in Fig. 7. It is remarked the good matching between simulation and analytical results when the simulated number of frame slots is 1000. Instead when Nslots = 100 the simulation results are slightly worse. This can be explained by the fact that the analytical framework developed in [8] assumes an infinite number of slots/frame. In this case the loop event probability is very low for CRDSA too. Thus for the 3 replicas case, CRDSA has essentially the same PLR performance and slope as ACRDA for Nslots = 1000 and slightly worse for the more practical case Nslots = 100. This confirms the conjecture that the asynchronous interference nature in ACRDA and CRA has no impact on the RA throughput. However when comparing in Fig. 8 the best simulated performance of CRDSA with Nrep = 3, Nslots = 100 to that of ACRDA (simulated only) with Nrep = 2 with a lognormal packet power distribution with σ = 3 dB, it is apparent that for a target PLR=10−4 , ACRDA has a 35 % better throughout than CRDSA. The ACRDA superior performance is obtained while operating in a truly asynchronous access mode instead of the slotted CRDSA mode. Furthermore, as discussed before, the fact that the number of ACRDA replicas can be reduced to 2 is reducing the demodulator complexity by an approximate 33 % factor. Given the positive impact of incoming packets power unbalance on performance, one can think of artificially using different realizations of the packet power randomization process for each replica transmitted by the same transmitter. In this way further diversity is created among the replica packets in addition to the location within the VF. This has the beneficial effect of removing the PLR floor for lognormal packet power distribution investigated in [8] as Fig. 8 (dotted/diamonds line) testifies. Some investigation about the performance impact of the gateway ACRDA demodulator window memory size has been performed in Fig. 9. As already found for E-SSA, a window size W of three frames seems to be the optimum choice [15]. As it is seen in Fig. 9, reducing the ACRDA demodulator window size W to 2 VFs reduces by about 10 % the throughput performance at PLR=10−4 while for W = 1 frame the performance loss becomes unacceptably large. A window size 2 < W ≤ 3 is therefore recommended. Another system parameter impacting the access latency is the number of slots per frame. Simulations have been performed for a VF composed by 64 slots and results compared to 100 slots. As anticipated, the reduction of the number of slots/frame slightly



increases the loop occurrence probability, as also explained analytically in [8]. This explains the observed increase in the PLR floor around 10−4 when using a 64 slots VF. The rest of this section discusses the delay performance of both ACRDA and CRDSA. We have considered ACRDA with 2-replicas configuration and CRDSA with 3-replicas configuration with Nslots = 100 for both ACRDA VF and CRDSA frame. In the simulator the delay is measured packetby-packet as the time interval from the moment a packet is placed in the transmitter input buffer to the moment the packet is successfully decoded at the receiver minus the propagation delay of the satellite link. As such, the delay results do not contain the delay that may be induced by a congestion control mechanism that may run before the transmitter output. In order to present a fair and clear comparison between ACRDA and CRDSA, the delay results are expressed as normalized to the frame length, and they exclude the signal propagation delay between the transmitter and the receiver. Note that, unless stated otherwise, the delay results are presented corresponding to the normalized MAC loads at which the PLR is less than or equal to 10−3 . Between the ACRDA baseline and its variant explained in this paper, Fig. 10 shows results for the variant that dictates first replica transmission at the beginning of the VF. Figure 11, however, shows results for both ACRDA baseline and its variant. Fig. 10-a (left handside plot) shows the CRDSA and ACRDA percentiles of the transmission delay for equally-powered packets and for various average MAC channel loads G. It clearly appears that for the 90 % percentile the ACRDA delay is reduced by a factor of 2.8 for G = 0.9 bits/symbol up to more than a factor of 10 for G = 0.3 bits/symbol. In case of lognormal packet power distribution with σ = 3 dB the delay simulation results are reported in Fig. 10-b (right handside plot); it is apparent that the ACRDA delay reduction w.r.t. CRDSA is comparable to the case σ = 0 shown in Fig. 10-a. Figure 11 shows delay percentiles for both ACRDA baseline and its 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 the beginning of the VF) will have instead a delay reduction factor of 2.8. For G = 0.3 bits/symbol the ACRDA baseline delay reduction factor compared to CRDSA is limited to 1.9 (w.r.t. a factor of 10 in the ACRDA variant). Looking at the MAC access delay performance of ACRDA, the variant scheme is definitely the preferable option. However, as discussed in Sect. II, the latency performance should, in general, be analyzed also considering congestion control algorithms and the type of traffic to be supported, which may be of non-Poisson nature. V. C ONCLUSIONS A novel RA scheme dubbed Asynchronous Contention Resolution Diversity ALOHA (ACRDA) has been described together with its key features and implementation aspects. With a similar signalling overhead and modulator complexity compared to CRDSA, ACRDA achieves slightly better throughput performance than CRDSA while operating in a truly asynchronous mode. This improved performance is achieved with

a sizeable reduction in the demodulator complexity since only two replicas are necessary. The transmission latency of the proposed scheme is also considerably improved with respect to CRDSA with a delay reduction ranging from a factor 2 to 9 depending 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 better allowing to achieve efficiency well in excess of 1 bits/symbol over a pure RA channel in the presence of Poisson traffic. The proposed ACRDA scheme proposed and analyzed in this paper may benefit from techniques recently proposed which can further enhance its performance. The exploitation in ACRDA of techniques such as soft combining of packet replicas proposed in [14] or the combining of the best replica packets chunks to generate a better packet of interest as suggested in [20] or the Coded Slotted ALOHA soft combining scheme [10] represent potential area of future investigation. Similarly one can consider the technique proposed in [13], [14] to pseudo-randomize the slot positions as a function of the transmitted data to remove the replica signalling overhead. This is particularly interesting in case small packets have to be transmitted. Finally the use of the bipartite graph-based framework introduced by Liva [9] for slotted ALOHA may be potentially extended to the asynchronous ACRDA case. Acknowledgments: The authors would like to thank Dr. Pantelis-Daniel Arapoglou for his support to the work reported in this paper. The authors are also thankful for the constructive comments and suggestions provided by the Editor and the anonymous reviewers which allowed to improve the quality of the paper. R EFERENCES [1] N. Abramson, ”The ALOHA System - Another Alternative for Computer Communication”, Proceedings of the AFIPS Fall Joint Computer Conference, Vol. 37, 1970, pp. 281-285. [2] G. L. Choudhury, and S. S. Rappaport, ”Diversity ALOHA - A Random Access Scheme for Satellite Communications,” IEEE Trans. on Comm., vol. COM-31, Mar. 1983, pp. 450-457. [3] R. De Gaudenzi, O. Del Rio Herrero, ”Advances in Random Access protocols for satellite networks”, International Workshop on Satellite and Space Communications, 2009, IWSSC 2009, Siena, Italy September 9-11, 2009, pp. 331-336. [4] E. Casini, R. De Gaudenzi and O. del Rio Herrero, ”Contention Resolution Diversity Slotted ALOHA (CRDSA): an Enhanced Random Access Scheme for Satellite Access Packet Networks”, IEEE Transactions on Wireless Communications, vol. 6, no. 4, pp. 1408-1419, April 2007. [5] E. Casini, R. De Gaudenzi and O. del Rio Herrero, D. Delaruelle, J.P. Choffray, ”Method of packet mode digital communication over a transmission channel shared by a pluraty of users”, US Patent number 8094672, Jan 10, 2012. [6] O. del R´ıo Herrero, R. De Gaudenzi, ”A High-Performance MAC Protocol for Consumer Broadband Satellite Systems”, In the Proc. of 27th AIAA International Communications Satellite Systems Conference, June 1-4 2009, Edinburgh (United Kingdom). [7] Digital Video Broadcasting (DVB); Second Generation DVB Interactive Satellite System; Part 2: Lower Layers for Satellite standard ETSI EN 301 545-2 V1.1.1 (2012-01). [8] O. del R´ıo Herrero, R. De Gaudenzi, ”Generalized Analytical Framework for the Performance Assessment of Slotted Random Access Protocols”, IEEE Trans. on Wireless Comm., Vol. 13, Issue 2, February 2014, pp. 809-821. [9] G. Liva, ”Graph-Based Analysis and Optimization of Contention Resolution Diversity Slotted ALOHA”, IEEE Trans. on Comm., Vol. 59, Issue 2, February 2011, pp. 477-487.



[10] E. Paolini, G. Liva, M. Chiani, ”High Throughput Random Access via Codes on Graphs: Coded Slotted ALOHA”, In the Proc. of the 2011 International Communication Conference, ICC 2011, June 5-9 2011, Kyoto, Japan. [11] H.-C. Bui, J. Lacan and M.-L. Boucheret, ”An enhanced multiple random access scheme for satellite communications”, In the Proc. of the 2012 Wireless Telecommunications Symposium (WTS), 18-20 April 2012. [12] H.-C. Bui, J. Lacan and M.-L. Boucheret, ”Multi-slot coded ALOHA with irregular degree distribution”, In the Proc. of the first International IEEE-AESS Conference in Europe on Space and Satellite Telecommunications (ESTEL), October 2012, Rome, Italy. [13] F. Ricciato and P. Castiglione, ”Pseudo-random Aloha for enhanced collision-recovery in RFID”, IEEE Communications Letters, Vol. 17, No. 3, March 2013, pp. 608-611. [14] P. Castiglione, F. Ricciato and P. Popovski, ”Pseudo-Random ALOHA for Inter-frame Soft Combining in RFID Systems”, In the Proc. of IEEE 2013 18th International Conference on Digital Signal Processing. 2013. [15] O. del R´ıo Herrero, R. De Gaudenzi, ”High Efficiency Satellite Multiple Access Scheme for Machine-to-Machine Communications”, IEEE Trans. on Aerospace and Electronic Systems, Vol. 48, No. 4, Oct. 2012, pp. 2961-2989. [16] O. del R´ıo Herrero, R. De Gaudenzi, ”Methods, apparatuses and system for asynchronous spread-spectrum communication”, US Patent number 7990874, Aug 2, 2011. [17] O. del R´ıo Herrero, R. De Gaudenzi, J. L. Pijoan Vidal, ”Design Guidelines for Advanced Random Access Protocols”, In the Proc. of the 30-th AIAA Internation Satellite Systems Communications Conference, Ottawa, Canada, September 24-27, 2012. [18] J. Massey, P. Mathys, ”The Collision Channel Without Feedback”, IEEE Trans. on Inform. Theory, Vol. IT-31, No. 2, March 1985, pp. 192-204. [19] C. Kissling, ”Performance Enhancements for Asynchronous Random Access Protocols over Satellite”, In the Proc. of 2011 International Communication Conference, ICC 2011, June 5-9 2011, Kyoto, Japan. [20] F. Clazzer and C. Kissling, ”Enhanced Contention Resolution ALOHA ECRA”, 9th International ITG Conference on Systems, Communications and Coding - SCC 2013, January 2013, Munich, Germany. [21] O. del R´ıo Herrero, E. Casini, R. De Gaudenzi, ”Contention Resolution Diversity Slotted Aloha Plus Demand Assignment (CRDSA-DA): an Enhanced MAC Protocol for Satellite Access Packet Networks”, 23rd AIAA International Communications Satellite Systems Conference, 2528 Sep. 2005, Rome (Italy). [22] ETSI TS 102 721-5 v1.1.1, ”Satellite Earth Stations and Systems; Air Interface for S-band Mobile Interactive Multimedia (S-MIM); Part 5: Protocol Specifications, Link Layer” (2011-12). [23] Digital Video Broadcasting (DVB); Second Generation DVB Interactive Satellite System (DVB-RCS2); Guidelines for Implementation and Use of LLS: EN 301 545-2,DVB Document A162, February 2013. [24] J.O. Irwin, ”On the Frequency Distribution of the Means of Samples from a Population Having any Law of Frequency with Finite Moments, with Special Reference to Pearson’s Type II”. Biometrika, Vol. 19, No. 3/4, 1927, pp. 225-239. [25] P. Hall, ”The Distribution of Means for Samples of Size N Drawn from a Population in which the Variate Takes Values Between 0 and 1, All Such Values Being Equally Probable”. Biometrika, Vol. 19, No. 3/4, 1927, pp. 240-245.

Tslot

PACKET # (i,1)

PACKET # (i,2)

PACKET # (i+1,1)

PACKET # (i,3)

PACKET # (i+1,2) PACKET # (i+2,1)


PACKET # (i+3,1)


PACKET # (i+3,3)

Tframe

(a) CRDSA Frame

Time offset between VF(i) and VF(i-1)

Tslot

Virtual Frame from user # i PACKET # (i,1)

PACKET # (i,2)

PACKET # (i,3)

Tframe PACKET # (i-1,1)

Tslot

Virtual Frame from user # (i-1) PACKET # (i-1,3)

PACKET # (i-1,2)

Tframe Tslot

Virtual Frame from user # (i+1) PACKET # (i+1,1)

PACKET # (i+1,2)

PACKET # (i+1,3)

Tframe

Time offset between VF(i) and VF(i+1)

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

Desired packet

Interf packet

Desired packet

Interf packet

Tslot Tframe

Fig. 4.

Example of loop event in ACRDA.



USEFUL PAYLOAD BITS

FEC DECODER DIGITAL DEMUX

ADC

SLIDING WINDOW SAMPLES MEMORY

P/S CONVERTER

BURST DEMODULATOR

DEMUX

REPLICA PACKET(S) SIGNALLING BITS

FEC ENCODING PACKET CHANNEL ESTIMATE

PREAMBLE SEARCHER

CARRIER LOCAL OSCILLATOR

REPLICA PACKET(S) INTERFERENCE CANCELLATION PROCESSOR

REPLICA PACKET(S) REGENERATION

REPLICA PACKET(S) CHANNEL ESTIMATOR

REPLICA PACKET(S) CHANNEL ESTIMATE

ACRDA PACKET DEMODULATOR CONTROLLER

Fig. 2.

ACRDA Demodulator functional block diagram

Virtual Frame from user # i

Tslot

PACKET # (i+1,1)

PACKET # (i+1,2)

PACKET # (i+1,3)

Tframe Tslot

Virtual Frame from user # (i-2) PACKET # (i,1)

PACKET # (i,2)

PACKET # (i,3)

Tframe Tslot

Virtual Frame from user # (i+1) PACKET # (i,1)

PACKET # (i,2)

PACKET # (i,3)

Tframe PACKET # (i-1,1)

Tslot

Virtual Frame from user # (i-3) PACKET # (i-1,3)

PACKET # (i-1,2)

Tframe Tslot

Virtual Frame from user # (i-1) PACKET # (i+1,1)

PACKET # (i+1,2)

PACKET # (i+1,3)

Tframe Tslot

Virtual Frame from user # (i+2) PACKET # (i+1,1)

PACKET # (i+1,2)

PACKET # (i+1,3)

Tframe

Twindow t

tnow ∆W

Fig. 3.

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



1 ACRDA Simulation ACRDA Analytical CRDSA Analytical CRDSA Simulation

Throughput − T [bits/symbol]

0.8

0.6

0.4

1.6 0.2

Simulated PDF N interf=1

1.4

Irwin−Hall PDF N interf=1 0

Simulated PDF N interf=2

1.2

0

0.2

0.4

Irwin−Hall PDF N interf=2

0.6 0.8 1 1.2 1.4 Average MAC Channel Load − G [bits/symbol]

1.6

1.8

2

Simulated PDF N interf=3 Irwin−Hall PDF N interf=3

1

(a) Throughput

PDF

Simulated PDF N interf=4 Irwin−Hall PDF N interf=4

0.8

0

10

0.6 −1

10

0.4

0

0

0.5

1

1.5

2

2.5

3

3.5

4

Average interference during PoI

Packet Loss Ratio [PLR]

−2

0.2

10

−3

10

−4

10

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

CRDSA Simulated ACRDA Simulated ACRDA Analytical CRDSA Analytical

−5

10

−6

10

0

0.2

0.4


1.6

1.8

2

(b) PLR Fig. 6. Simulation and analytical CRDSA and ACRDA performance for Nrep = 2, Nslots =100 (simulations), 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 = 3 frames and a window step ∆W = 0.15.



1.8 ACRDA, 3 rep, σ=0 dB ACRDA, 2 rep, σ=3 dB ACRDA, 3 rep, σ=3 dB ACRDA, 2 rep, σ=0 dB CRDSA, 3 rep, σ=3 dB CRDSA, 2 rep, σ=0 dB CRDSA, 2 rep, σ=3 dB CRDSA, 3 rep, σ=0 dB ACRDA, 2 rep, IP σ=3 dB

1 1.6

0.9 CRDSA Simulation Nslots=1000

1.4

CRDSA Analytical ACRDA Simulation Nslots=100

0.7

Throughput − T [bits/symbol]

Throughput − T [bits/symbol]]

0.8

ACRDA Analytical CRDSA Simulation Nslots=100

0.6 0.5 0.4

1.2

1

0.8

0.6

0.3 0.4

0.2 0.2

0.1 0

0

0

0.2

0.4


1.6

1.8

2

0

0.2

0.4


2

1.6

1.8

2

0

0

10

10

ACRDA, 3 rep, σ=0 dB ACRDA, 2 rep, σ=0 dB ACRDA, 2 rep, σ=3 dB ACRDA, 3 rep, σ=3 dB CRDSA, 2 rep, σ = 0 dB CRDSA, 2 rep, σ = 3 dB CRDSA, 3 rep, σ=0 dB CRDSA, 3 rep, σ = 3 dB ACRDA, 2 rep, IP σ=3 dB

−1

10

−1

10

−2

10 −2

10



1.8

(a) Throughput

(a) Throughput

−3

10

CRDSA Simulation Nslots=1000.

−4

10

CRDSA Analytical ACRDA Analytical CRDSA Simulation Nslots=100

−5

ACRDA Simulation N

10

−3

10

−4

10

−5

10

=100

slots

−6

10

−6

10

1.6

−7

0

0.2

0.4


1.6

1.8

2

(b) PLR Fig. 7. Simulation and analytical CRDSA and ACRDA performance for Nrep = 3, Nslots =100 and Nslots =1000 (simulations), 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 = 3 frames and a window step ∆W = 0.15.

10

0

0.2

0.4


(b) PLR Fig. 8. Simulation of CRDSA and ACRDA with Nrep = 2, 3 performance for 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, 3 dB and Poisson traffic, window size of W = 3 frames and a window step ∆W = 0.15. The red diamonds correspond to the case of independent lognormal power (IP) allocation for each replica packet.



1

Throughput − T[bits/symbol]

0.8

0.6

0.4

ACRDA 2 replicas, W=3, σ=0 dB ACRDA 2 replicas, W=2, σ=0 dB ACRDA 2 replicas, W=1, σ=0 dB

0.2

0

0

0.2

0.4


1.6

1.8

2

(a) Throughput 0

10

−1


10

−2

10

−3

10

−4

10

ACRDA 2 replicas, W=3, σ=0 dB ACRDA 2 replicas, W=2, σ=0 dB ACRDA 2 replicas, W=1, σ=0 dB 0

0.2

0.4 0.6 0.8 1 1.2 1.4 1.6 Average MAC Channel Load − G [bits/symbol]

1.8

2

(b) PLR 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, 3 frames and a window step ∆W = 0.15.



2

2

Color code:

Color code:

G=0.3 bits/symbol

1.8

G=0.7 bits/symbol

1.8

G=0.5 bits/symbol

G=0.9 bits/symbol

G=0.7 bits/symbol 1.6

G=1.1 bits/symbol 1.6

G=0.9 bits/symbol

G=1.3 bits/symbol G=1.5 bits/symbol 1.4 Delay normalized to the frame length

Delay normalized to the frame length

1.4

1.2

1

0.8 CRDSA 0.6

1.2

1

0.8

CRDSA

0.6

ACRDA

ACRDA 0.4

0.4

0.2

0.2

0

0

10

20

30 40 50 60 70 Probability in % that delay

Asynchronous Contention Resolution Diversity ... - Semantic Scholar

Asynchronous Contention Resolution Diversity ... - Semantic Scholar

Suggest Documents

Efficient Contention Resolution Protocols for ... - Semantic Scholar

Contention Resolution Diversity Slotted ALOHA - IEEE Xplore

Contention-free MAC Protocols for Asynchronous ... - Semantic Scholar

Polymorphic Contention Management - Semantic Scholar

Synchronization Without Contention - Semantic Scholar

Adversarial Contention Resolution for Simple ... - People.csail.mit.edu

Enhanced Contention Resolution Aloha - ECRA - Core

Contention Resolution with Bounded Delay - CiteSeerX

Unbounded Contention Resolution in Multiple-Access Channels

Reducing Controller Contention in Shared ... - Semantic Scholar

Resource Contention Detection and Management ... - Semantic Scholar

Contention Resolution with Bounded Delay - CiteSeerX

Modelling Contention Avoidance and Resolution in

Predicting Cache Contention with Setvectors - Semantic Scholar

Determinizing Asynchronous Automata - Semantic Scholar

Dynamic framework with adaptive contention ... - Semantic Scholar

Resource Contention Detection and Management ... - Semantic Scholar

Distance Adaptive Contention Window Mechanism ... - Semantic Scholar

Contention Window Analysis and Proposed ... - Semantic Scholar

Analytical Modeling of Contention-Based ... - Semantic Scholar

Beyond Contention: Extending Texture-Based ... - Semantic Scholar

RESOLUTION - Semantic Scholar

Asynchronous, Hierarchical and Scalable ... - Semantic Scholar

Asynchronous and distributed process improvement - Semantic Scholar