Cooperative transmissions emulate multi-antenna systems and can improve the quality of signal reception. In this paper, we propose and analyze a cross layer random access scheme, C-ALOHA, that enables cooperative transmissions in

the context of ALOHA system. Our analysis shows that over a fading channel C-ALOHA can improve the throughput by 30%, as compared to standard ALOHA protocol

Ercetin, Ozgur

Erçetin, Özgür

Gokturk, Sarper Muharrem

Gurbuz, Ozgur

Göktürk, Sarper Muharrem

Gürbüz, Özgür

English

Sabanci University Research Database

468 IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 6, JUNE 2008Throughput Analysis of ALOHA with Cooperative DiversityM. Sarper Gokturk, Ozgur Ercetin, and Ozgur GurbuzAbstract— Cooperative transmissions emulate multi-antennasystems and can improve the quality of signal reception. Inthis paper, we propose and analyze a cross layer random accessscheme, C-ALOHA, that enables cooperative transmissions inthe context of ALOHA system. Our analysis shows that over afading channel C-ALOHA can improve the throughput by 30%,as compared to standard ALOHA protocol.Index Terms— Wireless networks, random access schemes,cooperative communications.I. INTRODUCTIONCOOPERATIVE communications is one of the promisingtechniques that can enhance the performance of wirelessnetworks. Appropriate cross-layer medium access strategiesare required to exploit the physical layer advantages providedby cooperative communications [1]. The most significant dif-ference of a cooperative medium access protocol from a non-cooperative protocol is that while conventional protocols areavoiding collisions, a cooperative protocol requires intentionalcollisions to boost the packet success probability.In a wireless network, transmission errors occur either dueto packet collisions or due to channel fading/noise. Recentlyin [2], a practical technique is presented for differentiatingcollisions and channel errors. In this work, we exploit thecollision/error differentiation capability presented in [2] andpropose an ALOHA [3] based random access scheme, Co-operative ALOHA (C-ALOHA), which enables cooperativetransmissions in case of erroneous packet receptions to providerobustness to channel errors and improve the packet successprobability. In C-ALOHA, initial transmission of a packet iscarried out as in the ALOHA system. We assume that thereceiver recognizes whether packet transmission failure is dueto a collision or channel noise, and sends immediate collisionor error feedbacks, respectively. In case of an error feedback,cooperative transmissions are invoked, so that some of thenodes that have correctly overheard the transmission chooseto retransmit together with the source node in the next slot.Consequently, the packet success probability is improved andthe number of retransmissions is decreased significantly ascompared to a non-cooperative system.Enhancing the performance of medium access methods hasbeen investigated extensively in the literature, mainly focusingon collision avoidance, intelligent scheduling techniques andcollision resolution protocols. Cross-layer approaches thatManuscript received February 3, 2008. The associate editor coordinatingthe review of this letter and approving it for publication was J. Holliday. Thiswork was in part supported by TUBITAK Career Grant No: 105E093 andTUBITAK Grant No:105E192.The authors are with the Faculty of Engineering and Natural Sciences,Sabanci University, Istanbul, Turkey (e-mail: msgokturk@su.sabanciuniv.edu,{ogurbuz, oercetin}@sabanciuniv.edu).Digital Object Identifier 10.1109/LCOMM.2008.080174.exploit the novel physical layer findings, such as cooperativediversity, are gaining more interest. In [4], cooperative trans-missions are employed to provide diversity gain to a collisionresolution protocol presented in [5]. Also, recently, mediumaccess protocols enabling cooperation in 802.11 systems arepresented in [6], [7]. To the best of our knowledge, an analysisof successful packet transmission probability for a randomaccess method in a cooperative setting still does not exist.The contribution of this work is that a simple cross-layerALOHA based protocol, C-ALOHA is proposed, and analyti-cal derivation of the successful packet transmission probabilityis presented. C-ALOHA enables cooperative transmission forpacket retransmissions in case of erroneous receptions, andthus, provides robustness to ALOHA protocol against wirelesschannel impairments.II. PRELIMINARIESWe consider a wireless network of m nodes, where nodestransmit over a Rayleigh fading channel to a single receiveremploying a Maximal-Ratio-Combiner (MRC). Packets arrivefor transmission at each node according to an independentPoisson process with overall rate of λ, i.e., with rate λ/mat each transmitting node. Each packet is of equal size andrequires one time slot for transmission. All transmitters areassumed to be synchronized, and reception of each packetstarts at an integer time and ends before the next integer timeas assumed in the analysis of slotted ALOHA in [8]. Wealso assume that at the end of every slot, each node obtainsimmediate feedback from the receiver through an error-freechannel specifying whether: 1) the slot was idle (i), 2) atransmission occurred but the packet could not be successfullydecoded due to error (e), 3) multiple transmissions resulted incollision (c), 4) a packet was received successfully (s). Error-free feedback can be approximated by applying error controlcoding to the feedback packet. Furthermore, although notessential for correct protocol operation, immediate feedbackis assumed to simplify the analysis.In cooperative networks, the nodes that have correctlyoverheard the source transmission may cooperate with thesource by retransmitting the overheard packet to the receiver,so that the receiver can be provided with multiple copies ofthe same signal, resulting in diversity gain. We quantify theimprovement in successful packet reception probability due tocooperative transmission for varying number of cooperatingnodes, when BPSK modulation is employed. The approachfollowed here does not depend on the modulation scheme andany modulation scheme can be used instead of BPSK. Theaverage BER, P¯b, under Rayleigh fading for the BPSK receiverwith k-branch diversity using MRC is given by [9] P¯b(γ¯, k) =1π∫ π/20(1+ γ¯sin2φ)-kdφ, where γ¯ refers to the average SNR1089-7798/08$25.00 c© 2008 IEEEAuthorized licensed use limited to: ULAKBIM UASL - SABANCI UNIVERSITY. Downloaded on October 25, 2008 at 09:25 from IEEE Xplore.  Restrictions apply.GOKTURK et al.: THROUGHPUT ANALYSIS OF ALOHA WITH COOPERATIVE DIVERSITY 469per link, and k denotes the number of cooperating nodes.Assuming uniform bit errors and no forward error correction,the success probability of a µ bit packet can be obtained asPs(k) = [1−P¯b(γ¯, k)]µ, and the probability of packet error asPe(k) = 1−Ps(k). Channel SNR is assumed to be estimatedat the receiver for each node-receiver link, and to remainconstant for a time slot. Synchronization among transmittingnodes can be provided via techniques such as [10], and in caseof imperfect synchronization, one of the methods reviewed in[11] can be employed so that full diversity gain can still beachieved.III. ANALYSIS OF C-ALOHAIn this section, we present the throughput analysis of theC-ALOHA protocol in detail. We assume that each nodehas two separate buffers, and each buffer is assumed to beof one packet size for analysis purposes. Each generatedpacket directly goes to buffer B1; discarded if B1 is fullor stored otherwise. A transmitted packet is kept in B1until success feedback is received. All nodes in the networkoverhears the transmission of other nodes. In case a packetis correctly overheard, it is stored in buffer B2, replacing thecurrent packet in B2. Otherwise, B2 is emptied. Thus, B2always stores the correctly overheard packet in the previousslot. When the intended receiver sends an e feedback, eachnode that correctly overheard the transmission independentlytransmits the packet in B2 with probability qc. In case of a cfeedback, each node independently transmits the packet in B1with probability qr.We define the state of the system with respect to thetotal number of backlogged packets in the network, i.e., totalnumber of packets in B1. The probability that a packet arrivesat a node in x slots is qa(x) = 1−exλ/m. We assume that eachnew arrival is not directly transmitted but backlogged. Whenthe system is at state n, a successful packet reception occurswith probability Pn(s), which can be written by conditioningon the feedback from the receiver asPn(s) = Pn(s|fc)Pn(fc) + Pn(s|fi)Pn(fi)+ Pn(s|fe)Pn(fe) + Pn(s|fs)Pn(fs), (1)where Pn(fc), Pn(fi), Pn(fe), Pn(fs) refer to the probabilitythat c, i, e, s feedbacks are received at state n. These prob-abilities are also interpreted as the probability that collisionoccurred in the previous slot, the previous slot was idle,erroneous or success, respectively. First, we derive Pn(s) forALOHA considering channel errors, and then, derive Pn(s)for C-ALOHA.1) ALOHA: The probability of successful transmission atstate n is independent of the received feedback, but onlydependent on the current state. Therefore, the probability ofsuccess given the feedback, is same for each feedback, i.e.,Pn(s|fi) = Pn(s|fe) = Pn(s|fc) = Pn(s|fs) = nqr(1 −qr)n−1.Let n be the number of backlogged nodes at an arbitrarytime t0. The system can be at any state between 0 andn in the previous slot, t0 − 1, depending on the numberof packet arrivals during that slot. Assuming that packetsarrive at the system at the end of each slot, we define theprobability that j arrivals occurred in x slots in transitionto state n as Qa,x(n, j) =(m−(n−j)j)qa(x)j(1− qa(x))m−n.Also, probability that k nodes choose to transmit packets in theprevious slot, t0 − 1 is Qr(n, j, k) =(n−jk)qkr (1− qr)n−j−k,where qr is the probability that a node transmits the packetin B1. Having quantified Qa,x and Qr, we can give theprobability of receiving i, c, s, e feedbacks when the systemis at state n.Pn(fi) =n∑j=0Qa,1(n, j)Qr(n, j, 0), (2)Pn(fc) = 1− Pn(fi)−n∑j=0Qa,1(n, j)Qr(n, j, 1), (3)Pn(fs) =n∑j=0Qa,1(n, j)Qr(n, j, 1)Ps(1), (4)Pn(fe) =n∑j=0Qa,1(n, j)Qr(n, j, 1)Pe(1), (5)where Ps(1) and Pe(1) refer to the success and error prob-abilities of a single node transmission over a noisy fadingchannel, respectively. The intuition behind the derivation of(2), (3) and (4) are the same in the analysis of slotted ALOHA[8]. However, (5) is derived by noting that error feedback isreceived when there is a single transmission but it is corrupteddue to channel noise.2) C-ALOHA: The operation of the C-ALOHA systemwould be best explained by describing the response of thesystem to each feedback. In case of i, c and s feedbacks, eachnode transmits its packet in B1 with probability qr. However,in case of an e feedback each node that has correctly overheardthe source packet transmits the packet in B2 together withthe source node in the upcoming slot with probability qc.Note that the first occurrence of e feedback is always aftera single node (direct) transmission, whereas the followingoccurrences can be after either a direct or a cooperativetransmission. It can be easily shown that the probability ofreceiving an i and a c feedback are still given by (2), (3),respectively. The success probability given c, i and s feedbackis Pn(s|fc) = Pn(s|fi) = Pn(s|fs) = nqr(1 − qr)n−1, sinceafter collision, idle and success events C-ALOHA operates inthe same way as ALOHA.In case of an e feedback, the probability of success dependson whether or not cooperation is invoked. A packet may bereceived successfully after multiple erroneous trials, whichmay involve either cooperative or direct transmissions. Wedefine the period between the first occurrence of the e feedbackand the time s feedback is received as an error epoch. An errorepoch may consist of multiple erroneous transmissions but canhave only one successful transmission, which also designatesthe end of the error epoch. Let Qh(t) represent the probabilitythat t nodes correctly overhear the source packet, Qh(t) =(mt)Ps(1)tPe(1)m−t, and Qc(t, k) represent the probabilitythat k out of t nodes choose to involve in cooperation, andthe cooperative packet transmission is successful Qc(t, k) =(tk)qkc (1− qc)t−kPs(k+1).A transmission may be successful without requiring co-operation, in which case error epoch has length 1. TheAuthorized licensed use limited to: ULAKBIM UASL - SABANCI UNIVERSITY. Downloaded on October 25, 2008 at 09:25 from IEEE Xplore.  Restrictions apply.470 IEEE COMMUNICATIONS LETTERS, VOL. 12, NO. 6, JUNE 20080 10 20 30 40 50 6000.050.10.150.20.250.30.35Throughputn, number of backlogged nodesNumber of packets per slot  ALOHAC−ALOHA, q c=0C−ALOHA, q c=0.05C−ALOHA, q c=0.25Fig. 1. Throughput for varying number of backlogged nodes.probability of having an error epoch of length 1 is P (l=1) =∑nj=0 Qa,1(n, j)Ps(1). For x ≥ 2, in order to simplify theanalysis we assume that once a set of nodes chooses tocooperate with a source node, the same set of nodes continueto retransmit the packet until the end of the error epoch. ThenP (l=x) for x ≥ 2 can be givenP (l=x)=n∑j=0Qa,x(n, j)Pe(1)m∑t=1Qh(t)t∑k=1Qc(t, k)Pe(k+1)l-2+n∑j=0Qa,x(n, j)Pe(1)m∑t=0Qh(t) (1− qc)t Ps(1). (6)In the derivation of (6), we differentiate among the casesof cooperation and direct transmission employed within theepoch. The expected length of an error epoch is E{L} =∑∞x=1 xP (l = x). The proportion of time the system is inerror epoch is 1−Pn(fi)−Pn(fc). Since only one out of E{L}slots is a success, by renewal-reward theory the probability ofreceiving s feedback can be given asPn(fs) =1E{L} [1− Pn(fi)− Pn(fc)] . (7)Furthermore, Pn(fe) is also equal to 1− Pn(fs)− Pn(fc)−Pn(fi), and Pn(s|fe) isPn(s|fe)=m∑t=1Qh(t)t∑k=1Qc(t, k)+m∑t=0Qh(t) (1-qc)tPs(1),where the first and second terms represent the probabilities ofsuccess with cooperative transmission and direct transmission,respectively. Thus, the probability of successful transmissionin C-ALOHA can be determined by (1).IV. NUMERICAL RESULTSIn this section, we compare the throughput of C-ALOHAwith slotted ALOHA over a noisy fading channel. We considerindependent and identically distributed (i.i.d.) node-receiverlinks, with Rayleigh fading, average SNR of 25 dB, andcoherence time equal to a time slot. The packet size is setas 512 bits. The throughput is calculated for varying numberof backlogged nodes and different qc as depicted in Figure 1.It is clearly seen that ALOHA suffers from the channel errors,and the maximum throughput is decreased dramatically to0.255. C-ALOHA reaches a maximum of 0.33 under the samechannel conditions, slightly below the maximum throughputof slotted ALOHA in error-free channel (0.367). It is observedthat the maximum throughput of slotted ALOHA can beimproved by 20% by enabling error detection capability andimmediate source retransmission upon error feedback. Thiscorresponds to C-ALOHA with no cooperating nodes, i.e.,qc = 0. User cooperation provides a further 10% increasein the throughput, and thus, resulting in a 30% increase inthe maximum throughput of slotted ALOHA. Note that for agiven channel state and network of size m, there is a qc valuebelow which the system is underutilized, and above whichthe throughput can not be increased further. This is due to thefact that for a given channel state the cooperative transmissionis almost always successful when the number of cooperatingnodes is above a certain number, and adding additional nodesin the cooperating set does not provide any further gain.V. CONCLUSIONSIn this paper, we have proposed a cross-layer random accessmethod that incorporates cooperative transmissions into thewell known ALOHA system. We have derived analyticalexpressions for the successful packet transmission probabilityfor this protocol and analyzed the effect of random cooperationdecision on the system performance. We have shown that byexploiting the robustness of cooperative transmissions againstchannel impairments, the throughput of the ALOHA systemin a noisy fading channel can be improved by 30%.REFERENCES[1] F. H. P. Fitzek and M. D. Katz, Cooperation in Wireless Networks: Prin-ciples and Applications, 1st ed. Dordrecht, The Netherlands: Springer,2006.[2] K. Whitehouse, A. Woo, F. Jiang, J. Polastre, and D. Culler, “Exploitingthe capture effect for collision detection and recovery,” in Proc. Em-NetS-II, pp. 45-52, May 2005.[3] N. Abramson, “The Aloha system–another alternative for computercommunications,” in Proc. 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Commun., vol. 39, no. 10, pp. 1482-1493, Oct. 1991.[11] G. Jakllari, S. V. Krishnamurthy, M. Faloutsos, P. V. Krishnamurthy, andO. Ercetin, “A cross-layer framework for exploiting virtual MISO linksin mobile ad hoc networks,” IEEE Trans. Mobile Comput., vol. 6, no. 6,pp. 579-594, June 2007.Authorized licensed use limited to: ULAKBIM UASL - SABANCI UNIVERSITY. Downloaded on October 25, 2008 at 09:25 from IEEE Xplore.  Restrictions apply.

Throughput analysis of ALOHA with cooperative diversity

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