2196 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 11, NOVEMBER 2013

Beacon-Based Slotted ALOHA forWireless Networks with Large Propagation Delay

Hoki Baek, Student Member, IEEE, Jaesung Lim, and Sangyoon Oh, Member, IEEE

Abstract—In a wireless network with large propagation delayS-ALOHA(Slotted ALOHA) requires large guard time whichcauses lower normalized throughput. To reduce the large guardtime in the ISA-ALOHA [4], a time alignment mechanism wasproposed under the assumption of propagation delay estimation.In this letter, we propose a framed structure which is able toestimate propagation delay by employing coordinator beaconing.The framed structure consists of a time period for beaconing anda group of multiple time slots for random access. The proposedBeacon-based S-ALOHA(BS-ALOHA) can make packets gener-ated during the time of beaconing evenly distributed over therandom access period. Furthermore, we propose an analyticalmodel considering overhead due to coordinator beaconing timeand show that BS-ALOHA provides higher normalized through-put than both ALOHA and S-ALOHA employing the large guardtime.

Index Terms—Propagation delay, framed structure, slottedALOHA.

I. INTRODUCTION

UNLIKE terrestrial networks, the propagation delay inairborne and underwater networks is not negligible and is

dynamically changed owing to mobility of nodes. In common,these networks have a coordinator to which all nodes sendpackets and a well-known characteristic, space-time uncer-tainty, which results from large propagation delay [1].

In terrestrial networks, S-ALOHA uses a time slot whoselength is the almost same as transmission time of a packet.It then provides higher normalized throughput than ALOHA.However, if the propagation delay is a significant factor, theperformance can be different. In [2], simulation results showthat S-ALOHA yields the equal normalized throughput to thatof ALOHA when the propagation delay becomes large and thespace-time uncertainty problem cannot be resolved. Accordingto [3], when the guard time length is longer than transmissiontime of a packet in a slot, S-ALOHA even provides lowernormalized throughput than ALOHA.

ISA-ALOHA(Improved Synchronized Arrival slottedALOHA) [4] was proposed to reduce the large guard time byusing the time alignment mechanism which helps each nodeadjust the start time of transmission, i.e., a packet arrives

Manuscript received August 8, 2013. The associate editor coordinating thereview of this letter and approving it for publication was P. Chatzimisios.

This work was supported by the National Research Foundation ofKorea (NRF) grant funded by the Korea government (MSIP) (No.2013R1A2A1A01016423). This research was supported by the MSIP (Min-istry of Science, ICT & Future Planning), Korea, under the ITRC (InformationTechnology Research Center) support program supervised by the NIPA(National IT Industry Promotion Agency (NIPA-2013-H0301-13-2003)).

The authors are with the Graduate School of Information and Communica-tions, Ajou University, Suwon, Republic of Korea (e-mail: {neloyou, jaslim,syoh}@ajou.ac.kr).

Digital Object Identifier 10.1109/LCOMM.2013.101413.131802

at the start time of a slot at the coordinator. For the timealignment, Propagation Delay to Coordinator(PDC) shouldbe estimated. ISA-ALOHA assumed that each node canestimate the propagation delay by exchanging packets withcoordinator.

On the other hand, in a single-channel wireless networkwith large propagation delay, any specific mechanism forexchanging packets is required to estimate the propagationdelay. In this letter, we adapt a framed structure which isable to estimate propagation delay by employing coordinatorbeaconing. All nodes are assumed to be synchronized byGlobal Positioning System(GPS). The PDC should be obtainedfor time alignment even in the perfect time synchronized net-work. The framed structure has some advantages. Firstly, theframed structure is adequate to support coordinator beaconingby allocating a coordinator time slot which includes guardtime enough to resolve space-time uncertainty. The beaconingcan reduce the number of packet exchanges required for PDCestimation. Beacon message may include time informationused for PDC estimation and acknowledgment for successfulreception of packets. Secondly, the framed structure can pro-vide a periodic PDC estimation which can help dynamicallydetermine the error bound of PDC estimation, especially inhigh mobility environments.

In the proposed scheme, the framed structure consists ofa time period for beaconing and a random access periodwhich is a group of multiple time slots. Each node estimatesPDC during the beacon time period and executes the timealignment mechanism proposed in [4] during the randomaccess period. The proposed Beacon-based S-ALOHA(BS-ALOHA) can make packets generated during the time ofbeaconing evenly distributed over the random access period.Furthermore, we propose an analytical model consideringoverhead due to coordinator beaconing time and show thatBS-ALOHA provides higher normalized throughput than bothALOHA and S-ALOHA employing the large guard time.

II. BEACON-BASED SLOTTED ALOHA

We consider a single-channel single-hop wireless networkwith large propagation delay. Our network consists of acoordinator and multiple nodes. We assume that all nodes aresynchronized perfectly by GPS and that they transmit packetsof equal size to the coordinator. If all nodes are synchronized,BS-ALOHA can be applied to any networks and providesmore effective performance in the wireless networks with largepropagation delay, e.g., the airborne and underwater networks.

We define a number of variables for the framed structureof BS-ALOHA as shown in Fig. 1. Let tstart, Tframe,TB , TMAX RTT , and ts,j be the start time of a frame,

1089-7798/13$31.00 c© 2013 IEEE

BAEK et al.: BEACON-BASED SLOTTED ALOHA FOR WIRELESS NETWORKS WITH LARGE PROPAGATION DELAY 2197

Fig. 1. PDC estimation and time alignment in a frame of BS-ALOHA.

frame duration, beacon transmission time, maximum round-trip time of the maximum communication range R, and starttime of the j-th slot, respectively. TMAX RTT is given byTMAX RTT = 2R/c, where c is the signal propagation speed.The framed structure consists of a coordinator time slot and agroup of multiple time slots. The coordinator time slot whoseguard time length is TMAX RTT is for beaconing. After thecoordinator time slot of length TB + TMAX RTT , M slots oflength TS are available for random access. Including an initialdelay of length TMAX RTT enables the farthest node from thecoordinator to access the first slot. We define ti to be the timeat which a packet at the i-th node is generated, and ttx,i to bethe time at which the i-th node starts to transmit the packet.We also define tv,i as the virtual packet arrival time, which isthe time a packet generated by the i-th node would arrive ifthe packet was transmitted as soon as it was generated. Thus,tv,i is obtained by tv,i = ti + τi, where τi is the PDC of thei-th node.

All nodes can estimate PDC in every frame by usingcoordinator beaconing. As shown in Fig. 1, the coordinatorbroadcasts a beacon at tstart, the start of a frame, and the i-th node receives it at tB,i, the beacon arrival time. The PDCof the i-th node then is obtained by τi = tB,i − tstart. Byusing GPS and framed structure, periodic PDC estimation ispossible.

Next, we explain random access period in which eachnode executes the time alignment mechanism proposed in[4] to reduce guard time. In addition, we present distributionmethod of packets generated during the time of beaconing.BS-ALOHA evenly distributes these packets over the randomaccess period.

When the i-th node generates a packet, it determinesthe start time of transmission, ttx,i, based on tv,i and τi.Firstly, it checks whether tv,i happens to fall within theM slots available for transmission. For simplicity, let γ betstart + TB + TMAX RTT . If tv,i falls within the first M − 1slots, i.e., γ ≤ tv,i ≤ γ + (M − 1) × TS , the node selectsthe next slot to begin after tv,i. If tv,i falls within slot M ,i.e., γ + (M − 1) × TS ≤ tv,i ≤ γ + M × TS , the packetwill be transmitted in the first slot of the next frame, as thereare no more slots available in the current frame. Therefore, ifγ ≤ tv,i ≤ γ +M × TS , then the index k of the selected slot

is given by

k ={(⌈ (tv,i − γ)

TS

⌉)mod M

}+ 1. (1)

On the other hand, if tv,i < γ, i.e., the packet is generatedduring the time of beaconing, the node postpones transmissionand selects a slot based on tv,i. For this, we uniformly divideγ into M intervals (I1, · · · , IM ) and define TI as a length ofinterval, which is obtained by TI = (TB + TMAX RTT )/M .If tv,i is within Ik, the packet will be transmitted in slot kwhich is obtained by

k =⌈(tv,i − tstart)

TI

⌉. (2)

In this way, BS-ALOHA can evenly distribute packets gen-erated during the time of beaconing over the random ac-cess period. Consequently, BS-ALOHA can equalize collisionprobability of every slot and provide a fair packet delay byletting k be proportional to tv,i.

After selecting the slot, the node performs time alignmentto reduce guard time while resolving space-time uncertaintyby adjusting the start time of transmission so that the packetwill arrive at the beginning of a slot. If the slot k is selected,ttx,i is obtained by ttx,i = ts,k − τi.

For example, in Fig. 1, tv,2 and tv,3 are within slot 2 andM , respectively. Thus, node 2 selects slot 3. However, in caseof node 3, there are no more slots after slot M in the frame.Thus, node 3 selects the slot 1 of the next frame. Unlike node 2and 3, node 1 selects the slot j because tv,1 is within Ij . Afterselecting the slots for packet transmission, each node adjuststhe start time of transmission so that the packet will arrive atits beginning. Thus, ttx,1, ttx,2, and ttx,3 can be obtained byts,j − τ1, ts,3 − τ2, and ts,1 − τ3, respectively.

If all nodes are synchronized, BS-ALOHA can be applied toboth single-hop airborne networks and single-hop underwaternetworks by determining parameters: R, c, vMAX , and TP .In the airborne networks [5] [6], R is 300 nautical miles(nmi)and c is 3 × 108 m/s because Radio Frequency(RF) signal isused. On the other hand, in the underwater networks [4], Ris 1500 m and c is 1500 m/s because acoustic signal is used.We can set the values of vMAX and TP according to thegiven system parameters. Moreover, BS-ALOHA can supportacknowledgment by using a beacon message because it mayinclude acknowledgment for successful reception of packetsas well as time information used for PDC estimation.

III. PERFORMANCE ANALYSIS

We assume that infinite nodes generate packets accordingto a Poisson process at a rate of λ packets/s and that TB isnegligible. We also assume that all the packet losses are causedby collisions. We do not consider any packet retransmission.

We consider an additional guard time, TG, in a slot tocompensate for the drift of the estimated PDC due to the highmobility. Thus, TS is TP + TG, where TP is transmissiontime of a packet. Even if the GPS provides perfect timesynchronization, the estimated PDC at the start of a framecan be changed as all nodes move rapidly during a frame.The amount of the drift can be greatest when the two nodes

2198 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 11, NOVEMBER 2013

move in opposite directions with maximum velocity duringTframe. Thus, we set TG as

TG = 2vMAX × Tframe

c(3)

where vMAX is the maximum velocity of a node. We replaceTframe in (3) with TMAX RTT + M(TP + TG) as Tframe

contains TG recursively. After that, we can obtain TG by

TG =2vMAX(TMAX RTT +MTP )

c− 2MvMAX. (4)

We define normalized throughput, X , as the ratio of frametime used for successful packet transmission to frame duration.The normalized throughput of BS-ALOHA can be expressedas

X =E[S]× TP

Tframe(5)

where E[S] is the average number of successful slots in aframe and is given by

E[S] =M∑s=0

sP (S = s) (6)

where S is a random variable describing the number ofsuccessful slots and P (S = s) is the probability that thenumber of successful slots is s. We can obtain P (S = s)by

P (S = s) =

M∑b=s

P (S = s|B = b)× P (B = b) (7)

where B is a random variable describing the number of busyslots, P (S = s|B = b) is the conditional probability that thenumber of successful slots is s given that the number of busyslots is b, and P (B = b) is the probability that the number ofbusy slots is b. Since not all the busy slots are successful owingto collisions, we consider those b whose values are equal toor larger than s. In (7), P (S = s|B = b) is expressed as

P (S = s|B = b) =

(b

s

)ρs(1− ρ)b−s (8)

where ρ is the conditional probability that the number ofarrival packets in a slot is one given that the slot is busyas in [7]. Thus, ρ is expressed as

ρ =λTPGT e

−λTPGT

pB(9)

where TPGT is the amount of time, which is used for gener-ating packets arriving at a slot, and pB is the probability thata slot is busy. In S-ALOHA, the packets arriving at a certainslot were generated during the length of its previous slot, TS .Thus, TPGT of S-ALOHA is expressed as TPGT = TS . On theother hand, in BS-ALOHA, the packets arriving at a certainslot were generated during its corresponding TI as well asduring the length of its previous slot, TS . Thus, TPGT of BS-ALOHA is given by TPGT = TS +TI . The probability pB isobtained by

pB = 1− e−λTPGT . (10)

In (7), P (B = b) is expressed as

P (B = b) =

(M

b

)pbB(1− pB)

M−b. (11)

Fig. 2. Normalized throughput according to G (TP = 3.0 ms).

Fig. 3. Normalized throughput according to G (TP = 0.1 ms).

IV. NUMERICAL RESULTS

In this section, we compare BS-ALOHA with ALOHA, S-ALOHA employing large guard time, and ISA-ALOHA whichuses the assumptions that all nodes know their PDCs. ISA-ALOHA can provide higher normalized throughput than BS-ALOHA because it does not require overhead duration ofTB + TMAX RTT for coordinator beaconing time. Thus, weuse ISA-ALOHA as an ideal scheme to show the effect of theoverhead.

In order to show the effect of guard time, we use S-ALOHAemploying a guard time whose length is the same as the maxi-mum propagation delay given by TMAX RTT /2, i.e., R/c. Thenormalized throughput of ALOHA is Ge−2G and that of S-ALOHA is Ge−(1+α)G [3], where G is the offered load givenby λTP , and α is the ratio of the maximum propagation delayto TP . When α is larger than 1, S-ALOHA actually provides alower normalized throughput than ALOHA. In ISA-ALOHA,normalized throughput is Ge−(1+β)G, where β is the ratio ofthe guard time to TP . We assume that the guard time lengthof ISA-ALOHA is the same as TG of BS-ALOHA when Mis 100.

BAEK et al.: BEACON-BASED SLOTTED ALOHA FOR WIRELESS NETWORKS WITH LARGE PROPAGATION DELAY 2199

We determine several parameters based on Link-16 [5] andTactical Targeting Network Technology (TTNT) [6]. These arerepresentative military airborne communication systems. Allnodes can communicate directly because their networks aresingle-hop. In these systems, the maximum communicationrange is 300 nmi, where 1 nmi is 1.852 km and RF signal isused. Thus, the corresponding maximum propagation delay is1.852 ms. The F-16 Fighting Falcon equipped with Link-16has the maximum speed of 680 m/s (Mach 2.0). Therefore, weset R, c, and vMAX as 300 nmi, 3 × 108 m/s, and 680 m/s,respectively. We also consider two types of TP s: one whosetransmission time is longer than the maximum propagationdelay (3.0 ms) and another whose transmission is shorter (0.1ms).

Fig. 2 shows X according to G when TP is 3.0 ms, longerthan the maximum propagation delay. BS-ALOHA provideshigher X than S-ALOHA and ALOHA regardless of M asthe guard time is reduced by time alignment. Moreover, BS-ALOHA and the ideal ISA-ALOHA provides almost same Xeven if BS-ALOHA only considers the overhead due to thecoordinator beaconing time. We can also see that M does notsignificantly affect X of BS-ALOHA.

Fig. 3 shows X according to G when TP is 0.1 ms, smallerthan the maximum propagation delay. BS-ALOHA provideshigher X than S-ALOHA and ALOHA regardless of M . S-ALOHA provides a much lower X than ALOHA, as α ismuch larger than 1. When M is 1000, BS-ALOHA providesthe highest X except ISA-ALOHA. This means that X of BS-ALOHA is affected by Tframe. The longer Tframe providesthe higher X when TP is small. The difference of Xs betweenBS-ALOHA and ISA-ALOHA is not zero. However, it is stillvery small when M is large. This means that BS-ALOHAwith large M and ISA-ALOHA provide almost same X evenif BS-ALOHA only considers overhead due to the coordinatorbeaconing time.

V. CONCLUSIONS

In this letter, we adapt a framed structure which can estimatePDC periodically by employing coordinator beaconing andreduce guard time by executing the existing time alignmentmechanism based on the estimated PDC, not assumption.Furthermore, we propose an analytical model consideringoverhead due to coordinator beaconing time. Numerical resultsshow that BS-ALOHA always provides higher normalizedthroughput than both S-ALOHA and ALOHA. Moreover, BS-ALOHA with large M and ISA-ALOHA provide almost samenormalized throughput even if BS-ALOHA only considers theoverhead due to the coordinator beaconing time.

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