A Transmission Scheme for Continuous ARQ Protocols over Underwater Acoustic Channels

Transcription

1 A Tansmission Scheme fo Continuous ARQ Potocols ove Undewate Acoustic Channels Mingsheng Gao 1, Wee-Seng Soh 1 and Meixia Tao 2 1 Dept. of Electical & Compute Engineeing, National Univesity of Singapoe, Singapoe Dept. of Electonic Engineeing, Shanghai Jiao Tong Univesity, Shanghai, China 224 s: elegaom@nus.edu.sg; elesohws@nus.edu.sg; mxtao@sjtu.edu.cn Abstact Due to the half-duplex popety of the undewate acoustic channels, the classic stop-and-wait ARQ (SW-ARQ) and its vaiants ae geneally thought to be the only class of ARQ potocols that can be applied in undewate. When combined with the lage popagation delay popety of the undewate acoustic channels, the use of SW-ARQ and its vaiants makes the thoughput pefomance of undewate acoustic communication systems vey inefficient. In this pape, we popose a tansmission scheme that takes advantage of the long popagation delay in undewate to enable the use of continuous ARQ potocols ove undewate acoustic channels. Simulation esults show that ou poposed tansmission scheme allows much highe thoughput to be achieved than both the classic SW-ARQ and its vaiants, even when simple continuous ARQ potocols ae used. I. INTRODUCTION Fowad-eo-coection (FEC) and automatic epeat equest (ARQ) ae the two main eo-contol techniques that ensue the eliability of data tansmission in undewate acoustic links [1], [2]. Recently, thee has been some eseach on how FEC schemes can be applied to eliminate bust eos in undewate acoustic communication systems [3], [4]. Howeve, in any FEC scheme, the numbe of eoneous symbols in a eceived codewod cannot exceed a cetain bound, beyond which the eos cannot be coected. Theefoe, thee ae always some application scenaios that pefe the use of ARQ techniques to achieve the desied eliability [5]. In teestial RF communications wheeby popagation delays ae shot, only the stop-and-wait ARQ (SW-ARQ) potocol and its vaiants can be used when the links ae halfduplex [6]. In ode to impove the thoughput pefomance of half-duplex communication systems, seveal vaiants of the classic SW-ARQ have been poposed ove the yeas. Fo example, Mois [7] poposes that the tansmitte sends a goup of M packets, and waits fo the eceive to eply with the ACKs/NAKs fo these packets as a goup. Those packets that ae NAK ed ae then etansmitted with othe new packets to fom a new goup of M packets duing the next cycle. In this manne, as many as M packets can be tansmitted duing one ound-tip time and, hence, the thoughput efficiency is inceased. Howeve, if odeed delivey of packets to the uppe laye is needed, the eceive has to stoe the packets until they can be eaanged. In [8], Tuney poposes a scheme in which the tansmitte also sends out a goup of M packets and waits fo thei ACKs/NAKs, but only those packets that ae NAK ed ae etansmitted in the next cycle, i.e., no new packet is added. The advantage ove the pevious appoach is that the eceive now does not need the capability to buffe moe than M packets fo odeed delivey. Fo the case of undewate acoustic communications, since the modems ae mostly half-duplex, it is geneally thought that only SW-ARQ and its vaiants would be feasible. Fo instance, in [9], Stojanovic impoves the SW-ARQ vaiant in [7] by selecting the optimal packet size, which is a function of the communication ange, tansmission ate, and bit eo ate. In essence, these vaiants have meely optimized the classic SW-ARQ; while they have etained the SW-ARQ s suitability fo half-duplex links, they have also etained its undesiable popeties of low efficiency and high packet delay. In the undewate envionment, howeve, the undewate acoustic waves have a low popagation speed of appoximately 15 m/s, which esults in significant popagation delay. This is also the key eason why the SW-ARQ potocol and its existing vaiants pefom even moe badly in undewate, since a tansmitte always idles fo one ound-tip time while waiting fo the eceive s ACK(s)/NAK(s). In a natual manne, if a methodology can be devised that would enable a continuous ARQ despite of the channel s half-duplex popety, the tansmission efficiency could be geatly impoved. An impotant but often neglected popety in undewate acoustic communication is that, it is actually possible fo a pai of nodes to send packets that coss each othe in the medium, while each packet can still be coectly eceived by the othe node, so long as each node has finished its tansmission and has switched to listening mode by the time the packet aives. Motivated by this popety, we pesent a tansmission scheme whee a tansmitte altenates between tansmitting a data packet to the eceive, and listening fo an ealie packet s ACK/NAK, while one o moe othe packets ae still in tansit. This enables continuous ARQs to be implemented ove undewate acoustic channels. Although the appoach is unthinkable in half-duplex teestial wieless systems due to the much shote popagation delay, it has now become feasible in undewate by iding on its long popagation delay. It should be mentioned that, although many studies have been pefomed on continuous ARQs fo teestial communication systems, to the best of ou knowledge, no attempt has been made to imitate this continuous behavio in halfduplex undewate acoustic communication systems so fa. In this pape, we explain how ou poposed tansmission scheme /9/$ IEEE

2 can enable continuous ARQ potocols to be implemented ove half-duplex undewate acoustic channels. We also povide simulation esults to show that, even if we meely apply simple continuous ARQ potocols that ae now enabled by the poposed tansmission scheme, they can aleady achieve much highe thoughput than the classic SW-ARQ and its vaiants ove undewate acoustic channels. The est of this pape is oganized as follows. In Section II, we descibe the tansmission scheme in detail. In Section III, we explain how the system paametes of the tansmission scheme can be detemined. We then show in Section IV the simulation esults that we have obtained when we implemented seveal continuous ARQ potocols using ou poposed tansmission scheme, and compae them with the SW-ARQ and one of its vaiants. Finally, Section V concludes the pape. II. OUR PROPOSED TRANSMISSION SCHEME Conside an undewate communication system wheeby a tansmitte has an estimation of the initial popagation delay (denoted by p ) to its eceive, as well as the uppe bound of the elative adial velocity (denoted by v ) between the two nodes. Hee, we define v to be positive when the two nodes ae appoaching each othe. Fo convenience, we utilize the following notations in ou model desciption: v p : The popagation speed of undewate acoustic waves. δ and γ: The tansmission times of a data packet and an ACK/NAK packet, espectively. Note that thei eception times ae assumed to be the same as thei tansmission times, because v is usually much smalle than v p. p i : The popagation time of the i th data packet fom the tansmitte to the eceive. p i : The popagation time of the ACK/NAK packet fo the i th data packet fom the eceive to the tansmitte. t i : The idle peiod at the tansmitte afte sending the i th data packet. These idle peiods ae intoduced to avoid possible collisions between the data tansmissions and the ACK/NAK eceptions by the tansmitte when v >. t i : The idle peiod at the eceive afte acknowledging the i th data packet with eithe an ACK o a NAK. These idle peiods ae intoduced to avoid possible collisions between the eceptions of data packets and the ACK/NAK tansmissions by the eceive when v >. s: The maximum pemissible numbe of tansmitted, but not yet acknowledged, data packets; this is also efeed to as the window size. k : The maximum allowable total numbe of data packets that can be tansmitted in the cuent session (including etansmissions); if the tansmitte still has some emaining data packets to be sent when k is eached, it has to initialize a new session befoe it can continue to tansmit them. Theefoe, k should be set to a value that is sufficiently lage to accommodate the cuent session. As mentioned ealie, the classic SW-ARQ s low thoughput and high packet delay become much moe ponounced in the undewate acoustic channel, due to the long popagation delay. The poposed tansmission scheme, on the othe hand, Tansmitte Receive s =3 t 1 t 2 t 3 t 4 t 5 t 6 #1 #2 #3 #4 #5 #6 p 1 p 2 Fig. 1. p 1 p 3 p 4 p 2 #1 #2 #3 #4 #5 Data packet p 3 p 5 p 6 p 4 t 1 t 2 t 3 t 4 t 5 t 6 ACK/NAK The flow of the tansmission scheme. #7 p 7 #6 #7... Time... Time combats the effects of long popagation delay by having moe than one packet to be on-the-fly within the channel between the tansmitte and the eceive, at any instant. The flow of the tansmission scheme fo s =3is illustated in Fig. 1. Hee, we assume that the tansmitte has aleady acquied the contol of the channel successfully, and has a seies of packets to send to the eceive. Also, fo the ease of explanation, we assume that the ACKs/NAKs ae eceived eo-fee 1. Afte sending s data packets, the tansmitte switches to a stop-and-wait mode, in which it waits until it has eceived an ACK/NAK befoe tansmitting the next data packet. This eliminates the need fo explicit time-slot synchonization between the tansmitte and the eceive. The key diffeence fom the classic SW-ARQ potocol is that the ACK/NAK that the tansmitte expects is not the esponse fo the most ecently tansmitted data packet, but fo an ealie data packet. Fo example, afte tansmitting packet #3, the tansmitte waits to eceive the ACK/NAK fo packet #1. Fo the eceive, it tansmits the ACK/NAK immediately afte eceiving each data packet. Apat fom the time it spends on tansmitting the ACK/NAK, the eceive listens fo data packet at othe times. Ou novel appoach is simila to the juggling of objects between two hands; when juggling, a hand cannot be thowing one object while eceiving anothe object at the same time, which is simila to the half-duplex popety of the undewate acoustic channel. In addition, multiple objects can be juggled between two hands, much like the tansmission scheme s attempts to inject multiple data packets and ACKs/NAKs into the medium simultaneously. We shall efe to this tansmission scheme as the juggling-like stop-and-wait (JSW) scheme. Note that it is meely a tansmission scheme, athe than an ARQ potocol. Its tansmission stategy allows othe continuous ARQ potocols to be applied in half-duplex undewate acoustic links. Although it may appea that ou tansmission scheme equies an ACK/NAK fo evey packet, it can actually be futhe optimized. Fo example, we can goup multiple packets togethe to fom a packet tain, fo which the eceive only needs to etun a single ACK packet that contains cumulative/selective ACK infomation. It can be obseved fom Fig. 1 that the JSW scheme can function popely if and only if (i) t i γ fo 1 i s 1, (ii) t i fo all i s, and (iii) t i fo all i 1. 1 Although it is possible to extend ou potocol to include scenaios that conside coupted ACKs/NAKs, we will explain how this can be addessed in ou futue pape, due to space limitation.

3 Conditions (i) and (ii) ensue that the tansmitte is always in listening mode when an ACK/NAK aives; on the othe hand, condition (iii) ensues that the eceive is always in listening mode when a data packet aives. Ou main focus will be on the case whee v >. We will explain at the end of Section III how ou poposed scheme woks when v. Also, note that v is meely an uppe bound, meaning that the instantaneous elative adial velocity can still be negative even when v is positive. Fo v >, it is possible fo both t i and t i to decease ove time, with the fastest ate of decease occuing when the elative adial velocity is consistently at its uppe bound, i.e., v. Theefoe, given p, v, and k, it is cucial to choose an appopiate value fo s, as well as the appopiate inte-packet spacings to tansmit the fist s packets, so that the above thee conditions ae always met thoughout the entie tansmission session. III. DETERMINATION OF THE SYSTEM PARAMETERS We now pesent in detail how the system paametes of the JSW scheme can be calculated. Fo the ease of pesentation, we assume that the switching time between tansmit and eceive modes, t sw, is negligible. Note, howeve, that it can be fully accommodated in the following calculations by incopoating it within the tansmission time of an ACK/NAK, i.e., we can eplace the paamete γ with γ, whee γ = γ + t sw. A. Calculation of s Fo simplicity, the inte-packet spacings to tansmit the fist s packets (i.e., t 1,t 2,...,t s 1 ) ae made equal, with a value denoted by t. We will show in Section III-B how its appopiate value can be calculated. Fom Fig. 1, we have p 1 + p 1 + δ = sδ + t i + t s. (1) Since t s, the above can be futhe ewitten as p 1 + p 1 (s 1)δ + t i. (2) Thus, s can be expessed as p1 + p 1 s = +1, (3) δ + t whee p 1 and p 1 ae given by (4) and (5), espectively: v p p 1 = p v p + v (4) { p 1 = max p 1 v } (p 1 + δ),. v p + v (5) B. Calculation of t Fom Fig. 1, fo all k 2, we can obtain { p k = max p 1 v k 1 [ (k 1)δ + t i v p + v +(k s)γ.u(k s 1) ] }, (6) and { p k = max p 1 v k 1 [ p1 +kδ+ t v p + v i+(k 1)γ ] }, whee U(x) is a unit step function that etuns a if x<, and etuns a 1 othewise. It can be noted fom the above that, if the elative distance between the tansmitte and the eceive emains static, we have p k = p k = p fo all k 1. We can also make the following obsevations about p k and p k fo all k 2: k 1 p k = p 1 + (t i t i ) + [min(k, s) 1]γ (8) p k =(s 1)δ + s (7) k 1 t i + (t s+j t j) p 1 (9) j=1 The above two elations can be used to find t k fo all k s, and t k fo all k 1. Thus,wehave t s = p 1 + p 1 (s 1)δ t i (1) t k = p k+1 p k + t k γu(s k 1) (11) t s+k = p k+1 p k + t k (12) Fo a given v >, we can see fom (6) and (7) that, both p k and p k ae stictly deceasing functions with espect to k fo 1 k k. In light of (11) and (12), we have t s+k <t k, fo k s (13) t s+k <t k, fo k 1 (14) Equations (13) and (14) tell us that, both the sequences t k,t s+k,t 2s+k,... and t k,t s+k,t 2s+k,... (fo any k [1,s]) ae monotonically deceasing sequences. These imply that, fo any given t γ, if it can esult in t k and t k fo all k [k s +1,k ], then t k and t k also hold fo all k [1,k ]. Such t ( γ) always exists fo any given combination of p, v, and k that yields s 2. Note that fo the case whee s =1, the tansmission scheme degades to the conventional tansmission mode that is only suitable fo the classic SW-ARQ and its vaiants, and t no longe exists. In ode to obtain a value fo t that satisfies the above conditions fo a given set of p, v, and k, we use a numeical method as summaized in Fig. 2. As an illustated example, we exploe the values of s and t when the uppe bound of the elative adial velocity, v, vaies fom to 6 m/s, along with the following paametes: p =.6667 s (coesponding to an initial sepaation of 1 km), δ =.64 s, γ =.5 s, k = 1, and Δ=.1. Fom Fig. 3, we can see that t inceases monotonically as v vaies fom m/s to aound 5.6 m/s. Fig. 4, on the othe hand, shows that the window size, s, deceases monotonically as v inceases. When v goes beyond 5.6 m/s, the tansmission scheme degades to the classic stop-and-wait behavio, with s =1. In this case, t no longe exists, as can be seen in Fig. 3. By compaing Fig. 3 with Fig. 4 closely, we also obseve that the discontinuities in Fig. 3 occu at those points whee s changes.

4 2 Initializations: t γ, andsetp, v, δ, γ, k,andδ accodingly Iteations: 1) Compute s using (3) 2) if s =1 Execute SW-ARQ Go to End // t does not exist in classic SW-ARQ else fo each k [k s +1,k ] Compute t k and t k if t k and t k fo all k [k s +1,k ] Go to End // t found else t t +Δ Go to 1) End: Fig. 2. The algoithm fo detemining the initial inte-packet spacing, t. Initial inte packet spacing, t (s) Uppe bound of elative adial velocity, v (m/s) Fig. 3. The initial inte-packet spacing t vesus the elative adial velocity s uppe bound v fo p =.6667, δ =.64, γ =.5, andk = 1. Fom the discussion above, the following emaks can be made. Fistly, ou scheme does not equie accuate knowledge of the popagation delay, since we can always bias towads a smalle p, which will only esult in a smalle s. Secondly, it can be easily infeed that ou scheme can wok well when v >. Fov, the tansmitte and the eceive may eithe emain static elative to each othe (if v =), o they may dift futhe apat as time goes by. In eithe case, the conditions (i), (ii) and (iii) in Section II will always be met so long as all t i ae initialized to γ fo 1 i s 1, and s is given by 2p s = +1. (15) δ + t IV. SIMULATION RESULTS We have pefomed simulations using pogams witten in C++ to evaluate the benefits of ou poposed scheme. In ou simulations, we only conside point-to-point communications, and we assume that the two points ae within each othe s ange thoughout the session. The switching time between tansmit and eceive modes ae assumed to be negligible. We have also assumed that the data ate is 8 kbps, the data packet length is 512 bits, and the contol packet length (i.e., ACK/NAK) is 4 bits. The pefomance metic used is Window size, s Uppe bound of elative adial velocity, v (m/s) Fig. 4. The window size s vesus the elative adial velocity s uppe bound v fo p =.6667, δ =.64, γ =.5, andk = 1. thoughput, which we define as the atio of the total useful time to the total simulation time, whee the total useful time efes to the total tansmission time of all the data packets that ae coectly eceived duing the total simulation time. We have implemented two classic continuous ARQ potocols, namely, go-back-n (GBN-ARQ) and selective-epeat (SR-ARQ), which ae now made possible in half-duplex undewate acoustic channel by ou JSW scheme. We compae thei thoughput with the classic SW-ARQ and T-ARQ, unde both static and dynamic conditions, to demonstate the loss in efficiency if we wee to stick to the pevious peception that only non-continuous ARQ potocols may be applied in half-duplex undewate acoustic channels. We choose not to compae with the scheme in [9], which optimizes the packet length fo [7], because its thoughput can be inceased by having a lage goup size, M. The compaison will not be fai since this is achieved at the expense of having a much lage aveage esequencing delay at the eceive. In addition, the optimal packet size calculation in [9] loses its optimality when the nodes move. Fist, we conside the static case (i.e., the elative adial velocity is zeo), whee p k = p k = p fo all k 1. Hee, p is assumed to be.6667 s, and t i is set to γ fo 1 i s 1. We also assume that thee is an infinite data souce at the tansmitte. The total simulation time is 1,, s, and all the esults pesented ae aveaged ove 1 simulation uns. Fig. 5 illustates the thoughput of these potocols vesus packet eo ates (P e ) anging fom.1 to.2. Hee, the classic GBN-ARQ and SR-ARQ ae implemented based on ou JSW tansmission scheme, while the classic SW-ARQ and T-ARQ (with M =5) ae based on the conventional stopand-wait tansmission scheme whee the tansmitte-eceive pai ae not allowed to tansmit simultaneously. As expected, T-ARQ with M =5povides highe thoughput than classic SW-ARQ. This is because T-ARQ sends multiple data packets in each stop-and-wait cycle, while SW-ARQ sends only a single data packet in each cycle. Howeve, both of them have much lowe thoughput than GBN-ARQ and SR-ARQ. The supeio pefomance of the latte two potocols can be

5 Thoughput, η SR ARQ GBN ARQ T ARQ (M = 5) Classic SW ARQ Thoughput, η SR ARQ GBN ARQ T ARQ (M = 5) Classic SW ARQ Packet eo ate, P e Fig. 5. Thoughput vs. packet eo ate compaison among the fou diffeent ARQ potocols fo p = lagely attibuted to thei use of ou JSW tansmission scheme, which allows these continuous ARQs to opeate in an almost continuous manne without the need fo a full-duplex channel. Next, we conside a dynamic scenaio wheeby the adial velocity anges between and 6 m/s. Fig. 6 shows its impact on the thoughput of each of the fou diffeent ARQ potocols that we have simulated. At each data point, we hold the adial velocity constant, and measue the ARQ s thoughput, assuming that thee ae 5 data packets to be tansmitted, while p is.6667 s, P e is.5, and k is 1. Fom the figue, we can make seveal inteesting obsevations. Fistly, both GBN-ARQ and SR-ARQ can achieve much highe thoughput than T-ARQ and SW-ARQ when the adial velocity is less than 5.6 m/s. Howeve, thei thoughput degades to that of SW-ARQ when the adial velocity goes beyond 5.6 m/s. This can be attibuted to the fact that when the adial velocity is less than 5.6 m/s, the window size s is geate than one; thus, both GBN-ARQ and SR-ARQ can benefit fom ou JSW scheme, and opeate as continuous ARQ potocols. On the othe hand, when the adial velocity exceeds 5.6 m/s, s degades to one, essentially making these potocols opeate like SW-ARQ. Secondly, fo s>1, the thoughput of both GBN-ARQ and SR-ARQ expeiences stai-like descents as the adial velocity inceases. By compaing Fig. 4 and Fig. 6, we obseve that the discontinuities in thei thoughput occu at those adial velocities whee s deceases. This is because a smalle s implies that less packets can be placed into the pipeline, causing a noticeable dop in the thoughput. On the contay, the thoughput of both T-ARQ and SW-ARQ inceases as the adial velocity inceases, because less time is wasted on waiting as the ound-tip delay deceases faste. V. CONCLUSION In this pape, we popose a tansmission scheme fo undewate acoustic channels that enable the use of continuous ARQ potocols without the need fo a full-duplex channel. Ou scheme exploits the long popagation delay in undewate, and allows the tansmitte and the eceive to inject multiple data packets and ACKs/NAKs into the medium simultaneously Radial velocity (m/s) Fig. 6. Thoughput vs. elative adial velocity compaison among the fou diffeent ARQ potocols fo p =.6667 and P e =.5. in a juggling-like manne, even though the channel is halfduplex. We have also consideed the case wheeby the adial velocity between the tansmitte-eceive pai is non-zeo, and shown that the scheme woks coectly so long as the maximum adial velocity and the initial popagation delay ae known. It also does not equie any clock synchonization between the tansmitte-eceive pai. Ou simulation esults show that the poposed tansmission scheme allows much highe thoughput to be achieved than the existing stop-andwait ARQ appoaches, even when simple continuous ARQ potocols, namely GBN-ARQ and SR-ARQ, ae used. This implies that moe sophisticated continuous ARQ potocols that ae now made possible by ou tansmission scheme could potentially achieve even bette thoughput. ACKNOWLEDGMENT This eseach was suppoted by the Ministy of Education of Singapoe, unde AcRF Gant No. R REFERENCES [1] I. F. Akyildiz, D. Pompili, and T. Melodia, State-of-the-at in potocol eseach fo undewate acoustic senso netwoks, in Poc. WUWNet 6, Los Angeles, Califonia, USA, Sep. 26. [2] J. Poakis, E. Soze, J. Rice and M. Stojanovic, Shallow wate acoustic netwoks, IEEE Commun. Mag., vol.39,no.11,pp ,nov.21. [3] D. Pompili, T. Melodia, and I. Akyildiz, Routing algoithms fo delay-insensitive and delay-sensitive applications in undewate senso netwoks, in Poc. ACM Mobicom, 26. [4] A. F. Hais III, D. G. B. Meneghetti, and M. Zozi, Maximizing channel utilization fo undewate acoustic links, in Poc. IEEE OCEANS, June 27. [5] M. Zozi, Some esults on eo contol fo bust-eo channels unde delay constaints, IEEE Tans. Veh. Technol., vol. 5, no. 1, pp , Jan. 21. [6] S. Lin, D. J. Costello, J., and M. J. Mille, Automatic-epeat-equest eo contol schemes, IEEE Commun. Mag., vol. 22, pp. 5-17, Dec [7] J. M. Mois, Optimal blocklengths fo ARQ eo contol schemes, IEEE Tans. Commun., vol. 27, pp , Feb [8] P. F. Tuney, An impoved Stop-and-Wait ARQ logic fo data tansmission in mobile adio systems, IEEE Tans. Commun., vol. 29, pp , Jan [9] M. Stojanovic, Optimization of a data link potocol fo an undewate acoustic channel, in Poc. IEEE OCEANS, pp , Jun. 25.