Maximizing Channel Utilization for Underwater Aousti Links Albert F Hairris III Davide G. B. Meneghetti Adihele Zorzi Department of Information Engineering University of Padova, Italy Email: {harris,davide.meneghetti,zorzi}@dei.unipd.it Abstrat-Underwater aousti hannels suffer from long delays and high bit error rates. In addition to these hallenges, the unique bandwidth-distane relationship of underwater links makes straightforward appliation of traditional networking tehniques suboptimal. This paper presents an analysis of the appliation of three tehniques: forward error orretion, paket size adaptation, and paket train size adaptation in terms of their effets on hannel utilization in underwater aousti environments. Our analysis provides insight that an guide the design of MAC and routing protools. Results from simulations of the tehniques in ombination demonstrate how inreases in hannel utilization an be ahieved in the fae of underwater aousti hannel onstraints. Tehnial Area: 1.1 Other [Underwater Aousti Networks] I. INTRODUCTION A large number of appliations for underwater sensor networks exist [1]; however, due to limitations of the aousti hannel, providing effiient ommuniation is a hallenging problem. Propagation delay, absorption loss, and low bandwidth are only some fators that must be taken into aount in underwater aousti links. Developing protools that provide effetive ommuniation in terms of timeliness of data, reliability, and energy onsumption must take into aount these fators. One metri for ommuniation effiieny is hannel utilization. In the fae of limited bandwidth resoures, protools that require the hannel to be either idle, or used sending data that is not useful to the reeiving appliations, have a large negative impat on the system. The long propagation delays in underwater networks ause aknowledgment-based reliability mehanisms to severely redue the hannel utilization, due to the need to wait for response from the reeiver; however, the potentially high error rates of underwater hannels [2] require some reliability mehanism to be built into the network stak to support appliations with low tolerane for error. Tehniques to improve the hannel utilization in the fae of large propagation delays inlude using paket trains and forward error orretion (FEC) shemes, but understanding the impat of the various parameters, suh as paket size and the FEC strength, is an open problem. Additionally, properties unique to the underwater environment alter the onventional wisdom on how suh tehniques should be applied. In terrestrial radio networks, as the distane between the sender and reeiver inreases, assuming the transmit power is held onstant, the signal-to-noise ratio (SNR) at the reeiver dereases. Lower SNRs an ause more bit errors at the reeiver, depending on the hannel enoding sheme used for transmission. Lower data rate shemes tend to tolerate lower SNRs while maintaining aeptably low bit error rates. For underwater aousti links, in addition to this effet, the bandwidth available for transmitting the data also dereases with inreasing distane [3]. The ombination of these two effets has a large impat on the available data rates at given distanes for underwater networks. While previous work has attempted to minimize energy without onsidering hannel utilization [4], [5], [6], to minimize delay [2], or to maximize hannel utilization without onsidering the effets of the bandwidth-distane relationship [7], [8], none of this work ahieves optimal hannel utilization sine eah ignores a ritial aspet of the underwater hannel. The main ontribution of this work is an analysis of the effets of the bandwidth-distane relationship, high error rates, and long propagation delays on hannel utilization. We demonstrate the effets of these properties on the use of forward error orretion (FEC) and paket and paket train size adaptation. FEC an be adapted aording to the number of bit errors per blok the ode an orret. This optimal blok ode depends both on the error rate of the hannel and the bit rate available. Optimal paket size depends on the bit error rate of the hannel and the FEC ode used. Paket training an be used to mitigate the effets of long delays on effiieny while extending the amount of time before an error is reported to the sender. By arefully analyzing the relationships between these three tehniques and the effets of the underwater hannel harateristis on their appliation, we demonstrate how to design protools to maximize hannel utilization. The rest of this paper is as follows. Setion II briefly desribes related work in the area of effiient underwater ommuniations. Setion III presents the three adaptation mehanisms onsidered in this paper: forward error orretion, paket size adaptation, and paket train length adaptation. Setion IV presents the model of the underwater hannel used in the paper and disusses how the bandwidth-distane relationship and long propagation delays affet hannel utilization. Setion V presents the results of our simulations. Finally, Setion VI gives some onlusions and future diretions. 1-4244-635-8/7/$2. 27 IEEE Authorized liensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on Otober 17, 28 at 7:59 from IEEE Xplore. Restritions apply.
II. RELATED WORK Work in the design of underwater network protools is relatively new. Park et al. develop a MAC layer protool to attempt to deal with the long propagation delays [4]. This protool sends synhronization messages ontaining a transmission time shedule for eah node to attempt to avoid ollisions and unneessary delays. Harris et al. present a protool to allow nodes to use a low-power wakeup mode to onserve energy when idle [5] and an analysis of the effet of the bandwidth-distane relationship on routing deisions based on hop length for energy-effiient routing [6]. However, none of these works onsider hannel utilization. Heidemann et al. [2] provide a protool to attempt to minimize delay in underwater aousti networks. Pompili et al. [7] present a routing protool that attempts to minimize energy and maximize hannel utilization; however, this work does not onsider the effet of the bandwidth-distane relationship and uses fixed paket train sizes. Stojanovi [8] presents a paket train protool to attempt to inrease hannel utilization without an analysis of the use of FEC or the speifi effets of the bandwidth-distane relationship on the paket train sizes. III. MECHANISMS FOR INCREASING CHANNEL UTILIZATION We onsider three interrelated mehanisms for inreasing hannel utilization in this work: FEC, paket size adaptation, and paket train size adaptation. In order to quantify the effets on network performane, a metri must be hosen. In this paper, we onsider hannel utilization, whih is defined as the ratio of the amount of time the hannel is transmitting useful data that is suessfully reeived to the total amount of time the hannel is used (whih inludes the time the sender is either idle waiting for aknowledgments or transmitting data that is not used by this reeiver beause it is either redundant or is reeived in error). We ignore protool overhead for simpliity of notation; however, suh overhead an be trivially inluded and has minimal impat on the results. A. Forward Error Corretion and Paket Size Adaptation FEC is used primarily to avoid the need for retransmission due to bit errors in a paket and to redue the amount of time it takes to reover losses due to suh errors. Without any FEC, if a paket is reeived with bit errors, it is not useful to the reeiver. Therefore, if the data is needed, a retransmission must be performed. The round-trip time (i.e., the time it takes from when a node starts sending data to when it ends reeiving the orresponding aknowledgment) depends on the data rate of the hannel, determined by the bandwidth and the modulation, on the paket length, and on the propagation and proessing delays. If we let d be sum of the two-way propagation delay on the link, the proessing time of the paket at the reeiver, and the transmission time of the aknowledgment, the round-trip time an be omputed as follows: D t'r =d +R(1 where D is the number of bits transmitted before the sender stops and waits for an aknowledgment, and R is the data rate of the link. For high propagation delay links, suh as those present in the underwater environment, the propagation delay is the dominant omponent. Therefore, some redundany in the form of an FEC ode an be added to eah paket at little additional ost. Eah FEC blok ode has the apability to orret a number of transmission errors. In this work, we onsider Reed-Solomon odes [9], whih map an information blok onsisting of k symbols of L bits eah to a odeword of n > k L-bit symbols (where typially n = 2L), and whih an orret up to n-k symbol errors.' If the FEC blok ode is designed to orret more errors than atually our, the extra redundany added to the stream onstitutes a waste and redues the hannel utilization. Therefore, the FEC should ideally be adapted based on the error rate of the hannel. The effet of FEC on hannel utilization is ditated by the amount of redundany added to eah paket. Essentially, for eah kl appliation data bits, there is an additional (n- k)l bits of redundany added. Therefore, the hannel utilization in the absene of errors beomes: kl/r ' nl/r+d (2) If the probability that the FEC annot orret the bit errors in the paket is ep, the hannel utilization is as follows: (1 -ep)kl/r 8' nl/r+d (3) Note that ep depends not only on the bit error rate, but also on n, k and L, whih define the paket size and number of errors that an be orreted. The expressions in Equations (2) and (3) inorporate two mehanisms, namely, FEC and paket size adaptation. While it is ertainly possible to use eah of these tehniques independently, their tight relationship makes it appropriate to treat them together. Paket size adaptation has two primary effets. First, larger paket sizes send more data between aknowledgments, therefore reduing the fration of time that the hannel is unused. For an aknowledgment based protool on a half duplex link, suh as links in the underwater environment, if eah paket is independently aknowledged, i.e., there is no use of paket trains as desribed in the next subsetion, the hannel utilization is affeted by inreasing or dereasing n in Equation (2) with n = k. The hannel utilization inreases as n inreases, assuming no errors on the hannel. In the fae of errors, simply inreasing the paket size may not in fat inrease the hannel utilization. Consider Equation (3) with n = k, i.e., no error orretion apability. Inreasing n will lead to a orresponding inrease in ep (reall that ep depends on the bit error rate and the paket size). Any paket ontaining an error will onstitute wasted transmission time. Therefore, the inrease in paket error rate will potentially offset the gains in hannel utilization by 'For shortened odes, n < 2L, but the orretion apability is still (nk) /2 symbols. Authorized liensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on Otober 17, 28 at 7:59 from IEEE Xplore. Restritions apply.
inreasing the paket size. Therefore, the optimal paket size depends both on the round trip time and on the bit error rate of the link. Combining FEC with a larger paket size an potentially be used to inrease the hannel utilization beyond that if no FEC is used. B. Paket Train Length Adaptation Paket trains an be used to inrease hannel effiieny without inreasing the probability of paket error. The tehnique involves sending a number of individual pakets bak to bak before waiting for an aknowledgment. Seletive or umulative aknowledgments an then be used for eah of the paket trains. We hoose to use seletive aknowledgments sine they allow gap orretion [1], leading to better hannel utilization. The hannel effiieny when using paket trains, with the probability of paket error ep and paket train length T, is as follows: (1 -ep)tkl/r I' TnL/R+d (4) Equation (4) shows that inreases in T provide inreased hannel utilization. The ost of using longer paket trains is that the time it takes for the sender to learn about losses inreases with the length of the paket train as follows: tr dn+ (5) R Therefore, the main drawbak of using large paket trains is to delay the possible retransmissions. How muh this ost matters depends greatly on the appliation. A soft real-time appliation may have timing dependenies that require the use of short paket trains, whereas bulk data appliations, suh as FTP, may be able to tolerate far longer delays. C. Combined Effets on Channel Utilization The ombination of all three tehniques allows a large adaptation spae that an be used to inrease the hannel utilization depending on the link harateristis. Assuming a fixed data rate R, fixed propagation delay, and a fixed bit error rate, the effets of eah of the three adaptation mehanisms an be expliated. From Equation (4) it an be seen that inreasing the amount of data sent per paket, k, an inrease the hannel utilization; however, with an inrease in paket size also omes an inrease in paket error rate, ep, whih also depends on the relationship between n and k for the FEC blok ode used. Inreasing the amount of redundany per paket for the FEC, n -k, redues the hannel utilization in the fae of no paket errors, but an lead to the ability to use larger paket sizes (allowing an inrease in k) that might outweigh the redution in utilization due to the redundany added. Finally, inreasing the paket train length, T, dereases the amount of time spent waiting for aknowledgments and so inreases the hannel utilization, with a ost of inreased time before notifiation of a loss reahes the sender. The next setion haraterizes the effets of the underwater hannel on the data rate and the propagation delay. IV. DATA RATE AND PROPAGATION DELAY IN UNDERWATER CHANNELS Underwater aousti hannels differ from their terrestrial radio ounterparts in a number of different ways. In this work we fous on the long propagation delays and the relationship between the distane between two nodes and the bandwidth available for use on the link to highlight how underwater hannel harateristis affet hannel utilization. A. Propagation Delay Underwater aousti signals propagate at speeds depending on their depth in the water. This may lead to large differenes in propagation speed even for equal distanes, depending on the angle with respet to the z-axis of the transmission. The underwater propagation speed in m/s has been modeled aurately by Urik [11] as follows: = 1449.5 + 45.7t - 5.21t2 +.23t3 +(1.333 -.126t +.9t2)(S - 35) +16.3z +.18z2 where t is one tenth of the temperature of the water in degrees Celsius, z is the depth in meters, and S is the salinity of the water. The main fator that alters the speed of sound in water as depth hanges is the temperature of the water. For oeans, this interval is between 2 C and 22 C. However, hanges our at different rates in three different regions, the region above the thermoline, the thermoline itself, and the region below the thermoline [12]. The salinity for oeans is in the interval [32, 37] parts per thousand (ppt) with an average of 35 ppt [13]. Changes in the propagation delay affet d in Equation (3), with inreasing delays reduing hannel utilization. One important thing to note is that, unlike in terrestrial radio links, distane alone is not suffiient for determining delay times. It is possible in underwater links for a shorter link to have a longer delay. B. Bandwidth-Distane Relationship In underwater aousti environments, the bandwidth available to a link depends on the distane between the sender and the reeiver: as the distane dereases, the available bandwidth spetrum inreases, allowing for a greater link apaity. For typial terrestrial radio environments, shorter transmission distanes lead to either the ability to use lower power (due to less signal attenuation), or the ability to use higher bit rates (due to a higher signal-to-noise ratio), but the bandwidth available remains onstant. The frequeny omponent of the hannel is defined by the attenuation fator and the noise fator for the link. The SNR at a reeiver distane f from the transmitter an be modeled as follows [3]: (6) SNR(f, f) = N/A(f Af' (7) Authorized liensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on Otober 17, 28 at 7:59 from IEEE Xplore. Restritions apply.
where f is the frequeny, P is the transmitted power, and Af is the noise bandwidth at the reeiver. The AN produt, AN, determines the frequeny-dependent part of the SNR. For eah distane, there exists an optimal frequeny for whih the narrow-band SNR is maximum. Then, using this as the enter frequeny and following some definition of bandwidth (e.g., 3 db bandwidth), the maximum available bandwidth an be inferred. The attenuation fator A depends on the absorption loss on the underwater link. Thorp's formula is used to express the absorption oeffiient a(f) as follows [14]: 1 log a(f) =.11 f2 1+f2 + 44 41±f +2.75.1-4f2 +.3, where a(f) is given in db/km and f is in khz. The absorption oeffiient is the major fator that limits the maximum usable bandwidth at a given distane as it inreases very rapidly with frequeny. Using this absorption oeffiient, Urik models A in terms of the spreading loss and the spreading oeffiient k for a distane f and a frequeny f as follows [11]: 1log A = k 1log f + f 1loga(f), (9) where the first term is the spreading loss and the seond term is the absorption loss. The spreading oeffiient defines the geometry of the propagation (i.e., k = 1 is ylindrial, k = 2 is spherial, and k = 1.5 is pratial spreading [11]). The ambient noise in underwater environments is affeted by four omponents: turbulene (Nt), shipping (N5), waves (Nm), and thermal noise (Nth). The following formulae give the power spetral density of the four noise omponents in db re pupa per Hz as a funtion of frequeny in khz [15]: 1logNt(f) lologns(f) 1logNw(f) 17-3logf 4 + 2(s -.5) + 26 log f -6 log(f +.3) 5 + 7.5w1/2 + 2 log f -4 log(f +.4) 1 log Nth(f) = -15 + 2Ologf, and the overall noise power spetral density for a given frequeny f is as follows: P (8) N = Nt(f) +Ns(f) +Nw(f) +Nth(f) (11) The bandwidth, whih depends strongly on distane in underwater aousti links, affets the available data rate for the link, R in Equation (3). This has a major impat: inreased R dereases the transmission times for both the useful data reeived suessfully and for all data reeived in error and any redundany sent. Consider an example. As has been disussed, paket train length inreases an mitigate the effets of propagation delay on hannel utilization by inreasing the number of pakets transmitted bak to bak before waiting for an aknowledgment. Assume that there is some goal hannel utilization to be ahieved, and further assume that the bandwidth does not hange with distane between nodes on the link. Then, as.n S-r.9.8.7.6.5.4.3.2.1 2 4 6 8 1 12 14 16 18 2 Distane (m) Fig. 1. Channel utilization: error rate, FEC level, paket size 48 bytes the distane between the sender and reeiver is dereased, the propagation delay dereases aording to Equation (6). This orresponds to a derease in d in Equation (3) and an inrease in hannel utilization. Now, if the hannel utilization was already at the target value, the paket train size, T, ould be dereased. This may be desirable to derease the amount of time before the sender is made aware of a loss. However, for the underwater aousti links, dereasing the distane also inreases the bandwidth. This inrease orresponds to an inrease in R in Equation (3), whih dereases the hannel utilization. When the distane between the sender and reeiver shrinks, T an be dereased while still maintaining the same hannel utilization. However, beause the bandwidth inreases, the amount that T an be dereased is less than if the bandwidth were to remain onstant. V. NUMERICAL RESULTS To demonstrate the effets of the bandwidth-distane relationship, the high bit error rates, and the long propagation delays on the use of FEC, paket size adaptation, and paket train length, we produed the models desribed in the previous setions in C++. We ran a large number of experiments varying the distane between sender and reeiver from 1 m to 2 km and the bit error rate between 1-3 to 1-9. Variations in the parameters of the various adaptations were made as follows. The paket size was varied from 48 bytes to 128 bytes. The FEC error orreting level ((n -k)/2) was varied from to 2. Finally, the paket train length was varied from 1 to 1. In this paper, due to spae onstraints, we present a selet number of results the demonstrate the trends, baking up the design intuitions in the rest of the paper. To study the effets of paket train adaptation in isolation we present results from runs where the probability of bit error was zero and the paket size was 48 bytes. Additionally, no FEC was used (setting k _ n). The delay before the sender was notified of a loss grew from.3 s at 1 m to 2.73 s at 2 km for a train size of one. For a train size of 1, these delays grew to.17 s and 3.6 s respetively. Authorized liensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on Otober 17, 28 at 7:59 from IEEE Xplore. Restritions apply.
1 1 FEC level.8 F.8 FEC level.6 F.6.4 F.4.2 F.2 In In In 384 888 24 46 124 IMA No M 384 888 24 46 124 Fig. 2. Channel utilization: error rate 1-4, distane 1 m Fig. 4. Channel utilization: error rate 1-4, distane 5 m.9.8 FEC level, 1.8 FEC level.7.6.5.6.4.4.3.2.2.1 384 888 24 46 124 384 888 24 46 124 Fig. 3. Channel utilization: error rate 5 x 1-4, distane 1 m Fig. 5. Channel utilization: error rate 5 x 1-4, distane 5 m Figure 1 depits the hannel utilization as the distane between sender and reeiver is inreased along the z-axis (the reeiver goes deeper into the water). The lines loser to the top of the graph (representing higher hannel utilization) orrespond to inreasingly longer paket trains. Longer paket trains have signifiant effets for distanes between 1 m and 6 m. At the edges of these bounds they tend to onverge, beause the delay is either short enough to not require the use of paket trains, or long enough to negate the effet of a train size hange of only 1. Experiments run with longer paket trains at the larger distanes ahieved better hannel utilization, but at a muh higher ost in terms of the time before the sender was notified of a loss. As expeted, as distanes get shorter, the size of paket train needed to maintain a fixed hannel utilization did not shrink rapidly due to the inrease in bandwidth. We ran experiments where the bandwidth was held onstant and found the optimal train length. We then used this train length in experiments where the bandwidth did inrease with dereasing distane, as is the ase in underwater hannels. The resulting hannel utilizations were as muh as 16% lower than the optimal hoie when the hanging bandwidth was not taken into aount. Figures 2 and 3 depit the hannel utilization for various paket sizes and FEC levels with error probabilities of 1-4 and 5 x 1-4 respetively and paket train lengths of 1. The distane between the sender and the reeiver is 1 m along the z-axis. Two things to notie are that first, the longest paket size is not the optimal hoie in either ase. This is beause the inrease in the amount of data sent per paket does not outweigh the orresponding inrease in paket error, ep, even when FEC is used. Seond, while in these results, adding the overhead for FEC apable of orreting 2 errors outweighs the ost of transmitting the extra redundany, in other experiments, that extra redundany did not always equal higher hannel utilization. Figures 4 and 5 depit the hannel utilization for the same parameters as in Figures 2 and 3, but with the distane between sender and reeiver inreased to 5 m. The hannel utilization is severely dereased due to the long propagation delays. Additionally, the bandwidth has dereased. These two effets hange the optimal paket length from the shorter distane ases. Again, we performed experiments without hanging the bandwidth as distane dereased, found the optimal parameters for all three mehanisms, and the used those parameters while taking into aount the bandwidth-distane relationship and found the performane to be suboptimal. Authorized liensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on Otober 17, 28 at 7:59 from IEEE Xplore. Restritions apply.
.8 F.6 F.4 F.2 F FEC level 384 888 24 46 124 Fig. 6. Channel utilization: error rate 1-4, distane 5 m, paket train 1._N S-r 1 1.8 F.6 r.4 F.2 F FEC level No 384 888 24 46 124 Fig. 7. Channel utilization: error rate 5 x 1-4, distane 5 m, paket train 1 Finally, Figures 6 and 7 depit the hannel utilization for the same parameters as in Figures 4 and 5, this time with a paket train length of 1. This inrease in train length has a onsiderable effet on hannel utilization but auses no hange in the optimal paket length or FEC strength beause hanges in paket train length do not affet either the loss probability, bandwidth, or delay of the hannel. VI. CONCLUSION This paper has presented an analysis of the effets of three tehniques, namely, forward error orretion, paket size adaptation, and paket train length adaptation, in underwater aousti networks. This analysis and the simulation results that followed demonstrated how the ombination of all three tehniques an be used to mitigate the high error rate, long delay, and bandwidth-distane relationship of underwater hannels to inrease hannel utilization. Paket train length adaptation an be used to mitigate the effets of long delays without inreasing the paket error probability. However, this mitigation omes at the ost of an inrease in the amount of time that passes before the sender an be notified of a loss. Forward error orretion and paket size adaptation an be used to mitigate both the propagation delay and high bit error rates. Our study demonstrated that the optimal hoie of parameters for all three tehniques depends on the distane between the sender and the reeiver, whih affets both the bandwidth available and the propagation delay for the underwater links. Future diretions for this work are to use these insights to design MAC and routing protools to maximize hannel utilization. Suh protools should also onsider energy onsumption and end-to-end delay to provide omprehensive support for a large number of appliations. REFERENCES [1] I. Akyildiz, D. Pompili, and T. Melodia, "Underwater aousti sensor networks: Researh hallenges," Elsevier's Ad Ho Networks, vol. 3, no. 3, 25. [2] J. Heidemann, W. Ye, J. Willis, A. Syed, and Y Li, "Researh hallenges and appliations for underwater sensor networking," in Proeedings of the IEEE Wireless Communiations and Networkin Congerene, 26. [3] M. Stojanovi, "On the relationship between apaity and distane in an underwater aousti ommuniation hannel," in ACM International Workshop on UnderWater Networks (WUWNet), 26. [4] V. Rodoplu and M. Park, "An energy-effiient MAC protool for underwater wireless aousti networks," in MTS/IEEE OCEANS, 25. [5] A. F. Harris, M. Stojanovi, and M. Zorzi, "Why underwater aousti nodes should sleep with one eye open: Idle-time power management in underwater sensor networks," in ACM International Workshop on UnderWater Networks (WUWNet), 26. [6] A. F. Harris and M. Zorzi, "Energy-effiient routing protol design onsiderations for underwater networks," in IEEE Conferene on Sensor; Mesh and Ad Ho Communiations and Networks (SECON), 27. [7] D. Pompili, T. Melodia, and I. Akyildiz, "Routing algorithms for delay-insensitive and delay-sensitive appliations in underwater sensor networks," in Pro. ofacm Mobiom, 26. [8] M. Stojanovi, "Optimization of a data link protool for underater aousti networks," in MTS/IEEE OCEANS, 25. [9] B. Sklar, Digital Communiations: Fundamentals and Appliations, 2nd ed. Prentie Hall PTR, 21. [1] IEEE Computer Soiety, "RFC 3517: A Conservative Seletive Aknowledgment (SACK)-based Loss Reovery Algorithm for TCP," June 1997. [11] R. Urik, Priniples of Underwater Sound. MGraw-Hill, 1983. [12] The National Center for Atmospheri Researh, "Temperature of Oean Water," http:llwww.windows.uar.edu/tour/link=/earth/water/temp.html&edu=high. [13] Offie of Navel Researh, "Oean Water: Salinity," http://www.onr.navy.mil/fous/oean/water/salinityl.htm. [14] L. Berkhovskikh and Y. Lysanov, Fundamentals of Oean Aoustis. Springer, 1982. [15] R. Coates, Underwater Aousti Systems. Wiley, 1989. Authorized liensed use limited to: ELETTRONICA E INFORMATICA PADOVA. Downloaded on Otober 17, 28 at 7:59 from IEEE Xplore. Restritions apply.