Cooperative Transmission for Underwater Acoustic Communications

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.

Cooperative Transmission for Underwater Acoustic Communications Zhu Han, Yan Lindsay Sun+ , and Hongyuan Shi∗ , Electrical and Computer Engineering Department, Boise State University, Boise, ID, USA + Department of Electrical and Computer Engineering, University of Rhode Island, Rhode Island, USA ∗ Center for Decision Technologies, Steven Institute of Technology, Hoboken, NJ, USA Abstract— Underwater acoustic channels normally have low data rate, long propagation delay, severe multipath effect, and time varying fading. Cooperative transmission is a new wireless communication technique in which diversity gain is achieved by utilizing relay nodes as virtual antennae. In this paper, we investigate cooperative transmission techniques for underwater acoustic communications. First, we study the performance of several cooperative transmission schemes, originally designed for radio communications, in an underwater scenario. Second, by taking advantage of the low propagation speed of sound, we design a new wave cooperative transmission scheme. In this scheme, the relay nodes amplify the signal received from the source node, and then forward the signal immediately to the destination. The goal is to alter the multipath effect at the receiver. Third, we derive the performance upper bound for the proposed wave cooperative transmission scheme. The simulation results show that the proposed wave cooperative transmission has significant advantages over the traditional direct transmission and the existing cooperative transmission schemes originally designed for radio wireless networks.

I. I NTRODUCTION Underwater acoustic communications [1]–[5] are critical to a number of applications. Most early underwater acoustic systems are established for military applications. Recently, there is an increasing interest in building civilian underwater networks. Without relying on wires, acoustic networks are easy to deploy and present minimal hazards to surrounding moving objects. Typical civilian applications of underwater networks include offshore oil discovery, the detection of submerged objects, tsunami forcasting and alerts, underwater habitat and pollution monitoring, etc. Sound can travel longer distances in water than electromagnetive waves. However, underwater acoustic communication channels normally have limited bandwidth and a high level of reverberation that can cause severe signal dispersion in both time and frequency domains. Sound waves experience frequency-related attenuation. The propagation can be refracted by gradients of water conditions (i.e. salinity, temperature, etc.). Rays of sound from the same emitter arrive at the receiver through various paths depending upon their launching angles. Travel times along these paths can be significantly different because the speed of sound is several orders of magnitude lower than that of light. Scattered sound waves from various objects and geographic boundaries bring in additional challenges for signal reception. Furthermore, time-varying propagation happens due to the Doppler effect caused by sea surface motion and source/receiver movement. Underwater communication systems have evolved from analog to digital and from incoherent to coherent. Researchers and developers have improved systems to achieve larger bandwidth

for practical usage. Demonstrated results include 1kbps at 90km, 100kbps at 0.1km, and 500kbps at 60m [5]. Underwater acoustic communications are rapidly growing [6]–[8] motivated by the increasing demand for exploiting underwater environments. It is necessary to further improve the transmission rate and reliability in underwater acoustic communications. Recently, cooperative transmission [9]–[12] has gained a considerable amount of attention as a transmission strategy for future wireless networks. Its basic idea is that the relay nodes can help the transmission by sending a replica of the signals. Such a scheme takes advantage of the broadcast nature of wireless media, and exploits the inherent spatial and multiuser diversities. In this paper, we explore the possibility and benefits of utilizing cooperative transmission in the underwater environment. We believe that this technique, new to acoustic communications, can overcome many channel limitations and increase the overall throughput of underwater acoustic channels. Three different strategies of cooperative transmission, previously used in wireless communications, are evaluated in the underwater scenario. Moreover, based on the low propagation speed of sound, we propose a wave cooperative transmission in which the relay amplifies the source information when the sound wave passes, thus the destination can receive an additional multipath component of high strength. We derive the performance upper bound of the proposed scheme. Through simulations, we demonstrate the multipath effect under the influence of cooperative transmission. The proposed wave cooperative transmission has significant advantages over the traditional direct transmission and other cooperative transmission protocols originally used in wireless networks. The paper is organized as follows: In Section II, we provide the underwater acoustic channel models. In Section III, we describe three cooperative transmission protocols used in wireless communication, and propose the wave cooperative protocol for underwater communications. The performance upper bound is derived and implementation concerns are also discussed in this section. Simulation results are presented in Section IV, and Section V concludes the paper. II. U NDERWATER ACOUSTIC CHANNEL During the underwater sound propagation, the energy loss is caused by geometric spreading, attenuation, and other path related losses. The causes of attenuation are categorized into medium absorption and scattering. Among these factors, spreading and attenuation caused by absorption are relative stable for a given area.

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Depending on the spatial boundary of the body of water, the spreading loss can be modelled as either spherical for deep water or cylindrical for shallow water, corresponding to an inverse-square or inverse first power relation with the propagation range. The absorption loss between two locations is normally described as (1) I2 − I1 = −αd,

where I2 and I1 are the intensities in dB at two locations, d is the distance in kilometers between these locations and α is the absorption coefficient in dB per kilometer. The amount of absorbed energy by water is mainly affected by the viscosity of water and the sound frequency. Empirically, the absorption coefficient increases with sound frequency. Thorp’s formula [1]– [4] approximates the relation as: α=

44f 2 0.11f 2 + + 2.75 × 10−4 f 2 + 0.003 2 1+f 4100 + f 2

(2)

where f is the sound frequency in kilohertz. Sound can be scattered by particles and objects along the propagation path, resulting in energy loss. The amount and locations of scatterers in water can vary from time to time in a given area. Besides random scattering, a sound wave is refracted when traversing areas of different water conditions. This phenomenon is similar to the case in which a light ray bends its path when it travels through different media. The refraction of sound can be calculated using the sound speeds of the media. It follows Snell’s law: cos θ2 cos θ1 = , (3) c1 c2 where c1 and c2 are the sound speeds in media 1 and 2, θ1 and θ2 are the grazing angles at the boundary. The value of sound speed depends on three factors: water salinity, temperature, and density. Briefly speaking, sound speed increases with the increment of any one of the above three factors. Several empirical formulae have been proposed by oceanographists. Here we present Coppens equation as an example (refer to [14] for coefficient values) cO,S,T = c0 + c1 T + c2 T 2 + c3 T 3 + (c4 + c5 T + c6 T 2 )(S − 35) cD,S,T

=

2

cO,S,T + (c7 + c8 T )D + (c9 + c10 T )D +[c11 + c12 (S − 35)] · (S − 35) · T · D,

(4)

where D is the depth, S is salinity, and T is water temperature. The distribution of sound speed in ocean normally conforms to a general profile. However near shores and estuaries, sound speed profiles appear in irregular shapes [4]. With the knowledge of sound speed distribution and boundary conditions, the transmission loss of sound can be computed by solving the wave equation of the acoustic field. Most numerical solutions of the equation are based on ray theory, normal-mode theory, and the parabolic equation method. In Section IV we use a method based on the ray theory to calculate the sound transmission loss. In addition to energy loss, underwater sound propagation normally experiences time spreading and Doppler effects, both of which are important factors for acoustic communication

Base station

Acoustic Direct links

s Underwater sensor nodes

r

d

Acoustic Relay links

Fig. 1: Underwater acoustic cooperative transmission system systems at high frequency. The impact of time spreading depends upon the extent of the multipath effect, which in turn is affected by the configuration of a sound channel, i.e. depth of the source/receiver, distance between the source and receiver, and the shape of the ocean floor. The roughness of the sea surface and the sea floor can also lead to time spreading. The Doppler effects can be classified into frequency shifting and frequency spreading. Doppler shifting is induced by source/receiver motion, while Doppler spreading is caused by sea surface fluctuation, various processes near the sea surface, and source/receiver motion. A small change in source and receiver locations can result in interference fluctuation [5], thus can further alter the result from multipath superposition. III. U NDERWATER C OOPERATIVE T RANSMISSION A. Three Cooperative Transmission Protocols The system structure is illustrated in Figure 1. It contains a source node s, a relays node r and a destination node d. The cooperative transmission from the source to the destination is accomplished in two phases. In Phase 1, source s broadcasts information to both destination d and relay node r. The received signals Yd and Yr at destination d and relay r can be expressed as p (5) Yd = Ps Gs,d X + nd , and

Yr =

p Ps Gs,r X + nr ,

(6)

where Ps represents the transmit power from source s, X is the transmitted information symbol with unit energy at the source in Phase 1, Gs,d and Gs,r are channel gains from s to d and s to r respectively, nd and nr are the additive white Gaussian noises (AWGN). Without loss of generality, we assume same noise power, σ 2 , for all links. We also assume that channels are stable within each transmission frame. With direct transmission, the signal-to-noise ratio (SNR) of the direct transmission (s−d) can be expressed as ΓDT s,d =

Ps Gs,d , σ2

and the information rate of the direct transmission is ¡ ¢ Rs,d = W log2 1 + ΓDT s,d ,

where W is the bandwidth for information transmission.

(7)

(8)

where

Yr Xr = |Yr |

(10)

is the transmitted signal from the source to the destination with normalized energy in Phase 1, Gr,d is the channel gain from the relay to the destination, and n0d is the received noise in Phase 2. Substituting (6) into (10), we rewrite (9) as p p Pr Gr,d ( Ps Gs,r Xs + nr ) p + n0d . (11) Y2,d = Ps Gs,r + σ2 Using (11), the SNR of the relayed signal at the destination is given by: ΓAF s,r,d =

Pr Ps Gr,d Gs,r 2 σ (Pr Gr,d + Ps Gs,r

+ σ 2)

.

(12)

Therefore, based on (8) and (12), after combine the signals using maximal ratio combining (MRC), we have the information rate at the output of MRC as ¡ ¢ 1 DT AF (13) RAF s,r,d = W log2 1 + Γs,d + Γs,r,d . 2 In the decode-and-forward (DF) cooperative transmission [10], the relay decodes the source information received in Phase 1 and relay to the destination in Phase 2. The destination combines the direct transmission information and the relayed information together. The achievable rate can be calculated as: DF = max min{R1 , R2 } Rs,r,d 0≤ρ≤1

where

and

∙ ¸ Ps,d Gs,r R1 = W log2 1 + (1 − ρ2 ) σ2

R2 = W log2

Ã

1+

Ps Gs,d Pr Gr,d + σ2 σ2

(14)

(15)

! p 2ρ Ps Gs,d Pr Gr,d . + σ2 (16)

In the estimate-and-forward (EF) cooperative transmission [10], the relay, in Phase 2, sends an estimate of the received signal from Phase 1. The destination uses the relay’s information as side information to decode the direct transmission in Phase 1. From [11], the achievable rate can be written as: ¡ ¢ DT EF (17) REF s,r,d = W log2 1 + Γs,d + Γs,r,d , where

ΓEF s,r,d =

Ps Pr Gs,r Gr,d . σ2 [Pr Gr,d + Ps (Gs,d + Gs,r ) + σ2 ]

(18)

air water source

Delay profile w/o relay

destination relay

ground

Multipath power

In Phase 2, relay r forwards a copy of the signal and the receiver enhance the reception with this additional copy. Relay r can handle signals according to different strategies. In the amplify-and-forward (AF) cooperative transmission [10], the relay node amplifies Yr and forwards it to the destination with transmission power of Pr . The received signal at the destination is p (9) Y2,d = Pr Gr,d Xr + n0d ,

Multipath power


Delay profile with relay

Fig. 2: Illustration of Wave Cooperative Transmission B. Wave Cooperative Transmission Protocol The above three cooperative protocols were originally proposed for wireless networks. Based on the unique characteristics of the underwater acoustic channel, we propose a new protocol named wave cooperative (WC) transmission, in which • the relay node amplifies the received signal and immediately forwards it to the destination, instead of waiting till the next time slot. Since the speed of sound (∼ 1500m/s) is much smaller than the speed of light, the acoustic transmission delay is much higher than the processing delay. Amplifying and forwarding at the relay node will not introduce a noticeable additional delay along the source-relay-destination path. The signal from the direct transmission and the signal forwarded by the relay can be viewed as two paths from the viewpoint of multipath propagation. Consequently, as long as the receiver can efficiently catch those multipath signals (for example, the RAKE receiver used in the CDMA system), the received SNR can be potentially improved. Figure 2 illustrates the wave propagation of the proposed scheme, with a delay profile example. The wave cooperative transmission is different from multipath propagation because the paths caused by the relay node usually have much stronger signal strength than the original paths. The wave cooperative transmission is also different from the amplify-and-forward cooperative transmission in wireless networks, which forwards the message in the next time slot and thus does not interfere with the direct transmission. In the wave cooperative transmission, the rate can be given by: ¡ ¢ (19) RW C = W log2 1 + ΓW C , where ΓW C is the received SNR if the multiple paths can be resolved. Different from the rate in other cooperative transmission schemes, the rate of the waveform cooperative (WC) transmission does not have the 12 factor. This is because WC does not need an additional time slot to forward messages. To find the close form solution of ΓW C , we need to refine the acoustic channel model to obtain phase changes from reflection and scattering. In this paper, due to our page limit, we develop a performance bound instead. We assume that the signals received from the source-to-destination path and from the relayto-destination path can be perfectly resolved. As a result, the performance of the wave cooperative transmission is bounded by the sum of direct transmission SNR and relay path SNR as ΓW C ≤

Ps Gs,d Pr Ps Gr,d Gs,r . + 2 σ2 σ (Pr Gr,d + Ps Gs,r + σ2 )

(20)


Effect of Destination Location

Effect of Relay Location, Shallow Water 1.8

3.5 Direct AF DF EF WC

3

Direct AF DF EF WC

1.6 1.4

Channel Capacity

Channel Capacity

2.5

2

1.5

1.2 1 0.8 0.6

1 0.4 0.5

0 200

0.2

250

300 Destination Location

350

400

Fig. 3: Performance vs. Destination Location C. Implementation Concerns Due to the high latency, the volume of storage required for an underwater system using cooperative transmission can be much higher than that for a terrestrial counterpart. Here is a simple estimation. Let S denote the propagation speed, d be the distance between the transmitter and the receiver, R be the data rate, M be the number of relays, and Dprocess be the processing delay at each relay. The storage requirement at the receiver is approximately µ ¶ dR M(M − 1) + Dprocess · R · (21) Coststorage = S 2 For wireless communications, S = 3 × 105 km/s. Some typical settings are R = 250 kbps and d = 80m. Thus, a typical value of Coststorage is

M (M − 1) . (22) 2 In underwater acoustic communications, S = 1.5km/s. No research and commercial system can exceed 40 km·kbps as the maximum attainable range-rate product. Thus the typical value of Coststorage is (2.67 × 10−7 + Dprocess ) · R ·

40 M(M − 1) + Dprocess · R) · . (23) 1.5 2 From (22) and (23), we can see that the processing delay dominates the storage cost in wireless communications, but the propagation delay dominates the storage cost in underwater acoustic communications. In wireless communications, even if the processing delay is at the order of milliseconds, the storage requirement is 0.25M (M − 1)/2 kb, which is very small. But in underwater acoustic communications, if we neglect the processing delay in (23), the storage requirement is roughly (

M (M − 1) · 27kb. (24) 2 Thus the storage cost for cooperative transmission in underwater acoustic communications is not negligible. However it is tolerable as long as M is maintained as a small value. In other words, the number of relays should be limited for underwater acoustic communications. Despite requiring large volume of storage, using cooperative transmission for underwater systems achieves much higher SNR at the receiver than the conventional transmission method.

0

0

50

100

150 200 250 Relay Location

300

350

400

Fig. 4: Performance vs. Relay Location, Shallow Water Therefore, with the same reliability requirement, the transmission power can be greatly reduced. This is a major advantage for underwater networks since acoustic transmission consumes more power than passive sensing and data processing. Another concern for underwater acoustic communications is directional transmission. Due to the limited transmission angles, the relay nodes should locate close to the direct transmission path. This will reduce the delay spread of the multipath propagation. We will investigate the effects of directional transmission in the simulation section. IV. S IMULATION RESULTS The simulation system contains two major components: an acoustic field module and a communication channel module. In the acoustic field modeule we use Bellhop Gaussian beam tracing program [15] to compute the sound transmission loss based on the sound speed distribution, bathymetry (bottom topology), source depth, sound frequency and launching angles, receiver depth, the distance from the source to the receiver, and related media parameters. The sound speed profile used in our simulation is based on the Atlantic water sound-speed profile from the Barents Sea Polar Front experiment described in [13]. Water depth is maintained at 250m. The source emits 40kHz sound with launching angles within a 100 degree range facing the receiver. The depth of both the source and receiver increases from 0m to 250m. The program computes transmission loss at locations up to 2km away from the source. The output from the acoustic field module is then fed into the communication channel module. It evaluates the underwater acoustic channel based on the proposed methods in Section III. Here we assume that the overall power control of the source relay is 2W and the noise level is 10−5 W. In Figure 3, we show the channel capacity as a function of the distance from the source to the destination. Here the source depth is 1m, relay depth is 5m, and the receiver is at the surface. The relay is located 100m away from the source and on the line from the source to the destination. We can see that the link capacity drops as the distance increases. The AF protocol sometimes has better and sometimes has worse performance than the direction transmission, depending on the location of the destination. Compared with the direct transmission, the DF, EF, and WC protocols always have better or same performance. Among the DF, EF and WC protocols, the WC protocol has the


Effect of Relay Location, Deep Water

Effect of Relay Depth

3

1.8 Direct AF DF EF WC

Direct AF DF EF WC

1.6 1.4

2

Channel Capacity

Channel Capacity

2.5

1.5

1

1.2 1 0.8 0.6

0.5 0.4 0

0

50

100

150 200 250 Relay Location

300

350

400

0.2

0

50

100 150 Relay Depth

200

250

Fig. 5: Performance vs. Relay Location, Sea Bottom

Fig. 6: Performance vs. Relay Depth

best performance. Compared with the direct transmission, the WC protocol doubles the link quality in many cases. In Figure 4, we show the link capacity as a function of relay location near the surface at 1m depth. Here the source, relay, and destination have the same depth. The destination is located 400m away from the source, and the relay locates at 10m ∼ 390m along the line from the source to the destination. We can see that the AF and EF protocols have similar performances, except that the DF protocol has less link capacity than the direct transmission when the relay is far away from the source. This is because the decoding of the source’ information at the relay can contain errors. As a result, the link capacity drops if the destination combines the source and relay transmission. The proposed WC protocol always has the best performance. In Figure 5, we show the performances for nodes located near the sea floor, where the source, relay, and destination are 240m deep. We can see that the performance of direct transmission is poor and the relay can significantly improve the performance for all protocols. However, similar to Figure 3 and 4, the performance improvement has a breathing effect. In other words, the cooperative transmission can improve performance only when the relays are at certain locations. This may be due to the directional transmission of acoustic signals, and the bouncing of signals from the surface and bottom. In Figure 6, we show the effects of relay depth. Here the source is 1m deep and the destination is 400m away on the surface. The relay is located at 200m away and changes its depth. We can see that the relay has the best performance when it is 10m deep. This is because the relay can get the signal in time and can avoid severe multipath effects. When the relay is about half of the sea depth, the performance is also good. This is because the relay is on the path of multipath propagation. When the relay is too deep, the performance drops.

relay must locate close to the line-of-sight between the source and the destination. Second, the multipath effect of acoustic signal causes a breathing effect. Third, the storage overhead of cooperative transmission in underwater environment is much higher than that in wireless communications. Finally, the newly proposed wave cooperative transmission scheme outperforms the existing cooperative transmission schemes designed for wireless communications. REFERENCES

V. CONCLUSIONS Cooperative transmission is a new communication paradigm in wireless communications. In this paper, we investigated the effects of cooperative transmission on underwater acoustic communications. We studied the differences between direct transmission and cooperative transmission, and proposed a new cooperative transmission scheme for the underwater environment. Our study has shown several unique features of the cooperative transmission in underwater acoustic environment. First, when the acoustic signal transmission is directional, the

[1] E. M. Sozer, M. Stojanovic, and J. G. Proakis, “Underwater acoustic networks”, IEEE Journal of Oceanic Engineering, vol.25, no.1, p.p.72-83, Januray 2000. [2] J. Preisig, “Acoustic propagation considerations for underwater acoustic communications network development”, in Proceedings of the 1st ACM international workshop on Underwater networks, p.p.1-5, September 2006. [3] P. C. Etter, Underwater acoustic modeling and simulation, 3rd ed., Spon Press, Taylor & Francis Group, 2003. [4] R. J. Urick, Principles of underwater sound, 3rd ed., McGraw-Hill, Inc, 1983. [5] D. B. Kilfoyle and A. B. Baggeroer, “The state of the art in underwater acoustic telemetry,” IEEE Journal of Oceanic Engineering, vol.25, no. 1, pp.4-27, January 2000. [6] A. K. Morozov and J. C. Preisig, “Underwater acoustic communications with multi-carrier modulation”, OCEANS 2006, p.p.1-6, September 2006. [7] M. Stojanovic and L. Freitag, “Multichannel detection for wideband underwater acoustic CDMA communications”, IEEE Journal of Oceanic Engineering, vol.31, no.3, p.p.685-695, July 2006. [8] D. B. Kilfoyle, J. C. Preisig, and A. B. Baggeroer, “Spatial modulation experiments in the underwater acoustic channel”, IEEE Journal of Oceanic Engineering, vol.30, no.2, p.p.406-415, April 2005. [9] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity, Part I: System description,” IEEE Transactions on Communications, vol.51, no.11, pp.1927-1938, November 2003. [10] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: efficient protocols and outage behavior,” IEEE Trans. on Information Theory, vol.50, no.12, pp.3062-3080, December 2004. [11] M. A. Khojastepour, A. Sabharwal and B. Aazhang, “On the capacity of ‘cheap’ relay networks,” in Proc. 37th Annual Conference on Information Sciences and Systems, Baltimore, MD, March 2003. [12] Z. Han and H. V. Poor, “Coalition game with cooperative transmission: a cure for the curse of boundary nodes in selfish packet-forwarding wireless networks”, in Proceedings of WiOpt07, Limassol, Cyprus, April 2007. [13] G. Jin, J. F. Lynch, C. S. Chiu and J. H. Miller, “A theoretical and simulation study of acoustic normal mode coupling effects due to the Barents Sea Polar Front, with applications to acoustic tomography and matched-field processing,” Journal of the Acoustical Society of America, vol. 100, no. 1, pp.193-205, July 1996. [14] “Technical guides - speed of sound in sea-water,” the National Physical Laboratory. [Online]. Available: http://resource.npl.co.uk/acoustics/ techguides/soundseawater/content.html. [15] M. Porter. Heat, Light, and Sound Research, Inc. BELLHOP Gaussian beam/finite element beam code. ONR Ocean Acoustics Library. [Online]. Available: http://oalib.hlsresearch.com/.