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530 J. Opt. Soc. Am. A/Vol. 26, No. 3 /March 2009 S. Arnon and D. Kedar

Non-line-of-sight underwater optical wirelesscommunication network

Shlomi Arnon1,* and Debbie Kedar1

1Satellite and Wireless Communications Laboratory, Electrical and Computer Engineering Department,Ben-Gurion University of the Negev, P O Box 653, IL-84105 Beer-Sheva, Israel

*Corresponding author: shlomi@ee.bgu.ac.il

Received September 3, 2008; revised November 21, 2008; accepted December 30, 2008;posted January 12, 2009 (Doc. ID 101024); published February 12, 2009

The growing need for ocean observation systems has stimulated considerable interest within the research com-munity in advancing the enabling technologies of underwater wireless communication and underwater sensornetworks. Sensors and ad hoc sensor networks are the emerging tools for performing extensive data-gatheringoperations on land, and solutions in the subsea setting are being sought. Efficient communication from thesensors and within the network is critical, but the underwater environment is extremely challenging. Address-ing the special features of underwater wireless communication in sensor networks, we propose a novel non-line-of-sight network concept in which the link is implemented by means of back-reflection of the propagatingoptic signal at the ocean-air interface and derive a mathematical model of the channel. Point-to-multipointlinks can be achieved in an energy efficient manner and broadcast broadband communications, such as videotransmissions, can be executed. We show achievable bit error rates as a function of sensor node separation anddemonstrate the feasibility of this concept using state-of-the-art silicon photomultiplier detectors. © 2009 Op-tical Society of America

OCIS codes: 010.0280, 010.4450, 040.3780, 040.5250, 060.2605, 060.4510.

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. INTRODUCTIONathering data from the ocean has been of interest toan for many years for the purposes of scientific research

s well as for pollution monitoring, seismic studies, andil and gas pipeline maintenance and security [1–3]. Ex-sting underwater sensors are expensive, and their de-loyment and recovery can be extremely costly, reachings much as $25,000 per day for the use of a deep-oceanhip [4]. Commonly, these sensors are distributedparsely over the area of interest and retrieved infre-uently for data harvesting or, alternatively, attached toutonomous underwater vehicles affording high mobilitynd flexibility in deployment and data assimilation, butlso incurring delay in data retrieval and expense. How-ver, there are many emerging applications, such as secu-ity, surveillance, and oil pipeline monitoring, where fine-rained data profiles are needed in real time and,ometimes, around the clock. Wireless sensor networksWSN) are providing this kind of rich data in numerouserrestrial applications, and there is now growing interestn investigating the potential of underwater WSN [3–6].eidemann et al. propose a system solution for seismiconitoring of offshore oilfields and address many

etwork- and datalink-level issues for short-range com-unications.Partan et al. underline some of the major differences

etween terrestrial and underwater wireless sensor net-orks and raise the question of defining different metrics

or underwater applications, where equipment and de-loyment are major expenses making operational energyudgets less critical despite problems of onboard sensorattery power. Akyildiz et al. have extensively reviewed

1084-7529/09/030530-10/$15.00 © 2

ork done in underwater acoustic networks and high-ighted research challenges. They envisage a tiered archi-ecture with a hybrid communication model using above-ater gateways.Currently, research is being carried out on a number of

evels, from the design of robust, low-cost sensors to theevelopment of tailored communication protocols that ad-ress the special needs of underwater networking [7,8].xperimental work has been reported [7,9] demonstrat-

ng practical solutions to issues of sensor node orienta-ion, waterproofing, biofouling protection, and localiza-ion. The object of this paper is to focus on issues of theireless communication link at the physical layer, and weropose a novel non-line-of-sight (NLOS) optical solutionith unique features.Acoustic communication is the widespread method for

nderwater wireless communication, and ranges of hun-reds of kilometers can be attained. However, data ratesre restricted because of severe, frequency-dependent at-enuation and surface-induced pulse-spread from reflec-ion. Data rates of �20 kbs have been achieved for rangesf a kilometer in deep ocean and �300–500 bps foranges of up to 100 km in shallow water and 200 km ineep ocean [6]. The speed of acoustic waves in the ocean is1500 m/s so that long-range communications involveigh latency that poses a problem for synchronization andultiple access protocols. In practice most acoustic links

perate in half-duplex mode and, within a sensor net-ork, sensor-to-sensor communication is an unsolved is-

ue restricting network topologies to star configurationsith a base station at the hub. Time-varying multipath

nterference, shadow zones, bubble-cloud attenuation

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S. Arnon and D. Kedar Vol. 26, No. 3 /March 2009/J. Opt. Soc. Am. A 531

ear the surface, and potential harm to marine mammalsre further concerns associated with underwater acousticireless communication.In view of these limitations, optical wireless communi-

ation, also termed free space optics (FSO), is a promisinglternative for underwater links within a sensor network.lthough the high data rates characteristic of terrestrialnd space FSO are threatened by extremely high absorp-ion and scattering there is evidence that broadband linksan be achieved over moderate ranges. Hanson and Radic10] demonstrated 1 Gbs transmissions in a laboratoryxperiment with a simulated aquatic medium with scat-ering characteristics similar to oceanic waters. They ex-anded their study using Monte Carlo simulations to pre-ict longer-range underwater FSO performance withandwidths over 5 GHz for a range of 64 m in clear oceanater, dropping to 1 GHz for a range of 8 m in turbid har-or water. Demonstrations of oceanic FSO over ranges of100 m using a LED transmitter are cited [11]. Det-eiller, Vasilescu and Rus [7] describe experimental workn an underwater sensor network with hybrid acoustic-ptical wireless communication links, benefiting from theroadcast facility of the acoustic technology and the highata rates afforded by an optical point-to-point link. How-ver, when sensors are deployed on the seabed or main-ained at a near-fixed depth by buoyancy control, line-of-ight (LOS) may not be achievable or may be obstructedy floating platform infrastructure, etc.In this paper we investigate an innovative sensor net-

ork concept based on FSO with broadband capacity thatould be scalable. Transmission range restrictions arevercome by virtue of multiple hops, and reliable networkperation with no single point of failure or bottleneck isrovided by the broadcast nature of the transmission andedundancy in the sensor dispersal. Pivotal to the concepteveloped in this paper is the idea of non-line-of-sightNLOS) communication. We have presented an outline of

terrestrial NLOS optical wireless sensor networkherein backscattering of light by molecules and aerosols

n the atmosphere functions as a vehicle of communica-ion in a similar way to the deployment of numerous tinyeflecting mirrors [12], and we have examined multipleccess challenges and solutions in this context [13]. In theurrent work we extend this concept to the underwaternvironment, where the reflection is actuated by thecean–air surface, and evaluate the system feasibilityith a numerical example. In [14] we explored the feasi-ility of an underwater optical oceanic probing schemend reviewed the optical properties of the ocean that areundamental to the achievement of an operable sensoretwork.In Section 2 we will briefly expand on the properties of

he ocean relevant to FSO. In Section 3 we develop theathematical models for assessing the system link bud-

et. In Section 4 we present the bit error rate (BER) cal-ulation, and in Section 5 we evaluate system perfor-ance with a numerical example. In Section 6 we discuss

nd summarize the results and draw conclusions. Thereliminary study provides insight into the potential com-unication performance of a single node-to-node link, al-

hough much further work is needed to model the complex

ceanic surface and light–water interactions such as mul-iple scattering and solar radiance transmission.

. OCEANIC CHANNEL PROPERTIESight propagation in seawater is highly wavelength sen-itive, with transmittance falling from near 100% overeveral meters in clear ocean water for light of wave-engths 400–500 nm to near zero for turbid waters andavelengths below 300 nm and above 700 nm [15,16].his is due to the spectral dependence of scattering andbsorption caused by aquatic molecules and suspendedarticles. These properties display high variability that isepth dependent (up to an order of magnitude) as well asarying over time because of changing oceanic composi-ion and prevailing weather [17]. For the purpose of thisork we shall adopt, as typical figures, the values used in

10] (see Table 1). These were based on the findings re-orded in [18] for absorption and scattering coefficients��� and ����, respectively, from measurements made inhe spectral band centered at 530 nm. The total attenua-ion is described by the extinction coefficient c���, which iselated to ���� and ���� by the simple expression

c��� = ���� + ����. �1�

It is clear from any text on ocean optics that attributingsingle value to the extinction coefficient at a given wave-

ength is a gross oversimplification, and we note that thereferred wavelength for superior transmission of an op-ic signal ranges between 400 nm and 550 nm dependingn the precise water composition.

In a multiple scattering channel the optic power arriv-ng at the receiver is not only depleted by absorption andight scattered out of the propagating beam, but also aug-

ented by light scattered back into the beam after sev-ral scattering events. The precise nature of light recep-ion in these circumstances requires a detailed model ofhe scattering properties of the medium and is not arivial issue. The additional received light that has beenultiply scattered results in pulse stretching in the time

omain. We envisage a gated receiver scheme as will beescribed in Section 4 and so do not consider the later ar-iving multiply scattered optic power.

When light propagating through a medium encountersn interface between areas of different refractive indicest is partially transmitted (refracted) and partially re-ected in accordance with Fresnel’s law for dielectric me-ia and Snell’s law of refraction. To predict the behavior ofight at the ocean–air surface it is necessary to ascertainhe value of the seawater refractive index, which is de-endent on the water temperature and salinity. The fol-

Table 1. Hermite Polynomials of Order n

n Hn���

0 11 �

2 �2−13 �3−3�

4 �4−6�2+3

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532 J. Opt. Soc. Am. A/Vol. 26, No. 3 /March 2009 S. Arnon and D. Kedar

owing model has recently been proposed for the approxi-ation of the refractive index of seawater nw and is valid

or temperatures in the range 0 °C�Temp�30 °C, sa-inities in the range 0% �S�35%, and optical wave-engths in the range 400���700 nm [19]:

nw�S,Temp,�� = n0 + �n1 + n2Temp + n3Temp2�S

+ n4Temp2 +n5 + n6S + n7Temp

�+

n8

�2

+n9

�3 , �2�

here n0 to n9 are empirically verified constants. The val-es obtained vary from 1.32913 for Temp=30 °C, S=0%,=700 nm to 1.35093 for Temp=1 °C, S=34.998%, �404.7 nm.Considerable work has been devoted to studying the re-

ection of light from the atmosphere (primarily sunlight)y the sea surface, where sun zenith angle and windpeed are dominant factors. However, the reflection ofight from underwater at the ocean–air surface, which isentral to the NLOS communication concept, has scarcelyeen investigated to the best of the authors’s knowledge.ince the refractive index of air is lower than that of wa-er, some incident skylight will always penetrate the seand comprise a source of background illumination con-aminating a propagating underwater optical signal. Thisill vary greatly with depth, receiver parameters (field-f-view, pointing direction, filter bandwidth, etc.), andmbient conditions (sun zenith angle, season, latitude, at-ospheric conditions, etc.) but is not considered in this

aper because of the assumptions detailed in Section 4.In the reverse direction the opposite is the case and,

bove a critical incidence angle, total internal reflection

Fig. 1. (Color online) Line-of-

TIR) can be achieved as explained in Section 3. Never-heless, the reflecting surface has the same three-imensional contour regardless of the incident directionf the light of interest, and the geometry of this surfaceust be modeled if we wish to calculate the propagation

arameters of an optic signal. Sea surface height is mea-ured in the time domain at different locations around thelobe using buoys with accelerometers or magnetometers20,21], and is commonly considered to be Gaussian orayleigh in distribution [22,23]. Furthermore, the seaurface slope, which is of interest in this work since it de-ermines the reflection angles of incident light, is alsoidely considered to be Gaussian as a first-order approxi-ation [24], while the parameter characterizing sea

roughness” and consequent variance in surface slope ishe wind speed and direction variation. In the limit, theea surface has been modeled as a plane surface boundingsemi-infinite dielectric medium and surface emissivity

as been calculated accordingly [24].

. COMMUNICATION SYSTEM LINKUDGET

n this section we develop the mathematical expressionsith which we can derive the performance of the proposed

ystem.

. LOS Communication Linkhe common FSO link in optical wireless communicationystems between two points is a LOS link as illustrated inig. 1. The optical signal reaching the receiver is obtainedy multiplying the transmitter power, telescope gain, andosses, and is given by [25] as

OS) communication scenario.

sight (L

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S. Arnon and D. Kedar Vol. 26, No. 3 /March 2009/J. Opt. Soc. Am. A 533

PR�los = PT�T�R exp�− c���d

cos���� ARec cos���

2�d2�1 − cos��0��,

�3�

here PT is the average transmitter optical power, �T ishe optical efficiency of the transmitter, �R is the opticalfficiency of the receiver, d is the perpendicular distanceetween the transmitter and the receiver plane, � is thengle between the perpendicular to the receiver planend the transmitter-receiver trajectory, ARec is the re-eiver aperture area, and �0 is the laser beam divergencengle.

. Reflective Communication Linkn some communication scenarios LOS is not availableue to obstructions, misalignment, or random orientationf the transceivers. This would be a common circumstanceor underwater sensor nodes or in the case of mobile usersnd leads us to propose an inventive method for achievingcommunication link. In addition, the proposed method

ffords the advantages of point-to-multipoint links andence facilitates broadcast communication. The funda-ental idea of reflective communication is illustrated inig. 2. The laser transmitter emits a cone of light definedy inner and outer angles �min and �max in the upward di-ection. We assume that the sensor nodes self align sohat the transmitter faces vertically upward at all times.he light reaching the ocean–air surface illuminates annnular area and is partially bounced back in accordanceith the reflectivity property described below.At an interface between areas of different refractive in-

ices, propagating light is partially transmitted (re-racted) and partially reflected in accordance withresnel’s law for dielectric media. If the light is polarizedith the electric field of the light perpendicular to thelane of the diagram above (s-polarized), the reflection co-fficient is given by

Rs = �nW cos��i� − nA cos��t�

nW cos��i� + nA cos��t��2

= � sin��i − �t�

sin��i + �t��2

, �4�

here �i and �t are the angles of incidence and of trans-ission (the latter is derived from the former using

Fig. 2. (Color online) Refl

nell’s Law) and nA is the refractive index of air.If the incident light is polarized in the plane of the dia-

ram (p-polarized), the reflection coefficient is given by

Rs = �nW cos��t� − nA cos��i�

nW cos��t� + nA cos��i��2

= � tan��t − �i�

tan��t + �i��2

. �5�

he respective transmission coefficients are given by Ts1−Rs and Tp=1−Rp.Polarized light propagating through an aquatic channel

ould loose its polarization properties due to the scatter-ng nature of the medium, so that we can assume that theight reaching the ocean–air surface is totally unpolarizednd its reflectivity is then given by R= 1

2 �Rs+Rp�.When the refractive index in the incident medium is

igher than in the second medium, as with an underwa-er optic signal reaching the ocean–air surface, then, ifhe angle of incidence surpasses a critical value, TIR oc-urs and all the light will be reflected back as if the inter-ace were a perfect mirror. The critical angle is given by

�c = sin−1� nA

nW . �6�

eflectivity as a function of incidence angle for the data inable 1 is shown in Fig. 3.We propose to use the TIR phenomenon to achieve an

ffective communication channel. If �min��c then TIRill not be achieved and only some of the light will be re-ected back in accordance with Fig. 3. However, the opticath, and consequent attenuation, of light reflected atmin����c is shorter than for �c����max, so that atepth x below the ocean–air surface the light intensityistribution received by the receiver will be a complicatednterplay of reflectivity and attenuation.

. Reflective Channel with a Wavy Surfacen this section we add the effect of the waviness of the seaurface. The seminal works of Cox and Munk in the 1950sevealed the very-near Gaussian probability distributionunction (pdf) of the slope, and several works publishedince then have confirmed and extended these results26–28]. In those works the authors computed a Gram–

communication scenario.

ective

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534 J. Opt. Soc. Am. A/Vol. 26, No. 3 /March 2009 S. Arnon and D. Kedar

harlier series of approximate Gaussian distribution inrder to obtain an analytical model for the wave slopeensity distribution function that would accurately corre-pond to measured sea surface contours. The basic ex-ression for the slope pdf using the Gram–Charlier seriess given by

p��� = n=0

N � cn

n!Hn���1

�2�exp�−

�2

2 , �7�

here � is the normalized slope, cn are expansion coeffi-ients, and Hn��� are the nth-order Hermite polynomialsisted in Table 1. The normalized slope is given by

� =� − �̄

slope, �8�

here � is the slope angle with respect to nadir, �̄ is theean slope angle, and slope is the standard deviation.The wave slope pdf obtained from experimental data

iffers from the Gaussian model in a few significant wayshat reveal information regarding the surface contour.he two primary indicators of the deviation of the sea sur-

ace slope pdf from the classic Gaussian form are ex-ressed in the coefficients of skewness and kurtosis. Thekewness is notable in the downwind direction, but negli-ible in the crosswind direction. If the mean and variancef the pdf derived from the Gram–Charlier series corre-pond to the respective values of the best-fit Gaussian pdfhen c0=1/sqrt���, c1=c2=0, and Eq. (7) reduces to aaussian pdf with additional higher–order terms correct-

ng for skewness and kurtosis. In this paper we do not cor-ect for skewness and kurtosis because of the symmetry ofhe omnidirectional transmission. Similarly, we assumehe mean slope angle is zero, although it has been foundo be near zero (determined by the prevailing wind direc-ion and material properties of the seawater) in experi-ental upwind and downwind measurements.To gain a better understanding of the angular spread oftransmitted laser beam reflected from the sea surfacee performed Monte Carlo simulations, launching 105

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle of incidence θi[Deg]

Ref

lect

ivity

Rs

Rp

RT

ig. 3. (Color online) Graph showing reflectivity at the ocean–ir surface as a function of incidence angle �i using parameters inable 2.

hotons at angles of 1°–90° (with respect to the seabedurface) and computing the angle of reflection using Eqs.4)–(6) and data from Table 2. The angle of reflection is

easured from the sea surface normal. The probabilityensity function for the sea surface slope, derived usinghe first term of the Gram–Charlier series that was usedn our simulations, is shown in Fig. 4 for wind speeds of.93, 8.58, and 10.2 m/s.A graph showing the power reception at different re-

ected angles as a function of incident angle for a smoothea surface appears in Fig. 5. Below the critical angleittle light is reflected by the sea surface, but above theritical angle the launched photons are totally reflected athe precise angle predicted. (Note that the transmit angles measured from the seabed surface and not from its nor-

al, while the reflected angle is measured from the sur-ace normal, so that the reflected angle is the right-angle-omplement of the incidence angle.) In contrast, theesults of the simulations indicating the spread of reflec-ion angles as a result of a nonsmooth sea surface arehown in Fig. 6. The wind speed is 11.5 m/s.

It is evident from Fig. 6 that when the sea surface isodeled as wavy some light is, in fact, back-reflected be-

ause of the local surface slope. The forward-reflectedight propagates primarily at angles close to the right-ngle-complement of the incidence angle, but consider-ble angular spread is encountered. In addition to theharp contrast in the variation of the angle of arrival webserve that the angular spread results in considerableoss in received optic power when the reception angle ofhe receiver is limited. Photons arriving at differentngles will have traversed different optical paths so mul-ipath phenomena (e.g., pulse spread in the time domain)ill also be encountered and will further reduce power re-

eption when the receiver is pulse-gated.A more detailed analysis of the power reception and

ulse spread is beyond the scope of this paper, but clearly

Table 2. Parameters Used in NumericalCalculationsa

Parameter Typical Value

Extinction coefficient �m−1� Clear ocean 0.1514Temperature (°C) 10

Salinity (%) 3.5Refractive index 1.33643

Critical angle (degrees) 48.44Transmission wavelength (nm) 532Optical efficiency of transmitter 0.9

Optical efficiency of receiver 0.9Average transmitter power (W) 0.1

Pulse duration (ns) 1Data rate (Mbit per second) 0.5Receiver aperture area �m2� 0.01

Laser beam divergence angle (degrees) �0=68ransmitter inclination angles (degrees) �min=0 �max=68

Dark counting rate (MHz) 1Background counting rate (MHz) 1

Counting efficiency (%) 16Transmitter depth-h (m) 20

Receiver depth-x (m) 20

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S. Arnon and D. Kedar Vol. 26, No. 3 /March 2009/J. Opt. Soc. Am. A 535

arge receiver apertures and fields-of-view are indicateds a means for mitigating the received power loss causedy the angular spread of the light reflected from a wavyea surface.

. Received Signal in a Reflective Communication LinkNo Wave)n Fig. 2, sensor nodes are on the seabed or floating withuoyancy control, so when the transmitter is at depth hhe illuminated annular surface with equal power density

−40 −30 −20 −100

0.01

0.02

0.03

0.04

0.05

0.06

Slo

Pro

babi

lity

Den

sity

The first term

Fig. 4. (Color online) Graph showing probability de

t depth x is given by (

min max

ssp

tt

Aann = 2��h + x�2�1 − cos��max� − 1 + cos��min��

= 2��h + x�2�cos��min� − cos��max��. �9�

quation (9) describes the annular area taken from aphere of radius �h+x� that would have uniform powerensity in free space.If we model the ocean–air surface as smooth then �

�i, and we can derive the link budget for the sensor-to-ensor link as follows: using the variables defined in Eq.

10 20 30 40le [Deg]

ram−Charlier series

Wind speed 10.2 m/sec σslope

=11.5

Wind speed 8.58 m/sec σslope

=8.62

Wind speed 3.93 m/sec σslope

=7.5

unction of surface slope angle for three wind speeds.

3), we express the auxiliary function

fR�ref��� =PT cos���

Aann ��T�R exp − c���� h + x

cos�����1

2 � tan��t − ��

tan��t + ���2

+ � sin�� − �t�

sin�� + �t��2� , �min � � �C

�T�R exp − c���� h + x

cos����� , �c � � �max� , �10�

nd calculate the received power as

PR�ref��� = ��Rec aper area

fR�Ref���da. �11�

t the plane of the receiving sensor, node coverage is pro-ided within an annular area bounded by radii �hx�tan�� � and �h+x�tan�� �. Equation (11) can be

implified on the assumption that the receiver aperture ismall relative to �h+x�, yielding the approximate receivedower as

PR�ref��� � ARecfR�ref���. �12�

The reflective communication link provides the founda-ion for a powerful broadcast network. A single transmit-ing sensor node will communicate with a number of sen-

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536 J. Opt. Soc. Am. A/Vol. 26, No. 3 /March 2009 S. Arnon and D. Kedar

or nodes, determined by the sparsity of the sensor nodeispersion. Each receiving sensor node will be able to re-ay the received signal, using its transmitter, to a furtheropulation of nodes. Hence, by multiple hops, the signalan propagate long distances despite the limitations onhe range of each reflective communication link. Theoint-to-multipoint nature of the link yields a reliableetwork without a single point of failure or bottleneck.urthermore, in contrast to acoustic communications, op-ical communication networks can operate in full duplexnd with multiple carrier frequencies. Multiple carriers

0

20

40

60

80

0

0.2

0.4

0.6

0.8

1

Incident photon direction [Deg]

Nor

mal

ized

phot

onnu

mbe

r(W

ind

spee

d0

m/s

ecno

wav

e)

ig. 5. (Color online) Graph showing angular distribution of poident photon direction is measured from seabed surface, reflecte

0

20

40

60

80

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Incident photon direction [Deg]

Nor

mal

ized

phot

onnu

mbe

r(W

ind

spee

d11

.5m

/sec

)

ig. 6. (Color online) Graph showing angular distribution of poace. Incident photon direction is measured from seabed surface,

ould increase the payload on each sensor node, buthroughput could be greatly enhanced.

. BIT ERROR RATEhe simplest and most widespread modulation technique

n FSO is intensity modulation in the form of On–Off key-ng (OOK). The detection method is direct detection. Inur NLOS sensor network the harsh underwater environ-ent has forced us to employ very short, high-energy

ulses as our data-carrying medium. The pulse intensity

−50

0

50

Reflected photon direction [Deg]

ception resulting from reflection from a smooth sea surface. In-ton direction is measured from sea-surface normal.

−50

0

50

Reflected photon direction [Deg]

ception resulting from reflection from a simulated wavy sea sur-ed photon direction is measured from sea-surface normal.

wer red pho

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S. Arnon and D. Kedar Vol. 26, No. 3 /March 2009/J. Opt. Soc. Am. A 537

s assumed much higher than any background illumina-ion, so we do not detail the precise scenario in terms ofun zenith angle, etc. Stringent time synchronizationould be necessary to operate this pulse-gated regime.The detector is in the form of a silicon photomultiplier

SiPM) matrix [29,30]. SiPMs are built from avalanchehotodiode arrays on a common substrate. Each elementperates in Geiger mode and is decoupled from the neigh-oring cells by a quenching resistor. In common with tra-itional photomultiplier tubes (PMT), single photons cane detected and gains are around 106, but the supply volt-ge can be as low as 25 V, which is an order of magnitudeess than for traditional PMTs. We assume that all theells are synchronized and the detectors are modeled ashoton counters. The accepted stochastic model for coher-nt photon arrival in photon counters is the Poisson dis-ribution, where the photon arrival rate during the gatedeceiver slot of duration T is given by

rs =1

T�PR

RD�D

h�, �13�

here RD is the data rate, �D is the detector counting ef-ciency, PR is PR�ref or PR�los, h is Plank’s constant, and �

s the frequency of the photon, so that h� is the photonnergy. The BER is given by

Pe = P�one��−�

Vt

P� �one�d + P�zero��Vt

�

P� �zero�d�,

�14�

nd assuming equiprobable transmissions of binary “1”nd “0,” this leads to the following expression for theER:

0 10 20 3010

−2

10−1

100

101

102

103

104

105

106

107

108

Pho

tons

Fig. 7. (Color online) Graph showing number of r

BER = 0.5�n=1

NTH �r1T�n exp�− r1T�

n! �+ 0.5�

n=1+NTH

Nmax �r0T�n exp�− r0T�

n! � , �15�

here r1=rd+rbg+rs and r0=rd+rbg, and where NTH is thehreshold count between “0” and “1,” and rd and rbg rep-esent the sources of additive noise due to dark countsnd background illumination, respectively. If we assume aarge number of photons then according to the centralimit theorem the BER can be approximated by

BER =1

2erfc� r1T − r0T

�2��r1T + �r0T�� , �16�

here

erfc��� =2

���

�

�

exp�− �2�d�. �17�

. NUMERICAL EXAMPLEo assess the feasibility of a NLOS optical link as de-cribed above we performed numerical simulations. Thealues of the parameters are given in Table 2. We assumehe sensors are all deployed at a depth of 20 m in clearcean. Using Eq. (13) we calculate the expected number ofeceived photons as a function of sensor node separationor the reflective channel. In Fig. 7 we show these resultsraphically and add the parallel results for a LOS chan-el for comparison. Using Eq. (16) we compute the ex-ected BER as a function of sensor node separation for

50 60 70 80 90e [m]

The reflective communication linkLOS communication link

photons as a function of sensor node separation.

40Distanc

eceived

taa

lSatrsrtisstowf

ntpohayfll

f4wcbwg

6INwcptttsfpinbswbmodm

R

538 J. Opt. Soc. Am. A/Vol. 26, No. 3 /March 2009 S. Arnon and D. Kedar

he reflective channel. In Fig. 8 these results are shown ingraph and the parallel results for a LOS channel are

dded for comparison.It is evident from Fig. 7 that a single LOS underwater

ink using a pulse modulated laser transmitter and aiPM detector array in the receiver results in a consider-bly higher photon count for a given sensor node separa-ion than does a NLOS link. For instance, for a node sepa-ation of 30 m, 6,000 photons would be received from aignal in a LOS link, while only 9 would be received in aeflective link where the transmitter depth is 20 m andhe receiving nodes are also at a depth of 20 m. However,f a single point-to-point link were to fail the transmittedignal would be lost, while in the NLOS underwater sen-or network solution a number of nodes would be expectedo receive the signal. Even in the severe case of the failuref several nodes, with sufficient node redundancy thereould still be additional nodes that could relay the signal

arther.We observe an interesting phenomenon in which the

umber of received photons falls with node separation un-il a point (at �25 m) when the photon count increases,eaks, and falls again. We attribute this to the interplayf increased attenuation with optical path on the oneand, and increased reflectivity when the incidence anglet the ocean–air surface is greater on the other hand. Be-ond some distance the attenuation dominates and the re-ective link performs in a way similar to that of the LOS

ink. The resultant BER is affected dramatically.In Fig. 8 we see that BER values of 10−4 are obtained

or the NLOS reflective link when the node separation is0 m, while a BER of 10−4 could be achieved in a LOS linkhen the node separation is 60 m. This leads us to con-

lude that some coding or network protocol solution woulde necessary to render the NLOS link viable in an under-ater sensor network with node dispersals at the depthsiven in the example.

0 10 20 3010

−12

10−10

10−8

10−6

10−4

10−2

100

Bit

erro

rra

te

The reflective communication linkLOS communication link

Fig. 8. (Color online) Graph showing

. SUMMARY AND CONCLUSIONSn this paper we have described a model for the LOS andLOS photon counting bit error probability in an under-ater sensor network that takes into consideration the

hannel characteristics and the communication systemarameters. We can see that an increase in node separa-ion increases dramatically the BER of the communica-ion system for both configurations. The results indicatehat networks of underwater sensors using laser links toerve wireless mobile users are feasible at high data ratesor medium distances of up to 100 m. Many aspects of theroposed NLOS underwater sensor network remain to benvestigated, including rigorous modeling of the reflectiveature of the ocean–air surface and a study of achievableit rates. However the fundamental concept has beenhown to be feasible and the range limitations of under-ater FSO can be combatted by applying a multi-hoproadcasting network paradigm. Further work modelingultiple scattering in different oceanic channels and

cean surface roughness as well as considering solar ra-iance penetration should refine the analysis and yieldore accurate numerical results.

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