Underwater Wireless Optical Communication ... - WordPress.com

1620

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 9, DECEMBER 2008

Underwater Wireless Optical Communication Channel Modeling and Performance Evaluation using Vector Radiative Transfer Theory Sermsak Jaruwatanadilok, Member, IEEE

Abstract—This paper presents the modeling of an underwater wireless optical communication channel using the vector radiative transfer theory. The vector radiative transfer equation captures the multiple scattering nature of natural water, and also includes the polarization behavior of light. Light propagation in an underwater environment encounters scattering effect creating dispersion which introduces inter-symbol-interference to the data communication. The attenuation effect further reduces the signal to noise ratio. Both scattering and absorption have adverse effects on underwater data communication. Using a channel model based on radiative transfer theory, we can quantify the scattering effect as a function of distance and bit rate by numerical Monte Carlo simulations. We also investigate the polarization behavior of light in the underwater environment, showing the significance of the cross-polarization component when the light encounters more scattering. Index Terms—underwater communication, radiative transfer, polarization, scattering, wireless optical communication

I. I NTRODUCTION

W

IRELESS communication under water has tremendous applications such as communication among divers, unmanned underwater vehicles (UUV), submarines, ships, and underwater sensors. Some of these UUVs and sensors are deployed to gather important data such as real-time videos and environmental and security data which may be time sensitive. Also, information on the remote control of these UUVs and submarines may be relayed through wireless communication. Therefore, efficient and high speed communications are required for handling underwater data transmission of large amounts of data with as small a delay as possible. Traditionally, wireless underwater data communication employs acoustic waves. Because an acoustic wave has low loss in the water, its range of communication can be very long [1]– [3]. However, it has several disadvantages. The acoustical communication channel has a narrow bandwidth; therefore, it can only handle a relatively low bit rate [2]. Also, the acoustic wave speed in water is slow (1500 m/s), which results in latency in communication. To accommodate a higher bit rate, a higher frequency has to be considered. A possible candidate is the optical frequency. It has been reported in a

Manuscript received February 15, 2008; revised September 8, 2008. This work was supported in part by the Office of Naval Research (N00014-07-10428), and the National Science Foundation (ECS-0601394). The author is with the Department of Electrical Engineering, University of Washington, Seattle, WA, 98195 phone: 206-616-5606; fax: 206-543-3842 (e-mail: [email protected]). Digital Object Identifier 10.1109/JSAC.2008.081202.

specific case that the range of communication can be up to 425 m [4]. However, even this kind of range is enough for communication among UUVs and divers in scenarios such as search and rescue operations in a disaster in a concentrated area. In this case, real-time, high quality images are crucial. High rate data transmission among underwater nodes and the buoy is therefore necessary. Optical wireless communication is possible in water, especially in the blue/green light wavelengths because it suffers less attenuation in water compared to other colors [5]. Compared to acoustic waves, it propagates faster in the water (2.255 × 108 m/s) and offers a larger bandwidth. However, an optical wave is subjected to more absorption and scattering than an acoustic wave. The effects of the scattering in water are two fold. First, it attenuates the transmitted signal reducing signal to noise ratio. Second, it creates the inter-symbol-interference (ISI) effect corrupting the signal waveform. Therefore, the characterization of light propagation through an underwater channel that includes the absorption and scattering effects is crucial to analyze the wireless optical communication in underwater environments. Most previous studies modeled the wireless optical communication under water using extinction factor, which is the reduction of the intensity of light as a function of optical distance [4],[6],[7]. These models, therefore, can capture only the effect of signalto-noise ratio on the communication channel. However, the dispersion effect needs to be included, and it is significant in some cases. The dispersion, which results from the multiple scattering of light from the particulate matter, creates the inter-symbol-interference which disturbs the integrity of the transmitted signal. This is a significant effect causing an increase in bit-error-rate, which is more pronounced in high bit rate communication. We employ the vector radiative transfer (VRT) theory which can capture both the attenuation and multiple scattering effects. The VRT also takes into account the polarization. Thus, the polarized optical signal communication can be modeled and evaluated. We investigate the characteristics of underwater media pertinent to the construction of our channel model. Then, we apply the derived channel response to simulate underwater digital communication and the performance of the communication is investigated. II. U NDERWATER CHANNEL MODEL The channel model we use involves both scattering and absorption of light in underwater environments and the noises.

c 2008 IEEE 0733-8716/08/$25.00

Authorized licensed use limited to: Univ of Puerto Rico Mayaguez - Library. Downloaded on March 26, 2009 at 19:39 from IEEE Xplore. Restrictions apply.

JARUWATANADILOK: UNDERWATER WIRELESS OPTICAL COMMUNICATION CHANNEL MODELING AND PERFORMANCE EVALUATION

Fig. 2.

1621

Plane parallel geometry.

The modified Stokes vector I is given by Fig. 1.

Additive noise channel model.

I = [I1

The absorption phenomenon is due to both the background media which is sea water and the suspended particulates in sea water. The scattering of light also takes place because of the presence of these suspended particulates. After characterizing the particles residing in sea water which is explained below, we employ the radiative transfer theory to capture the light scattering and absorption behaviors under such an environment. The radiative transfer theory has been used previously to investigate the light propagation in random scattering media [8]. It also has been used for channel modeling in free space optics [9],[10]. The relatively same concept applies here; however, an underwater environment can be much more complex than free space. In the channel model schematic shown in Fig. 1, the received signal y(t) is given by y(t) = x(t) ⊗ h(t) + n(t)

(1)

where x(t) is the input sequence, h(t) is the impulse response, and n(t) is the additive noise. The symbol ⊗ denotes the convolution. The impulse response h(t) is derived using the vector radiative transfer equation which is explained in Section III. The important parameter for the vector radiative transfer equation is the Mueller matrix which describes the scattering characteristics of the channel. To calculate the Mueller matrix, the characteristics of scattering particles which are the index of refraction, the particle density, and the particle distribution are required. In underwater environments, the composition of suspended particulate matters is complex and varies in location and time. It is explained in Section IV. Finally, the noise of the underwater communication is discussed in Section V. III. V ECTOR RADIATIVE TRANSFER EQUATION We employ the vector radiative transfer theory which explains the behavior of wave propagation and scattering in a discrete random medium. The frequency-domain pulse-vector radiative transfer equation in a plane-parallel problem as illustrated in Fig. 2 is given by [9].

0 ≤ τ ≤ τo

V ]T

E2 E2∗ 2ReE1 E2∗

2ImE1 E2∗ ]T

(3)

where E1 and E2 are vertically and horizontally polarized electric fields, the symbol denotes complex conjugate, and T is the transpose operator of a matrix. The cosine of the polar angle is μ = cos θ. The optical distance τ is defined as τ = ρσt z where ρ is the number density, σt is the average total cross section of a single particle, and z is the actual distance. The optical depth τo is defined by τo = ρσt L where L is length of the random medium. The Mueller matrix S is given by S1 S2 (4) S= S3 S4 where the submatrices S1 , S2 ,S3 , and S4 are given by 2 2 |f11 | |f12 | S1 = (5) 2 2 |f21 | |f22 | ∗ ∗ Re(f11 f12 ) −Im(f11 f12 ) (6) S2 = ∗ ∗ ) −Im(f21 f22 ) Re(f11 f12 ∗ ∗ 2Re(f11 f21 ) 2Re(f12 f22 ) (7) S3 = ∗ ∗ 2Im(f11 f21 ) 2Im(f12 f22 ) ∗ ∗ ∗ ∗ Re(f11 f22 + f12 f21 ) −Im(f11 f22 − f12 f21 ) S4 = ∗ ∗ ∗ ∗ Im(f11 f22 + f12 f21 ) −Re(f11 f22 − f12 f21 ) (8) The scattering amplitudes f11 , f12 , f21 , and f22 are calculated using Mie solution [11]. These scattering amplitudes depend on the index of refraction of particles and the size. Given a size distribution, we can calculate the scattering amplitude for each size and obtain an average. The term Fo represents the incident light (9) Fo = S(μ, φ, 1, 0)Io where Io is the incident modified Stokes vector. For lefthanded circular polarized light 1]

T

(10)

The solution to Eq. (2) can be separated into reduced (coherent) intensity and diffuse (incoherent) intensity. The solution to the coherent intensity is the portion of light that escapes the multiple scattering effect; therefore, it obeys

0 −1

for

= [E1 E1∗

U

Io = [1/2 1/2 0

ω ∂ + 1 + (μ − 1)i I(ω, τ, μ, φ) μ ∂τ τo 2π 1 S(μ, φ, μ , φ )I(ω, τ, μ , φ )dμ dφ = + Fo (τ, μ, φ) exp(−τ )

I2

(2)

∂ Iri = −Iri ∂τ


(11)

1622


Thus, the solution becomes Iri = Io f (ω, τ ) exp (−τ ) δ (φ) δ (μ − 1)

(12)

where f (ω, τ ) is the pulse shape function. The solution to the diffuse intensity can be calculated by solving Eq. (2) with the following boundary conditions I(τ = 0) = 0 for 0 ≤ μ ≤ 1 I(τ = τo ) = 0 for − 1 ≤ μ ≤ 0

(13)

Physically, Eq. (13) shows that there is no diffuse intensity coming into the slab of random medium at the boundary. The time-dependent diffuse intensity can be calculated by applying a Fourier transform to the solution of Eq. (2) 1 ω Id (tn , τ ) = Id (ω, τ ) exp i τ − iωtn dω (14) 2π τo Note that tn is the normalized time tn = tc/L. The normalized time tn = 1 indicates the travel time from one side of the random medium (z = 0) to the other side (z = L). To obtain the diffuse Stokes vector Id numerically, we solve Eq. (2) with the boundary conditions stated in Eq. (13) using the discrete ordinates method [12]. We also numerically integrate the Muller matrix with respect to the φ dependence as expressed in Eq. (15). 2π

L(μ, μ ) =

S(μ, μ , φ − φ)d(φ − φ)

(15)

0

As a result, Eq. (2) reduces to ω ∂ + 1 + (μ − 1)i μ Id (ω, τ, μ) ∂τ τo 1 L(μ, μ )Id (ω, τ, μ )dμ = for 0 ≤ τ ≤ τo

(16)

By applying the Gauss quadrature formula to μ dependent in Eq. (16), the μ-domain is discretized into 2N numbers. Thus, we obtain a first-order differential equation in the form of d I + AI = B exp(−τ ) dτ where

where F OV is the field of view of the receiver. μo = cos θo , θo is the closet angle to zero. The exact value of θo depends on the number of gauss quadratures (N ). There is a tradeoff in calculation time and accuracy and resolution of the most forward Stokes vector. As N increases, we get a more accurate result of the most forward Stokes vector. However, we encounter a larger dimension of the matrix equation, which results in an increase of computation time. Through out this paper, we use N = 40, which results in the most forward angle of 3.14 degrees. IV. C HARACTERISTICS OF WATER AND PARTICLES IN AN UNDERWATER ENVIRONMENT

The characteristics of water and particulate matters in an underwater environment have been a subject of several studies for decades [14]–[20]. We sort the materials of interest by the effects they cause: absorption and scattering. The materials creating absorption are (1) underline pure water or sea water, (2) planktonic components, (3) detrital components, (4) mineral components, and (5) colored dissolved organic matter (DOM). The materials creating scattering are (1) planktonic components, (2) detrital components, and (3) mineral components. A. Pure water

−1

+ Fo (μ) exp(−τ )

Stokes vector Iri and the incoherent Stokes vector Id (t, τ, μ) at discrete angle μj , −N ≤ j ≤ N . Our analysis concentrates on the received Stokes vector at the most forward angle. It contains the combination of the coherent and incoherent Stokes vectors Ireceived = Iri + Id (μo ) × πF OV 2 (18)

(17)

⎤ Id (ω, τ, μ−N ) ⎦ , Bj = Fo (μj ) , : I=⎣ μj Id (ω, τ, μN ) 1 ω L(μj , μk ) and Aj,k = . 1 + (μj − 1)i − μj τo μj ⎡

The solution to Eq. (17) consists of the particular solution and the complementary solution. By imposing the boundary conditions in Eq. (13), we can find the complete solution. The details on solving Eq. (17) are given in [13] and will not be discussed here. An important step is the scattering amplitude calculation using Mie scattering with the information on particle size distribution and the index of refractions of background water and particles given in Section IV. The solutions we obtained from the radiative transfer equation are the coherent

The absorption of pure water is wavelength dependent. The measurements are tabulated in [14]. The data suggest that the absorption is much larger for the higher wavelength region (λ > 600 nm). This limits the possible use of the optical wave to a lower wavelength region. It was shown that the absorption from planktonic components at a lower wavelength [15] also narrows the possible wavelength used to the region of about 500-600 nm, the blue-green region. B. Sea water: the refractive index Because we intend to model underwater ocean water, we employ the model for the refractive index for sea water in [16], which depends of salinity, temperature, and wavelength. n(S, T, λ) = n0 + n1 + n2 T + n3 T 2 S + n4 T 2 n8 n5 + n6 S + n7 T n9 + 2 + 3 + λ λ λ

(19)

where S is the salinity in ppt (part per thousand or 0/00 ), T is the temperature in degrees Celsius, and λ is the wavelength in nanometers. The coefficients have the following values: n0 = 1.31405, n1 = 1.779 × 10−4 , n2 = −1.05 × 10−6 , n3 = 1.6 × 10−8, n4 = −2.02 × 10−6, n5 = 15.868, n6 = 0.01155, n7 = −0.00423, n8 = −438, n9 = 1.1455 × 106 .



14

2

10

10

|S1|2

Planktonic Detrital Mineral

12

|S2|2 Specific intensity

10 Particle number

1623

10

10

8

10

0

10

−2

10

6

10

4

10

−4

0

5

10 15 20 Diameter of particles (μm)

25

10

30

Fig. 3. Particle distribution for particulate matter in underwater environment.

C. Planktonic components The details of planktonic components can be found in Table 1 of [17], which is a compilation of the average diameter, refractive index, and concentration data from several references. Plaktonic components contribute to both the absorption effect and the scattering effect. The diameter of planktonic components ranges from 0.07 μm to 27.64 μm. D. Detrital and mineral components The size distribution of detrital and mineral components is modeled using hyperbolic function [18]. The particle size ranges from 0.05 μm to 20 μm . Their dielectric properties are listed in [17]. The real part of the index of refraction for a detrital component and a mineral component are 1.3851 and 1.5715, respectively. The imaginary part of the index of refraction for both obeys

Fig. 4. ment.

0

50 100 150 Scattered angle (degrees)

200

Scattering amplitudes of particulate matter in underwater environ-

We calculate the scattering functions (S1 and S2 ) using Mie solution [11] at the 532 nm wavelength and plot the results in Figure 4. The average mean cosine is 0.1348 and the Albedo is 0.9767. The extinction coefficient ρ σt is 0.30547 . Because the underwater environments vary tremendously from location to location, this model serves as a representative of a natural body of water according to the data provided by references. The vector radiative transfer model is still valid for other underwater environments. However, the scattering amplitudes and, consequently, the Mueller matrix have to be recalculated. V. S IGNAL NOISE UNDERWATER

where λ is the wavelength in nm

There are many sources of noise that disturb the optical communication system under water. Here, we discuss each noise and give the expression for its variance [6],[21]. The variance of noise translates into the noise power spectrum which we can use in the bit transmission simulation. The modeled noise consists of (1) background noise, (2) dark current noise, (3) thermal noise, and (4) shot noise.

E. Colored dissolved organic matter (CDOM)

A. Background noise

Colored dissolved organic matter is a significant factor in the absorption, especially at the interface of ocean water and the run-off from river. There are two components of the yellow substance: fulvic and humic acids [19]. The absorption coefficient of both can be written as

The background noise consists of the blackbody radiation and the ambient light under water whose primary source is the refracted sunlight from the surface of the water. The background noise power can be written as

n (λ) = 0.0010658 exp (−0.007186λ)

fulvic : a0f Cf exp (−kf λ) ;

(20)

humic : a0h Ch exp (−kh λ) (21)

where a0f = 35.959 m2 mg is the specific absorption coeffi cient of fulvic acid kf = 0.0189 nm−1 , a0h = 18.828 m2 mg is the specific absorption coefficient of humic acid, kh = 0.01105 nm−1 , Cr and Ch are concentrations of fulvic and humic acids, respectively, in milligrams per cubic meter (parameters found for several locations in [20]). The loss from CDOM is incorporated into the imaginary part of the background medium (sea water). From the information above, we assume that all the particles are spherical with size distribution shown in Fig. 3. The number density ρ is 1.1262 × 1014 m−3 , which is the summation of the number of particles of every particle type.

PBG = PBG

solar

+ PBG

blackbody

(22)

The variance of the background noise is 2 σBG = 2qPBG B

(23)

where is the responsivity, λ is the wavelength, h = 6.6261× 10−34 J · s is the Planck’s constant, the electron charge q = 1.6 × 10−19 coulombs, η = 0.8 is the quantum efficiency of the detector, and B is the electronic bandwidth. 1) Solar background noise: The solar background noise power is PBG

solar

2

= Ar × F ovF ac × ΔλTF Lsol

(24)

where Ar = πD 4, D is the diameter of the aperture (20 cm in our calculations), F ovF ac = π(F OV 2 ), Δλ is the optical


1624


filter bandwidth, and TF is the optical filter transmissivity. The 2 solar radiance Lsol (watts/m ) is given by [6] Lsol =

(25) 2

blackbody

=

2hc2 α × F ovF ac × Ar TA TF Δλ λ5 [exp (hc/λkT ) − 1]

(26)

where c = 2.25257 × 108 is the speed of light in the water, TA = exp (−τo ) is the transmission in water, k = 1.381 × 10−23 is the Boltzmann’s constant, and α = 0.5 is the radiant absorption factor. B. Dark current noise Dark current noise is the noise presence at the detector (photo diode). The variance of the dark current noise is 2 = 2qIDC B σDC

THE DATA COMMUNICATION

A. Significance of the incoherence component

ERLf ac exp (−KDw ) π

where E is downwelling irradiance (watts/m ), R is underwater reflectance of the downwelling irradiance, Lf ac is the factor describing the directional dependence of the underwater radiance, K is the diffuse attenuation coefficient, and Dw is depth. For a wavelength of 532 nm, E = 1440 watts/m2 , R = 1.25%, and Lf ac = 2.9 in the horizontal direction [6]. 2) Blackbody radiation background noise: The noise power from blackbody radiation is PBG

VI. E FFECTS OF CHANNEL ON THE OPTICAL SIGNAL AND

(27)

where IDC = 1.226 × 10−9 Ampere.

First, we investigate the significance of the incoherent wave with respect to the coherent wave. The calculations here assume that the laser transmits continuous left-handed circularpolarized (LHCP) light. The coherent wave Iri is the portion of the wave that propagates through media without a scattering effect. This portion of the wave is only subject to attenuation. Therefore, it retains the original signal without distortion. However, its magnitude reduces exponentially as a function of optical depth (extinction coefficient multiplied by range). The incoherent wave Id results from both the scattering and attenuation in the media, and because of these effects, it suffers from distortion. It is also attenuates exponentially as a function of optical depth but at a slower rate because of the positive contribution from scattering. In practice, it is very difficult to separate them. However, in most cases, one will be a dominant component while the other marginally contributes. The plot in Fig. 5 shows the magnitude of coherent component, copolarized incoherent component (LHCP), and cross-polarized incoherent component (right-handed circular-polarized RHCP) of the received signal as a function of distance. Fig. 5(a) illustrates the case where FOV of the receiver is 10 mrad. It shows that at a distance beyond 50 meters, the incoherent component is more dominant. A shorter distance is reached when FOV is 50 mrad as shown in Fig. 5(b). FOV dictates the amount of incoherent component that the receiver gathers since wider FOV means that the receiver captures more multiply scattered light which usually arrives from a wider angle.

C. Thermal noise (Johnson noise) B. Impulse responses and signal wave forms

The variance of the thermal noise is σT2 H =

4kTe F B RL

(28)

where we assume that the equivalent temperature Te is 290K, F = 4 is the noise figure of the system, and RL = 100Ω is the load resistance. D. Current shot noise Shot noise exists when the received signal is present. The variance of current shot noise is 2 σss = 2qPs B

(29)

where Ps is the signal power. The total noise variance is the combination of all the noise sources. Therefore, the variance in current noise in the detector without any optical signal is given by 2 2 σ02 = σT2 H + σDC + σBG

(30)

Because of the shot noise presence, the variance in current noise in the detector for receiving an optical signal is given by 2 2 2 σ12 = σT2 H + σDC + σBG + σss (31)

To investigate the pulse wave propagation, the frequencydomain vector radiative transfer equation is solved for 16000 frequencies. The total bandwidth calculated is 6.4 GHz which is sufficient for the intended 1 Gb/s communication simulations. Then, the time-domain Stokes vector can be calculated using Eq. (14) and the impulse response is calculated from Eq. (18). The peak transmitted power is 1 Watt. The impulse responses for distances of 30 m and 50 m are illustrated in Figure 6. These impulse responses include both coherent and incoherent intensity. In the case of 30 m distance, the optical depth is 9.1641, and in the case of 50 m distance, the optical depth is 15.2735. The time scale is adjusted so that the time durations in both figures shown are equal (0.05 μs). There are noticeable differences in the behavior of both the co-polarized component and the cross-polarized component. In the 30 m case, the co-polarized component intensity dramatically reduces as a function of time when compared to that of the 50 m case. This reflects the amount of inter-symbol-interference which is substantial in 50 m. Also, when compared between 30 m and 50 m, the peak of the co-polarized impulse response reduces by about 20 dB, while the peak in the cross-polarized impulse response reduces only less than 10 dB. This shows the effect of multiple scattering on the increase of the cross-polarized component. This information can potentially be used to evaluate the



(a)

(a)

0

−40 Co−po X−po Coherent

−40

−60

−60

−70

−80

−80

−100

−90

−120

−100

−140 0

20

40 60 Distance (m) (b)

80

−110 0.13

100

0

0.14

0.15 0.16 time (μ s) (b)

0.17

0.18

−50 Co−po X−po Coherent

−20

Co−pol Cross−pol

−60

−40

−70

−60

−80 dB

Intensity (dB)

Co−pol Cross−pol

−50

dB

Intensity (dB)

−20

−80

−90

−100

−100

−120

−110

−140 0

Fig. 5. mrad.

1625

20

40 60 Distance (m)

80

−120 0.22

100

Magnitude of received signal (a) FOV =10 mrad, (b) FOV = 50

application of polarization to the communication. Examples of received signal waveforms through the underwater channel under different water conditions are shown in Figs 7 and 8 for transmission rates of 1 Gb/s and 100 Mb/s, respectively. They illustrate the distortion of the received signal as the distance of communication increases. The difference in transmission bit rates is obvious because the ISI strongly affects the higher bit rate transmission. Note that these are noise-free received signals for illustration of the distortion effect. In our bit-errorrate calculation explained in the next section, the noise is added before the detection process. C. Data communication simulations and bit-error-rate Monte Carlo simulations of the data communication are performed. A stream of 10,000 random bits is convolved with the impulse response. Then, the signal is integrated over a symbol period and the noise is added. We perform 50 independent simulations for each distance and bit rate, resulting in 500,000 total transmitted bits in each case. Although the vector radiative transfer also provides cross-polarization information, we consider only the co-polarized wave. We calculate the biterror-rate in communication using on-off keying modulation and 4-level amplitude modulation. 4-level amplitude modulation is performed by assigning four different signal levels for two data bits. The results are shown in Fig. 9. As expected, as the distance increases, the signal to noise ratio decreases and the distortion increases. Therefore, the bit-error-rate increases. At a given distance, we also found that the increase of FOV

Fig. 6.

0.23

0.24 0.25 time (μ s)

0.26

0.27

Impulse response (a) distance = 30 m, (b) distance = 50 m.

improves the bit-error-rate performance. That is because the more FOV, the larger the received signal. From these results, we can predict the distance at which a data communication at a particular bit rate is feasible under this underwater condition. It suggests that although the 4-level amplitude modulation could double the capacity of data transmission, it suffers more error in the transmission. VII. C ONCLUSIONS In this paper, we investigate underwater optical wireless data transmission. The underwater channel is modeled using vector radiative transfer theory which includes the multiple scattering effects and polarization. The multiple scattering effect results in inter-symbol-interference which strongly deteriorates the data communication. The details of underwater channel characterization are explained including the characteristics of particulate matter and sea water, and noises in the underwater environments. The data transmission and the received signal waveform are simulated showing the effect of the inter-symbol interference as functions of data rate and distance. The corresponding bit-error-rate performance is investigated illustrating the limitation of data communication as the distance increases. We found that as the distance increases, the bit-error-rate performance degrades as expected. From the results, it is possible to predict the distance at which the data transmission is feasible given a bit rate and field of view. Furthermore, multi-level amplitude modulation can be modeled and evaluated in a similar fashion. We simulated the 4-level amplitude modulation and found that although it can


1626


(a)

(a)

1.2

1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0

−0.2 0

2

4 6 Time (ns) (b)

−4

x 10

8

10

−0.2 0 −4

x 10

4

4

3

3

2

2

1

1

0

134

136

−6

7

x 10

138 Time (ns) (c)

20

140

0

142

140

160

−6

8

x 10

40 60 Time (ns) (b)

180 200 Time (ns) (c)

80

100

220

240

7 6

6 5

5

4 4

3 2

3

1 2

254

256 258 Time (ns)

260

262

0

340

360

380 Time (ns)

400

420

Fig. 7. Waveform of received signal propagated through under water at 1 Gb/s (a) transmitted bit, (b) at distance 30 m, and (c) at distance 50 m.

Fig. 8. Waveform of received signal propagated through under water at 100 Mb/s (a) transmitted bit, (b) at distance 30 m, and (c) at distance 50 m.

increase the capacity of the communication, the bit-error-rate performance is worse than that of on-off keying modulation.

[6] J. W. Giles and I. N. Bankman, “Underwater optical communications systems. Part 2: basic design considerations,” IEEE Military Communications Conference, Atlantic City, NJ, USA, pp. 1700–5, 2005. [7] N. Fair, A. D. Chave, L. Freitag, J. Preisig, S. N. White, D. Yoerger, and F. Sonnichsen, “Optical modem technology for seafloor observatories,” OCEAN, Boston, MA, USA, 2006. [8] A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Applied Optics, Vol. 40, pp. 5495–502, 2001. [9] S. Jaruwatanadilok, U. Ketprom, Y. Yuga, and A. Ishimaru, “Modeling the point-to-point wireless communication channel under the adverse weather conditions,” IEICE Transactions on Electronics, Vol. E87-C, pp. 1455–62, 2004. [10] U. Ketprom, Y. Kuga, S. Jaruwatanadilok, and A. Ishimaru, “Propagation model of the optical wave through dense fog in an urban environment,” URSI-APS, Albuquerque, NM, USA, p. 122, 2006. [11] H. C. Van de Hulst, Multiple Light Scattering, Vol. I and II, Academic, New York, 1980. [12] A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE Press, Piscataway, New Jersey and Oxford University Press, Oxford,

R EFERENCES [1] H. Ochi, Y. Watanabe, and T. Shimura, “Experiments of underwater acoustic communication using 16-QAM,” 8th International Congress on Acoustics, Kyoto, Japan, 2004. [2] I. F. Akyildiz, D. Pompili, and T. Melodia, “Underwater acoustic sensor networks: research challenges,” Ad Hoc Networks, Vol. 3, pp. 257–79, 2005. [3] T. J. Hayward and T. C. Yang, “Underwater acoustic communication channel capacity: a simulation study,” AIP Conference Proceedings, La Jolla, CA, USA, pp. 114–21, 2004. [4] M. A. Chancey, Short Range Underwater Optical Communication Links, M.S. Thesis in Electrical Engineering, North Carolina State University, 2005. [5] K. S. Shifrin, Physical Optics of Ocean Water, American Institute of Physics, New York, 1988.



(a)

0

10

−2

10

FOV=50, BR=100 FOV=100, BR=100 FOV=50, BR=1000 FOV=100, BR=1000

−4

10

−6

10

10

20

0

30 Distance (m) (b)

40

50

10

−2

BER

10

1627

England, an IEEE-OUP Classic Re-issue, 1997. [13] R. L. Cheung and A. Ishimaru, “Transmission, backscattering, and depolarization of waves in randomly distributed spherical particles,” Applied Optics, Vol. 21, pp. 3792–3798, 1982. [14] R. M. Pope and E. S. Fry, “Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements,” Applied Optics, Vol. 36, pp. 8710–23, 1997. [15] J. R. Apel, Principles of Ocean Physics, Academic Press, Suffolk, UK, 1987. [16] Q. Xiaohong and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Applied Optics, Vol. 34, pp. 3477–80, 1995. [17] D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Applied Optics, Vol. 40, pp. 2929–45, 2001. [18] D. Risovic, “Effect of suspended particulate-size distribution on the backscattering ratio in the remote sensing of seawater,” Applied Optics, Vol. 41, pp. 7092-7101, November, 2002. [19] V. I. Haltrin, “Chlorophyll-based model of seawater optical properties,” Applied Optics, Vol. 38, pp. 6826–32, 1999. [20] K. L. Carder, R. G. Steward, G. R. Harvey, and P. B. Ortner, “Marine Humic and Fulvic-Acids - Their Effects on Remote-Sensing of Ocean Chlorophyll,” Limnology and Oceanography, Vol. 34, pp. 68–81, January, 1989. [21] H. Manor and S. Arnon, “Performance of an optical wireless communication system as a function of wavelength,” Applied Optics, Vol. 42, pp. 4285–94, 2003.

−4

10

FOV=50, BR=100 FOV=100, BR=100 FOV=50, BR=1000 FOV=100, BR=1000

−6

10

10

20

30 Distance (m)

40

50

Fig. 9. Bit error rate as a function of distance and field of view. BR is bit rate in Mb/s, ex BR=100 means transmission bit rate is 100 Mb/s. (a) on-off keying, (b) 4-level amplitude modulation.

Sermsak Jaruwatanadilok (M’03) received the B.E. degree in telecommunication engineering from King Mongkut’s Institute of Technology, Ladkrabang, Thailand, in 1994, the M.S. degree in electrical engineering from Texas A&M University, College Station, in 1997, and the Ph.D. degree in electrical engineering from the University of Washington, Seattle, in 2003. He is currently a Research Assistant Professor at the University of Washington. His research interests are optical wave propagation and imaging in random medium, as well as optical and microwave remote sensing.
