On Path Loss of NLOS Underwater Wireless Optical Communication Links Shijian Tang, Yuhan Dong, Xuedan Zhang Shenzhen Key Laboratory of Information Science and Technology Department of Electronic Engineering, Tsinghua University, China Email:
[email protected], {dongyuhan, zhangxuedan}@sz.tsinghua.edu.cn Abstract—In practical underwater wireless optical communications (UWOC), the non-line-of-sight (NLOS) link which utilizes the sea surface to reflect the beam has been presented recently but not fully studied yet. In this paper, we investigate the path loss of NLOS UWOC links based on the Monte Carlo simulations taking the effects of both random sea surface slopes and scattering properties of seawater into account. Numerical results suggest that the random surface slopes induced by the wind may strongly corrupt the received signal. This detrimental effect can be dismissed by scattering light as the attenuation length increases where the multiple scattering light dominates in the received signal. Index Terms—Underwater wireless optical communications, non-line-of-sight, path loss
I. I NTRODUCTION Underwater wireless optical communications (UWOC) has been studied and considered as an alternative technology to traditional acoustic methods recently. The UWOC systems will achieve high data rate within short link ranges. Most previous works (see [1], [2] and reference therein) only focus on the performance of line-of-sight (LOS) UWOC links which are hard to implement in practice due to the obstructions especially when the optical source and detector are located on the seabed. Then Arnon et al. [3] proposed a non-line-of-sight (NLOS) scheme to transmit data using reflected beam from sea surface. This NLOS geometry can be used for configuration of submarine networks. However, an ideal assumption of stable sea surface and negligible scattering has been made in their work, which may differ from the realistic systems. In this paper, we consider the effects of wind-generated random sea surface slopes and scattering characteristic of seawater and investigate the path loss performance of NLOS UWOC links with link geometry of surface reflection studied in [3]. Monte Carlo approach has been adopted to simulate the interactions of photons with sea surface and seawater and then evaluate the system performance. Numerical results demonstrate that the random sea surface slopes may increase the path loss and deteriorate received signal as wind speed increases. While the scattering light can diminish this negative effect as the attenuation length increases, and then release the negative effect of wind speed on system performance. Our This material is based on the work supported by the National Natural Science Foundation of China (61201184). Corresponding author: Dr. Xuedan Zhang, Email:
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study is beneficial for reliability enhancement and performance evaluation for NLOS UWOC links. II. C HANNEL M ODEL A. NLOS Link Geometry The geometry of NLOS link is depicted in Fig. 1. The source and detector are located on the seabed below the sea level with depth d and separated by distance L. θ is the angle between the seabed and beam axis with θ = arctan(2d/L)1 . After illuminating the air-sea surface, and optical beam emitted by the source is reflected and then detected by the receiver. The wind may roughen the air-sea surface and change the slopes randomly, which will degrade the beam. Meanwhile The light also suffers absorption and scattering through the propagation trajectory mentioned above. The divergence angle of a well collimated laser source is 0.01 degrees and the field of view (FOV) of the detector is 180 degrees. The refractive indices for air and seawater are set as na = 1 and nw = 1.33, respectively.
Random air-sea interface d
Seabed L
Source
Detector
Fig. 1.
The geometry of NLOS link.
B. Random Sea Surface Model The capillary waves and gravity waves generated by the wind will result in the random surface slopes which can be modeled as a set of small facets. Based on the measurement from Cox and Munk [4], an isotropic Gaussian distribution has been adopted to model the slopes of random sea surface 1 We assume that the direction of beam axis from the source matches the detector position when the sea surface is calm without any slopes.
[5] with the expression as p(zx , zy ) =
zx2 + zy2 1 exp − 2πσ 2 2σ 2
!
(1)
where (zx , zy ) represents the slope of sea surface in the Cartesian coordinate (x, y, z) with zx = ∂z/∂x and zy = ∂z/∂y. σ 2 = 0.003 + 0.00512U is the isotropic variance of slopes where U denotes the wind speed above the surface in unit of meters per second. Note that the slopes for the actual sea surface are asymmetric in the up/down wind and cross wind directions [6]. However, the surface asymmetry has negligible effects on the NLOS system performance when the observation angle is not close to the horizon [7]. Meanwhile, it is also notable that the Gaussian distribution of slopes should be corrected by adding Gram-Charlier series when the effects of skewness and kurtosis are considered. For simplicity, we ignore the effects of skewness and kurtosis in this paper, and directly employ the isotropic form of slope distribution as in (1). Then the probability distribution of the directions of the normal of the facet can be derived from (1) as tan φ2 1 exp − tan φ sec2 φ (2) p(θ, φ) = 2πσ 2 2σ 2 where θ and φ are the azimuth angle and zenith angle of the normal of the facet, respectively. C. Monte Carlo Approach In this paper, we adopt the Monte Carlo approach to model the NLOS UWOC channels. Numerous photons are generated to simulate the absorption and scattering of the medium as well as the reflection events between photons and sea surface, through which the path loss of NLOS link is obtained statistically. The tracking of the trajectory for each photon is summarized as follows. Initially a set of photons is generated with specific position (x, y, z), emitting direction and unit weight for each photon. Then each photon interacts with the seawater and sea surface2 with the attributes of each photon (position, direction and weight) changing along the propagation. The tracking of each photon will stop either the weight is below specific threshold (10−6 in this paper) or the photon reaches the detector. For the former case, the photons are excluded from simulation. While for the latter case, the basic attributes of each photon will be recorded. The path loss is obtained through summing the weight of all arrived photons and then normalized by the total transmit weight. The main purpose of the Monte Carlo approach is to simulate the interactions of each photon with both seawater and random sea surface. The interactions between photons and seawater include the processes of absorption and scattering, which can be simulated similar to the works in [8], [9]. In addition, the Henyey-Greenstein function [6, eq. (3.34)] is 2 Note that there may exist a number of photons which do not hit the sea surface and reach the detector by only interacting with seawater.
utilized as the scattering phase function of seawater to model the channel temporal dispersion. Another key event is the interaction between each photon and random air-sea interface characterized by (1) and (2). When the photons strike the sea surface modeled by a facet, the direction of the facet normal can be obtained by θ
=
ξφ
=
2πξθ Z φ pφ (φ)dφ
(3)
0
where ξθ and ξφ are two uniformly distributed random variables in [0, 1], and pφ (φ) is the marginal probability distribution of φ derived from (2). Note that (1) only describes the slopes distribution when the photons hit the surface vertically, otherwise the slopes distribution should be adjusted according to the approach in [10]. The adjustment of slope distribution can be equivalently treated as the modification of photon weight with details in [5]. After the direction of normal is determined, the direction of reflected photons can be achieved from the incident direction and facet normal based on Snell’s Law. Since the interactions between the beam and surface include reflection and refraction, each reflected photon should be weighed by the reflection coefficient to take into account the effect of refraction. The corresponding reflection coefficient is given by ( h i2 h i2 1 sin(θi −θt ) 1 tan(θt −θi ) + , (θi < θc ) 2 sin(θ +θ ) 2 tan(θ +θ ) i t i t R= (4) 1, (θi ≥ θc ) where θi is the angle between the direction of incident photon and surface normal, and θt is the angle between reflected photon and surface normal. θc = arcsin(na /nw ) is the critical angle of the interface with na and nw as the refractive index of air and seawater, respectively. Note that the rough sea surface may cause each reflected photon hitting the sea surface again which is referred to as multiple reflection process. Therefore, the phenomenon of multiple reflection occurs if a photon emitted from sea bottom still has an upward reflection direction after interacting with the surface. A more accurate scheme might need to be utilized to model the multiple reflection process by setting up a series of facets in specific area with certain spatial resolution of facet size (typical value of spatial resolution ranges from 0.01 m for capillary wave to 1 m for gravity waves) [6]. However, we neglect the trajectories among the multiple reflection events in this work since the link range is larger enough than the spatial resolution. We therefore assume that a photon may hit the sea surface again immediately during the multiple reflection process without internal trajectories and only reconsider its directions. The spatial correlation of slopes introduces wave shadowing which is however ignored since it only affects the path loss when the incident photon is near horizon. Furthermore, the photons are absorbed without any reflections when they hit the seabed.
−30 −40
Path Loss [dB]
−50 −60 −70 −80 −90 −100 10
Calm surface without scattering Rough surface with scattering Rough surface without scattering 20
30
40
50
60
70
80
Link Range [m]
Fig. 2. The path loss for a 20 m depth NLOS link in clean ocean with U = 3 m/s.
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account based on the Monte Carlo simulations. From this figure, we can observe that the random surface generated by the wind strongly degrades the path loss. This is obvious that the random sea surface will diverge the collimate beam. While the scattering light can release this degradation of path loss since the photons diverged by the sea surface may be scattered back into the receiver aperture. Fig. 3 depicts the path loss for various wind speed U in coastal water. The path loss performance degrades for large values of wind speed. This is due to the fact that large wind speed may increase the slope variance and then disperse the beam more heavily in spatial domain. Three curves with various wind speed in Fig. 3 converge to each other as the attenuation length L increases, which suggests that the scattering light may diminish the negative effects caused by the increment of wind speed. This is intuitive since the multiple scattering light becomes dominant in this regime as the attenuation length increases. Therefore the negative effects of the wind speed on the path loss performance can be released by the scattering light, which improves the system reliability. IV. C ONCLUSION
Path Loss [dB]
−55 −60 −65 −70 −75 −80 10
Calm surface Rough surface U = 3 m/s Rough surface U = 10 m/s 15
20
25
30
35
40
45
Link Range L [m]
Fig. 3. U.
The path loss for a 10 m depth NLOS link in coastal with various
III. S IMULATION R ESULTS We consider the NLOS UWOC system with link geometry shown in Fig. 1, and evaluate the path loss performance based on the Monte Carlo approach mentioned above. The characteristics of seawater are summarized as following parameters b = 0.037 m−1 and c = 0.151 m−1 for clean ocean as well as b = 0.219 m−1 and c = 0.398 m−1 for coastal [6]. Fig. 2 demonstrates the path loss of NLOS links in three cases of calm surface (no slopes) without scattering light, random surface (U = 3 m/s) with and without scattering light, respectively. The first case of calm surface without scattering light can be analyzed by the approach in [3] and our results agree with that work. In the case of random surface without scattering light, we omit the interaction between the photons and medium, and only simulate the reflection of random surface. The weight of each received photon is adjusted by multiplying exp(−cl) where c is the attenuation coefficient and l is the corresponding propagation length. In the case of random surface with scattering light, both the interactions of photons between the medium and surface are taken into
In this paper, we have investigated the path loss of NLOS links by taking into account the effects of random sea surface slopes and small forward angle scattering of seawater. Numerical results based on Monte Carlo simulation demonstrate that the surface slopes proportional to the wind speed may strongly degrade the path loss while the multiple scattering light will diminish this degradation. Furthermore, the negative effects of win speed can be released in the regime of large attenuation length. These results are plausible for the NLOS UWOC systems design. R EFERENCES [1] B. Cochenour and L. Mullen, “Channel response measurements for diffuse non-line-of-sight (NLOS) optical communication links underwater,” in Proc. OCEANS Conf. 2011, Waikoloa, HI, Sept. 2011, pp. 1-5. [2] S. Tang, Y. Dong, and X. Zhang, “On link misalignment for underwater wireless optical communications,” IEEE Commun. Letts., vol. 16, no. 10, pp. 1688-1690, 2012. [3] S. Arnon and D. Kedar, “Non-line-of-sight underwater optical wireless communication network,” J. Opt. Soc. Amer. A, vol. 26, no. 3, pp. 530539, 2009. [4] C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the Sun’s glitter,” J. Opt. Soc. Amer., vol. 44, no. 11, pp. 838-850, 1954. [5] C. Mobley, B. Gentili, H. Gordon, Z. Jin, G. Kattawar, A. Morel, P. Reinersman, K. Stamnes, and R. Stavn, “Comparison of numerical models for computing underwater light fields,” Appl. Opt., vol. 32, no. 36, pp. 7484-7504, 1993. [6] C. Mobley, Light and Water: radiative transfer in natural waters. San Diego, CA: Academic Press/ Elsevier Science, 1994. [7] R. W. Preisendorfer and C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Oceanogr., vol. 16, pp. 12931316, 1986. [8] C. Gabriel, M. Khalighi, S. Bourennane, P. Lon, and V. Rigaud, “MonteCarlo-based channel characterization for underwater optical communication systems,” J. Opt. Commun. Netw., vol. 8, no. 1, pp. 1-12, 2013. [9] W. Cox, “Simulation, modeling, and design of underwater optical communication systems,” Ph.D. dissertation, North Carolina State University, Raleigh, 2012. [10] G. Plass, G. Kattawar, and J. Guinn, “Radiative transfer in the earth’s atmosphere and ocean: influence of ocean waves,” Appl. Opt, vol. 14, no. 8, pp. 1924-1936, 1975.
