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Channel capacity study of underwater wireless optical communications links based on Monte
Carlo simulation
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2012 J. Opt. 14 015403
(http://iopscience.iop.org/2040-8986/14/1/015403)
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IOP PUBLISHING JOURNAL OF OPTICS A: PURE AND APPLIED OPTICS
J. Opt. 14 (2012) 015403 (7pp) doi:10.1088/2040-8978/14/1/015403
Channel capacity study of underwaterwireless optical communications linksbased on Monte Carlo simulationJing Li1,2, Yong Ma1,2, Qunqun Zhou1,2, Bo Zhou1,2 andHongyuan Wang1
1 Electronic and Information Department, Huazhong University of Science and Technology,1037 Luoyu Road, Wuhan 430074, People’s Republic of China2 National Laboratory for Opto-electronics, Huazhong University of Science and Technology,1037 Luoyu Road, Wuhan 430074, People’s Republic of China
E-mail: [email protected]
Received 10 August 2011, accepted for publication 30 November 2011Published 22 December 2011Online at stacks.iop.org/JOpt/14/015403
AbstractChannel capacity of ocean water is limited by propagation distance and optical properties.Previous studies on this problem are based on water-tank experiments with different amountsof Maalox antacid. However, propagation distance is limited by the experimental set-up andthe optical properties are different from ocean water. Therefore, the experiment result is notaccurate for the physical design of underwater wireless communications links. This letterdeveloped a Monte Carlo model to study channel capacity of underwater opticalcommunications. Moreover, this model can flexibly configure various parameters oftransmitter, receiver and channel, and is suitable for physical underwater opticalcommunications links design.
Keywords: channel capacity, underwater wireless optical communications, Monte Carlosimulation
(Some figures may appear in colour only in the online journal)
1. Introduction
There is an increasing emphasis on monitoring theunderwater world for scientific, commercial and militarypurposes [1–3]. High data rates communication betweenvarious underwater vehicles and sensors is essential [4].Traditional acoustic transmission technology cannot meetthe bandwidth requirement. Optical wireless communicationprovides an ideal alternative since its carrier frequency ishigher by orders of magnitude [5, 6]. Unfortunately, thepropagation of light in water suffers from both absorption andscattering. The delayed arrival of scattering light relative toballistic light will result in a scattering effect which causesimage blurring and pulse stretching [7–9]. Therefore, theunderwater optical communication channel exhibits low-passcharacteristics and the channel capacity is limited.
One approach for evaluating the channel capacity isto measure the frequency at which the channel responsedecreases by half, or the −3 dB frequency [9]. A laboratorytank experimental study has been made by Mullen et aland the channel capacity of the propagation of modulatedlight in water has been measured [9]. Different amountsof Maalox antacid are added to simulate various waterturbidities. The experimental study of underwater wirelesslight communication gives the characteristics of propagationof light fields and verifies that data rates up to 1 GHz canbe achieved at ranges up to 15 attenuation lengths in theco-polarized reception set-up. However, several variables ofthe water-tank experiment are fixed, including the propagationdistance, receiver field of view and receiver position. Thisis not sufficient for the study of underwater wirelessoptical communication over a wide range of environmentalconditions. Moreover, the channel capacity measured in the
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J. Opt. 14 (2012) 015403 J Li et al
tank with fixed and limited propagation distance is consideredto approximate the condition of varied sea water opticalproperties (namely absorption coefficient and scatteringcoefficient). Whereas for most physical systems, channelcapacity estimation is needed for varied propagation distancewith fixed optical properties. Given the same attenuationlength cd (the product of attenuation coefficient c andpropagation distance d), scattering time delay for a biggerattenuation efficient is supposed to be a nearly scaled versionof that for a smaller one. Thus, generally the channel capacityof a real undersea communications link is different from thatmeasured in the laboratory. Besides, the experimental methodcannot reveal the effect of different transmitter–receiverconfigurations. These are the reasons why we developed acomputer simulation model to flexibly evaluate and study thechannel capacity of undersea communications links.
The Monte Carlo method is the most general solutionfor radiance transfer equation of light propagation inscattering media [10–14]. It has several advantages over theexperimental method. First, related variables can be adjustedconveniently according to real configurations [15]. Second,since a large number (generally 107) of photons is evaluated,the Monte Carlo model can reveal the statistical nature of thescattering channel [16]. Therefore, the Monte Carlo method issuitable for the study of underwater wireless communicationlinks and it is chosen in the study to evaluate the channelcapacity of optical communication links in the sea [17].
The remainder of this paper is organized as follows.Section 2 gives the design details of Monte Carlo radiativetransfer model in the underwater optical channel. Section 3validates our Monte Carlo model against the water-tankexperiment’s result. Section 4 presents a channel capacitystudy of various ocean waters. Discussions of water type’simpact on channel capacity are also given in this section.Section 5 makes the conclusion.
2. Design of Monte Carlo radiative transfer model
Our aim is to analyze the effect of propagation distanceand underwater optical property on channel capacity basedon the Monte Carlo method. The statistical model evaluatesthe receiving intensity by accumulating each photon’s weightwhen it hits the receiver. Thus, the key is to develop thescattering model for every single photon, which is brieflydescribed below.
The Monte Carlo scattering model for every singlephoton is divided into three phases. In the first phase, thescattering direction and random path length between twosuccessive scattering positions is calculated. The scatteringdirection is determined by the azimuth angle θ and thescattering angle ψ . The azimuth angle is sampled from theuniform distribution from 0 to 2π , whereas the scatteringangle calculation is divided into two cases. The scatteringangle of the emitting photon is treated as a special case.In this case, the photon is injected into the sea and itsscattering angle is uniformly sampled between 0 and thedivergence angle of the laser. Otherwise, as the photon isscattered in the sea, the scattering angle is sampled from a
Figure 1. The local and global coordinates of single-photonscattering model.
random distribution obeying the Henyey–Greenstein phasefunction [18]. While the angular distribution of light intensitycaused by multiple scattering obeys the Mie phase function, itis the common method using the Henyey–Greenstein functionto approximate. It should be noted that, to simplify theproblem, the divergence of the laser is set as 0 in this paper.Thus, the initial direction of the photons is along the directionfrom the transmitter to the receiver.
In the second phase, the scattering direction is convertedfrom local to global, as illustrated in figure 1. The azimuthangle θ and the scattering angle ψ is obtained relative tothe local coordinates x′y′z′, where the z′ axis is along theincidence direction. Thus, the outgoing scattering directionneeds to be adjusted relative to the global coordinates xyz. Theorigin of the global coordinates is set as the emitting pointwith the z axis from transmitter to receiver.
In the third phase, the photon is moved from the currentposition to the next position according to the scatteringdirection and random path length. Meanwhile, the photonweight W is adjusted according to single-scattering albedo,namely ω = b/c or ω = b/(a + b), where a, b and c arethe absorption coefficient, the scattering coefficient and theattenuation coefficient, respectively.
The above two phases are recursively evaluated untileither of two boundary conditions is satisfied, i.e. photondeath or reception. As the number of scattering increases, theweight of the photon decreases and has less contribution tothe final statistical data. Thus, a photon is termed as death ifit is less than a predefined weight Wmin. In this paper, Wminis set as 10−10 to balance both simulation time and statisticalaccuracy. Photon reception is determined by the status of thephoton hitting the receiving plane. If the photon is locatedwithin the receiving aperture and the scattering angle is lessthan the field of view (FOV), the photon is received.
Since there are massive photons to be traced and manyof them are supposed never to arrive at the receiver aperturewithin the limited FOV, i.e. have little contribution for the totalreceiving signal amplitude. In other words, vast launchingphotons (≥107) are needed for evaluating the stochasticcharacteristics of the receiving photons at the receiver. Thesimulation will be time-consuming and the result is notprecise. Therefore, we utilize the semi-analytic approachproposed by Pool et al [19]. Once a photon is traced intothe interaction volume restricted by the receiver’s FOV, asmall but finite fraction of the photon will be directed tothe receiver without further scattering. The probability of theportion is defined by the volume scattering function (VSF)
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Figure 2. Plot of the received signal amplitude and the ballistic component as a function of attenuation length. (a) Result reported inMullen’s tank experiment [10] and (b) result from Monte Carlo simulation. Receiving intensity of 11 different modulation frequencies from0 to 1 GHz are measured in (a) and (b). Attenuation length cd is defined as the product of attenuation coefficient and the propagationdistance.
of the medium and the small solid angle subtended by thedetector aperture. By this method 105 photons are sufficientfor our simulation. Thus the computational efficiency of thesimulation is improved significantly.
3. Model validations
For channel capacity study of underwater wireless opticalcommunications links, the initial effort is made by awater-tank experiment. Given the predefined propagationdistance and optical property, the received signal intensitiesare measured for various modulation frequencies. Therecorded result implies that the scattered underwater channelis low pass but cannot reveal the effect of propagation distanceand water quality on channel capacity. To validate our model,the parameters of the Monte Carlo model are set in accordancewith the water-tank experiment and the results are comparedwith the recorded experimental one.
To compare with Mullen’s water-tank experiment studyof received signal amplitude, the simulation is taken using thesame group of attenuation lengths cd, i.e. 1.0, 2.0, 4.0, 7.7,10.6, 12.8, 15.4, 17.6, 20.1, 22.0, 26.4, 30.4, 34.4, 38.4, 42.1,45.8, 50.9 and 56.4 and a refractive index n of 1.33 [9]. Therespective signal amplitude is accumulated over 1 ns which isthe typical integration time of PMT. The receiving of a photonstarts from the arrival of the ballistic signal. The propagationdistance d is set to the length of the tank, i.e. 3.66 m. Theaperture of the receiving iris is 50 mm and the field of view ofthe receiver is 8◦ (full angle). The asymmetry factor g is setas 0.9 [16]. Moreover, the sampling interval of the program isset as 10 ps and the number of emitted photons is 105.
In order to evaluate the channel capacity by our model,a comparison of the model and the experimental result isperformed. Mullen’s work [9] presents two results for us tocompare. First, it gives the receiving intensity as a functionof attenuation length (optical depth) for different modulationfrequencies, as illustrated in figure 2(a). Second, the −3 dBfrequency (frequency at which the modulation depth falls to
0.5) versus attenuation length is also given, as illustrated infigure 3(a). Therefore, our model validation process is dividedinto two phases, namely receiving intensity validation andwater-tank channel capacity validation. The first phase can testthe reliability of the signal amplitude, while the second phasecan examine the validity of time-resolved receiving profile.
Figure 2(b) presents the received signal amplitudecomputed from the Monte Carlo simulation result. Theintensity of the ballistic signal is plotted in figure 2(b)as well, which obeys the exponential decaying rule ofexp(−cd), where c is the attenuation coefficient and d isthe propagation distance in the water tank. All intensitieshave been normalized. The curve set above the slant lineis corresponding to the received intensity with differentmodulation frequencies, while the line below corresponds tothe ballistic component. The same conclusion can be made bythe Monte Carlo simulation as the previous section shows. Thereceiving intensity decreases while the modulation frequencyincreases. It implies that a light pulse with higher modulationfrequency >100 MHz may help suppress forward scatteredlight. This result is consistent with the conclusion presentedin Mullen’s water-tank data [9].
In compliance with the tank experiments, we can observefrom the simulation that, as the attenuation length increases,the scattering component gradually dominates the receivedsignal’s amplitude over the ballistic one. In other words,if the attenuation coefficient is fixed, the scattering effectis growing drastically quickly as the propagation distanceincreases. Although the tank experiment cannot give thedetailed time-resolved profile of this phenomenon, it can beanalyzed in our simulation, as presented in section 4. Togetherwith the fact that the scattering component of the underwaterwireless optical channel results in a low-pass filter-likeresponse, it can be inferred from these two conclusions thatthe cutoff frequency decreases as the propagation increasesundersea.
The simulation result fits Mullen’s published experi-mental one well except for the value of attenuation length
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Figure 3. Plot of the −3 dB frequency (frequency at which the modulation depth falls to 0.5) versus attenuation length. (a) Result given inMullen’s tank experiment [9] and (b) result from Monte Carlo simulation. Note that (a) measures both the co-polarized and cross-polarizeddata and our simulation only calculates the previous one.
of 10.6. This difference is due to the randomness of theMonte Carlo simulation model. Meanwhile, the simulationresult is about an order of magnitude greater than that ofthe experimental one. This can be explained by the differentnormalization method and the predefined photon weight usedin the simulation. In the experiment, the data is comparedto a pre-measured light intensity without adding impurities;while we directly take the light intensity of the first attenuationlength for easy handling.
Moreover, we validate our model by calculating thechannel capacity from the simulated time domain profile.For an underwater optical communications link study, onecommon measure of the channel capacity is the frequencyat which the channel response decreases by a factor of 2, orthe −3 dB frequency [9]. Once the impulse response functionis simulated by our model, the frequency spectrum H(f ) iscalculated and channel capacity is evaluated by taken thevalue at the −3 dB point.
Figure 3 illustrates the channel capacity measuredby Mullen (figure 3(a)) and calculated by our program(figure 3(b)) for seven attenuation lengths. The curves areplotted using piece-wise cubic interpolation. It should bementioned that figure 3(a) presents both the co-polarized andcross-polarized data, whereas our program is only capable ofcalculating the previous one, because polarization cannot bespecified in the Monte Carlo simulation. The simulation resultis nearly in accordance with the water-tank measurement.The difference between the experimental and simulationresults can be explained by theoretical approximations ofthe Henyey–Greenstein function and limited photon samplesused in the stochastic simulation. In compliance with the tankresult, the channel capacity decreases from about 1 GHz to200 MHz as the attenuation length increases from 15.4 to 56.4.Thus it can come to another conclusion that channel capacitydecreases as the attenuation length increases undersea. Morespecifically, it is the increase of the scattering coefficient that
Table 1. Optical properties for three ocean water types used in thesimulation [20].
Water type a (m−1) b (m−1) c (m−1)
Clear oceana 0.114 0.0374 0.1514Coastal oceanb 0.179 0.220 0.399Harbor waterc 0.366 1.829 2.195
a Bahamas (station 8, tongue of the ocean, 1.6 km deep).b Catalina channel (station 11).c San Diego harbor (station 2040).
causes the decrease of channel capacity, which will be fullydescribed in section 4.
4. Simulation results and discussion
Using the above-mentioned model, a simulation experimentis carried out to study the relationship between the channelcapacity of ocean water and the propagation distance. Onceparameters regarding the transmitter–receiver configurationare defined, the corresponding channel response h(t) can beevaluated by piling photon trajectories arriving at the receiverlens with limited aperture.
The optical property of true water is used instead of thatof the experimental water doping by Maalox suspension. Asshown in table 1, our simulation evaluates three kinds ofocean water, i.e. clear ocean, coastal ocean and harbor water.Absorption coefficients and scattering coefficients measuredin three hydrologic stations are used [20]. In typical oceanwaters, the anisotropy factor g for the Henyey–Greensteinfunction satisfies 0.75 ≤ g ≤ 0.95 [21, 22]. Here, we take thetypical value g = 0.9 [16]. Meanwhile, high time resolutionis required for bandwidth evaluation more than several GHz.Thus, we set the sampling time interval to 10 ps by whichthe channel capacity below 100 GHz can be evaluated. Otherparameters regarding the configuration between transmitterand receiver are the same as the tank experiment, i.e. field of
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Figure 4. Impulse response for clear ocean with attenuation length cd = 15.4 and scattering coefficient b = 0.0374. (a) is the impulse timeresponse profile, (b) is the filtered envelope for time response and (c) is the frequency response calculated by FFT.
Figure 5. Impulse response for coastal ocean with attenuation length cd = 15.4 and scattering coefficient b = 0.220. (a) is the impulse timeresponse profile, (b) is the filtered envelope for time response and (c) is the frequency response calculated by FFT.
Figure 6. Impulse response for harbor water with attenuation length cd = 15.4 and scattering coefficient b = 1.829. (a) is the impulse timeresponse profile, (b) is the filtered envelope for time response and (c) is the frequency response calculated by FFT.
view of the receiver FOV = 8◦ (full angle) and the diameterof lens d = 50 mm. It should be noted that full collimationbetween transmitter and receiver are presumed.
4.1. Simulation results for three ocean waters
The receiving impulse response profiles are calculated forthree ocean water types. Figures 4(a)–6(a), respectively,depict the typical simulation results for clear ocean, coastalocean and harbor water when attenuation length cd = 15.4.The vertical coordinate represents the normalized receivingintensity. The horizontal coordinate denotes the receiving timerelative to the arriving instant of the ballistic component,which is set as the origin. It can be observed that thetime-resolved profile patterns for three ocean waters aregenerally different. For clear ocean, the ballistic componentdominates the receiving amplitude, followed by a scatteringcomponent tail whose amplitude is much smaller and less
significant, as illustrated in figure 4(a). For coastal ocean,a scattering component peak which is comparable to theballistic component emerges, as shown in figure 5(a). Thisis due to the increase of the scattering coefficient incoastal ocean. For harbor ocean, the ballistic componentis attenuated severely and hardly noticeable, whereas thescattering component depicts a wide receiving peak, as shownin figure 6(a).
It should be noted that high frequency oscillations exist inthe receiving pulse response. It indicates the high frequencycomponent corresponding to random white Gaussian noiseintroduced by the simulation. To get a better view of theprofile pattern difference in three ocean waters, we adopt aButterworth low-pass filter for digital filtering of data. Topreserve the frequency component generated by the channelresponse, the filter is designed with pass-band frequency ωp =
10 GHz, stop-band frequency ωs = 100 GHz and pass-bandlosses Rp ≤ 0.1 dB, stop-band attenuation Rs ≥ 20 dB. The
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Figure 7. Channel capacity in three ocean waters with 14attenuation lengths. It is plotted by means of piece-wise cubicinterpolation.
results of this processing are shown in figures 4(b), 5(b) and6(b), respectively. The amplitude is also normalized.
The plots in figures 4(b)–6(b) clearly show that thereceiving signal for an undersea communications linkcontains two components: ballistic component and scatteringcomponent. Different types of sea waters generally can becharacterized by the amounts of these two components.As the scattering coefficient is small enough (e.g. clearocean), the scattering component is negligible and only aballistic peak emerges. With the increase of the scatteringcoefficient (e.g. coastal ocean), two components’ receivingpeaks exist simultaneously. When the scattering coefficientis large enough (e.g. harbor water), the ballistic peak isinsignificant and the scattering peak dominates the profile.
To calculate the channel capacity for different waterswith predefined propagation distance, we then evaluate thefrequency response of the filtered signal with FFT (fastFourier transform). The results of this technique are illustratedin figures 4(c), 5(c) and 6(c). Once more, the response isnormalized and the frequency corresponding to 0.5 is taken asthe channel capacity. It can be noticed that, with the increasingof scattering coefficient, the channel capacity decreases. Infact, the scattering coefficient in tank experiments is generallycomparable to or greater than that of the harbor water. Thisis due to the limited tank length and over-doping of Maalox.Therefore, although tank results can provide a candidatereference for system design, the channel capacity measuredin the laboratory cannot be applied to a physical underseacommunications link directly.
4.2. Analysis of results
While figures 4–6 illustrate the typical simulation result ofocean water, the complete result of channel capacity forvarious optical depths is calculated and plotted in figure 7.The calculated points are connected by piece-wise cubicinterpolation. It can be seen that, for a specific water, channelcapacity decreases as attenuation length increases, i.e. channelcapacity decreases as propagation distance increases.
Figure 7 reveals several important aspects for consid-eration involving underwater wireless communications links
design. First, the channel capacity of ocean water decreasessignificantly with the increase of the scattering coefficient.Generally, the channel capacity of clear ocean is a little largerthan that of the coast ocean with the same attenuation length.Also the channel capacity of harbor water is less than thatof coast ocean by an order of magnitude. Therefore, goodwater quality is crucial for high capacity communication links.For the set of attenuation lengths used in the simulation,the channel capacities of optical communication in clear andcoast ocean are on the order of several hundreds of MHz;it is on the order of several tens of MHz in harbor water.Specifically, the channel capacity of clear ocean can achieveGHz as the attenuation length is less than about 15, whichimplies that GHz communication is possible in clear ocean forcommunication distances within 100 m. Second, for a givenocean environment, channel capacity approximately exhibitsan exponential decay as propagation distance increases. Thisprovides us with an easy estimation method in communicationdesign for physical underwater optical links.
5. Conclusion
This paper proposed a Monte Carlo model for channelcapacity evaluation in underwater optical communications.The simulation program based on the model is also developed.The simulation result and the water-tank experiment’s resultexhibit a reasonable agreement. Moreover, the Monte Carlomodel is utilized to simulate the channel capacity for threetypes of ocean waters, namely clean ocean, coastal ocean andharbor water. The simulations show that the water qualityplays a significant role in channel capacity. As the waterbecomes more turbid, the channel capacity budget shoulddecrease simultaneously. The results indicate that the channelcapacities for clean water, coastal ocean and harbor waterare of the order of hundreds of MHz, tens of MHz andMHz, respectively. The developed model and the programcan benefit better understanding of the underwater opticalchannel and the practical design of an underwater opticalcommunications link.
Acknowledgments
The authors would like to thank the National NaturalScience Foundation of China under grant no. 61078062 andthe National High Technology Research and DevelopmentProgram of China under grant no. 2006AA09Z142.
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