Optical plankton: an optical oceanic probing ... - SPIE Digital Library

Journal of Applied Remote Sensing, Vol. 1, 013541 (8 October 2007)

Optical plankton: an optical oceanic probing scheme Debbie Kedar and Shlomi Arnon Satellite and Wireless Communication Laboratory Department of Electrical and Computer Engineering Ben-Gurion University of the Negev P.O Box 653,IL-84105, Beer-Sheva, ISRAEL Phone: 972-8-6477773 ; Fax 972-8-6472949 [email protected]; [email protected] Abstract. In this paper, we evaluate the possibility of a wireless sensor network concept operating in the oceanic environment. A population of underwater sensor nodes, termed "optical plankton," form a distributed sensor network characterized by the deployment of many miniature and low-cost sensors capable of profiling the particulate composition in the immediate marine environs. The stimulation of backscatter signals from the surrounding medium is one principle of operation studied, but the potential for additional probing methods is discussed. The optically probed signal is communicated to a base station, where the large number of received signals is fused to obtain an accurate estimate of the nature of the local aqueous medium. The many similarities and differences between the atmospheric and oceanic sensing and wireless communication environments are discussed and the distinctive features of an oceanic probing system are underlined. Specific scientific applications are briefly reviewed. The challenges to be met are addressed in general and a focused analysis of the specific issue of multi-access interference (MAI), common to all optical wireless-based sensor networks, is presented. Novel analytical approaches have been employed to evaluate and quantify the MAI. It is the object of this paper to assess the feasibility of a novel miniaturized oceanic probing system and explore some of the challenges. It would appear that the proposed scheme could be the basis of an innovative oceanic probing method and fill a niche not as yet catered for with existing technologies. Keywords: Marine optics, backscattering, optical wireless communication, MAI, lidar, wireless sensor networks.

1 INTRODUCTION Gathering data regarding the physical, chemical, topological and biological parameters characterizing the ocean has been of interest to man for many years. The enhanced global environmental awareness witnessed over recent decades has further driven the quest for a better understanding of the ocean’s properties and processes and their influence on global issues such as climatic changes and the health of the planet Earth. The study of marine ecosystems, ensuring port security, monitoring oil pipelines and leaks of hazardous materials in transit are a few of the motivations for profiling the concentrations and distributions of substances in the ocean as well as collecting data on local water temperature, pressure and water circulation patterns. An easily deployed and relatively low cost sensing system in the form of a distributed wireless sensor network (WSN) would cater for an emerging need for extensive time- and space- profiled data on the marine environment as well as freshwater. In most dictionaries, the word "ocean" is given two basic interpretations; firstly it describes the bodies of water covering some 70% of our planet, and secondly it is used figuratively to represent an immense expanse or vast space or quantity without apparent limits. Indeed the most cursory review of the categories of oceanic environments, from nutrient-rich and turbid coastal waters to clear deep ocean waters with different life forms and

© 2007 Society of Photo-Optical Instrumentation Engineers [DOI: 10.1117/1.2803234] Received 13 Jun 2007; accepted 2 Oct 2007; published 8 Oct 2007 [CCC: 19313195/2007/$25.00] Journal of Applied Remote Sensing, Vol. 1, 013541 (2007)

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particulate composition would be an ambitious task and well beyond the scope of this paper. This can be inferred from Fig. 1 which shows schematically on a timescale from seconds to hundreds of years and on a spatial scale spanning ten orders of magnitude a few of the oceanic processes which can be observed [1]. Superposed on the elliptical areas indicating the timescale and spatial range of these processes are rectangles representing the spatial and temporal sampling capabilities of existing observation platforms in use today. A grey dotted rectangle delineates high temporal- and spatial-resolution measurements that are not catered for with existing measuring systems, and could be addressed by our proposed probing concept. These measurements include high resolution measurements of fluorescence decay times, which will enable detection of hydrocarbons in water due to oil pollution, or monitoring the physiological status of algae photosystems. The evolution over time and space of contaminant plumes can be traced with high resolution enabling remedial action to be taken at early stages of an event. These and other applications will require low-cost and easily deployable sensing systems such as can be provided by WSNs. Amongst the numerous techniques for sensing the ocean, both remotely and in situ, many are concerned with the optic properties of seawater and of the many organisms and substances suspended in it. The depth of penetration of solar illumination determines the degree of photosynthetic life that can be supported, and is itself determined by the absorption and scattering properties of the seawater and its contents. Light transmission is highly wavelength sensitive, due to the spectral dependence of scattering and absorption, falling sharply from near 100% per meter in clear ocean water for light of wavelengths 400 – 500nm to near zero for turbid waters and wavelengths below 300nm and above 700nm [2], [3]. The amount of light scattered between 900 and 1800, that is in the backward direction, is an important inherent optical property, which is independent of the spatial distribution of the impinging radiation. Measurements of this phenomenon have been considered a reliable indication of the irradiance reflection, the remote sensing reflectance, the particulate composition of the vicinity and hence the bulk index of refraction of the local body of water and are treated in greater detail in references [4] - [7]. The addition of ancillary information such as photosynthetic pigment concentration, gathered on the same measuring platform further enhances the usefulness of backscattering data.

Fig. 1. Schematic temporal-spatial representation of oceanic processes (in ellipses) and sampling capabilities of three platforms (in rounded rectangles), showing "grey area" which could be served by optical sensor networks. Adapted from reference [1].

Journal of Applied Remote Sensing, Vol. 1, 013541 (2007)

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In contrast to scientists exploring the oceanic composition, underwater photographers consider light scattered in the backward direction to be a major source of image degradation. One tactic to overcome the blurring of underwater images due to the reception of backscattered light is using range-gated lidar, whereby a pulse of light is fired at the object to be imaged while the camera is gated to accept the reflected light only during a short time interval determined by when light reflected from the object is anticipated to arrive at the camera aperture. Thus, the unwanted backscatter light from the intervening medium is not received and the image quality is greatly improved [8]. The concept of lidar is familiar in atmospheric probing, where light backscattered from aerosols and particles is received and used to profile the composition of the atmosphere [9], [10]. However, underwater lidar for the purpose of probing oceanic particulate composition has not been applied widely, although a few research efforts have been reported both in the sphere of earth science [11] and for pollution monitoring using fluorescence measurements [12]. We will outline a novel miniaturized probing method, based on the lidar concept but embedded in a sensor network concept and thus augmented with the accompanying versatility and easy deployability. A major drawback in using lidar underwater, by comparison with atmospheric systems, is the very high attenuation of light in seawater. This has also severely hampered the wide application of underwater optical wireless communication (OWC). Recently, renewed interest has been expressed in this field, particularly for military applications [14]. The need for underwater wireless communications, such as between submarines and networked sensors, has been met in the past using sonar communication. However, with sonar (acoustic) communication only limited data rates are possible, so that for present day communication needs a carrier that can support high data rates, such as radio and optical wireless communication, is sought. Sonar communication is also unsuitable for applications where compact and inexpensive systems are needed because, unlike OWC equipment, its hardware is bulky and costly. Seawater is almost totally opaque to radio frequency waves so that only OWC remains as a potential alternative to sonar communications for short ranges underwater. Another important development promoting OWC is the emergence of inexpensive highly luminescent light-emitting-diodes (LEDs) at a number of wavelengths. These light sources have low power requirements while delivering several watts of optic power. We have recently published research proposing a novel atmospheric probing concept, which we have named "laser firefly clusters" [10], [14]. The laser firefly cluster is a mobile, flexible and versatile distributed sensing system, whose purpose is to profile the chemical and particulate composition of the atmosphere for pollution monitoring, meteorology, detection of contamination and scientific research. The fireflies are deployed in situ at the altitude of interest, and evoke a backscatter response from aerosols and molecules in the immediate vicinity using a coded laser signal. In this paper we investigate the potential of an underwater miniature distributed sensor system modeled on the laser firefly concept and termed "optical plankton". We have established that there is a growing interest in probing the ocean’s particulate composition, which will call for low-cost and easily deployable sensor systems. However, the marine environment is a challenging communication channel, and we wish to study the potential of a low-cost, easily deployable, intelligent wireless sensor networks to perform the task of oceanic probing. In the next section we outline the special features of distributed sensing and briefly describe the concept of optical plankton. In section three we elaborate on the proposed optical plankton system and discuss the major problems arising, and possible solutions as well as niche applications that can be addressed. In section four we present a numerical example demonstrating the theoretical feasibility of optical plankton, focusing of the issue of multiple access interference (MAI) and discuss the results. In the fifth section we summarize.


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2 DISTRIBUTED SENSING FOR PARTICULATE PROBING The essential feature of a distributed sensor system is the amalgamation of sensing, communication and data processing functions within each miniature sensor node [15], [16]. A very large number of sensor nodes is deployed within a region of interest where they record a parameter of interest, which may be temperature, salinity, magnetic field strength, acceleration or one or more of many other possible measurable variables. The data may be sensed continuously, sporadically or on demand, and then stored or transmitted according to some predetermined plan or as needed. The cumulative data can provide a comprehensive picture of the spatial and temporal spread of the parameter under investigation, and measurement accuracy is enhanced by the high redundancy of samples. The areas of application include medical, agriculture, home security and environmental monitoring to name a few, and atmospheric probing for meteorological, scientific and pollution studies is potentially a prime candidate. Equally, monitoring the chemical, physical and biological composition of the ocean is of interest to scientists, environmentalists and law enforcement authorities. The data may be communicated from one sensor to another or directly to a more sophisticated base station (BS) where central data processing and decision-making is performed, and control mechanisms or alarms may be activated. Energy-efficient wireless communication is essential for the functioning of autonomous sensor nodes and low cost per node is crucial considering the large number of nodes deployed. The extent, spatial and temporal resolution, processing capabilities, low cost, scalability and autonomy of wireless sensor networks render them a different generation of monitoring technologies that can address new sensing needs as well as complementing existing techniques. Rather than challenging existing data-gathering equipment in reliability, robustness and longevity, the distributed sensor network meets the needs of extensive sensing tasks, high resolution parameter profiling and intelligent data-fusing in an inexpensive way and in a readily deployable fashion. 2.1 Optical plankton for oceanic probing The optical plankton are miniature semiconductor laser devices with photodiodes, communication control and data processing facilities incorporated. A bloom of hundreds of plankton is deployed in the marine environment/estuary/lake at a location of interest. A probing signal from the sensor node (plankton) elicits backscatter, which is the sought data indicating the particulate composition in the immediate neighborhood of the shoal in our current study. The location of each sensor node must be calculated and could be obtained from reflected interrogation signal transit times and from the spatial position of the return signal on a matrix detector. The data-carrying signals from each node to the BS must be distinguished from one another, for instance using CDMA-type codes, to minimize MAI. A basic sensing task of the optical plankton is to evoke a backscatter signal from the molecules, air bubbles and particles in its immediate vicinity, but additional sensors may be co-located on the node, including additional optical sensing platforms such as fluorescence sensing yielding photosynthetic pigment concentration and augmenting the information gathered from the probed location. Emitted light is reflected backwards, or backscattered, by the different particles and the backscattered light is received on the optical plankton, where it is processed and stored. The need for a low-cost, miniature in situ probing system that can profile the composition of oceanic waters is evident. From Fig. 1 we can see that spatial resolution of millimeters to meters, and temporal sampling of seconds to hours over periods of days is not currently served by existing platforms. The growing interest in gliders and Lagrangian self-recording floats for multidimensional, high resolution, portable and scalable platforms further corroborates the existence of a niche for oceanic probing systems of the nature of optical plankton [6], [15].


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The severe attenuation of propagating light in seawater restricts the transmission range so that the cluster of optical plankton will not be able to stray far from the BS. However, the BS may be connected to other BS’s in a network with wired connections using optical fiber, and subsequently connected to a mooring, autonomous underwater vehicle (AUV), glider or other platform. In this paper we focus our analysis onto assessing the operability of a cluster of sensor nodes (or shoal of optical plankton) communicating with a single BS. We assume that the numerous other technical challenges of deploying the nodes, etc. have been addressed within the overall system design and do not relate to these, albeit non-trivial, design issues herein. The media of the atmosphere and the ocean are similar as channels for OWC in that in both cases absorption by particles and molecules, scattering by the air/water and suspended matter and turbulence due to the changing refractive index of the medium due to eddies attenuate and spread a pulse of light. However, there are distinct differences in the requirements of a communication system operating in each medium. In the following we will contend with the similarities and differences in the context of a distributed sensing system with the objective of probing the composition of the medium, which is also the communication channel.

3 THE PROPOSED SYSTEM In this introductory paper, the operability of an optical plankton shoal-BS unit will be examined theoretically from the four constituent viewpoints of the probing task, the data communication with a BS, the location determination and the multi-access interference. Additional issues will need to be addressed in future work. To this end we will first summarize some basic relations and research results in marine optics. The attenuation of light propagating in an aquatic medium is wavelength dependant and a result of the cumulative effects of absorption and scattering, governed by the absorption and scattering coefficients α (λ ) and b(λ ) respectively. The total attenuation is described by the extinction coefficient

c(λ ) , which is related to α (λ ) and b(λ ) by the simple relation [3] c ( λ ) = α (λ ) + b (λ )

(1)

In accordance with Beer’s Law, the reduction in radiant flux, Φ , with distance r from a source is proportional to the initial radiant flux, the distance traversed and the coefficients governing extinction by absorption and scattering. This can be summarized as

⎡ ( ∂Φ (r , λ ) )abs + ( ∂Φ (r , λ ) ) scatt ⎤ c (λ ) = − ⎢ ⎥ Φ (r , λ )∂r ⎣ ⎦

(2)

where the loss of radiant flux has been separated into loss due to absorption

( ∂Φ(r , λ ) )abs and loss due to scattering ( ∂Φ(r , λ ) )scatt . The loss of radiant energy due to

absorption is rectilinear, while the energy loss due to scattering has directional properties described in the volume scattering function (VSF) β (ϑ , ϕ ) where ϑ and ϕ are the polar and azimuthal angles of scattering respectively. Recalling the following definitions for the irradiance Einc impinging on an infinitesimal area dS, and the radiant intensity I emanating into an infinitesimal solid angle dΩ


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dΦ dS dΦ I= dΩ Einc =

we can write

(Wm-2)

(3)

(Wsr-1)

(4)

β (ϑ , ϕ ) due to unit scattering volume dV as β (ϑ , ϕ ) =

dI (ϑ , ϕ ) Einc dV

(m-1 sr-1)

(5)

Noting that dV = dSdr and d Ω = sin ϑ dϑ dϕ , and assuming that scattering is axially symmetric so that the volume scattering function has no azimuthal dependence, we can now define the inherent optical property b(λ ) in terms of the VSF for a given wavelength π

b = 2π ∫ β (ϑ ) sin ϑ dϑ

(6)

0

Further distinguishing between scattering in the forward and backward hemispheres, represented by subscripts F and B respectively, such that

b = bF + bB

(7)

we may now define the backscatter coefficient as π

bB = 2π

∫ β (ϑ ) sin ϑ dϑ

(8)

π /2

3.1 The probing task The accurate measurement of the backscatter coefficient is notoriously difficult involving summing many small-angle-shifted irradiance measurements. A simple linear relation between the scatterance at 1200 and the backscatter coefficient of different oceanic water types and with different suspended particle distributions has been uncovered by Oishi [18]. Boss and Pegau [4] further elaborated on this observable and measurable phenomenon and posed theoretical validation on the basis of the small variation in the ratio of the VSF and the backscatter coefficient around 1200 with different common particle distributions coupled with the insensitivity of this ratio to the contribution of the water matrix to the overall VSF at that angle. While more accurate measures are now possible with recently developed specialist test equipment [19], the approximate result using irradiance measurements at one angle will be the basis of our optical plankton proposal since we are seeking compact, mobile and inexpensive methods of obtaining data on the oceanic composition. The probe signal is a narrow-divergence-angle light source, while the on-board receiver will have a narrow fieldof-view receiver tilted at 300 to the perpendicular so as to capture the light scattered at 1200 and originating in a small "slice" of the adjacent water. The arrangement is sketched in the enlarged insert in Fig. 2. It is clear that the distance from the scattering volume to the sensor is of the order of magnitude of the transmitter-receiver separation on the optical plankton, so


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that a miniature sensor node of the order of millimeters in size would elicit and receive backscatter from a volume only millimeters away. Thus the attenuation due to the propagation medium would be low, and the received backscatter would faithfully represent local oceanic composition.

Fig. 2. Schematic illustration of a shoal of optical plankton transmitting data signals to a base station receiver showing aperture, spectral filter and matrix detector. A detail of the probing signal is in the enlarged insert.

3.2 The data communication to the base station Once the data has been sensed it must be wirelessly transmitted to the BS. In contrast to atmospheric OWC, the restriction on transmitter power due to eye-safety considerations is not an impediment and lasers or LEDs emitting several watts of power can be used [13]. The scattering nature of seawater would spread laser light and degrade the beam quality rapidly, so that we consider the use of less costly highly luminescent LEDs to be preferable. Moreover, the optical plankton would be likely to be in a constant state of drift in the water so that tracking and alignment issues would be alleviated with a large divergence communicating beam as could be obtained with a LED. It could be argued that wired communication using optical fibers would mitigate many of the problems encountered in wireless communication and could simultaneously combat the inherent problem of driftinduced sensor node dispersion, but this would be at the expense of the considerable system flexibility, versatility, scalability and simplicity afforded by wireless communication and is suitable for a different overall approach.


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The choice of transmission wavelength is not straightforward. It is commonly accepted that blue-green wavelengths suffer less absorption in seawater than longer wavelengths, but they also suffer more scatter from tiny particulates and bubbles in the water. Additionally, aquatic particles such as chlorophyll, algae, or phytoplankton have specific absorption patterns, which might lead to an absorption minimum at different wavelengths [20]. Furthermore, the wavelength-sensitive characteristics of the receiver photodiode are an important factor in achieving a viable communication link and, for instance, the quantum efficiency of silicon photodiode detectors for red light is generally twice its value at blue light. In conclusion, the best wavelength for the desired application depends on the implementation and the environment, and should preferably be determined experimentally. A numerical treatment of the complex trade-offs in system design and system performance analysis using commercial off-the-shelf components can be found in [21].

3.3 Sensor node location Since the optical plankton will not be able to transmit to the BS beyond a range determined by the optical properties of the local seawater and the sensor node LED characteristics, it may not be necessary to invest in a sensor node location contrivance. The transmission range would then be the spatial resolution of the data sampling. However, if the precise location of each optical plankton is required, this can be achieved using an interrogation signal from the BS that is retroreflected from the sensor node; the delay in return indicates the transit distance and the return signal location on a detector matrix indicates the angular position relative to the BS. If we allow the BS to bear an array of tens of LEDs, then we could overcome the significant attenuation of the light encountered on the double journey from the BS to the node and back. In its simplest form this would only require the installation of a polished retroreflecting mirror on the base of the optical plankton. On this point it is essential to acknowledge the widespread issue of biofouling on optical surfaces that limits the operational lifetime of underwater instruments and requires consideration in system design.

3.4 Multi-access interference A major problem encountered in distributed sensor networks where numerous sensor nodes communicate their data simultaneously to a BS is multi access interference (MAI). One possible solution would be by orthogonally coding the data signals from each sensor node. Since the co location of two or more sensor nodes in the cone defining the field-of-view (FOV) of one pixel in the matrix detector could cause MAI, this could be combated by using a detector with many pixels. The consequent FOV cone would then be very small and only few sensor nodes would be likely to be co-located. Hence, short orthogonal codes would suffice and the encoder on the node would not be very complex. However, we consider this regime to be impractical in the optical plankton system; firstly because the highly scattering and attenuating medium would distort the signal and make decoding very hard, and secondly because the short transmission range would necessitate very dense deployment of nodes in order to glean adequate data, and then many plankton would be co located in a FOV cone and long orthogonal codes would be needed. Therefore we propose a solution in the form of spectral diversity. Narrow spectral ranges could be allotted to each optical plankton for transmission of data, while the BS could apply filters in turn to open a time window for each spectral transmission (see Fig. 2). Other sources of illumination (fluorescence, Raman scattering etc) would likewise be filtered out although interfering unmodulated light would not be very troublesome as it could be easily rejected by a simple algorithm at the base station receiver. If two or more plankton operating at the same wavelength are in the same FOV cone of a single detector in the matrix, there are three possible scenarios: i) they are so close that the


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aggregate return signal is just a multiple of the individual signal – this is in fact advantageous; ii) they are sufficiently far apart that they can easily be separated; iii) they cause multi-access interference and then their return signals are rejected and the BS filter is tuned to another wavelength. Regarding the timing of the data signals; we could avoid interrogation-triggered data transmissions to simplify the optical plankton’s communication control circuitry, by sporadic and repeated transmission of data by each optical plankton at random intervals. The duration of signal repetition sequences would be timed to capture a time slot at each spectral range.

4 NUMERICAL EXAMPLE AND DISCUSSION In order to evaluate the viability of the optical plankton concept we first examine the relationship between the node density, the number of pixels in the detector matrix and the number of co located sensors. Next we infer the scale of the spectral diversity and consequent complexity of the system. The maximum distance of a sensor node from the BS from which a transmitted signal can be detected is a function of the optical properties of the medium and the power and divergence of the source. We term this variable M and calculate the average number of nodes co located in the FOV cone of a single detector in the matrix as a function of it. Defining PT as the signal power of the plankton’s data-carrying transmitter, PRmin as the sensitivity of the individual photodiode in the BS receiver’s matrix detector and accordance with Beer’s Law, M can be written as

M=

⎛ P 1 ln ⎜ T c(λ ) ⎜⎝ PRmin

For instance, for c (λ ) = 0.2m

−1

c(λ ) as in equation 2, then in

⎞ ⎟⎟ ⎠

(9)

a maximum transmission range of 3m could be achieved

with a PT / PRmin ratio of 1.8, while this ratio would need to be 7.4 for a transmission range of 10m. We define the node volumetric density as D (m-3), and define the average number of nodes co located in the FOV cone of a single detector in the matrix as N. Assuming the FOV cone half angle of the receiver, determined by the optics and detector matrix size, is γ we can now define

⎡ π DM 3 ⎛ γ ⎞⎤ N =⎢ tan 2 ⎜ 2 ⎟ ⎥ ⎝ n ⎠⎦ ⎣ 3

(10)

where [x] implies the nearest integer to x and the detector matrix is assumed to be a square array of n x n pixels. Having established N, we proceed to determine the optimal number of wavelengths in our spectral diversity scheme, Λ . In the ensuing calculation we ignore the "self-shading" that would be caused by plankton blocking the transmission of other co-located plankton and hence derive upper bound performance data. The number of possible combinations of optical plankton data transmission wavelengths λi ;


i = 1, 2,...Λ in N is written

[N ]

Cλi . The number

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λi , and resulting in MAI at that wavelength is qi. We can now derive the probability of MAI for a given N and Λ to be of optical plankton transmitting at the same

Λ

N

i =1

qi = 2

p ( MAI ) = ∑ p(λi ) ∑ p (qi )

(11)

where p ( qi ) is the a priori probability of qi optical plankton transmitting at the same

λi

and

p(λi ) is the a priori probability of λi. If each

λi

is equiprobable equation 11 reduces to p ( MAI ) =

N

∑ p(q ) . In the interest of i

qi = 2

simplicity of system design we wish to work with a minimal value for Λ while for best performance we wish to minimize p(MAI). We have calculated

N

Cλi for N from 2 to 6 and

Λ from 2 to 4 and computed the resultant p(MAI) assuming equiprobable λi .

Fig. 3. Graph showing average number of co located sensors in a single detector FOV cone as a function of maximum transmission range for three values of sensor node density D; detector matrix size 4 x 4 pixels, total receiver FOV = 0.1 rad.

Figure 3 shows average number of co located sensors in a single detector FOV cone as a function of maximum transmission range up to a maximum value of 5 meters for sensor node densities of 1000 m-3, 2000 m-3 and 5000 m-3, and for a 4 x 4 pixel array detector matrix and with a total receiver FOV cone half angle of 0.1 radians. With this narrow FOV receiver, no more than five optical plankton would be expected to be co located in one detector FOV cone for transmission ranges of 5 meters, even with a 4 x 4 pixel array when the node density is 1000 m-3. The range at which less than two optical plankton would be expected to be co located in one detector FOV cone is 3.35 meters and would drop to 2.7 meters if the node


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density were raised to 2000 m-3. Increasing the node density to 5000 m-3, which can be considered a limiting case, would lead to approximately five optical plankton co located in one detector FOV cone for a transmission range of 3 meters, rising to 25 for a 5 meter transmission range system.

Fig. 4. Graph of probability of multi-access interference (MAI) and probability of NO multi-access interference (NMAI) vs. average number of co located sensors for three spectral diversity schemes.

Figure 4 shows the probability of obtaining MAI, p(MAI), as a function of the average number of co-located optical plankton, N, which, in turn, reflects the system and environmental parameters through M, as described in equation 10, for three different values of Λ . As one would expect, p(MAI) increases with N for a given Λ as more plankton with the same data transmission wavelength will be co located in one detector FOV, and decreases with Λ for a given N as the spectral diversity reduces the incidence of interference. The tradeoff between simplicity of system design (fewer wavelengths) and increased dud transmissions (MAI) will be dependant on the redundancy in the system. For instance, in the case of N = 3 it may be worth using a 4-wavelength system rather than a 3-wavelength system and reduce p(MAI) by 33% from 0.3 to 0.2, while if N = 6 and there is sufficient redundancy to support a p(MAI) of near 0.5, the reduction of p(MAI) from 0.536 for a 3-wavelength system to 0.417 for a 4-wavelength system (around 12%) may not justify the additional complexity. It should be noted that MAI does not necessarily contradict the acceptability of the transmission. In future work distinction will be made between cases where two, three and more co located plankton transmitting at the same wavelength cause MAI and a graded penalty will be attributed to the transmissions where the MAI is likely to be more contaminating. It should also be noted that, if MAI results in the rejection of a transmission, the probability of successful data signal reception is not simply (1- p(MAI)) since there are combinations of optical plankton where one or more λi are not present so that when the filter


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in the BS is tuned to that

λi

there will be no data signal reception regardless of the number of

optical plankton present. We have added to the same figure the probabilities of no MAI, p(NMAI) encountered. As N increases, the probability of a combination of λi with no MAI falls, but this is more severe for lower values of Λ . The data is summarized in Fig. 5.

Fig. 5. Graph of ratio of probability of NO multi-access interference (NMAI): probability of multi-access interference (MAI) vs. average number of co located sensors.

The efficacy of using a larger Λ is clearly evident in that the ratio p(NMAI)/p(MAI), which is shown as a function of N, is consistently higher for larger values of Λ . This metric encompasses the disadvantage of a high incidence of MAI coupled with the benefit of a higher probability of wavelength combinations with no MAI and is thus may be considered a suitable measure of "performance".

5 SUMMARY In this paper we have sketched a novel distributed sensing scheme for profiling the marine environment based on lidar methods and termed "optical plankton". We have expanded on the niche that such a system could fill within the growing area of oceanic studies and discussed the requisite design features to render a wireless sensor network suitable to the underwater environment. By addressing the potential obstacles to the proposed underwater optical oceanic probing scheme, we have described a plausible sensor network arrangement and have demonstrated the feasibility of optical plankton with a brief numerical study. We have focused on possible solutions to the problem presented by MAI and investigated the potential of a spectral diversity scheme using a novel analytical approach. Future work is required to validate the theoretical approach in an experimental study.


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