Work on channel modelling and characterisation

The modelling and characterisation of UOWC is the main step towards understanding the behaviour of the channel in order to implement the UOWC system successfully. There has been a significant amount of work conducted over the years in this area, experimentally, analytically or numerically (simulation). In terms of experimental work in characterising the underwater channel, the pioneering work has been conducted by a team in Naval Undersea Warfare Centre, USA [27, 28]. From the laboratory test conducted, the feasibility of the system operating in MHz range was demonstrated. At Naval Air Systems Command (NAVAIR), Cochenour and his team have been doing extensive experiments since 2006. Initially, they conducted an experiment based on a 3.66 m water tank for measuring temporal dispersion. From the preliminary results obtained from the experiment, they managed to prove that multiple scattering are not significant when the data rate is 1 Mbps. However

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they highlighted that their observations were limited to a short distance of 3.66 m and the pointing inaccuracies were only 5 [29]. Next in [18, 30] they investigated the spatial distribution and temporal dispersion and measured the beam spread function (BSF). They proposed a theoretical model for BSF which is accurate to 12 attenuation length (AL). In 2013, further effort was taken in conducting an experiment to characterise the temporal dispersion using a high dynamic range and high sensitivity equipment. The work was then expanded to study the effect of transmitter and receiver misalignment, receiver FOV and scattering particles on temporal dispersion.

Apart from experimental work, there is also a considerable amount of work reported in modelling the UOWC using the MC method. This technique of modelling the underwater channel is preferred as it is simpler when the difficulties and high cost experimental setup can be avoided [31, 32]. This also solves the limited propagation distance issues and limited freedom in varying system parameters [33].

An early work pioneered by Jarutanawadilok used vector RTE that includes the polarisation effect in modelling the UOWC channel. In his work, MC simulation was used to quantify the effect of scattering by investigating the bit-error-rate (BER) performance [34]. Hanson and Radic also used MC simulation to measure the temporal dispersion in UOWC links apart from their experimental work [35]. They concluded that for moderate ranges a data rate of more than 1 Gbps can be achieved. In [36], the impulse response of the underwater channel

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was investigated by using semi-analytic MC to improve the efficiency of the MC simulation. His simulation results were compared with the experimental data obtained in [37] where reasonable agreement was achieved.

In [38] the path loss and frequency response of UOWC were studied in various types of water. The effect of receiver aperture and receiver FOV are investigated. They demonstrated that the FOV significantly affects the path loss and bandwidth. It was concluded that for a collimated beam several GHz bandwidth can be achieved for on-axis locations. Similarly, in [39], MC method was used to investigate the performance of diffuse channel. In their model, they incorporated several system variables such as transmitter (Tx) and receiver (Rx) characteristics. They studied the delay spread of the channel and concluded that it was negligible except in turbid water. In addition to that, the path loss performance and the bandwidth performance of reflective NLOS links were also investigated in [40, 41].

A closed form double Gamma function to model the impulse response for coastal and turbid water was proposed by Tang et al. in [42]. He used MC simulation to compare the results and observed agreement between them. A further step was taken in [43, 44] in which a weighted Gamma function was proposed to model the impulse response of the UOWC multiple-in-multiple-out (MIMO) links.

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In addition to the simulation works, few mathematical models have been developed in understanding UOWC. Doniec et al. proposed a signal strength model where he considered the source effects in the equation [45]. However, it is limited to clear water only. A mathematical formulation of MC model was proposed by Dalgleish et al. to calculate the impulse response over a wide range of operational and environmental scenarios. They also proposed a stochastic process detector noise model that shows good agreement with the experimental validation [31, 32 and 44] .

Contrary to most of the work done to model the channel horizontally, a vertical link is considered by Johnson et al. in channel modelling where a mathematical model to calculate the variations of the attenuation coefficient due to the water depth is proposed [47]. Recently, a stochastic model was proposed in [48] that can be used to study the spatial and temporal distributions of photons. This model includes ballistic photons, single scattering and multiple scattering in their derivations where it it can be treated as a generic model for UOWC. Table 2.5 summarises the work done in channel modelling and characterisation highlighting their contribution.

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Table 2.5: Summary of works on channel modeling and characterisation.

Year Author Method Links Contributions (Parameter studied) 2008 Hanson [35] _Experiment MC Collimated _LOS Impulse Response _{Path Loss}

2008 Jarutanawadilok [34] Vector RTE Collimated _LOS Path Loss _BER

2012 Cox [38] MC Collimated _LOS Frequency Path Loss Response

2012 Cochenour [14] Experimental Collimated LOS Diffuse NLOS

Frequency Response Beam spread

Function

2013 Gabriel [39] MC Diffuse NLOS _{Impulse response} Path Loss

2013 Li [36] Semi analytic _MC Collimated _LOS Impulse response

2013 Doniec [45] Experimental _Analytical Diffuse NLOS Signal Strength

2013 Tang [40] MC Diffuse NLOS Impulse response

2013 Johnson [47] Numerical Analytical

Experimantal Collimated

Path Loss (vertical)

2014 Dalgleish [31] Analytical MC

Experimental Collimated Impulse response

2014 Dong [44] MC Diffuse MIMO Impulse response

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