Seasonal Temperature Dependence of Availability of Under-Water Visible Optical Communications through Egypt Nile River Water

Underwater visible optical communications become very important for their high velocity and more data rate. But the optical is suffering from the high water attenuation. For optical communication. Pure water is the best of the ten water types with wavelengths λ = 455 and 486 mm . The Nile river water is a pure water without salinity (fresh water). The temperature of the water is daily changes and so the performance of optical communication underwater becomes temperature-dependent. A simplified expression very good accuracy of Egypt Nile water to determine the water refractive index, water dispersion, water attenuation, received optical power, and SNR as direct temperature dependence is done. The optical channel loss model is used to determine the received optical power and the ray trace model is used to define optical radiation pattern. The equation of optical received power by ray trace is the same as that by using the optical channel loss model except for the transmitter gain of them are different. F or λ=486nm with water temperature varying from 4 o C to 30 o C, the corresponding refractive index decreases from 1.3399 to 1.3379 (so, the optical velocity under fresh water increases from 2.239*10 8 m/s to 2.2423*10 8 m/s), dispersion decreases from 0.6492 to 0.6459 (ps/m nm), attenuation factor decreases from 0.0378 m -1 to 0.0345m - 1 and so the required transmitted optical power due to attenuation for 800 m long shrinks to 7.4 %. The Effect of temperature becomes more evident with more link distance. The required transmitted power to achieve the required SNR increases with the more data rate. To overcome the unavailability of the link due to water temperature, the transmitted power must be controlled by the daily water temperature. In this study, the temperature dependence of the performance of the optical link and a simulation proposed example design is done. loss


I Introduction
The underwater visible optical communications become very more important to the degree there are multi researches to develop this technology [1]- [10]. Until now, the aims of researches are optical communication underwater links with large distance and high data rate (bit rate) [11]. Underwater communications are required in many applications such as the transfer of messages and speech transmission between submarine ships [8]. The main challenge of this technology is the high water attenuation (absorption and scattering) of optical waves [3]. Also the varying seasonal water temperature (approximately from 5 o C to above 30 o C). The blue/green band of 430 to 550 nm gives a lower attenuation of the visible spectrum [3], [9] and the leader wavelengths are λ=455 and 486 nm (with pure water [9], [12]. Water attenuation (α m -1 ) depends upon the type of water. Pure water is one of the tenth water types [13].
Water is classified according to the attenuation coefficient (αFW) [1]. The Nile River water is fresh water (pure water without salinity and perhaps there is very little particulate concentration). Pure water has an absorption greater than scattering [14] and in the pure sea water (Cc=0.005 and α=0.043 m -1 [10], [15]). The value of αFW increases with the temperature at wavelength λ=455nm while it decreases with temperature at wavelength λ=486nm. And so, with λ=455nm, as the water temperature increases, the allowed link distance, the received power and the SNR are lowered but vice versa with λ=486 nm. The speed of the optical wave in water is approximately 0.75 of the speed of light in vacuum (where water refractive index around 1.34) and it increases with increasing both temperature and wavelength. The dispersion of water decreases slowly with temperature and so the allowed data rate increases with temperature.
The Beer's law [1], [15] is used with a link distance less than the diffusion length [9], [15]. But the modified Beer-Lambert law is used with a link distance greater than the diffusion length. [3], [9] With a narrower transmitter half-power angle (φ1/2) the power density becomes better, also, the underwater channel could be regarded as a non-dispersive medium [3] Single LED is generally modeled by means of a generalized Lambertian radiation pattern [11]. The receiver cross-section area is small (around 400cm 2 ) and so the distributions of both the received power density and SNR are approximately uniform inside the received area. The link availability of the required transmitted power is the smaller value of the required transmitted power due to attenuation and due to SNR. The pass optical loss model [16], [17] gives the received optical power and the SNR therefore the availability of the optical link and the ray trace model [9], [11], [18], [19] is used to study the power pattern through the propagation distance.

In this study
The optical wave propagation under-water is studied by using both the ray trace model [9], [18], [19]and the optical channel model [1], [20]. The equation of received power of the ray trace model is converted into the format of the optical channel losses model. The difference between the two models is the transmitter gain. The ray trace model gives a good description of the optical transmission. . A simplified expression with very well accuracy for fresh water (Egypt Nile River water) to define the water refractive index (nFWT), water dispersion (DFWT), water attenuation (αFWT), received optical power (Pr) and SNR as a direct temperature dependence are done for temperature changes from 5 o C to 40 o C (seasonal changes in temperature) with leader wavelengths (λ=455 and 486nm) and without particulate concentration (i.e. Cc=0 mg/m 3 ). A proposed simulation design of underwater optical communication links is done. (1) Where, 1 = 0 + 1 2 + ( 2 + 3 ) + 4 2 + 5 3 = 1 + 10 −8 { 1 2 ( 2 − 2 ) + 3 2 ( 2 − 4 ) } Constants a1 -a5 and k1-k4 are stated in Appendix A.1.1. As the temperature and wavelength increase, the refractive index decreases as shown in Fig.1 and as explained in [13]. Therefore the optical wave velocity increases with water temperature.
ii-The dispersion of unguided wave is considered as the material dispersion (DFW) [22] ; Fig.2, as the temperature increases, the dispersion decreases slowly. While as the wavelength increases, the dispersion decreases. Therefore the data rate (Br) increases slowly with temperature.

II.1.2Attenuation of fresh water
Attenuation of fresh water is the summation of the absorption (aFWT m -1 ) and scattering (bFWT m -1 )

IV-Water losses
If the propagation is a line of sight (LOS) and with link distance (L) less than the diffusion distance (Ldiffusion, Ldiffusion=15/α [9]), the water losses are calculated by the famous Beer's law {loss= e -αL , where, L (m) and α (m -1 ) [1], [9], [15]}. Otherwise the modified Beer's law is used [9]. Note: LOS means a component of the light propagation is referred to as the portion of the light radiated by the transmitter that arrives directly within the field of view (FOV) of the receiver [11].
The diffusion length (Ldiffusion) decreases with temperature (with λ=455) but Ldiffusion increases with temperature (λ=486nm). The value of Ldiffusion =429.41 m (for λ=455nm , T=5 o C), 370.23 (for λ=455nm , T=305 o C), 398.77m (for λ=486nm , T=5 o C), and 424.63m (for λ=486nm , T=30 o C). Note, Ldiffusion at 5 o C for λ=455 nm greater than that at λ=486 nm and vice versa for T=30 o C, where from Fig.3, with T< 12 o C, αFW at λ=486 > αFW at λ=455. From reference [9], we noticed that the propagation loss factor independent of the half-power angle of the transmitter (φ1/2) where the value of propagation loss factor with φ1/2 =5 0 equally with that φ1/2=10 o as explained in Appendix B.  The received optical power (power budget) [1], [16], [17] P R = P t G t G r ( λ 4π R ) 2 e −αR η T η R (18) Where, transmitter gain, Gt =(π Dt /λ) 2 , receiver gain, Gt =(π Dr /λ) 2 [17], [31], Dt and Dr are the geometric diameters of transmitter and receiver, respectively. Equation (18) [18] Optical power density transmitted by LED can be expressed as [9], [11], [18], [19]; and Φ1/2 is the half-power angle of the transmitter From Eq.21, GT independent upon the wavelength and GT is a function of θ and φ1/2 At receiver with Beer's law, the power density (Pr density) is; P r density = P t G T 4πR 2 e −αR η t (23) Where, e -αR is the medium (water) losses. The received optical power P r = P t G T 4πR 2 e −αR A r eff η t η r (24) Where, ηr is the quantum efficiency of the receiver, Ar eff {Ar eff = Ar cos(γ)}, Ar is the physical receive area, γ is the angle between the perpendicular to the receiver plane area and the ray which incident on the receiver area. Equation (18) can be rewritten as; The format of Eq.24 is the same format of Eq.25, but, Gt=(π Dt /λ) 2 instead of GT= 2(m+1)cos m (θ) The value of GT decreases with higher values of half-power angle (φ1/2) and large values of in alignment angle (θ) as shows in Fig.4. Also Fig.4 indicates that after the specific value of angle θ (θ=8 o ) the gain The parameter m rapidly decreases with φ1/2 as shown in Fig.5.
Also, Table 1 indicates that GT increases by reducing the value of φ1/2 (φ1/2 is reduced by selecting the LED or by using lenses [9]). The increasing factor of GT due to reducing φ1/2 is; increasing factor of G T due to reduce φ 1/2 , = 10 log { G T atφ 1/2 =5 0 Note 6: From Fig.4 and Table 1, at specific values of angle θ the increasing factor becomes less one. And so, the φ1/2 must be chosen to optimize with θ The field of view of the receiver (FOVr) must be greater than the field of view of an LED, FOVTX = φ1/2 [11]. The field of view of a receiver (FOVRx) is defined as the angle between the points on the detection pattern, where the directivity is reduced to 50% [11].
The maximum incident angle θmax to avoid the geometric losses must be less than φ1/2; θmax = cos -1 (L/Rmax) where, Rmax = { (L 2 +(Dr/2) 2 } 0.5 (27) Note 7; some references state that, the received power Eq.20 multiplied by rect(FOVr /FOVr) [9], [18], [19] but by using the ratio of receiving area to the transmitted area and the centroid losses are useful for power losses. Where the value of rect(FOVr /FOVr) = 1 if FOVt less than FOVr and rect(FOVr /FOVr) = 0 if FOVt > FOVr [11]   The dimensions of the received area are around cm 2 and so the received power density can be considered equally through the receiver area as shown in Fig.6 a) λ=455 nm b) λ=486 nm We noticed that for the same value of F, as T increases, the corresponding available distance decreases. With distance link (L=500m), parameter Log(F) is the smallest at λ=486 nm as shown in Fig.7. The dependence of distance L on T becomes little with λ=455 and 486 nm as shown in Fig.7. As expected, the required value of the parameter Log(F) to give propagation distance L=500 m increases with T.
The received optical power (PR) also, can be defined as [22], [36] = ℎ ⁄ Thus, the value of SNR increases with Pt , Dt and Dr while SNR decreases with distance (R), water attenuation factor (αFWT) , wavelength (λ), and data rate (Br) As expected the value of SNR decreases with T (where, attenuation increases with T) with wavelength 455nm, while SNR increases with temperature with λ=486nm as shown in Fig.8. Also, the value of SNR > SNRmin for λ= 455 and 487nm. The dimensions of the received area are around tenths of cm 2 and so the SNR can be considered equally through the receiver as shown in Fig.9.    (30) Where, σ is the source line width (nm), Dm material dispersion ( ps/m nm), Br is the data rate (Gb/s) and R is the distance (m).

II.3 Availability of link
The link becomes available with SNR>SNRmin andPr>Prmin where, Pr min is the minimum required received power (receiver sensitivity) and SNRmin is the lowest SNR with the required BER. (as example, Sensitivity = -43 dm = 50nW [18] Therefore the final required transmitted power Pt req is the smaller value of ( Pt req Prmin , Pt req SNR req) Therefore, Deff = 20.2cm (less than Dr , no geometric losses) , Ar= 0.03465 m 2 , Ar eff = 0.03465 m 2 m= 181.806 and GT= 2(m+1) (L/R) m = 365..6

Conclusion
The underwater visible optical communications are affected by the water temperature. As the water temperature increases, the link distance decreases with λ=455nm but it increases with λ=455nm. So the link availability depends upon the daily and seasonal temperature. With freshwater (Egypt Nile River water), the best wavelength is λ=486nm. To overcome the unavailability of the link due to the water temperature, the transmitted power must be controlled by the daily water temperature. As the data rate increases, the link distance decreases. With wavelength λ=486nm, the link can be greater than 500 m with a data rate =1Gbps. Appendix B Modified Beers law and the effect of φ1/2 on the water losses Losses factor at λ=532nm is [21] with pure water (Cc=0.005mg/m 3 ) and with clean water ( Cc=0.31 mg/m 3 ) With φ1/2 = 5 o Losses pure water = 0.1999999 exp(-0.0657156 z)+0.0046431 exp(-0.2633946 z) (B1.1)