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The safety of submerged buoy is higher than traditional buoy. The most important problem for submerged buoy is that signal will be attenuated greatly due to ocean wave fluctuation and seawater. On the basis of ocean wave model, propagation characteristics of electromagnetic wave in seawater channel for submerged buoy is analyzed in this letter. It includes the propagation properties of electromagnetic wave in seawater and across the air-sea interface. The results show that the VHF frequency band, first order sea level and water depth of less than 10 cm are acceptable for submerged buoy.

Marine information construction is in the stage from Digital Ocean to Smart Ocean. As a result, the study of ocean sensors is blooming [

Since most of the ocean buoys have a certain distance from the coast, and the space-based link can cover a wide range, the most effective way of real-time information transmission for ocean buoys is space-based link [

In this letter, we focus on the seawater channel characteristics for submerged buoy. First, the ocean wave model is given. Then, channel characterizations in seawater and across the air-sea interface are analyzed. Finally, the comprehensive simulation and analysis are presented.

In actual environments, the ocean wave will fluctuate with the wind. The main way to describe ocean wave is wave spectrum S ( ω , θ ) [

a = 2 S ( ω , θ ) Δ ω Δ θ (1)

where S ( ω , θ ) = S ( ω ) D ( θ ) , S ( ω ) is power spectrum, and D ( θ ) is direction spectrum [

S ( ω ) = α g 2 ω 5 e x p [ − β ( g U ω ) 4 ] (2)

where α = 8.1 × 10 − 3 , g is gravity acceleration, β = 0.74 and U is the wind speed above sea surface.

D ( θ ) = 2 π c o s 2 θ (3)

Theoretically, θ can range from -π to π, but in reality most of ocean energy distributes in the range from − π 2 to π 2 .

The simulation results of ocean wave with different wind speeds are shown in

Seawater is a conductive medium which has a great impact on the electromagnetic waves propagation. Because the Maxwell equations are the basic theory of the electromagnetic wave propagation, we use these equations to calculate and analyze the propagation properties of electromagnetic wave in seawater.

The permittivity of seawater can be calculated by an extension Debye formula called Havirial-Negami, which is expressed as [

ε s w = ε s w ∞ + ε s w 0 − ε s w ∞ 1 + ( j 2 π f τ s w ) 1 − α − j σ s w 2 π f ε 0 (4)

where

ε s w 0 ( T , S ) = ε s w 0 ( T ) a ( T , S ) ,

ε s w ∞ ( T ) = 87.134 − 0.1949 T − 0.01276 T 2 + 0.0002491 T 3 ,

a ( T , S ) = 1 + 1.16 × 10 − 5 T S − 3.65 × 10 − 3 S + 3.21 × 10 − 5 S 2 − 4.23 × 10 − 7 S 3 ,

τ s w ( S , T ) = τ ( 0 , T ) b ( S , T ) ,

τ ( 0 , T ) = 1.77 × 10 − 11 − 6.09 × 10 − 13 T + 1.10 × 10 − 14 T 2 − 8.11 × 10 − 17 T 3 ,

b ( S , T ) = 1 + 2.28 × 10 − 5 T S − 7.64 × 10 − 4 S − 7.76 × 10 − 6 S 2 + 1.11 × 10 − 8 S 3 ,

σ s w ( S , T ) = S ( 0.18 − 0.0015 S + 2.09 × 10 − 5 S 2 − 1.28 × 10 − 7 S 3 ) × exp ( ( T − 25 ) ( 0.02 + 0.00013 ( 25 − T ) + 2.46 × 10 − 6 ( 25 − T ) 2 − S ( 1.85 × 10 − 5 − 2.55 × 10 − 7 ( 25 − T ) + 2.55 × 10 − 8 ( 25 − T ) 2 ) ) )

and ε 0 = 8.854 × 10 − 12 , ε ∞ = 4.9 , α = 0 , S is salinity (‰) and T is temperature (˚C).

It is obvious that the permittivity of sea water has a relationship with frequency, temperature and salinity of seawater. We choose the most common case of seawater, a temperature of 15˚ and a salinity of 35‰, as the simulation condition. The result is given in

Seawater is an electrical conductive medium where electromagnetic waves generate conduction current. Therefore, the Helmholtz equations of sea water are used.

∇ 2 E = ( j ω μ σ − k 2 ) E = − ω 2 μ ε ( 1 − j σ ω ε ) E = − ω 2 μ ε e c E (5)

∇ 2 H = ( j ω μ σ − k 2 ) H = − ω 2 μ ε ( 1 − j σ ω ε ) H = − ω 2 μ ε e c H (6)

where μ = μ 0 is permeability and ε e c = ε [ 1 − j σ / ω ε ] is the equivalent complex permittivity of seawater. With this parameter, we can consider seawater as an equivalent medium. The equivalent complex wave number is

k ′ c = ω μ ε e c (7)

and the propagation constant is

γ = j k ′ c = α + j β (8)

where α is attenuation constant and β is phase-shift constant. From (5) to (8), we can obtain

α = ω μ ε 2 [ 1 + ( σ ω ε ) 2 − 1 ] (9)

β = ω μ ε 2 [ 1 + ( σ ω ε ) 2 + 1 ] (10)

Substituting the above results into the plane wave expression, we can obtain,

E = E 0 e − γ z = E 0 e − α z e − j β z (11)

where z is propagation distance. As can be seen in (11), the magnitude of the electric field strength decays exponentially with increasing propagation distance, and phase rotation occurs.

Some works have simulated the propagation of electromagnetic waves in seawater, but these works focus on the acoustic frequency band [

From

Furthermore, we simulate the amplitude attenuation with different depth in seawater. The result is shown in

For submerged buoy, electromagnetic waves are not only attenuated in seawater but also refracted through the air-sea interface. Since refraction will also produce attenuation, a study in propagation across air-sea interface is essential. The polarization mode of the incident wave field will have a great impact on the characteristics of transmitted wave field. Horizontal polarization and vertical polarization are two basic polarizations. Other polarization modes can be obtained by superposition of these two modes.

The refraction coefficient is defined as the ratio of amplitude of refracted wave to incident wave as the Fresnel formula shows [

T ⊥ = 2 η 2 c o s θ 1 η 2 c o s θ 1 + η 1 c o s θ 2 (12)

T ∥ = 2 η 2 c o s θ 1 η 2 c o s θ 2 + η 1 c o s θ 1 (13)

where θ 1 is the angle of incidence, θ 2 is the angle of refraction which can be obtained from the Snell Law,

s i n θ 1 s i n θ 2 = ε 2 ε 1 (14)

where ε 1 is equal to the dielectric constant in freespace and ε 2 is the permittivity of seawater. η 1 and η 2 are intrinsic impedance which is the ratio of amplitude of the electric field to the magnetic field, and the equivalent complex intrinsic impedance η c can be expressed as

η c = μ ε e c = μ ε − j ( σ ω ) (15)

We simulated the total propagation characteristics of electromagnetic wave at a certain point, including the amplitude attenuation and phase shift both in seawater and across the ocean surface.

The simulation results are shown in

The safety of traditional marine buoys is an important problem. In this regard, submerged buoy seems to have a better development prospect. However, many problems need to be overcome, such as a reliable information transmission. This letter analyzes the propagation characteristics of electromagnetic wave in seawater channel for submerged buoy. Amplitude variation and phase fluctuation of the communication signals are characterized. The results show that the VHF frequency band, first order sea level and water depth of less than 10cm are acceptable for submerged buoy. Such prior knowledge could help us to select a suitable algorithm for adaptive anti-rolling servo control and optimize waveform for resisting dynamic seawater attenuation.

This work was supported by the National Natural Science Foundation of China (61671263) and Tsinghua University Initiative Scientific Research Program (20161080057).

The authors declare no conflicts of interest regarding the publication of this paper.

Zhan, Y.F. and Pan, X.H. (2019) Propagation Characteristics of Electromagnetic Wave in Seawater Channel for Submerged Buoy. Journal of Computer and Communications, 7, 72-81. https://doi.org/10.4236/jcc.2019.710007