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1.Introduction
Maritime communication technology has gained great development since the 1980s. According to relevant data released by the International Marine Science Organizations in recent years，more than 40，000 vessels worldwide have installed communications equipment and 464 ports in 127 countries and regions have conducted such communications.
Figure 1
Under the impetus of new technologies such as frequency management，real-time frequency selection，selective calling，digital communications networking，microelectronics，and large scale integrated circuits，the performance of the communication equipment on the ship is more advanced，the functions are more perfect，the operation is more simple，the reliability of the equipment is greatly improved，and the single equipment can be organically integrated to form an integrated communication system or a data communication network.
Figure 2 A novel architecture of marine communications network
Under the communication network architecture shown in Figure 2，it is equally possible for all users at sea to communicate using conventional maritime wireless communications networks and marine satellite communications networks，but unlike existing marine communications networks，this architecture proposes new land mobile communications technology to create new high-speed broadband links via reefs or offshore platforms，airships，drones and other relay nodes，especially for islands with rich reefs such as the South China Sea.
2.Signal Attenuation Model
2.1 The basic model
The calm ocean and the turbulent ocean may cause different attenuation for the signal reflect off the ocean. We assume that only the shape of ocean surface will affect the signal reflection.
When we consider a turbulent ocean，several factors of turbulence affect the signal. The following mathematical model shows the signal attenuation due to the wave height.
Therefore，
Where：
represents the strength of the signal，
indicates the height of waves，
describes the reduction of signal strength，which is the coefficient.
represents the original signal strength.
The height of wave may affect how signal reflect off the ocean and how much strength loss due to the reflection.
2.2 Connect sea surface condition with signal attenuation
Symbols：
Specular reflection coefficient
Diffuse reflection coefficient
Specular reflection coefficient considering the curvature of the Earth Diffuse reflection coefficient considering the curvature of the Earth
Incident angle of electromagnetic wave
Reflection angle of electromagnetic wave
Wavelength
Average wave height
h Small fluctuations in calm seas
Seawater dielectric constant
Vertically polarized Fresnel reflection coefficient
D Earth curvature factor
G Sea surface roughness
k Coefficient
In the initial simple model，we establish the initial formula by using the average height（ ）of the waves and the incident angle（φ）. In general，
2.2.1 Specular Reflection
For a calm ocean，we can approximately equate the electromagnetic reflection process with specular reflection. The loss value of the specular energy（ ）component relative to the direct signal energy component may be expressed as：
①
The specular reflection coefficient is derived from the formula by Ament Con（1953）. The specular reflection coefficient is related to the average height and the incidence angle of the electromagnetic wave. The formula is as follows：
②
Later，it was found in the literature that Miller and other researchers had corrected the coefficient. Using the zero-order Bessel function ，it was determined that the modified specular reflection coefficient was closer to the real condition than the previous one. The revised formulas are as follows：
③
④
Then，we put the value of into ，and the final specular reflection coefficient as follows：
⑤
The vertical polarization Fresnel reflection coefficient is related to the dielectric constant of the seawater. So，we need to consider the influence of ，that is：
⑥
The loss value of specular reflection energy component relative to direct signal energy component（ ）can be obtained by replacing and into equation①：
In addition，the curvature of the earth itself will also affect the specular reflection coefficient（Kerr，1951），. We use D to represent the earth's curvature factor. Therefore，the formula of the specular reflection coefficient of the curvature of the earth is given as follows：
2.2.2 Diffuse Reflection
For the turbulent sea，we need to discuss the effect of the fast water on the electromagnetic wave. From the wave itself，we summarize the main two factors：the influence of wave height on electromagnetic wave and the influence of wave shape on the incident angle of electromagnetic wave. During the discussion，we found that the roughness of the sea surface（g）included the height of the wave and the incident angle of the wave and equated the reflection process of the electromagnetic wave with diffuse reflection. Similarly，the loss values of the diffuse（ ）reflection energy component relative to the direct signal energy component may be expressed as：
Roughness of the sea surface g is：
The diffused reflection coefficient derived from Hasper（2010）those two variables---- the incident angle and the reflection angle of electromagnetic wave reflection are used here：
At the same time，we need to consider the curvature factor of the earth in the same way as the specular reflection coefficient，and the relation between the diffuse reflection coefficient of the earth curvature factor and the specular reflection is as follows：
The diffuse reflection coefficient，which considers the curvature factor of the earth，can be enlarged in to：
=
After the integration，we can get the loss value of diffuse reflection energy component relative to direct signal energy component（ ）. The expression is as follows：
2.3 Ocean Waves Model
Ocean is continuous changing，which the waves are the most obvious. However，unlike the heat，the changing of waves is sometimes randomly. In another word，factors that affect the waves are not such straightforward. Wind-generated waves where occur on the surface of ocean are significantly common.
According to Pierson and Moskowitz（1964），Pierson-Moskowitz spectrum illustrates the relationship between wave spectra and wind speeds of a fully developed sea.
Where ，g is the gravitational acceleration， and . We can use the Matlab to get the figure of p-m spectrum，which shows the relation of wave spectral density（ ）and its frequency . It means the area of the figure represent the significant wave height， is integrated：
2.4 Conclusions and Results
From the topic，we think that the first reflection intensity should be compared between the turbulent sea level and the calm sea level，which is equivalent to the calculation of the loss of the two kinds of sea surface to the electric wave reflection. Meanwhile，considering that the ionosphere condition is approximately the same，the frequency of the electromagnetic wave emitted at a same degree. Therefore，we only need to consider the loss changes caused by the sea surface itself.
From the previous solution and b = ，therefore
The known quantities are：
By using MATLAB，the attenuations are：
Therefore，obviously the strength of the first reflection off a turbulent ocean is lower than the calm ocean. Since the results above show the fact that turbulent ocean absorb signal around 10 %（0.199-0.09）which is more than calm ocean. 2.5 Considering the Ionosphere
During reflection process，the wave enters into the ionosphere. Moreover，it could also be affected by the season，time of the day，and solar condition. In this part，we mainly discussed the ionosphere factor，which influenced by those three variables. Ionosphere has 3 basic layers：D，E，F. Layer D is the lowest layer of the ionosphere，which is more affected by solar radiation. When the solar activity is strong，more ions can be produced. But these ions are mostly neutralized，so the degree of ionization is relatively low. So，it has less impact on high frequency waves. And when there is no solar radiation，the most obvious character is that the high frequency waves emitted in the distance are not received during the day.
E is a middle layer，100 to 150 kilometers from the ground. At night，due to the decrease in solar radiation，the E layer begins to disappear. After consulting the literature，we know that the neutralization of the underlying ions is stronger. Therefore，the height of the E layer will be higher at night than in the daytime.
F is 150 to more than 500 km above the ground and is the main reflection layer of high frequency electromagnetic waves. Due to the strong solar reflectivity during the day，this layer can be divided into F1 and F2 layers. However，at night，the solar radiation is weak，so the layers merged into one.
The figure below illustrates the process：
The intensity of solar activity also affects the ionizing degree of ionosphere. The solar radiation on the ionosphere changes with seasonal factors. In general，ionizes of the ionosphere affected by sunlight in summer are higher than that in winter. The closer that layers to the solar radiation，the higher the degree of ionization they will have. Because of that，the reflection of high-frequency electromagnetic waves is more likely to happen.
So，we considered that F layer is the most aspect. Assuming that the ion production rate per unit volume is Q：
Where
represents effective ionization’s cross section of the gas，
n represents gas number density，
s represents local ionizing radiation intensity.
Because the degree of ionization changes over time，we have a continuous equation of degree of ionization：
Where
N represents the total amount of ionospheric electrons
v represents electronic movement speed
L represents the total number of electrons that have collided and disappeared We could get an equation as follow：
3.Multi-hop Communication with SNR restriction
3.1 Initial SNR
We have known that the signal is sent by a 100-watt constant carrier，thus the initial signal to noise ratio is ：
3.2 Improve the Signal Attenuation Model
Until now，we only consider the influence of ocean surface. In this section，the effect caused by ionosphere and the spread in free space will be added into the consideration.
The loss due to the spread in free space can be found in a formula ，we assume the frequency is 30 Hz and the distance for one hop is 1000 km，then is equal to .
Where， is the reduction rate due to the free space spread， is under the condition of calm ocean，and is the rate regard to the ionosphere.
3.3 Multi-hop Communication
In this part，the number n should be considered into the formula. Therefore， ， .
By using Matlab，we can get the maximum number is 4.
Reference Lists：
[1] Ament Con，J.，Global morphology of ionospheric scintillation，Proc. IEEE，1953，50，240-259.
[2] Driessen J. R.，Ship detection with high-resolution HF sky-wave radar. IEEE，2010.
[3] Hasper，W. Some new experimental research of HF backscatter propagation in crirp.2010 Asia-Pacific Radio Science Conference-Proceedings，2010：13-16.
[4] Kerr，J.M，Radio Ray Propagation in the Ionosphere，Mc Graw-Hill Book Company，New York，1951.
[5] Pierson，D. G. and Moskowitz，G. J. The scintillation of the radio transmissions from Explorer 7，J. Atmos. Terrest. Phys.，1964，24，278-282.
Maritime communication technology has gained great development since the 1980s. According to relevant data released by the International Marine Science Organizations in recent years，more than 40，000 vessels worldwide have installed communications equipment and 464 ports in 127 countries and regions have conducted such communications.
Figure 1
Under the impetus of new technologies such as frequency management，real-time frequency selection，selective calling，digital communications networking，microelectronics，and large scale integrated circuits，the performance of the communication equipment on the ship is more advanced，the functions are more perfect，the operation is more simple，the reliability of the equipment is greatly improved，and the single equipment can be organically integrated to form an integrated communication system or a data communication network.
Figure 2 A novel architecture of marine communications network
Under the communication network architecture shown in Figure 2，it is equally possible for all users at sea to communicate using conventional maritime wireless communications networks and marine satellite communications networks，but unlike existing marine communications networks，this architecture proposes new land mobile communications technology to create new high-speed broadband links via reefs or offshore platforms，airships，drones and other relay nodes，especially for islands with rich reefs such as the South China Sea.
2.Signal Attenuation Model
2.1 The basic model
The calm ocean and the turbulent ocean may cause different attenuation for the signal reflect off the ocean. We assume that only the shape of ocean surface will affect the signal reflection.
When we consider a turbulent ocean，several factors of turbulence affect the signal. The following mathematical model shows the signal attenuation due to the wave height.
Therefore，
Where：
represents the strength of the signal，
indicates the height of waves，
describes the reduction of signal strength，which is the coefficient.
represents the original signal strength.
The height of wave may affect how signal reflect off the ocean and how much strength loss due to the reflection.
2.2 Connect sea surface condition with signal attenuation
Symbols：
Specular reflection coefficient
Diffuse reflection coefficient
Specular reflection coefficient considering the curvature of the Earth Diffuse reflection coefficient considering the curvature of the Earth
Incident angle of electromagnetic wave
Reflection angle of electromagnetic wave
Wavelength
Average wave height
h Small fluctuations in calm seas
Seawater dielectric constant
Vertically polarized Fresnel reflection coefficient
D Earth curvature factor
G Sea surface roughness
k Coefficient
In the initial simple model，we establish the initial formula by using the average height（ ）of the waves and the incident angle（φ）. In general，
2.2.1 Specular Reflection
For a calm ocean，we can approximately equate the electromagnetic reflection process with specular reflection. The loss value of the specular energy（ ）component relative to the direct signal energy component may be expressed as：
①
The specular reflection coefficient is derived from the formula by Ament Con（1953）. The specular reflection coefficient is related to the average height and the incidence angle of the electromagnetic wave. The formula is as follows：
②
Later，it was found in the literature that Miller and other researchers had corrected the coefficient. Using the zero-order Bessel function ，it was determined that the modified specular reflection coefficient was closer to the real condition than the previous one. The revised formulas are as follows：
③
④
Then，we put the value of into ，and the final specular reflection coefficient as follows：
⑤
The vertical polarization Fresnel reflection coefficient is related to the dielectric constant of the seawater. So，we need to consider the influence of ，that is：
⑥
The loss value of specular reflection energy component relative to direct signal energy component（ ）can be obtained by replacing and into equation①：
In addition，the curvature of the earth itself will also affect the specular reflection coefficient（Kerr，1951），. We use D to represent the earth's curvature factor. Therefore，the formula of the specular reflection coefficient of the curvature of the earth is given as follows：
2.2.2 Diffuse Reflection
For the turbulent sea，we need to discuss the effect of the fast water on the electromagnetic wave. From the wave itself，we summarize the main two factors：the influence of wave height on electromagnetic wave and the influence of wave shape on the incident angle of electromagnetic wave. During the discussion，we found that the roughness of the sea surface（g）included the height of the wave and the incident angle of the wave and equated the reflection process of the electromagnetic wave with diffuse reflection. Similarly，the loss values of the diffuse（ ）reflection energy component relative to the direct signal energy component may be expressed as：
Roughness of the sea surface g is：
The diffused reflection coefficient derived from Hasper（2010）those two variables---- the incident angle and the reflection angle of electromagnetic wave reflection are used here：
At the same time，we need to consider the curvature factor of the earth in the same way as the specular reflection coefficient，and the relation between the diffuse reflection coefficient of the earth curvature factor and the specular reflection is as follows：
The diffuse reflection coefficient，which considers the curvature factor of the earth，can be enlarged in to：
=
After the integration，we can get the loss value of diffuse reflection energy component relative to direct signal energy component（ ）. The expression is as follows：
2.3 Ocean Waves Model
Ocean is continuous changing，which the waves are the most obvious. However，unlike the heat，the changing of waves is sometimes randomly. In another word，factors that affect the waves are not such straightforward. Wind-generated waves where occur on the surface of ocean are significantly common.
According to Pierson and Moskowitz（1964），Pierson-Moskowitz spectrum illustrates the relationship between wave spectra and wind speeds of a fully developed sea.
Where ，g is the gravitational acceleration， and . We can use the Matlab to get the figure of p-m spectrum，which shows the relation of wave spectral density（ ）and its frequency . It means the area of the figure represent the significant wave height， is integrated：
2.4 Conclusions and Results
From the topic，we think that the first reflection intensity should be compared between the turbulent sea level and the calm sea level，which is equivalent to the calculation of the loss of the two kinds of sea surface to the electric wave reflection. Meanwhile，considering that the ionosphere condition is approximately the same，the frequency of the electromagnetic wave emitted at a same degree. Therefore，we only need to consider the loss changes caused by the sea surface itself.
From the previous solution and b = ，therefore
The known quantities are：
By using MATLAB，the attenuations are：
Therefore，obviously the strength of the first reflection off a turbulent ocean is lower than the calm ocean. Since the results above show the fact that turbulent ocean absorb signal around 10 %（0.199-0.09）which is more than calm ocean. 2.5 Considering the Ionosphere
During reflection process，the wave enters into the ionosphere. Moreover，it could also be affected by the season，time of the day，and solar condition. In this part，we mainly discussed the ionosphere factor，which influenced by those three variables. Ionosphere has 3 basic layers：D，E，F. Layer D is the lowest layer of the ionosphere，which is more affected by solar radiation. When the solar activity is strong，more ions can be produced. But these ions are mostly neutralized，so the degree of ionization is relatively low. So，it has less impact on high frequency waves. And when there is no solar radiation，the most obvious character is that the high frequency waves emitted in the distance are not received during the day.
E is a middle layer，100 to 150 kilometers from the ground. At night，due to the decrease in solar radiation，the E layer begins to disappear. After consulting the literature，we know that the neutralization of the underlying ions is stronger. Therefore，the height of the E layer will be higher at night than in the daytime.
F is 150 to more than 500 km above the ground and is the main reflection layer of high frequency electromagnetic waves. Due to the strong solar reflectivity during the day，this layer can be divided into F1 and F2 layers. However，at night，the solar radiation is weak，so the layers merged into one.
The figure below illustrates the process：
The intensity of solar activity also affects the ionizing degree of ionosphere. The solar radiation on the ionosphere changes with seasonal factors. In general，ionizes of the ionosphere affected by sunlight in summer are higher than that in winter. The closer that layers to the solar radiation，the higher the degree of ionization they will have. Because of that，the reflection of high-frequency electromagnetic waves is more likely to happen.
So，we considered that F layer is the most aspect. Assuming that the ion production rate per unit volume is Q：
Where
represents effective ionization’s cross section of the gas，
n represents gas number density，
s represents local ionizing radiation intensity.
Because the degree of ionization changes over time，we have a continuous equation of degree of ionization：
Where
N represents the total amount of ionospheric electrons
v represents electronic movement speed
L represents the total number of electrons that have collided and disappeared We could get an equation as follow：
3.Multi-hop Communication with SNR restriction
3.1 Initial SNR
We have known that the signal is sent by a 100-watt constant carrier，thus the initial signal to noise ratio is ：
3.2 Improve the Signal Attenuation Model
Until now，we only consider the influence of ocean surface. In this section，the effect caused by ionosphere and the spread in free space will be added into the consideration.
The loss due to the spread in free space can be found in a formula ，we assume the frequency is 30 Hz and the distance for one hop is 1000 km，then is equal to .
Where， is the reduction rate due to the free space spread， is under the condition of calm ocean，and is the rate regard to the ionosphere.
3.3 Multi-hop Communication
In this part，the number n should be considered into the formula. Therefore， ， .
By using Matlab，we can get the maximum number is 4.
Reference Lists：
[1] Ament Con，J.，Global morphology of ionospheric scintillation，Proc. IEEE，1953，50，240-259.
[2] Driessen J. R.，Ship detection with high-resolution HF sky-wave radar. IEEE，2010.
[3] Hasper，W. Some new experimental research of HF backscatter propagation in crirp.2010 Asia-Pacific Radio Science Conference-Proceedings，2010：13-16.
[4] Kerr，J.M，Radio Ray Propagation in the Ionosphere，Mc Graw-Hill Book Company，New York，1951.
[5] Pierson，D. G. and Moskowitz，G. J. The scintillation of the radio transmissions from Explorer 7，J. Atmos. Terrest. Phys.，1964，24，278-282.