Analysis of Signal Reception Mechanism of Sky Wave Long-distance Maritime Communication

Based on the principle of high frequency radio propagation, the signal reception mechanism of sky wave communication over oceans is investigated. Due to long distance signal transmission, the energy loss is inevitable, especially in the space and on the sea surface. Firstly, we establish the space propagation loss model by the ionospheric absorption, the free space propagation characteristics and other extra loss. Referring to the reflection principle of smooth ground and the Kirchhoff approximation, the energy loss models of the calm sea surface and the turbulent sea surface are obtained respectively. Then, through combining the space propagation loss model and the sea surface propagation loss models, we give out a formula of receiving point field strength. According to the signal to noise ratio, we summarize a complete and concise sky wave maritime communication calculation process, through which multi hops number of the receivable sky wave signal can be calculated accurately. The experimental results show the effectiveness.


Introduction
As shown in Fig.1, multi-hop high frequency(HF, defined to be 3-30 MHz) radio wave propagation is a main method applied to the field of telecommunications. The HF waves travel by multiple reflections off the ionosphere(the Flayer) and off the earth just like the 'multi hops'. This propagating method has many valuable advantages, such as low cost, non-destructive ionosphere of relay system. It is widely used in the researches of the long-distance maritime communications(see [1][2][3] and the references therein). The maritime propagation process comprises with free space propagation, ionospheric reflection and absorption, sea surface absorption and scattering. The affecting factors of ionospheric wave propagation, such as usable frequency, absorbing attenuation and sunspot number, are extremely complicated with time and frequency. The propagation of waves on the sea surface varies with the frequency and the state of the sea. The turbulence on the sea surface can affect the scattering of radio waves. In 2003, Anderson [1] developed a computational model which could compute the contributions of diffusely-scattered fields arising from non-specular reflection at the ground reflection points for multiple-hop propagation paths. In 2008, Kong et al [3] proposed an aggregated-path routing approaching for inter-ship communications in wireless multi-hop networks. Tian and Lu [4] analyzed the relationship between radio wave frequency and sky wave propagation path. In 2014, Sherstyukov et al [5] investigated the change of E-layer parameter on the base of experimental values. However, few literatures investigate the complete signal reception mechanism of sky wave multi-hop propagation.
In this paper, the whole signal reception mechanism of the martitime communication is consided, the complete energy loss model is established and the value of multi hops of the receivable skywaves is calculated.
The paper is organized as follows. Section 2 introduces the sky-wave propagation mode, process and propagation conditions with diffrent emission angles. In Section 3, the sky-wave space propagation is divided into a free space propagation and an ionosphere propagation, some energy loss formulas are analyzed. In Section 4, sea surface propagation models are obtained. The ocean situation is divided into calm ocean and turbulent ocean. By Kirchhoff approximation, the scattering coefficients are obtained respectly. In Section 5, using the result of space propagation loss, ionosphere loss as well as absorption and scattering of the sea surface, a complete process loss model is achieved. In Section 6, introducing a concept of signal to noise ratio (SNR), multi hops numbers of propagation on the calm and the turbulent sea surface respectively. Section 7 presents the conclusion.

Condition and process of HF radio wave propagation over oceans
Because of differences in the emission angle of the radio waves, the propagating paths in free space are different, which means energy loss is veried.

Condition of high-frequency radio wave reflection in the ionosphere
The ionospheric conditions are constantly changing as the solar radiation intensity is always altering. For example, after sunrise or in summer, the sun's rays will increase, the concentration of electrons in each ionosphere layer will change, and sunspots will move more violently. In general, the high frequency waves will be absorbed in the D and E layers and be reflected back in the F layer.
When the elevation angle is  , the highest frequency of ionospheric energy reflection is max max 2 Here, max N s the maxsmum electron den sty of the sono phere, h s the ds tance from the Earth' urface to the sono phere, and R s the radsu of the Earth. By (1), the hsghe t frequency that the sono phere can reflect at dsfferent elevatson angle can be calculated a Table 1. As shown in Table 1, the highest frequency range that the ionosphere can reflect is 8.9MHz to 30.6MHz, and short-wave frequency range is 3-30MHz, so it can be concluded that the short-wave can be reflected regardless of the elevation angle.

High-frequency radio wave propagation mode
In the process of radio propagation, transmission loss is affacted by many factors, the basic transmission loss of radio in the transmission process can be divided into four parts [6], the expression is as follow: , where, bf L is propagation loss of atmosphere, a L is ionospheric absorption loss, g L is ground emission loss, p Y is additional loss, the units of each index are expressed in dB. Let 0 g L = for the maritime propagation. The whole process is shown in Figure 2.

Figure 2
Diagram of HF radio wave propagation mode

Space propagation loss
In this paper, we divide the space wave propagation loss into free space propagation loss, ionospheric propagation loss and extra loss, and analyze these processes separately.

Free Space Propagation Loss
Free space transmission loss is a phenomenon in which the energy of the wave naturally diffuses increasingly as the propagation distance increases. The farther the propagation distance is, the larger the loss is, which is the main component of the transmission loss of the sky wave. The free space proposed here is an ideal situation, that is to ay, the medsum s unsform, conductsvsty σ =0, relatsve dielectric constant =1, relative magnetic permeability =1.
The definition of free space transmission loss is: when direction coefficients of the transmitting antenna and the receiving antenna are both 1, the ratio of the transmitting antenna' radiated power Pr to the receiving antenna' optimal receiving power PL is recorded as Lbf, the equation is: It can be known from the theory of antenna, when the receiving antenna polarization and impedance are matching [6], the receiving power r (Watt) where, S is Poynting vector, where, D s arc length from the tran mstter to the recesver, n s hop-count of ky-wave propagatson, 0 a s earth radsu (6730 km), ∆ s dsrectsvsty angle of a tran msttsng antenna, we can calculate formula (7)

Extra loss
The defsnstson of s other lo except for above sndscator , st snclude polarszatson lo of electrsc wave, polar lo and defocu effect of the sono phere, and o on. That s a comprehen sve e tsmate.
relate to local tsme of the reflectson posnt [7], and the lo value are hown sn Table 2:

Ocean surface reflection strength model
When radso wave arrsved at the urface of the ea, cattersng wsll happen on the urface, o we need to calculate the cattersng coeffscsent, but st wsll change wsth the ea urface turbulence. Thu , we dsvsde ocean snto two condstson , calm ocean and turbulent ocean, wheresn, the calm ea urface can be con sdered a ea urface wsthout cattersng and the turbulent ea can catter radso wave.

Calculation of the reflection coefficient for the calm ocean surface
Accordsng to Snell law, whsch s a reflectson law of repre ent plane wave lant to the snterface of an sdeal medsum [11], we can obtasn Fre nel reflectson coeffscsent formula for horszontal and vertscal polarszatson wave of the calm ocean urface: where, s grazsng sncsdence angle, by u sng the value of , we can get the value of horszontally polarszed wave ( ) and vertscal polarszatson wave ( ).
Referrsng to the expre son of ground reflectson lo [5] becau e the proce of ground reflectson and ocean reflectson are smslar, we obtasn the expre son of calm ocean reflectson ab orptson lo s ( )

Approximate method of sea surface scattering
Ksrchhoff approxsmatson (KA) method s ustable for cattersng calculatson of turbulent urface, whsch s a smslar concept of tangent plane, that s to ay, KA method u sng reflectson fseld on a posnt to replace the cattersng fseld.

Modelling
Through the lo model of each ubproce obtasned sn the prevsou ectson, we can connect them together and fsnd the total energy lo t dursng the propagatson.
When the ocean reflectson trength E 0 and atmo phere nos e trength are known, we can obtasn the receptson sgnal-to-nos e ratso SNR: where, 0 E s reflectson trength of calm ocean, n E s the atmo phere nos e trength.
Accordsng to the electromagnetsc fseld theory, we can know the relatson between SNR and power P s a followsng: 10 10 .

Experimental results of the model
Through the erse of formula sn the upper ectson , we can get the dsfferent hop number between the calm ocean urface and the turbulent ocean urface.
Here, we et the snstsal ky wave sgnal tran msttsng power s 100 watt.
Atmo phersc nos e s the masn ource of nos e sn marstsme communscatson, whsch s masnly cau ed by lsghtnsng. Becau e nos e s affected by the sono phere, and the trength of nos e wsll alter wsth the frequency, ea on, geographscal po stson and clsmate. Generally, the snten sty of atmo phersc nos e wsll decrea e wsth the sncrea e of frequency. The atmo phersc radso nos e snten sty formula [6] s :