RU2461124C1 - Method of information transfer in conditions of reflections (versions) - Google Patents

Abstract

FIELD: radio engineering.

SUBSTANCE: method is implemented as per means for selection of clock frequency values of pseudorandom sequence (PRS) of complex phase-shift signal, at which considerable attenuation of influence of fade-outs is provided due to reflections of signals from sea water surface under certain operating conditions of communication channel. On-line selection of PRS clock frequency values F_T is performed during pre-start preparation and possibility of changing PRS clock frequency values F_T in normal operation mode at changing the radio channel parameters taking place at various locations of space vehicle and sea-based subscriber station.

EFFECT: improving interference immunity of satellite radio channel of L-band.

3 cl, 5 dwg

Description

The invention relates to radio engineering, in particular to methods for receiving multipath signals in the L-frequency range (1.5 / 1.6 GHz), and can be used in systems of mobile satellite communications, navigation and data transmission to improve the quality of reception of digital information transmitted complex phase-manipulated signals in the conditions of their reflections, mainly from the sea surface, as well as from other types of the underlying surface in the absence of shading objects (for example, for the steppe, tundra, snow plain, etc.).

With multipath propagation, the received signal experiences fading, which significantly worsen the conditions for transmitting information, as a result of which the reliability of the received information sharply deteriorates, and its transmission speed drops. This circumstance determines the fundamental importance of taking into account the influence of signal reflections from the sea surface during energy calculations and selecting the characteristics of the radio channels of satellite information transmission systems, as well as the development of methods to increase the noise immunity of receiving fading signals in such systems.

A known method for estimating the level of multipath fading in the L-band due to reflections of the signal from the sea surface [Karasawa Y., Shiokawa T. Characteristics of L-band multipath fading due to sea surface reflection. IEEE Transactions on Antennas and Propagation, 1984, vol. AP-32, No. 6, pp. 618-623), which presents a technical solution for determining energy losses in a radio channel depending on the elevation angle, gain of the receiving antenna of the subscriber station, height and tilt of the sea wave. This technical solution is selected as the first analogue to the claimed method.

The disadvantage of the above first analogue is that it provides an estimate of the level of fading only of the harmonic signal and does not take into account the real structure of the signals currently used in satellite communication, navigation and data transmission systems, and, moreover, it does not propose a method of reducing the effect of fading in a marine satellite radio channel.

A known method of transmitting information in a multipath channel [Patent RU No. 2118052 C1, IPC Н04В 7/015 of 07.25.1996], selected as the second analogue. In this technical solution, to mitigate the effect of multipath in communication systems, complex phase-manipulated signals are used based on the phase manipulation of the carrier pseudo-random sequence with the corresponding correlation transformation on the receiving side. The specified second analogue is the closest in combination of essential features and the achieved result and is selected as a prototype to the claimed method.

The disadvantage of the prototype is that it is not effective enough in marine satellite communication, navigation and data transfer systems, since it does not take into account the specifics of the sea reflecting surface, which is almost always in motion (excited) and therefore cannot be described by any regular function.

The technical problem to which the claimed invention is directed is to achieve a significant attenuation of the effect of multipath fading in the L-band satellite channel due to reflections of signals from the sea surface and, as a result, increasing the noise immunity of receiving fading signals in mobile satellite communication systems, navigation and data transmission.

The technical result of the invention is to increase the noise immunity of a satellite radio channel of the L-band in the conditions of reflections of signals from the sea surface due to the fact that the clock frequency of the pseudorandom sequence (PSP) F _t of the complex phase-shift signal emitted from the spacecraft is selected based on the condition of ensuring the weakening effect of fading at a prior data on the parameters of the radio channel averaged during the operation of the spacecraft (SC) and subscriber station (AS) th home.

The essence of the claimed invention is as follows.

The sea surface is almost always in motion, i.e. is statistically rough and is therefore described using the apparatus of random functions. In this case, the signal reflected from such a surface is also random, while its statistical characteristics substantially depend on the ratio of the parameters of the uneven surface and the radio waves incident on it [Zubkovich SG "Statistical characteristics of radio signals reflected from the earth's surface." M .: Sov. Radio, 1968, p. 57].

The criterion for surface roughness is the Rayleigh parameter [Papa R.J., Lennon J.F. The dependence of rough surface scattering on surface height statistics and correlation function. - IEEE Transactions on Antennas and Propagation, 1987, vol. AP-35, No. 2, p. 240]:

,

,

волновое число в свободном пространстве;Where

free space wave number;

λ is the wavelength of the incoming signal;

h _in - the rms value of the height of the sea waves;

, α - угол места космического аппарата.θ _p , θ _p are the angle of incidence and the angle of reflection (scattering) of the incident wave, measured from the vertical direction, so

, α is the elevation angle of the spacecraft.

For u << 1, the sea surface practically creates a mirror coherent reflection at an angle equal to the angle of incidence, and for u >> 1 it scatters the energy of the incident signal in all directions. In this case, reflection from the surface is incoherent scattering, i.e. random process with a distribution depending on its statistical characteristics.

A sea wave in the general case consists of a main (primary) wave and shorter (secondary) waves superimposed on it (Fig. 3). However, since in the L-range the Rayleigh parameter characterizing the degree of surface roughness is much smaller for secondary waves than for the main one, their influence on the main wave can be neglected. In addition, we assume that the surface of the sea is uniformly rough, i.e. all its sections have the same height characteristics. In this case, the value of h _{is the} same over the entire surface.

When irregularities are large in comparison with the wavelength (h _in > λ / 4) and gentle slopes, and there is no shadowing of some surface elements with others, as is the case in the L-range, we can use the approximation-based method to calculate the reflected field Kirchhoff [see the above book of Zubkovich S.G., p.35]. In this case, the patterns of formation of the reflected signal can be described by geometric optics and by superposition of elementary reflections from many separate planes tangent to the surface of the sea wave at its corresponding points.

Random parameters characterizing the state of the sea surface are the height of the crests of the sea waves and their slope relative to the horizon, given by the rms values of h _in and β _in , as well as the correlation interval of the surface l ₀ , i.e. such a distance between points of a random surface at which the statistical relationship between them becomes negligible.

. В дальнейшем используется соотношение H=4h_в.The size of the irregularities is characterized by the height H of their maximum range from the foot to the top. In oceanology, for different types of waves, the ratio h _in / N is taken equal to 0.19-0.24 [see the above-mentioned book of Zubkovich SG, p. 70], whence it follows that the wave height H is related to h _{in the} ratio

. In what follows, the ratio H = 4h _in .

The standard deviation of the tilt of the sea wave β _in is determined on the basis of statistical data on the oceans collected in a literature over a long period of time. So, in the case when the wave height H varies from 1 to 4 m, which prevails most of the time, the rms value of the slope of the sea waves varies between 0.04-0.07 [Karasawa Y., Shiokawa T., Characteristics of L- band multipath fading due to sea surface reflection. - IEEE Transactions on Antennas and Propagation, 1984, vol. AP-32, No.6, p.620].

The fade level Fd of the received signal due to its reflections from the sea surface is determined from the following equation:

,

,

where p is the probability with which during the communication session the level of fading in the radio channel does not exceed the calculated value;

- плотность распределения вероятностей нормированной огибающей U_фл флюктуирующего сигнала, поступающего на корабельную антенну,

- the probability distribution density of the normalized envelope U _fl fluctuating signal supplied to the ship's antenna,

where φ is the phase difference due to the path difference between the direct signal U _p and the coherent component U _{k of the} reflected signal;

I ₀ (x) is the modified zero-order Bessel function;

- нормированная амплитуда когерентной составляющей отраженного сигнала,

- the normalized amplitude of the coherent component of the reflected signal,

Where

is the normalized voltage value at the output of the correlator in the interval (0, τ ₀ );

τ ₀ = 1 / F _t - the duration of the element of the complex phase-manipulated signal;

F _t - the clock frequency of the pseudo-random sequence;

B _c = F _t / R _t - the base of a complex phase-shifted signal;

R _t - the speed of information transmission in the channel;

τ = L _x / c is the delay in the arrival of the reflected signal to the input of the receiver due to the travel difference between the direct and reflected signals to the receiving point;

c is the propagation velocity of electromagnetic waves;

- разность хода между прямым и отраженным сигналами до точки приема;

- the path difference between the direct and reflected signals to the receiving point;

θ _a is the angle between the direction to the spacecraft and the direction of arrival of the reflected signal;

- расстояние между приемной антенной и элементарной площадкой отражения;

- the distance between the receiving antenna and the elementary reflection platform;

H _a - antenna installation height above mean sea level;

G (2α) is the gain of the receiving antenna in the direction of the specular reflection point relative to the direction to the spacecraft;

F (θ _p ) is the Fresnel reflection coefficient from the sea surface for waves with circular polarization in the L-band.

A circularly polarized wave can be represented as two linearly polarized waves, whose amplitudes are equal, the plane of polarization is mutually perpendicular, and the phases are shifted by an angle π / 2. As the orthogonal components of the signal, vertical and horizontal polarization components are used, for which

in this case, the orthogonal components of the complex Fresnel reflection coefficient are determined by known formulas:

- вертикальная составляющая;

- vertical component;

- горизонтальная составляющая,

- horizontal component

where ε is the dielectric constant of sea water;

γ is the specific conductivity of sea water [S / m].

Dispersion of the normalized incoherent component of the reflected signal

,

,

where φ _p is the scattering angle in the horizontal plane;

A is the area of the reflecting section of the sea surface;

- удельная эффективная площадь рассеяния поверхности моря,

- specific effective area of dispersion of the sea surface,

;Where

;

- дисперсия наклона морской волны;

- variance of the slope of the sea wave;

S (θ _p , θ _p ) is the function of shading the incoming signal by sea waves [Smith B.G. Geometrical shadowing of a random rough surface. - IEEE Transactions on Antennas and Propagation, 1967, vol. AP-15, No. 5, p.671].

Thus, the claimed method allows to evaluate the level of multipath fading Fd in the satellite radio channel of the L-band (figure 4), as well as to determine such values of the clock frequency of the pseudorandom sequence F _t complex phase-shift signal, which provides a significant reduction of the effect of fading in the communication channel (Fig .5) and, as a consequence, an increase in its noise immunity under conditions of reflections from the sea surface.

The values of the parameters of the radio channel according to the first embodiment of the invention are selected as a result of averaging their values during the operation of the spacecraft and sea-based speakers, and according to the second embodiment, as a result of measuring their values.

Devices (the applicant does not claim to protect them - approx. The applicant) for implementing variants of the claimed method of transmitting information in the conditions of reflections are illustrated by the following figures:

- figure 1 presents the General structural diagram of a device for implementing the claimed method of transmitting information under reflection conditions according to claims 1, 2 of the formula;

- figure 2 presents a structural diagram of a device for transmitting information in the conditions of reflections that implements the claimed method according to claim 3 of the formula;

- figure 3 presents a model of a sea wave;

- figure 4 shows the qualitative dependence of the level of fading Fd from elevation angle α for the case of an excited sea surface (H = 1 m) with β _b = 0.04-0.07;

- figure 5 shows qualitatively the attenuation of the influence of reflections in the marine satellite channel of the L-band when using complex phase-shifted signals with a clock frequency of the pseudo-random sequence F _t .

A device for implementing the inventive method according to claims 1, 2 of the formula comprises a unit 1 for generating and emitting a complex phase-manipulated signal with a clock frequency of a pseudo-random sequence F _t , configured to generate a pseudo-random sequence with a clock frequency F _t and a unit 2 for receiving and processing a complex phase-manipulated signal with the clock frequency of the pseudo-random sequence F _t made with the possibility of generating a pseudo-random sequence with a clock frequency F _t (figure 1).

A device that implements the claimed method according to claim 3 of the formula and shown in figure 2, further comprises a control panel 3 clock frequency of the pseudo-random sequence F _t , communication line equipment 4, computing unit 5, meter 6, wave height H, meter 7, tilt sea wave relative to the horizon line β _in and the meter 8 of the elevation angle of the spacecraft α.

The unit 1 for generating and emitting a complex phase-manipulated signal with a clock frequency of the pseudo-random sequence F _t on the spacecraft generates and emits a complex phase-manipulated signal with a clock frequency of the pseudo-random sequence F _t and is configured to generate an SRP with a clock frequency of F _t .

The unit 2 for receiving and processing a complex phase-shifted signal with a clock frequency of a pseudo-random sequence F _t at a sea-based subscriber station receives and processes a complex phase-manipulated signal with a clock frequency of a pseudo-random sequence F _t and is configured to generate a bandwidth with a clock frequency of F _t .

Control panels 3 clock frequency PSP F _t connected to the control inputs of unit 1 for generating and emitting a complex phase-manipulated signal with a clock frequency of a pseudo-random sequence F _t and block 2 for receiving and processing a complex phase-manipulated signal with a clock frequency of a pseudo-random sequence F _t on KA and AS, respectively. The control panels form commands (control signals) that are supplied to the control inputs of blocks 1 and 2 to generate the clock frequency of the pseudo-random sequence F _ti , where i = 1, 2 ... N, N is the number of states of the communication channel, using controlled PSP generators included in the composition of blocks 1 and 2, based on the calculation of F _ti made by computing unit 5. (The above-mentioned controlled PSP generators are not shown in Figs. 1 and 2, since, according to the applicant, this is not necessary - the applicant’s note.

Computing unit 5 calculates the frequency values of the pseudo-random sequence F _ti corresponding to the specific conditions of the radio channel that occur at various locations of the spacecraft and the sea-based subscriber station and a priori data on the parameters of the radio channel - sea wave height H, sea wave tilt relative to the horizon line β _in and the elevation angle α of the spacecraft averaged over the life of the spacecraft and sea-based ASs or their measured values.

The equipment of the communication line 4, located on a spacecraft or sea-based subscriber station and connecting control panels 3 with a frequency of SRP F _t on a spacecraft and on a sea-based AS, is capable of transmitting information about the values of the clock frequency of the pseudorandom sequence F _ti . Moreover, as the equipment of the communication line, a standard radio information transmission line can be used. In this way, an operative adjustment of the clock frequencies F _{t is} ensured during the normal operation when the location of the spacecraft and / or sea-based subscriber station changes.

The functioning of the device in dynamic mode, which implements the claimed method according to claim 3 of the formula, is as follows.

The meter 6 of the height of the sea wave H, the meter 7 of the inclination of the sea wave β _in and the meter 8 of the elevation angle of the spacecraft α measure the indicated parameters H, β _in and α, respectively. Based on the measurement of these parameters, the computing unit 5 calculates the clock frequency of the pseudo-random sequence F _ti corresponding to the specific conditions of the radio channel, which occur at different locations of the spacecraft and sea-based subscriber station.

We show the possibility of carrying out the invention, i.e. the possibility of its industrial application.

Units 1 for generating and emitting a complex phase-manipulated signal with a clock frequency of SRP F _t and 2 for receiving and processing a complex phase-manipulated signal with a clock frequency of SRP F _{t are} known from the prototype or from the following information sources: L. Varakin "Communication systems with noise-like signals." - M .: Radio and communications, 1985, p. 329-343; "Global Navigation System NAVSTAR." - "Foreign Radio Electronics", 1980, No. 8, p. 59-63.

We show a rule (method) by which a control panel 3 of the frequency of the pseudo-random sequence F _t and a controlled generator of the SRP can be obtained.

The control panel 3 frequency PSP F _t , the task of which is to select the value of the clock frequency F _t , in the simplest case is a driver of the control signal, for example, the voltage supplied to the control inputs of blocks 1 and 2, and specifically to the control inputs of the PSP generators. This control signal (voltage value), arriving, for example, on the varicap of the master crystal oscillator, which is part of the controlled PSP generator, changes its clock frequency to the required value (see, for example, Altshuller GB and other “Crystal oscillators” - M.: Radio and Communications, 1984, p.145-150). Another technical solution is also possible for changing the clock frequency of the memory bandwidth, described, for example, in the book Golembo V.A., Kotlyarov V.L., Shvetsky B.M. "Piezoelectric amplitude-to-digital temperature transducers." - Lviv: LSU, 1977, p.171 and consisting in the use of a controlled frequency divider, i.e. frequency divider with an arbitrary division factor. Note that the specified divider operates with a control signal in the form of a binary code, therefore, in this case, the control panel 3 of the SRP frequency F _t must generate control commands in binary code (or incorporate an amplitude-to-digital converter for converting a constant control voltage to binary code ) The specified frequency divider can be installed at the output of the controlled generator PSP, thus setting the desired value of the clock frequency F _t

Essentially, controlled PSP generators are known and widely used: see, for example, patent RU No. 1840447 A1, IPC Н04В 5/02 of 05/28/1979, patent RU No. 1840167 A1, IPC Н04М 13/00, H04L 7/00 from 01/22/1985

However, in the indicated sources of information their structure is not fully disclosed, therefore the applicant, for concreteness, also cited the obvious rule (method) for constructing such a controlled generator of bandwidth.

The equipment of the communication line 5, which provides information on the clock frequencies of the memory bandwidth F _ti , is known, see, for example, information sources: Penin P.I. "Digital Information Transmission Systems". Textbook for universities. - M .: Owls. Radio, 1976, p. 342-345; Spilker J. "Digital Satellite Communications". Per. from English - M .: Communication, 1979, p. 15-21.

The computing unit 5, which provides the calculation of the clock frequencies of the memory bandwidth F _ti , is described in the application materials at a functional level, and its implementation involves the use of a programmable tool. Such programmable tools are known: a personal computer, computers, see, for example, information sources: Pyatibratov A.P., Gudyno L.P., Kirichenko A.A. "Computing systems, networks and communications." - M.: Finance and statistics. 2004, p.1-273; Pool L. "Work on a personal computer." Per. from English - M .: Mir, 1986, p. 73-88.

The measuring instrument 6 of the height of the sea wave H is known: see, for example, A. Zagorodnikov "Radar survey of sea waves." - L .: Gidrometeoizdat, 1978, p. 141-158; Vanaev A.P., Chernyavets V.V. “Determination of wave parameters by a combined system for measuring ship speed and wave height.” - “Shipbuilding”, 1993, No. 8-9, p.6-8; RU patent No.2328757 C2, IPC G01W 1/04, G01C 13/00, B63B 22/00 dated 09/04/2006

The measure of the inclination of the sea wave β _in is known: see, for example, patent RU No. 2231033 C2, IPC G01L 11/00, G01P 5/00 from 09/17/2002; RU patent No.2328757 C2, IPC G01W 1/04, G01C 13/00, B63B 22/00 dated 09/04/2006

The measuring instrument 8 of the elevation angle of the spacecraft α is a direction finder (see, for example, “Handbook of Radio Electronic Systems.” Edited by B.X. Krivitsky, vol. 2. - M .: Energia, 1979, p.165-169) ; RU patent No. 2144200 C1, IPC G01S 3/14, G01S 3/74 dated 06/17/1999

Claims (3)

1. A method of transmitting information under reflection conditions, which consists in emitting from a spacecraft a complex phase-manipulated signal with a clock frequency of a pseudorandom sequence F _t , receiving signals directly and reflected from the sea surface at a sea-based subscriber station, and processing the total fluctuating signal with subsequent isolation of the transmitted message, characterized in that the value of the clock frequency of the pseudorandom sequence F _t emitted from the spacecraft complex fa the manipulated signal is determined based on the conditions for ensuring the weakening of the effect of fading in the radio channel with probability p according to the formula:

where p is the probability with which during the communication session the effect of fading in the radio channel does not exceed the calculated value;
Fd is the depth of fading of the received signal due to its reflections from the sea surface;

the probability distribution density of the normalized envelope U _fl fluctuating signal supplied to the ship's antenna,
where φ is the phase difference due to the path difference between the direct signal U _p and the coherent component U _{k of the} reflected signal;
I ₀ (x) is the modified zero-order Bessel function;

normalized amplitude of the coherent component of the reflected signal,
Where

,
is the normalized voltage value at the output of the correlator in the interval (0, τ ₀ );
τ ₀ = 1 / F _t - the duration of the element of the broadband signal;
F _t - the clock frequency of the pseudo-random sequence;
B _c = F _t / R _t - the base of a complex phase-shifted signal;
R _t - the speed of information transmission in the channel;
τ = L _x / c is the delay in the arrival of the reflected signal to the input of the receiver due to the travel difference between the direct and reflected signals to the receiving point;
C is the propagation velocity of electromagnetic waves;

- the path difference between the direct and reflected signals to the receiving point;
θ _a is the angle between the direction to the spacecraft and the direction of arrival of the reflected signal;

- the distance between the receiving antenna and the elementary reflection platform;
H _a - antenna mounting height above mean sea level;
G (2α) is the gain of the receiving antenna in the direction of the specular reflection point relative to the direction to the spacecraft;
F (θ _p ) is the Fresnel reflection coefficient from the sea surface for waves with circular polarization in the L-band;
the complex orthogonal components of the Fresnel reflection coefficient from the sea surface for waves with circular polarization are determined by the expressions:

vertical component;

horizontal component
where ε is the dielectric constant of sea water;
γ is the specific conductivity of sea water [S / m];

- Rayleigh parameter;

- wave number in free space;
λ is the wavelength of the incoming signal;
h _in - the rms value of the height of the sea waves;
θ _p , θ _p - respectively, the angle of incidence and angle of reflection of the radio waves incident on the sea surface, measured from the vertical direction;

,
where α is the elevation angle of the spacecraft;
in its turn:

variance of the normalized incoherent component of the reflected signal,
where φ _p is the scattering angle in the horizontal plane;
A is the area of the reflecting section of the sea surface;

specific effective scattering area of the sea surface,

- variance of the slope of the sea wave;
S (θ _p , θ _p ) is the function of shading the incoming signal by sea waves;
G ² (θ _p , φ _p ) is the square of the gain of the receiving antenna in the direction of the reflecting section of the sea surface with area A;
at the same time, the values of the radio channel parameters used in the calculation formulas — the height of the sea wave H, the inclination of the sea wave relative to the horizon line β _в and the elevation angle α of the spacecraft α are selected averaged over a priori data during the functioning of the spacecraft and a subscriber-based sea-based station at their given locations, also known as the radiation pattern of the receiving antenna G (θ _a ) and the height of its installation above the mean sea level H _a . 2. The method according to claim 1, characterized in that the values of the radio channel parameters used in the calculation formulas are selected at different locations of the spacecraft and the sea-based subscriber station, which are used when changing the location of the spacecraft and the sea-based subscriber station. 3. A method of transmitting information under reflection conditions, which consists in emitting from a spacecraft a complex phase-manipulated signal with a clock frequency of a pseudorandom sequence F _t , receiving signals directly and reflected from the sea surface at a sea-based subscriber station, and processing the total fluctuating signal with subsequent isolation of the transmitted message, characterized in that the determined height aqua H, aqua inclination β relative to the horizon _in a place location Dialing of a marine station, determine the elevation angle of the spacecraft α, and the clock frequency of the pseudo-random sequence F _t of the complex phase-shift signal emitted from the spacecraft is determined based on the condition of ensuring the weakening of the effect of fading in the radio channel with probability p according to the formula:

where p is the probability with which during the communication session the effect of fading in the radio channel does not exceed the calculated value;
Fd is the depth of fading of the received signal due to its reflections from the sea surface;

the probability distribution density of the normalized envelope U _{fl of the} fluctuating signal supplied to the ship’s antenna, where φ is the phase difference due to the path difference between the direct signal U _p and the coherent component U _{k of the} reflected signal;
I ₀ (x) is the modified zero-order Bessel function;

normalized amplitude of the coherent component of the reflected signal,
Where

,
is the normalized voltage value at the output of the correlator in the interval (0, τ ₀ );
τ ₀ = 1 / F _t - the duration of the element of the broadband signal;
F _t - the clock frequency of the pseudo-random sequence;
B _c = F _t / R _t - the base of a complex phase-shifted signal;
R _t - the speed of information transmission in the channel;
τ = L _x / c is the delay in the arrival of the reflected signal to the input of the receiver due to the travel difference between the direct and reflected signals to the receiving point;
C is the propagation velocity of electromagnetic waves;

- the path difference between the direct and reflected signals to the receiving point;
θ _a is the angle between the direction to the spacecraft and the direction of arrival of the reflected signal;

- the distance between the receiving antenna and the elementary reflection platform;
N _a - antenna installation height above mean sea level;
G (2α) is the gain of the receiving antenna in the direction of the specular reflection point relative to the direction to the spacecraft;
F (θ _p ) is the Fresnel reflection coefficient from the sea surface for waves with circular polarization in the L-band;
the complex orthogonal components of the Fresnel reflection coefficient from the sea surface for waves with circular polarization are determined by the expressions:

vertical component;

horizontal component
where ε is the dielectric constant of sea water;
γ is the specific conductivity of sea water [S / m];

- Rayleigh parameter;

free space wave number;
λ is the wavelength of the incoming signal;
h _in - the rms value of the height of the sea waves;
θ _p , θ _p - respectively, the angle of incidence and angle of reflection of the radio waves incident on the sea surface, measured from the vertical direction;

where α is the elevation angle of the spacecraft;
in its turn:

variance of the normalized incoherent component of the reflected signal,
where φ _p is the scattering angle in the horizontal plane;
A is the area of the reflecting section of the sea surface;

specific effective scattering area of the sea surface,
Where

- variance of the slope of the sea wave;
S (θ _p , θ _p ) is the function of shading the incoming signal by sea waves;
G ² (θ _p , φ _p ) is the square of the gain of the receiving antenna in the direction of the reflecting section of the sea surface with area A;
at the same time, the current values of the radio channel parameters are used in the calculation formulas - the height of the sea wave H, the inclination of the sea wave relative to the horizon line β _in and the elevation angle of the spacecraft α and the known type of the radiation pattern of the receiving antenna G (θ _a ) and its height above average sea level N _a .

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