CN103684632A - Modeling method for Ka waveband channel from deep-space spacecraft to earth - Google Patents

Abstract

The invention provides a modeling method for a Ka waveband channel from a deep-space spacecraft to the earth. The method includes building a deep-space relay network framework from the deep-space spacecraft to the earth; determining channel composition of a network according to the deep-space relay network framework and a transmission environment; determining factors and parameters, influencing Ka waveband channel modeling, in each channel; according to the determined influencing factors and parameters, building a Ka waveband channel model from the deep-space spacecraft to the earth. Influence of Doppler effect on modeling is fully taken into consideration, so that the built Ka waveband channel model has strong effectiveness, a theoretical basis is provided for a Ka waveband deep-space communication relay network, and Ka waveband channel model has great applicative significance in studying signal modulation, coding mode and power control technology of the Ka waveband deep-space communication relay network.

Description

A kind of deep space spacecraft is to the Ka band channel modeling method of the earth

Technical field

The present invention relates to deep space communication field, relate in particular to a kind of deep space spacecraft to the Ka band channel modeling method of the earth.

Background technology

In recent years, along with development and the increase to bandwidth demand of survey of deep space, the personnel of more and more research satellite systems start to utilize Ka wave band to carry out ground null link.In order to design and to optimize Ka band satellite link in deep space communication, a fair understanding and the dynamic behavior modeling of propagation channel is very important.At present, the Ka band channel modeling method for deep space spacecraft to the earth, has only considered the impact of the factors such as weather, shade, does not consider Doppler effect, and the model validity that causes current modeling method to be set up is lower.

Summary of the invention

The object of the present invention is to provide a kind of deep space spacecraft to the Ka band channel modeling method of the earth, the lower problem of model validity of setting up to the Ka band channel modeling method of the earth to solve current deep space spacecraft.

For solving the problems of the technologies described above, a kind of deep space spacecraft provided by the invention, to the Ka band channel modeling method of the earth, comprising: build deep space spacecraft to the deep space junction network framework of the earth; The channel of determining this network to deep space junction network framework and the transmission environment of the earth according to deep space spacecraft forms; Determine the factor and the parameter that in each several part channel, affect the modeling of Ka band channel; According to the influencing factor of determining in previous step and parameter, build deep space spacecraft to the Ka band channel model of the earth.

Preferably, described structure deep space spacecraft to the method for the deep space junction network framework of the earth is: deep space spacecraft is divided into deep space relaying backbone network and earth's surface network to the deep space junction network of the earth; Described deep space relaying backbone network (Deep Space Relaying Backbone Network, DSRBN) refers to the network between deep space spacecraft and near-earth relay spacecraft; Described earth's surface network (Earth Surface Network, ESN) comprises near-earth relay spacecraft, earth station and tellurian network.

Preferably, the described channel of determining this network to deep space junction network framework and the transmission environment of the earth according to deep space spacecraft forms, and comprising: deep space spacecraft is divided into the channel between channel, near-earth relay spacecraft and the ground station between deep space spacecraft and near-earth relay spacecraft to the channel of the deep space junction network of the earth.

Preferably, when satellite that near-earth relay spacecraft is geostationary orbit, the channel between described near-earth relay spacecraft and ground station adopts rician fading channel; When satellite that near-earth relay spacecraft is native to this world stationary orbit, the channel between described near-earth relay spacecraft and ground station adopts rayleigh fading channel.

Preferably, the factor and the parameter that in described definite each several part channel, affect the modeling of Ka band channel, comprising: the factor that affects Ka band satellite Channel Modeling in the channel between near-earth relay spacecraft and ground station comprises: system noise, first is apart from the loss that declines of loss, atmospheric absorption loss, rain; Corresponding parameter is: the ground system noise temperature T of system noise _sys, the first near-earth relay spacecraft apart from loss and the distance d between ground station, atmospheric absorption loss L _atmwith the rain loss L that declines _r; The factor that affects Ka band satellite Channel Modeling in channel between near-earth relay spacecraft and deep space spacecraft comprises: second distance loss, Doppler frequency shift, solar scintillation; Corresponding parameter is: the near-earth relay spacecraft of second distance loss and the distance d between deep space spacecraft _sc, be subject to the carrier frequency f of Doppler frequency shift impact _dthe I that affects with solar scintillation _rician.

Preferably, according to influencing factor parameter, structure deep space spacecraft to the Ka band channel model of the earth is:

$P_r=\frac{P_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{Amp}}{A}_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_\mathrm{<figure-callout\; id="2"\; label="t\; A\; sc"\; filenames="2013106246706100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">t</figure-callout>}}{A}_{\mathrm{sc}}^{}{}_2^{}{\mathrm{\&epsiv;}}_{\mathrm{sc}}^2{A}_g{\mathrm{\&epsiv;}}_g}{V_D^2{c}^2{d}_{\mathrm{sc}}^2{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="2013106246706100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">d</figure-callout>}}^2}\&CenterDot;f_D^2{f}^2{\left({\mathrm{kT}}_{\mathrm{sys}}\right)}^{-1}{(L_r+L_{\mathrm{atm}})}^{-1}$

Wherein, P _rthe Ka wave band energy that earth station receives, P _{sc_t}it is the energy of a deep space Spacecraft Launch; ε _ampit is the efficiency of amplitude of near-earth relay spacecraft; A _{sc_t}it is the antenna area of the deep space spacecraft that transmits; ε _{sc_t}it is the antenna efficiency of the deep space spacecraft that transmits; A _scand A _grespectively the area of near-earth relay spacecraft and ground-plane antenna, ε _scand ε _grespectively the efficiency of near-earth relay spacecraft and ground-plane antenna; F is carrier frequency; K is Boltzmann constant; V _dit is the relative speed between spacecraft; C is the light velocity.

The beneficial effect of technique scheme of the present invention is as follows:

The present invention is based on deep space junction network framework deep space spacecraft is divided into two different parts to the deep space channel of the earth, this is a kind of special polymorphic channel model that is applied to non-homogeneous communication environments.In deep space junction network, simulate Ka band satellite channel, and weather conditions have been considered, shade, the impact on Channel Modeling of the many factors such as Doppler frequency shift and solar scintillation, thereby the deep space spacecraft of setting up is to the Ka band channel model of the earth, this model can effectively reduce the error rate of signal transmission, there is very strong validity, for Ka wave band deep space communication junction network provides theoretical foundation, and the signal modulation of Ka wave band deep space communication junction network, coded system and power control techniques research are had to very large use meaning.

Accompanying drawing explanation

Fig. 1 is that a kind of deep space spacecraft of the present invention is to the Ka band channel modeling method schematic flow sheet of the earth;

Fig. 2 is that deep space spacecraft is to the deep space junction network configuration diagram of the earth.

Embodiment

For making the technical problem to be solved in the present invention, technical scheme and advantage clearer, be described in detail below in conjunction with the accompanying drawings and the specific embodiments.

As shown in Figure 1, a kind of deep space spacecraft provided by the invention, to the Ka band channel modeling method of the earth, comprising:

S1: build deep space spacecraft to the deep space junction network framework of the earth;

S2: the channel of determining this network to deep space junction network framework and the transmission environment of the earth according to deep space spacecraft forms;

S3: determine the factor and the parameter that affect the modeling of Ka band channel in each several part channel;

S4: according to the influencing factor of determining in previous step and parameter, build deep space spacecraft to the Ka band channel model of the earth.

As shown in Figure 2, building deep space spacecraft to the method for the deep space junction network framework of the earth is: deep space spacecraft is divided into deep space relaying backbone network 4 and earth's surface network 5 to the deep space junction network of the earth; Deep space relaying backbone network 4(Deep Space Relaying Backbone Network, DSRBN) refer to the network between deep space spacecraft 1 and near-earth relay spacecraft 3, wherein, deep space spacecraft refers to the distance of the earth's core O and is greater than 2 * 10 ⁶the spacecraft of km; Earth's surface network 5(Earth Surface Network, ESN) comprise near-earth relay spacecraft 3, ground station 6 and tellurian network.

Shown in Fig. 1 in method, the channel of determining this network to deep space junction network framework and the transmission environment of the earth according to deep space spacecraft forms, and comprising: deep space spacecraft is divided into the channel between channel, near-earth relay spacecraft and the ground station between deep space spacecraft and near-earth relay spacecraft to the channel of the deep space junction network of the earth.Preferably, when near-earth relay spacecraft 3 is the satellite of the earth 2 stationary orbits, in this case, near-earth relay spacecraft 3 is relative static with ground station 6, wherein the signal of transmission is by LOS(sighting distance) route determines, so the channel between near-earth relay spacecraft 3 and ground station 6 adopts rician fading channel; When near-earth relaying space flight 3 devices are the satellite of native to this world 2 stationary orbits, in this case, near-earth relay spacecraft 3 is not relative static with ground station 6, have multipath effect, so the channel between near-earth relay spacecraft 3 and ground station 6 adopts rayleigh fading channel in signal transmission.

To Ka wave band, the transmission in each several part channel is analyzed below, to illustrate factor and the parameter that affects the modeling of Ka band channel in how to confirm each several part channel:

1) in the channel between near-earth relay spacecraft and ground station, affect factor and the parameter of the modeling of Ka band channel

The factor that affects Ka band satellite Channel Modeling in channel between near-earth relay spacecraft 3 and ground station 6 comprises: system noise, first is apart from the loss that declines of loss, atmospheric absorption loss, rain; Corresponding parameter is: the ground system noise temperature T of system noise _sys, the first near-earth relay spacecraft apart from loss and the distance d between ground station, atmospheric absorption loss L _atmwith the rain loss L that declines _r;

It is specially:

A) system noise temperature T _sysfor:

T _sys＝T _eq+T _atm (1)

In formula, T _eqfor noise of equipment temperature; T _atmfor atmospheric noise temperature.

B) the rain loss L that declines _rfor:

L _r＝γ _rA _r(R _r,θ) (2)

In formula, γ _rbe the rainfall proportion of goods damageds, it is by rate of rainall R _rdetermine and can be obtained by statistics; A _r(R _r, θ) be the wave trajectory length through rain layer, A _r(R _r, be θ) by rate of rainall R _rbe connected elevation angle theta and determine.Because rainfall attenuation L _rfollow logarithm normal distribution, rainfall attenuation L _rprobability density function (pdfs) be:

$p_r=F\left(\ln L_r\right)={\&Integral;}_{\ln L_r}^{\&infin;}\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="2013106246706100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">r</figure-callout>}}\sqrt{2\mathrm{\&pi;}}}\exp (-\frac{{(\ln L_r-m_r)}^2}{2{\mathrm{\&sigma;}}_r^2})\mathrm{dx}---\left(3\right)$

σ wherein _r, m _rbe respectively rainfall attenuation L _rvariance and average, can be by rainfall proportion of goods damageds γ _r, rate of rainall R _r, connect elevation angle theta and obtain.The long-time statistical of rainfall attenuation can be expressed as:

$p_r^{\mathrm{LT}}=\left\{\begin{array}{cc}\frac{1}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_r}\frac{1}{L_r}\exp (-\frac{{(\ln L_r-m_r)}^2}{2{\mathrm{\&sigma;}}_r^2})& L_r>0\\ 0& L_r\&le;0\end{array}\right.---\left(4\right)$

C) atmospheric absorption loss L _atmfor:

$L_{\mathrm{atm}}\&ap;\left\{\begin{array}{cc}\frac{275}{275-T_{\mathrm{atm}}}& T_{\mathrm{atm}}<275\\ \&infin;& T_{\mathrm{atm}}\&GreaterEqual;275\end{array}\right.---\left(5\right)$

Wherein, T _atmfor atmospheric noise temperature.

D) signal transmits between near-earth relay spacecraft and ground station, the energy P that can receive on ground _rfor:

P _r＝P _Ampε _AmpA _scε _scA _gε _g(λd) ^-2(kT _sys) ^-1(L _r+L _atm) ^-1 (6)

In formula, P _ampenter the energy of near-earth relay spacecraft; ε _ampit is the efficiency of amplitude of near-earth relay spacecraft; A _scand A _grespectively the area of spacecraft and ground-plane antenna, ε _scand ε _grespectively the efficiency of spacecraft and ground-plane antenna; λ is the wavelength of radio wave (Radio Frequency, RF); K is Boltzmann constant;

To sum up, bring formula (1) (2) (3) into rainfall that formula (6) is, the pass between atmosphere and the energy that receives is:

$P_r=\left\{\begin{array}{cc}{\mathrm{\&alpha;}}_r\frac{1}{(T_{\mathrm{eq}}+T_{\mathrm{atm}})}\frac{275-T_{\mathrm{atm}}}{{\mathrm{\&gamma;}}_r{A}_r(R_r,\mathrm{\&theta;})(275-T_{\mathrm{atm}})}& T_{\mathrm{atm}}<275\\ 0& T_{\mathrm{atm}}\&GreaterEqual;275\end{array}\right.---\left(7\right)$

α wherein _r=P _ampε _ampa _scε _sca _gε _gk ^-1(λ d) ^-2.

2) in the channel between deep space spacecraft and near-earth relay spacecraft, affect factor and the parameter of the modeling of Ka band channel

The factor that affects Ka band satellite Channel Modeling in channel between near-earth relay spacecraft and deep space spacecraft comprises: second distance loss, Doppler frequency shift, solar scintillation; Corresponding parameter is: the near-earth relay spacecraft of second distance loss and the distance d between deep space spacecraft _sc, be subject to the carrier frequency f of Doppler frequency shift impact _dthe I that affects with solar scintillation _rician, be below specifically described:

According to the transmission environment of the channel channel between deep space spacecraft and near-earth relay spacecraft, this channel can be configured to awgn channel.First, for deep space communication spacecraft, outstanding feature of this section of channel is longer transmission path, this will cause very large path attenuation to signal transmission, produce second distance loss, consider the jumping between near-earth relay spacecraft and deep space spacecraft, the energy that near-earth relay spacecraft receives is P _{sc_r}, adopt following formula to calculate:

$P_{\mathrm{sc}\_r}=\frac{P_{\mathrm{sc}\_t}{A}_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_t}{A}_{\mathrm{sc}-r}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_r}}{{\mathrm{\&lambda;}}^2{d_{\mathrm{sc}}}^2}---\left(8\right)$

In above formula, P _{sc_r}it is the energy that near-earth relay spacecraft receives; P _{sc_t}it is the energy of deep space Spacecraft Launch; λ is RF wavelength; d _scit is the distance between near-earth relay spacecraft and deep space spacecraft; A _{sc_t}and A _{sc_r}it is respectively the antenna area that transmits and receives spacecraft; ε _{sc_t}and ε _{sc_r}it is respectively the antenna efficiency that transmits and receives spacecraft.

Secondly, because there is relative motion between spacecraft, so carrier frequency f is subject to the impact of Doppler frequency shift.Be subject to the carrier frequency f of Doppler frequency shift impact _dcan be expressed as:

$f_D=f\frac{V_D}{c}---\left(9\right)$

In formula (8), V _dbe the relative speed of spacecraft, c is the light velocity, can obtain:

$\mathrm{\&lambda;}=\frac{V_D}{f_D}---\left(10\right)$

$P_{\mathrm{sc}\_r}=\frac{P_{\mathrm{sc}\_t}{A}_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_t}{A}_{\mathrm{sc}-r}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_r}{f_D}^2}{{V_D}^2{d_{\mathrm{sc}}}^2}---\left(11\right)$

Finally, in deep space junction network, signal is also subject to the impact of solar scintillation.General, we represent by scintillation index the impact that solar scintillation brings.Make m represent scintillation index, when m<0.1, can obtain scintillation index and Lai Si index I _ricianpass be:

$I_{\mathrm{rician}}=\frac{\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="2013106246706100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}}{1-\sqrt{1-m^2}}---\left(12\right)$

By formula (11), can be found out, scintillation index and Lai Si index are inversely proportional.When m≤0.1, solar scintillation does not almost exert an influence to channel, therefore now can regard the channel between deep space spacecraft and near-earth relay spacecraft as Gaussian channel; When m>0.1, in order to compensate the impact of solar scintillation on radio signal, when communicating link design, need to give the link margin of the reserved 0.4dB of Ka wave band, could complete normally communication.

By the above-mentioned transimiison analysis to Ka wave band, we can obtain total expression formula of the received energy of ground station, from the Ka band channel model of deep space space flight 1 Qi Dao ground station 6, are:

$\begin{array}{c}{P}_r=\frac{P_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{Amp}}{A}_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_\mathrm{<figure-callout\; id="2"\; label="t\; A\; sc"\; filenames="2013106246706100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">t</figure-callout>}}{A_{\mathrm{sc}}}^{}{{}_{}}^2{{\mathrm{\&epsiv;}}_{\mathrm{sc}}}^2{A}_g{\mathrm{\&epsiv;}}_g}{{V_D}^2{c}^2{d_{\mathrm{sc}}}^2{d}^2}{f_D}^2{f}^2{\left({\mathrm{kT}}_{\mathrm{sys}}\right)}^{-1}{(L_r+L_{\mathrm{atm}})}^{-1}\\ =\frac{P_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{Amp}}{A}_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_\mathrm{<figure-callout\; id="2"\; label="t\; A\; sc"\; filenames="2013106246706100003DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">t</figure-callout>}}{A_{\mathrm{sc}}}^{}{{}_{}}^2{{\mathrm{\&epsiv;}}_{\mathrm{sc}}}^2{A}_g{\mathrm{\&epsiv;}}_g}{{V_D}^2{c}^2{d_{\mathrm{sc}}}^2{d}^2}m(f,f_D,P_0)\end{array}---\left(13\right)$

Wherein, P _rthe Ka wave band energy that earth station receives, P _{sc_t}it is the energy of a relay spacecraft transmitting; ε _ampit is the efficiency of amplitude of near-earth relay spacecraft; A _{sc_t}it is the antenna area of the deep space spacecraft that transmits; ε _{sc_t}it is the antenna efficiency of the deep space spacecraft that transmits; A _scand A _grespectively the area of spacecraft and ground-plane antenna, ε _scand ε _grespectively the efficiency of spacecraft and ground-plane antenna; F is carrier frequency; K is Boltzmann constant; V _dit is the relative speed between spacecraft; C is the light velocity; P ₀it is system unavailability ratio; M (f, f _d, P ₀) be multiplication factor, along with frequency increases and increases.

To sum up, the present invention is based on deep space junction network framework deep space spacecraft is divided into two different parts to the deep space channel of the earth, this is a kind of special polymorphic channel model that is applied to non-homogeneous communication environments.In deep space junction network, simulate Ka band satellite channel, and weather conditions have been considered, shade, the impact on Channel Modeling of the many factors such as Doppler frequency shift and solar scintillation, thereby the deep space spacecraft of setting up is to the Ka band channel model of the earth, this model can effectively reduce the error rate of signal transmission, there is very strong validity, for Ka wave band deep space communication junction network provides theoretical foundation, and the signal modulation of Ka wave band deep space communication junction network, coded system and power control techniques research are had to very large use meaning.

What deserves to be explained is, method provided by the invention is equally applicable to whole deep space relayed communications network, the i.e. Ka band channel modeling from earth surface network to other planetary surface networks, if for whole deep space communication network, will be divided into from earth surface network to other planetary surface networks earth's surface network, deep space relaying backbone network and planetary surface network three parts, wherein, earth's surface network, deep space relaying backbone network are identical with above described network, and planetary surface network (PSN) comprises the network on airborne vehicle, planetary surface entity and the planet that approaches planet.Obviously, now the Ka band channel from the earth to other planetary surface networks except above described near-earth relay spacecraft and the channel ground station, near-earth relay spacecraft and approach the channel between the deep space spacecraft of planet, also comprises and approaches the deep space spacecraft of planet and the channel between planetary surface network.Wherein, Ka band signal is similar to the transmission in the channel between near-earth relay spacecraft and ground station approaching the deep space spacecraft of planet and the transmission in the channel between planetary surface network, repeats no more herein.

It is more than the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, do not departing under the prerequisite of principle of the present invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (6)

1. deep space spacecraft, to a Ka band channel modeling method for the earth, is characterized in that, comprising:

Build deep space spacecraft to the deep space junction network framework of the earth;

The channel of determining this network to deep space junction network framework and the transmission environment of the earth according to deep space spacecraft forms;

Determine the factor and the parameter that in each several part channel, affect the modeling of Ka band channel;

According to the influencing factor of determining in previous step and parameter, build deep space spacecraft to the Ka band channel model of the earth.

2. a kind of deep space spacecraft as claimed in claim 1 is to the Ka band channel modeling method of the earth, it is characterized in that, described structure deep space spacecraft to the method for the deep space junction network framework of the earth is: deep space spacecraft is divided into deep space relaying backbone network and earth's surface network to the deep space junction network of the earth;

Described deep space relaying backbone network refers to the network between deep space spacecraft and near-earth relay spacecraft;

Described earth's surface network comprises near-earth relay spacecraft, earth station and tellurian network.

3. a kind of deep space spacecraft as claimed in claim 2 is to the Ka band channel modeling method of the earth, it is characterized in that, the described channel of determining this network to deep space junction network framework and the transmission environment of the earth according to deep space spacecraft forms, and comprising: deep space spacecraft is divided into the channel between channel, near-earth relay spacecraft and the ground station between deep space spacecraft and near-earth relay spacecraft to the channel of the deep space junction network of the earth.

4. a kind of deep space spacecraft as claimed in claim 3 is to the Ka band channel modeling method of the earth, it is characterized in that, when satellite that near-earth relay spacecraft is geostationary orbit, the channel between described near-earth relay spacecraft and ground station adopts rician fading channel; When satellite that near-earth relay spacecraft is native to this world stationary orbit, the channel between described near-earth relay spacecraft and ground station adopts rayleigh fading channel.

5. a kind of deep space spacecraft as claimed in claim 3, to the Ka band channel modeling method of the earth, is characterized in that, affects factor and the parameter of Ka band channel modeling in described definite each several part channel, comprising:

The factor that affects Ka band satellite Channel Modeling in channel between near-earth relay spacecraft and ground station comprises: system noise, first is apart from the loss that declines of loss, atmospheric absorption loss, rain; Corresponding parameter is: the ground system noise temperature T of system noise _sys, the first near-earth relay spacecraft apart from loss and the distance d between ground station, atmospheric absorption loss L _atmwith the rain loss L that declines _r;

The factor that affects Ka band satellite Channel Modeling in channel between near-earth relay spacecraft and deep space spacecraft comprises: second distance loss, Doppler frequency shift, solar scintillation; Corresponding parameter is: the near-earth relay spacecraft of second distance loss and the distance d between deep space spacecraft _sc, be subject to the carrier frequency f of Doppler frequency shift impact _dthe I that affects with solar scintillation _rician.

6. a kind of deep space spacecraft as claimed in claim 5, to the Ka band channel modeling method of the earth, is characterized in that, according to influencing factor parameter, structure deep space spacecraft to the Ka band channel model of the earth is:

$P_r=\frac{P_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{Amp}}{A}_{\mathrm{sc}\_t}{\mathrm{\&epsiv;}}_{\mathrm{sc}\_t}{A}_{\mathrm{sc}}^2{\mathrm{\&epsiv;}}_{\mathrm{sc}}^2{A}_g{\mathrm{\&epsiv;}}_g}{V_D^2{c}^2{d}_{\mathrm{sc}}^2{d}^2}\&CenterDot;f_D^2{f}^2{\left({\mathrm{kT}}_{\mathrm{sys}}\right)}^{-1}{(L_r+L_{\mathrm{atm}})}^{-1}$

Wherein, P _rthe Ka wave band energy that earth station receives, P _{sc_t}it is the energy of a deep space Spacecraft Launch; ε _ampit is the efficiency of amplitude of near-earth relay spacecraft; A _{sc_t}it is the antenna area of the deep space spacecraft that transmits; ε _{sc_t}it is the antenna efficiency of the deep space spacecraft that transmits; A _scand A _grespectively the area of near-earth relay spacecraft and ground-plane antenna, ε _scand ε _grespectively the efficiency of near-earth relay spacecraft and ground-plane antenna; F is carrier frequency; K is Boltzmann constant; V _dit is the relative speed between spacecraft; C is the light velocity.

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