**3. Dynamic link calculation**

#### **3.1 Dynamic link formulas of interest**

This section provides a summary of the dynamic link model of interest [6]. More detailed derivation of other variables, especially UVZBD, UVYBD, and UVXBD, can be found in [5]. For station elevation angle, either LV or SV elevation or cone angle (EL or theta or ϴ), and LV or SV clock or azimuth angle (AZ or Phi or Ф), we have1

$$\text{Cone Angle} = \frac{180^0}{\pi} \cos^{-1} \left( \frac{\underline{\text{UVZBD}} \cdot (-\underline{\text{S}} \underline{\text{R}})}{|\underline{\text{S}} \underline{\text{R}}|} \right) \text{in Deg} \tag{1}$$

$$\text{EL} = 90^0 - \frac{180^0}{\pi} \cos^{-1} \left( \frac{\underline{\text{GS}} \cdot \underline{\text{SR}}}{|\underline{\text{GS}}| \* |\underline{\text{SR}}|} \right) \text{ in Deg} \tag{2}$$

$$\varphi = \frac{180^0}{\pi} \tan 2^{-1} \left( \frac{\text{UVXBD} \cdot (-\underline{\text{SR}})}{|\underline{\text{SR}}|}, \frac{\text{UVYBD} \cdot (-\underline{\text{SR}})}{|\underline{\text{SR}}|} \right) \text{in } \text{Deg} \tag{3}$$

Clock Angle ¼ Ф � Offset

#### **3.2 Tracking signals and link analyses along the trajectory**

As mentioned in the introduction, there are three separate tracking signals along the flight trajectory that we need to analyze ensuring that they have adequate link margins of three dB or more. Most of the present DLA covers only two stages of launch coverage and neglecting the third stage coverage. The requirement for third stage tracking is explained below:

<sup>1</sup> The authors would like to thank Dr. James Yoh for his derivation of these formulas.

1.From liftoff to the end of LOS, the waveform for this link is generally a digital FM or BPSK for telemetry downlink as defined in the Range Commander Council (RCC) 119-88 [2]. The liftoff to LOS 5 link margin plot is shown in the left half of **Figure 3** for five different ground stations.

2.From the end of LOS to NASA TDRSS at geosynchronous orbit, the telemetry link is a BPSK or QPSK (telemetry + data) which is sent from LV to TDRSS to be relayed to White Sands or Goddard ground station (WSGT/GRGT), as shown in the second right half of the **Figure 3** and in more link details in

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle*

*DOI: http://dx.doi.org/10.5772/intechopen.92462*

3.For the third link after SV payload separation, when the satellite or SV starts its transfer orbit, the tracking link from the SV payload (or bus) to an AFSCN ground station will be in SGLS, Unified S-Band (USB), or a NSGLS waveform as described in more detail in [3, 4]. For a more secure tracking, SV normally will be using SGLS link for tracking as described in [4], with a MEO satellite in **Table 2** as an example. A commercial and less secure SV launch may use USB

**Table 1**.

**Table 2.**

**167**

*Link budgets for SGLS TT&C uplink and downlink services [4].*

#### **Figure 3.**

*TLM dynamic link margin from TEL4 to TDRSS versus mission elapsed time.*


#### **Table 1.**

*LV to TDRSS range TLM link (based on NASA source).*

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle DOI: http://dx.doi.org/10.5772/intechopen.92462*



**Table 2.** *Link budgets for SGLS TT&C uplink and downlink services [4].*

1.From liftoff to the end of LOS, the waveform for this link is generally a digital FM or BPSK for telemetry downlink as defined in the Range Commander Council (RCC) 119-88 [2]. The liftoff to LOS 5 link margin plot is shown in the

left half of **Figure 3** for five different ground stations.

*Satellite Systems - Design, Modeling, Simulation and Analysis*

*TLM dynamic link margin from TEL4 to TDRSS versus mission elapsed time.*

**Figure 3.**

**Table 1.**

**166**

*LV to TDRSS range TLM link (based on NASA source).*


For the uplink, where the transmit antenna is located on the ground, the antenna

*c*

� � � � in dBi (5)

<sup>4</sup><sup>π</sup> <sup>∗</sup> <sup>f</sup>*<sup>C</sup>* <sup>∗</sup> SR � �<sup>2</sup> " # in dB (6)

can be easily directed to an LV or SV. This transmit antenna is likely to be a directional high gain dish antenna for connectivity with an LV or SV located possibly far away. In **Table 3**, line 9, a typical ground station has a large parabolic

*Gt* <sup>¼</sup> <sup>10</sup> <sup>∗</sup> log 10 <sup>η</sup> <sup>∗</sup> <sup>π</sup> <sup>∗</sup> <sup>f</sup>*<sup>C</sup>* <sup>∗</sup> <sup>D</sup>

where η = average antenna efficiency (0.70 in the calculation in **Table 3**); fC = uplink frequency, in Hz; D = antenna diameter, in m; and c = speed of light, in

For the downlink, the transmit antenna is typically an omnidirectional antenna that covers a larger portion of the sky or the Earth, in which case the antenna gain is small (e.g., 2 dBi) and is either specified as in line 9 of **Table 3** or can be interpolated from values extracted from a table of antenna gain pattern with a specific AZ,

In general, there are terms that may be added to **Tables 2** and **3**. For example, the uplink transmit antenna in **Table 3** may have two more loss terms, namely, radome loss to account for any loss for a radome and pointing loss to account for any pointing error in directing the boresight of the antenna. For **Table 3** they are both negligible and ignored except for the polarization losses. The transmit and receive polarization losses (lines 14 and 22, respectively, in **Table 3**) can be

The signal path traverses through the transmission medium, in between transmit

where fC = carrier frequency, in Hz; c = velocity of light, in m/s; and SR = slant

At L and S bands, the atmospheric loss is very small, at less than 0.001 dB/Km or

The transmit signal, after accounting for the space and atmospheric losses, and its signal path terminates at the antenna of either the ground station, the SV, or the LV receiving system. Before considering the characteristics of the receive antenna

and receive systems. When the distance between transmit and receive systems increases, the signal beam has an angular spread which decreases the signal power collected by a receiving antenna. We know that the portion of the transmission medium near the ground station depends on the Earth's atmosphere which attenuates the signal to different degrees, dependents on the frequency, the altitude of the GS, and the angle of the signal path through the atmospheric (GS elevation angle). Beyond the Earth's atmosphere, the signal path traverses through the space with little atmospheric attenuation, only with free space loss to account for. Therefore, there are essentially two losses through the transmission medium, namely, the space loss to account for the spreading of the signal beam and the additional atmospheric loss [7].

*LS* <sup>¼</sup> <sup>10</sup> <sup>∗</sup> log 10 *<sup>c</sup>*

0.1 dB/100Km for a link availability of better than 98% [8].

antenna dish with a gain Gt = 43.94 dBi using the following formula.

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle*

*DOI: http://dx.doi.org/10.5772/intechopen.92462*

EL, and MET, using a mission specific launch trajectory.

accounted for as one-single combined receive polarization loss.

**4.1 Transmission medium and losses**

range between GS and SV, in m.

**4.2 Received isotropic power**

**169**

m/s.

#### **Table 3.**

*Typical C/No for uplink and downlink budgets.*

or NSGLS for SV tracking instead of using SGLS waveform. **Table 3** shows link budget for uplink and downlink C/No example for tracking links 1 and 2. **Table 2** shows SGLS telemetry, tracking, and command (TT&C) link budget for tracking link 3 for a MEO satellite. If the SV is using a USB or a NSGLS [3], the tracking waveform can be an AQPSK signal with telemetry on the I channel and ranging on the Q channel.

#### **4. Basic link parameters and formulas**

This section describes the basic link parameters including LV or SV transmitter power amplifier gain (Pt), transmitter antenna gain (Gt), space loss (Ls), received isotropic power (RIP), and received (C/No = SNR).

A modulation signal or information data is generated at a ground station, in an LV or in an SV. This modulation signal will be used to modulate onto the radio frequency (RF) carrier to become a modulated transmit signal. This transmit system will be consisting of a high-power amplifier (HPA) which amplifies the signal to generate an output power expressed in dBW (conversion from Watts to dBW is simply dBW = 10\*log10(Watts)); some cables and circuits with a loss and an antenna with a gain are added together as shown below. The output from the transmit system is therefore an effective isotropic radiated power or EIRP, which can be found in either the uplink or the downlink of an LV or an SV tracking system.

$$\text{EIRP} = P\_T + L\_C + G\_t \text{ in dBW} \tag{4}$$

where Gt = transmit antenna gain, in dBi; LC = transmit circuit loss, in negative dB; and PT = HPA output power, in dBW.

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle DOI: http://dx.doi.org/10.5772/intechopen.92462*

For the uplink, where the transmit antenna is located on the ground, the antenna can be easily directed to an LV or SV. This transmit antenna is likely to be a directional high gain dish antenna for connectivity with an LV or SV located possibly far away. In **Table 3**, line 9, a typical ground station has a large parabolic antenna dish with a gain Gt = 43.94 dBi using the following formula.

$$G\_t = 10 \ast \log 10 \left[ \eta \ast \left( \frac{\pi \ast \mathbf{f}\_C \ast \mathbf{D}}{c} \right) \right] \text{ in dBi} \tag{5}$$

where η = average antenna efficiency (0.70 in the calculation in **Table 3**); fC = uplink frequency, in Hz; D = antenna diameter, in m; and c = speed of light, in m/s.

For the downlink, the transmit antenna is typically an omnidirectional antenna that covers a larger portion of the sky or the Earth, in which case the antenna gain is small (e.g., 2 dBi) and is either specified as in line 9 of **Table 3** or can be interpolated from values extracted from a table of antenna gain pattern with a specific AZ, EL, and MET, using a mission specific launch trajectory.

In general, there are terms that may be added to **Tables 2** and **3**. For example, the uplink transmit antenna in **Table 3** may have two more loss terms, namely, radome loss to account for any loss for a radome and pointing loss to account for any pointing error in directing the boresight of the antenna. For **Table 3** they are both negligible and ignored except for the polarization losses. The transmit and receive polarization losses (lines 14 and 22, respectively, in **Table 3**) can be accounted for as one-single combined receive polarization loss.

#### **4.1 Transmission medium and losses**

The signal path traverses through the transmission medium, in between transmit and receive systems. When the distance between transmit and receive systems increases, the signal beam has an angular spread which decreases the signal power collected by a receiving antenna. We know that the portion of the transmission medium near the ground station depends on the Earth's atmosphere which attenuates the signal to different degrees, dependents on the frequency, the altitude of the GS, and the angle of the signal path through the atmospheric (GS elevation angle). Beyond the Earth's atmosphere, the signal path traverses through the space with little atmospheric attenuation, only with free space loss to account for. Therefore, there are essentially two losses through the transmission medium, namely, the space loss to account for the spreading of the signal beam and the additional atmospheric loss [7].

$$L\_S = 10 \ast \log 10 \left[ \left( \frac{c}{4\pi \ast \mathbf{f}\_C \ast \mathbf{SR}} \right)^2 \right] \text{ in dB} \tag{6}$$

where fC = carrier frequency, in Hz; c = velocity of light, in m/s; and SR = slant range between GS and SV, in m.

At L and S bands, the atmospheric loss is very small, at less than 0.001 dB/Km or 0.1 dB/100Km for a link availability of better than 98% [8].

#### **4.2 Received isotropic power**

The transmit signal, after accounting for the space and atmospheric losses, and its signal path terminates at the antenna of either the ground station, the SV, or the LV receiving system. Before considering the characteristics of the receive antenna

or NSGLS for SV tracking instead of using SGLS waveform. **Table 3** shows link budget for uplink and downlink C/No example for tracking links 1 and 2. **Table 2** shows SGLS telemetry, tracking, and command (TT&C) link budget for tracking link 3 for a MEO satellite. If the SV is using a USB or a NSGLS [3], the tracking waveform can be an AQPSK signal with telemetry on the I

This section describes the basic link parameters including LV or SV transmitter power amplifier gain (Pt), transmitter antenna gain (Gt), space loss (Ls), received

A modulation signal or information data is generated at a ground station, in an LV or in an SV. This modulation signal will be used to modulate onto the radio frequency (RF) carrier to become a modulated transmit signal. This transmit system will be consisting of a high-power amplifier (HPA) which amplifies the signal to generate an output power expressed in dBW (conversion from Watts to dBW is simply dBW = 10\*log10(Watts)); some cables and circuits with a loss and an antenna with a gain are added together as shown below. The output from the transmit system is therefore an effective isotropic radiated power or EIRP, which can be found in either the uplink or the downlink of an LV or an SV tracking

where Gt = transmit antenna gain, in dBi; LC = transmit circuit loss, in negative

EIRP ¼ *PT* þ *LC* þ *Gt* in dBW (4)

channel and ranging on the Q channel.

*Satellite Systems - Design, Modeling, Simulation and Analysis*

isotropic power (RIP), and received (C/No = SNR).

**4. Basic link parameters and formulas**

*Typical C/No for uplink and downlink budgets.*

dB; and PT = HPA output power, in dBW.

system.

**168**

**Table 3.**

and the receiver, a good indication of the signal strength is given by the received isotropic power. RIP is simply the transmitter EIRP after subtracting off the losses of the transmission medium, i.e.

$$\text{RIP} = \text{EIRP} + L\_{\text{S}} + L\_{A} \text{ in dBW} \tag{7}$$

*<sup>N</sup>*<sup>0</sup> <sup>¼</sup> <sup>k</sup> dB <sup>þ</sup> <sup>10</sup> <sup>∗</sup> log ð Þ *TS* in dBW*=*Hz (11)

where k = Boltzmann's constant in dB = �228.6 dBW/KHz.

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle*

such as telemetry and ranging to evaluate their performance.

**5. Space vehicle link services**

*DOI: http://dx.doi.org/10.5772/intechopen.92462*

perform accurate ranging.

**5.1 SNR and link margin calculation**

power."

**171**

Using Eqs. (9) and (11), the ratio C/N0 at the receiver input is obtained in **Table 3**, line 31. It represents the final product before going into specific service(s)

For many SVs, we are interested in their uplink and downlink services. **Table 2** shows an example, taken from an IEEE paper [4]. This is the standard link budget, where the ground station is an AFSCN [3] remote tracking station (RTS) using SGLS waveform [3, 4]. The waveform is described in an AFSCN interface control document (ICD) [3] and is implemented in DLA, although other waveforms can be readily incorporated. The uplink has two services of interest—carrier and command —while the downlink has three services of interest: carrier, ranging, and telemetry. In general service margins are calculated for these five services. For the SGLS waveform, command is coupled with ranging and modulated on the uplink carrier; therefore command is also turned around at the SV along with ranging. This SGLS turnaround process explains the reason that **Table 2** shows a power allocation for command in the downlink and no calculation for its margin. As a result, downlink power allocated to command is essentially wasted while robbing power from other downlink services. The requirements and service margins for command and telemetry are expressed in Eb/N0, since it is the bit error rate (BER) that counts for both cases. The carrier and ranging are expressed in C/No given by a specific station. For ranging, it is the autocorrelation value between the decoded ranging code and the transmitted ranging code that needs to be maximized in order to successfully

**Table 2** represents uplink and downlink budgets for SGLS TT&C. Let us address the important aspects of the calculation of uplink and downlink services in the next few subsections. The role of modulation indices is to divide up the power for allocation to services. The modulation index is expressed in radians so that it can go right in as an argument in a sinusoidal or Bessel expression. If the modulation indices of all services are zero radians, no power is allocated to the services, and the carrier retains all the link power calculated in Section 4. If the modulation indices of services are not zero, portions of the power are taken from the carrier and allocated to the services. The remaining power stays with the carrier as the "residual carrier

After SV separation, we are dealing with the SV uplink and downlink using SGLS or NASA Unified S-Band waveforms as described in [3, 4]. For telemetry service, the requirement is SNR = Pservice/NoB = Eb Rb/NoB = Eb/No in dB. For carrier and ranging, the requirements are stated in terms of C/No as mentioned before. For acquisition, the uplink carrier loop bandwidth could be as high as +/� 100 KHz, while its tracking bandwidth could be as small as a few Hz. For the station the carrier tracking loop bandwidth is about 20–50 Hz, as in **Table 2** in line 36. For ranging, the bandwidth of 10 Hz represents ranging tracking loop bandwidth (**Table 2**, line 56), which corresponds to the sampling rate of the autocorrelation

where LA is the atmospheric loss extracted from tables or curves, in negative dB (very small at 0.02 dB/Km per Datron chart in L and S bands). Ls can also be obtained from the Datron calculator [8].

#### **4.3 Receive system and performance**

The last portion of **Table 3** addresses the receiving system and assesses how well it performs. This section involves with the calculation of the signal strength and the noise strength, resulting in the ratio of signal power over noise power density (C/N0). In general, we first address the signal power and then the noise power density. Line 21 provides for the receive antenna size consistent with the receive antenna gain to be calculated later. The next parameter in **Table 3** is the polarization loss, which accounts for the mismatching between the polarization axial ratios of the received signal and the receiving system. The axial ratio is the ratio of the major axis of an ellipse to its minor axis. For circularly polarized signal, the ratio should be 0 dB. Any deviation from 0 dB results in a polarization loss. Line 23 shows the values of receive antenna gain. For downlink in which the receive antenna is a dish antenna located at GS, Gr is calculated using the standard dish antenna equation (similar to Eq. (6) for Gt).

$$G\_r = 10 \ast \log 10 \left[ \eta \ast \left( \frac{\pi \ast \mathbf{f}\_C \ast \mathbf{D}}{c} \right) \right] \text{ in dBi} \tag{8}$$

where η = average antenna efficiency (assumed to be 0.6 in the calculation in **Table 3**); fC = downlink frequency, in Hz; D = antenna diameter, in m; and c = velocity of light, in m/s.

At the end, the received power at the antenna feed is just the sum of RIP, minus the polarization loss, plus the receive antenna gain, i.e.

$$\mathbf{C} = \mathbf{RIP} + L\_P + \mathbf{G}\_r \text{ in dBW} \tag{9}$$

where LP is the polarization loss, in negative dB.

For the downlink transmit antenna on the SV, as in the case of uplink receive antenna, the SV antenna is a broad beam Earth coverage (EC) omnidirectional type of SV antenna, with a gain of 2 dBi (see line 23 of **Table 3**).

For the noise power density (N0), we need to calculate the system temperature (TS) measured at the antenna feed. The system temperature is the sum of antenna sky temperature (TA) and the composite temperature from antenna line loss (LL) and low noise amplifier noise figure (NF) which are referred to the antenna feed. In linear quantity, TS is given by [1].

$$T\_S = T\_A + \left(\mathbf{10^{(L\_L + NF)/10}} - \mathbf{1}\right) \* \mathbf{290} \text{ in } \text{Deg} - \mathbf{K} \tag{10}$$

where NF = low noise amplifier noise factor, in dB and LL = line loss, in dB. The noise density (N0) is given by

*Dynamic Link from Liftoff to Final Orbital Insertion for a MEO Space Vehicle DOI: http://dx.doi.org/10.5772/intechopen.92462*

$$N\_0 = \text{k}\bar{\text{dB}} + 10 \ast \log\left(T\_{\text{S}}\right) \text{in dBW/Hz} \tag{11}$$

where k = Boltzmann's constant in dB = �228.6 dBW/KHz.

Using Eqs. (9) and (11), the ratio C/N0 at the receiver input is obtained in **Table 3**, line 31. It represents the final product before going into specific service(s) such as telemetry and ranging to evaluate their performance.
