Link budget
The carrier-to-noise ratio, CNR in dB, is calculated per the equation described in TR 38.821 Section 6.1.3.1, given by
\[\begin{equation} CNR=EIRP+Rx\frac{G}{T}-k-PL_{FS}-PL_{A}-PL_{SM}-PL_{SL}-PL_{AD}-B \end{equation}\]
where:
\(CNR\) is the carrier to noise ratio (also sometimes termed as SNR or signal to noise ratio) in dB
\(EIRP\) is the effective isotropic radiated power in dBW
\(Rx\frac{G}{T}\) is the antenna-gain-to-noise temperature in dB/K of the receiver
\(k\) is the Boltzmann constant with the value of -228.6 dBW/K/Hz
\(PL_{FS}\) is the free space path loss (FSPL) in dB
\(PL_{A}\) is the atmospheric path loss due to gases
\(PL_{SM}\) is the shadowing margin in dB
\(PL_{SL}\) is the scintillation loss in dB
\(PL_{AD}\) is the additional loss in dB
\(B\) is the channel bandwidth in dBHz (i.e., \(10\log_{10}(BW),\) where \(BW\) is bandwidth in Hz)
\(Rx\frac{G}{T}\) is obtained using the expression
\[\begin{equation} Rx\frac{G}{T}=G_{rx}-N_{f}-10\log_{10}\!\left(T_{0}+\left(T_{a}-T_{0}\right)\times 10^{-0.1\times N_{f}}\right) \end{equation}\]
where:
\(G_{rx}\) is the receive antenna gain in dBi.
\(N_{f}\) is the noise figure in dB
\(T_{0}\) is the ambient temperature in degrees Kelvin, set to \(290\) by default
\(T_{a}\) is the antenna temperature in degrees Kelvin.
The \(CNR\) expression is used in both directions i.e., terrestrial to satellite and satellite to terrestrial. The expressions below provide the formula for \(EIRP\) if the input is provided as \(EIRPDensity\) [dBW/MHz]
\[\begin{equation} EIRP\;[\text{dBW}]= EIRPDensity\;[\text{dBW/MHz}]+10\log_{10}(BW\;[\text{MHz}]) \end{equation}\]
Uplink Link Budget¶
The uplink link budget computes the signal quality from the UE to the satellite. Per 3GPP TR 38.821 Table 6.1.2, the uplink carrier-to-noise ratio is given by
\[\begin{equation} \left(\frac{C}{N}\right)_{\!UL} = EIRP_{UE} + \left.\frac{G}{T}\right|_{sat}\!(\theta) - 10\log_{10}(k) - 10\log_{10}(B_{Hz}) - L_{total} \end{equation}\]
where:
\(EIRP_{UE} = P_{Tx,UE} + G_{UE,Tx}\) is the UE effective isotropic radiated power in dBW. \(P_{Tx,UE}\) is the UE transmit power (total power, not a density) and \(G_{UE,Tx}\) is the UE transmit antenna gain in dBi.
\(G/T|_{sat}(\theta) = G_{sat,abs}(\theta) - 10\log_{10}(T_{sys,sat}) - NF_{sat}\) is the satellite receiver gain-to-noise temperature in dB/K, where \(G_{sat,abs}(\theta) = G_{max} + G_{rel}(\theta)\) is the absolute satellite antenna gain at off-boresight angle \(\theta\).
\(B_{Hz}\) is the channel bandwidth in Hz.
\(L_{total}\) is the total path loss (free-space path loss + shadow fading + clutter + additional losses) in dB, computed identically to the downlink.
The key differences between the downlink and uplink link budgets are summarized below.
| Parameter | Downlink | Uplink |
|---|---|---|
| Transmitter | Satellite | UE |
| Receiver | UE | Satellite |
| EIRP type | Density (dBW/MHz) | Total (dBm) |
| Whose G/T | UE G/T | Satellite G/T |
| Bandwidth in SNR | Cancels out | Remains |
A key distinction is that the satellite EIRP is specified as a density (dBW/MHz), so the bandwidth term cancels when computing DL SNR. In contrast, the UE EIRP is a total power (dBm), so the UL SNR depends explicitly on the channel bandwidth.
Example 1: Link budget for UE at Nadir Point; No interference; 2GHz S Band.
| Simulation Parameters | LEO 600km | LEO 1200km |
|---|---|---|
| Satellite coordinates (x, y, z) (User Input) | 0, 0, 600 | 0, 0, 1200 |
| UE coordinates (x, y, z) (User Input) | 0, 0, 0 | 0, 0, 0 |
| Frequency (User Input) | S-Band, n256 | S-Band, n256 |
| Terrestrial environment (User Input. Default based on sec 6.1.1.3 of 38.821) |
Rural | Rural |
| LOS probability (User Input. Per LOS probability in 3GPP TR 38.811 sec 6.6.1) |
1 | 1 |
| Antenna Aperture Radius(m) (User Input. Default based on Table 6.1.1.1-2 of 38.821) |
1 | 1 |
| EIRP density (dBW/MHz) (User Input. Default based on Table 6.1.1.1-1 of 38.821) |
34 | 40 |
| Bandwidth B (User Input. Default based on Table 6.1.3.2-1 of 38.821) |
30 | 30 |
| EIRP (dBW) \(= EIRP[dBW/MHz] + 10\log_{10} B[MHz]\). Per TR 38.821 section 6.1.3.1-5 |
48.77 | 54.77 |
| Elevation angle (Per Elevation angle formulas provided in 3GPP TR 38.811 sec 6.6.2) |
90 | 90 |
| Angular Antenna Gain \(G(\theta)\), (dB) (Per Bessel function formulas provided in 3GPP TR 38.811 sec 6.4.1) |
0 | 0 |
| Slant range \(d\) (Km) (Per slant height formulas provided in 3GPP T1 38.811 sec 6.6.2) |
600 | 1200 |
| Free space pathloss (dB), \(PL_{FS}\) (Per Free space pathloss formulas provided in 3GPP TR 38.811 sec 6.6.2) |
154.8 | 160.82 |
| Shadow loss (dB), \(PL_{SM}\) (Per Shadow loss formulas provided in 3GPP TR 38.811 sec 6.6.2) |
0.39 | 0.39 |
| Additional Loss(dB), \(PL_{AD}\) (User Input. Default based on Table 6.1.3.2-1 of 38.821) |
0 | 0 |
| Total Pathloss, L (dB) \(L = PL_{FS} + PL_{SM} + PL_{AD}\) |
155.19 | 161.21 |
| Rx Antenna Gain (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
0 | 0 |
| Noise figure \(N_f\) (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
7 | 7 |
| Rx Antenna Temp \(T_a\) (K) (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
290 | 290 |
| RX equivalent antenna Temp, \(T\) [\(dBK\)] (Per TR 38.821 section 6.1.3.1) |
31.62 | 31.62 |
| Receiver G/T \((dB/K)\) (Per RX G/T formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
\(-\)31.62 | \(-\)31.62 |
| Boltzmann constant \(k\) [\(dBW/K/Hz\)] | \(-\)228.6 | \(-\)228.6 |
| Carrier to Noise Ratio, CNR
(dB) (Per CNR formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
15.78 | 15.76 |
Example 2: Link budget for UE at Off Nadir Point; No interference; 2GHz S Band.
| Simulation Parameters | LEO 600km | LEO 1200km |
|---|---|---|
| Satellite coordinates (x, y, z) (User Input) | 0, 0, 600 | 0, 0, 1200 |
| UE coordinates (x, y, z) (User Input) | 17,18, 0 | 64,34, 0 |
| Frequency (User Input) | S-Band, n256 | S-Band, n256 |
| Terrestrial environment (User Input. Default based on sec 6.1.1.3 of 38.821) |
Rural | Rural |
| LOS probability (User Input. Per LOS probability in 3GPP TR 38.811 sec 6.6.1) |
1 | 1 |
| Antenna Aperture Radius(m) (User Input. Default based on Table 6.1.1.1-2 of 38.821) |
1 | 1 |
| EIRP density (dBW/MHz) (User Input. Default based on Table 6.1.1.1-1 of 38.821) |
34 | 40 |
| Bandwidth B (User Input. Default based on Table 6.1.3.2-1 of 38.821) |
30 | 30 |
| EIRP (dBW) \(= EIRP[dBW/MHz] + 10\log_{10} B[MHz]\). Per TR 38.821 section 6.1.3.1-5 |
48.77 | 54.77 |
| Elevation angle (Per Elevation angle formulas provided in 3GPP TR 38.811 sec 6.6.2) |
87.64 | 86.54 |
| Angular Antenna Gain \(G(\theta)\), (dB) (Per Bessel function formulas provided in 3GPP TR 38.811 sec 6.4.1) |
\(-\)4.2 | \(-\)10.26 |
| Slant range \(d\) (Km) (Per slant height formulas provided in 3GPP TR 38.811 sec 6.6.2) |
600.51 | 1202.19 |
| Free space pathloss (dB), \(PL_{FS}\) (Per Free space pathloss formulas provided in 3GPP TR 38.811 sec 6.6.2) |
154.81 | 160.84 |
| Shadow loss (dB), \(PL_{SM}\) (Per shadow loss formulas provided in 3GPP TR 38.811 sec 6.6.2) |
0.39 | 0.39 |
| Additional Loss(dB), \(PL_{AD}\) (User Input. Default based on Table 6.1.3.2-1 of 38.821) |
0 | 0 |
| Total Pathloss, L (dB) \(L = PL_{FS} + PL_{SM} + PL_{AD}\) |
155.20 | 161.23 |
| Rx Antenna Gain (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
0 | 0 |
| Noise figure \(N_f\) (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
7 | 7 |
| Rx Antenna Temp \(T_a\) (K) (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
290 | 290 |
| RX equivalent antenna Temp, \(T\) [\(dBK\)] (Per TR 38.821 section 6.1.3.1) |
31.62 | 31.62 |
| Receiver G/T \((dB/K)\) (Per RX G/T formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
\(-\)31.62 | \(-\)31.62 |
| Boltzmann constant \(k\) [\(dBW/K/Hz\)] | \(-\)228.6 | \(-\)228.6 |
| Carrier to Noise Ratio, CNR
(dB) (Per CNR formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
11.58 | 5.49 |
Example 3: Link budget with UE at Off Nadir Point with Interference; 2GHz S Band.
The calculations proceed exactly per Example 2 up to CNR. Once CNR is computed, interference is added and to obtain CNIR.
| Simulation Parameters | LEO 600km | LEO 1200km |
|---|---|---|
| Satellite coordinates (x, y, z) (User Input) | 0, 0, 600 | 0, 0, 1200 |
| UE coordinates (x, y, z) (User Input) | 17,18, 0 | 64,34, 0 |
| Frequency (User Input) | S-Band, n256 | S-Band, n256 |
| Terrestrial environment (User Input. Default based on sec 6.1.1.3 of 38.821) |
Rural | Rural |
| LOS probability (User Input. Per LOS probability provided in 3GPP TR 38.811 sec 6.6.1) |
1 | 1 |
| Antenna Aperture Radius(m) (User Input. Default based on Table 6.1.1.1-2 of 38.821) |
1 | 1 |
| EIRP density (dBW/MHz) (User Input. Default based on Table 6.1.1.1-1 of 38.821) |
34 | 40 |
| Bandwidth B (User Input. Default based on Table 6.1.3.2-1 of 38.821) |
30 | 30 |
| EIRP (dBW) \(= EIRP[dBW/MHz] + 10\log_{10} B[MHz]\). Per TR 38.821 section 6.1.3.1-5 |
48.77 | 54.77 |
| Elevation angle (Per Elevation angle formulas provided in 3GPP TR 38.811 sec 6.6.2) |
87.64 | 86.54 |
| Angular Antenna Gain \(G(\theta)\), (dB) (Per Bessel function formulas provided in 3GPP TR 38.811 sec 6.4.1) |
\(-\)4.2 | \(-\)10.26 |
| Slant range \(d\) (Km) (Per slant height formulas provided in 3GPP TR 38.811 sec 6.6.2) |
600.51 | 1202.19 |
| Free space pathloss (dB), \(PL_{FS}\) (Per Free space pathloss formulas provided in 3GPP TR 38.811 sec 6.6.2) |
154.81 | 160.84 |
| Shadow loss (dB), \(PL_{SM}\) (Per shadow loss formulas provided in 3GPP TR 38.811 sec 6.6.2) |
0.39 | 0.39 |
| Additional Loss(dB), \(PL_{AD}\) (User Input. Default based on Table 6.1.3.2-1 of 38.821) |
0 | 0 |
| Total Pathloss, L (dB) \(L = PL_{FS} + PL_{SM} + PL_{AD}\) |
155.20 | 161.23 |
| Rx Antenna Gain (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
0 | 0 |
| Noise figure \(N_f\) (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
7 | 7 |
| Rx Antenna Temp \(T_a\) (K) (User Input. Default based on Table 6.1.1.1-3 of 38.821) |
290 | 290 |
| RX equivalent antenna Temp, \(T\) [\(dBK\)] (Per TR 38.821 section 6.1.3.1) |
31.62 | 31.62 |
| Receiver G/T \((dB/K)\) (Per RX G/T formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
\(-\)31.62 | \(-\)31.62 |
| Boltzmann constant \(k\) [\(dBW/K/Hz\)] | \(-\)228.6 | \(-\)228.6 |
| Carrier to Noise Ratio, CNR
(dB) (Per CNR formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
11.58 | 5.49 |
| Carrier to Interference Ratio, CIR
(dB) (User Input. Per TR 38.821 section 6.1.3.1) |
5 | 5 |
| Carrier to Noise plus Interference Ratio,
CNIR (dB) (Per CNIR formulas provided in 3GPP TR 38.821 sec 6.1.3.1) |
4.14 | 2.23 |
Link Budget Calculations: Example 1 LEO 600¶
We consider the satellite co-ordinates as \((0, 0, 600)\) km, and the UE co-ordinates as \(\left(0, 0, 0\right)\)km. The elevation angle is calculated as arctan of the ratio of the satellite altitude to the distance between the satellite and the UE in the XY plane.
\[\begin{equation} \alpha =\sin^{-1}\!\left(\frac{D}{Ru \times L}\right) =90^{\circ} \end{equation}\]
Where,
\[\begin{equation} Ru = \sqrt{x_{ue}^{2} + y_{ue}^{2} + z_{ue}^{2}} \end{equation}\]
\[\begin{equation} L = \sqrt{\left(x_{sat} - x_{ue}\right)^{2} + \left(y_{sat} - y_{ue}\right)^{2} + \left(z_{sat} - z_{ue}\right)^{2}} \end{equation}\]
\[\begin{equation} D = \sqrt{\left(x_{sat} - x_{ue}\right)\cdot x_{ue} + \left(y_{sat} - y_{ue}\right)\cdot y_{ue} + \left(z_{sat} - z_{ue}\right)\cdot z_{ue}} \end{equation}\]
\[\begin{equation} \alpha =90^{\circ} \end{equation}\]
The slant height used in NetSim is per 38.811, equation 6.6-3, i.e.
\[\begin{equation} d=\sqrt{R_{E}^{2}\sin^{2}\!\left(\alpha \right)+h_{o}^{2}+2h_{o}R_{E}}-R_{E}\sin\!\left(\alpha \right) \end{equation}\]
For a link between a ground station and a LEO satellite operating at 600 km with elevation angle \(\alpha =90^{\circ}\).
\[\begin{multline} d=\sqrt{\left(6.371\cdot 10^{6}\right)^{2}\cdot \sin^{2}\!\left(90^{\circ}\right)+\left(6\cdot 10^{5}\right)^{2}+2\cdot \left(6\cdot 10^{5}\right)\left(6.371\cdot 10^{6}\right)}\\ -6.371\cdot 10^{6}\sin\!\left(90^{\circ}\right) \end{multline}\]
\[\begin{equation} d=600 \text{ km} \end{equation}\]
The free space pathloss \(PL_{FS}\) for a channel with \(d=600\) km is
\(F_{Low}=2170,\; F_{High}=2200, \; f_{c}=\frac{2170+2200}{2}\)=\(2.185\) GHz
\[\begin{equation} PL_{FS}=32.45+20\log_{10}\!\left(f_{c}\right)+20\log_{10}\!\left(d\right) \end{equation}\]
\[\begin{equation} 32.45+20\log_{10}\!\left(2.185\right)+20\log_{10}\!\left(600\times1000\right)=154.8 \text{ dB} \end{equation}\]
The receiver antenna \(G/T\) is given by the expression
\[\begin{equation} Rx\frac{G}{T}=G_{rx}-N_{f}-10\log_{10}\!\left(T_{0}+\left(T_{a}-T_{0}\right)\times 10^{-0.1\times N_{f}}\right) \end{equation}\]
We know \(T_{0}=290\), and when we apply \(T_{a}=290\), we obtain
\[\begin{equation} Rx\frac{G_{rx}}{T}=0-7 - 10\log_{10}\!\left(290\right)= -31.62 \text{ dB/K} \end{equation}\]
We know that bandwidth \(B \;[\text{dBHz}]=10\times \log_{10}\!\left(B\;[\text{Hz}]\right)=10\times \log_{10}\!\left(30\times 10^{6}\right)=74.77\) dBHz
The shadow margin \(PL_{SM}\) is calculated per the tables available in section 6.6.2 of 38.811. The given example is based on the Rural scenario, with a LOS probability of 1 and an elevation angle of \(90^{\circ}\). The standard deviation chosen from the table is 0.72. We then generate a zero-mean Gaussian random variable with input standard deviation of 0.72. In this case, the random shadow loss drawn is 0.54 dB
Angular antenna gain, \(G(\theta )=0\)
MaxAntennaGain=0,
And finally we obtain \(CNR\) as
\[\begin{equation} CNR=EIRP+G\!\left(\theta \right)-\text{MaxAntennaGain}+Rx\frac{G}{T}-k-PL_{FS}-PL_{SM}-PL_{AD}-B \end{equation}\]
Substituting we get
\[\begin{equation} CNR=48.77+0+\left(-31.62\right)-\left(-228.6\right)-154.8-\left(0.39\right)-0-74.77=15.78 \text{ dB} \end{equation}\]
Link Budget Calculations: Example 2 LEO 1200¶
We consider the satellite co-ordinates as \((0, 0, 1200)\) km, and the UE co-ordinates as \(\left(64, 34, 0\right)\) km. The elevation angle is calculated in NetSim as follows
\[\begin{equation} \theta =86.54^{\circ} \end{equation}\]
The slant height used in NetSim is per 38.811, equation 6.6-3, i.e.
\[\begin{equation} d=\sqrt{R_{E}^{2}\sin^{2}\!\left(\alpha \right)+h_{o}^{2}+2h_{o}R_{E}}-R_{E}\sin\!\left(\alpha \right) \end{equation}\]
For a link between a ground station and a LEO satellite operating at 1200 km with elevation angle \(\alpha =86.54^{\circ}\).
\[\begin{multline} d=\sqrt{\left(6.371\cdot 10^{6}\right)^{2}\cdot \sin^{2}\!\left(86.51^{\circ}\right)+\left(12\cdot 10^{5}\right)^{2}+2\cdot \left(12\cdot 10^{5}\right)\left(6.371\cdot 10^{6}\right)}\\ -6.371\cdot 10^{6}\sin\!\left(86.51^{\circ}\right) \end{multline}\]
\[\begin{equation} d=1202.19 \text{ km} \end{equation}\]
The free space pathloss \(PL_{FS}\) for a channel with \(d=1202.19\) km is
\(F_{Low}=2170,\; F_{High}=2200, \; f_{c}=\frac{2170+2200}{2}\)=\(2.185\) GHz
\[\begin{equation} PL_{FS}=32.45+20\log_{10}\!\left(f_{c}\right)+20\log_{10}\!\left(d\right) \end{equation}\]
\[\begin{equation} 32.45+20\log_{10}\!\left(2.185\right)+20\log_{10}\!\left(1202.19 \times1000\right)=160.84 \text{ dB} \end{equation}\]
The receiver antenna \(G/T\)is given by the expression
\[\begin{equation} Rx\frac{G}{T}=G_{rx}-N_{f}-10\log_{10}\!\left(T_{0}+\left(T_{a}-T_{0}\right)\times 10^{-0.1\times N_{f}}\right) \end{equation}\]
We know \(T_{0}=290\), and when we apply \(T_{a}=290\), we obtain
\[\begin{equation} Rx\frac{G_{rx}}{T}=0-7 - 10\log_{10}\!\left(290\right)= -31.62 \text{ dB/K} \end{equation}\]
We know that bandwidth \(B\;[\text{dBHz}]=10\times \log_{10}\!\left(B\;[\text{Hz}]\right)=10\times \log_{10}\!\left(30\times 10^{6}\right)=74.77\) dBHz
The shadow margin \(PL_{SM}\) is calculated per the tables available in section 6.6.2 of 38.811. The given example is based on the Rural scenario, with a LOS probability of 1 and an elevation angle of \(86.54^{\circ}\). The standard deviation chosen from the table is 0.72. We then generate a zero-mean Gaussian random variable with input standard deviation of 0.72. In this case, the random shadow loss that we draw is 0.54 dB.
Angular antenna gain, \(G(\theta )= -10.26\)
MaxAntennaGain=0,
And finally we obtain \(CNR\) as
\[\begin{equation} CNR=EIRP+G\!\left(\theta \right)-\text{MaxAntennaGain}+Rx\frac{G}{T}-k-PL_{FS}-PL_{SM}-PL_{AD}-B \end{equation}\]
Substituting we get
\[\begin{equation} CNR=54.77-10.26+\left(-31.62 \right)-\left(-228.6\right)-160.84-\left(0.39\right)-0-74.77=5.49 \text{ dB} \end{equation}\]