Link Budget
Reference: CCSDS 401.0-B-30 (RF and Modulation), ITU Radio Regulations, ECSS-E-ST-50-05C
1. Link Budget Methodology
1.1 Friis Transmission Equation
The received power at the ground station is derived from the Friis equation:
P_rx = P_tx + G_tx + G_rx - L_fs - L_atm - L_point - L_pol - L_imp
Where:
P_rx = Received power (dBm)
P_tx = Transmitter output power (dBm)
G_tx = Transmit antenna gain (dBi)
G_rx = Receive antenna gain (dBi)
L_fs = Free space path loss (dB)
L_atm = Atmospheric attenuation (dB)
L_point = Pointing loss (dB)
L_pol = Polarization mismatch loss (dB)
L_imp = Implementation loss (cable, connector, filter) (dB)
1.2 Free Space Path Loss Derivation
L_fs = 20*log10(4*pi*d/lambda) [dB]
= 20*log10(4*pi*d*f/c)
= 32.45 + 20*log10(f_MHz) + 20*log10(d_km)
For UHF (437 MHz) at slant range 2000 km:
L_fs = 32.45 + 20*log10(437) + 20*log10(2000)
= 32.45 + 52.81 + 66.02 = 151.28 dB
For S-band (2.4 GHz) at slant range 2000 km:
L_fs = 32.45 + 20*log10(2400) + 20*log10(2000)
= 32.45 + 67.60 + 66.02 = 166.07 dB
1.3 Slant Range Geometry
* Satellite (h = 550 km)
/|
/ |
Slant / | h = 550 km
Range d / |
/ |
/ El. |
GS *------/--------* Subsatellite point
Earth surface (R_E = 6371 km)
d = sqrt((R_E + h)^2 - R_E^2 * cos^2(El)) - R_E * sin(El)
| Elevation (deg) |
Slant Range (km) |
UHF FSPL (dB) |
S-band FSPL (dB) |
| 5 (minimum) |
1932 |
151.0 |
165.8 |
| 10 |
1510 |
148.8 |
163.6 |
| 20 |
1023 |
145.4 |
160.2 |
| 45 |
620 |
141.1 |
155.9 |
| 90 (zenith) |
550 |
140.0 |
154.8 |
2. Atmospheric and Propagation Effects
2.1 Atmospheric Attenuation
| Effect |
UHF (437 MHz) |
S-band (2.4 GHz) |
Notes |
| Tropospheric (dry air) |
0.05 dB |
0.10 dB |
At 10 deg elevation |
| Rain attenuation (99.9%) |
0.0 dB |
0.3 dB |
ITU-R P.838, moderate climate |
| Cloud/fog |
0.0 dB |
0.05 dB |
Negligible at both bands |
| Ionospheric scintillation |
0.5 dB |
0.1 dB |
Worst case, high solar activity |
| Total atmospheric |
0.55 dB |
0.55 dB |
|
2.2 Faraday Rotation
Faraday rotation of linearly polarized signals through the ionosphere:
theta_F = 2.36e4 * TEC / f^2 [radians]
Where:
TEC = Total Electron Content = 50 TECU (daytime, moderate solar)
f = frequency in Hz
For UHF (437 MHz):
theta_F = 2.36e4 * 50e16 / (437e6)^2 = 6.18 rad = 354 deg (SEVERE)
For S-band (2.4 GHz):
theta_F = 2.36e4 * 50e16 / (2.4e9)^2 = 0.20 rad = 11.8 deg (manageable)
Impact: UHF must use circular polarization to avoid Faraday rotation nulls.
The monopole on the satellite is linearly polarized; ground station Yagi should be
circularly polarized, incurring 3 dB axial ratio loss in worst case.
2.3 Polarization Loss
| Configuration |
Loss (dB) |
| Circular TX – Circular RX (co-pol) |
0.0 |
| Linear TX – Circular RX |
3.0 |
| Circular TX – Linear RX |
3.0 |
| Cross-polarized (worst case) |
> 20.0 |
For UHF: Linear (sat) to Circular (GS) = 3.0 dB loss (accounted in budget)
For S-band: Circular patch (sat) to Circular dish (GS) = 0.5 dB (axial ratio imperfection)
3. UHF Link Budget (437 MHz Downlink)
3.1 Detailed Budget
| # |
Parameter |
Symbol |
Value |
Unit |
| 1 |
TX Power |
P_tx |
30.0 |
dBm |
| 2 |
TX Cable + Connector Loss |
L_tx |
-0.5 |
dB |
| 3 |
TX Antenna Gain (monopole) |
G_tx |
0.0 |
dBi |
| 4 |
TX Pointing Loss |
L_point_tx |
-1.0 |
dB |
| 5 |
EIRP |
|
28.5 |
dBm |
| 6 |
Free Space Path Loss (5 deg el.) |
L_fs |
-151.0 |
dB |
| 7 |
Atmospheric Loss |
L_atm |
-0.55 |
dB |
| 8 |
Polarization Loss |
L_pol |
-3.0 |
dB |
| 9 |
Total Path Loss |
|
-154.55 |
dB |
| 10 |
RX Antenna Gain (9-el Yagi) |
G_rx |
14.0 |
dBi |
| 11 |
RX Cable + Connector Loss |
L_rx |
-1.0 |
dB |
| 12 |
RX Pointing Loss |
L_point_rx |
-0.5 |
dB |
| 13 |
Received Power |
P_rx |
-113.55 |
dBm |
| 14 |
System Noise Temperature |
T_sys |
500 |
K |
| 15 |
Boltzmann Constant |
k |
-228.6 |
dBW/K/Hz |
| 16 |
Noise Spectral Density |
N_0 |
-201.6 |
dBW/Hz |
| 17 |
Data Rate (9600 bps) |
R |
39.8 |
dB-Hz |
| 18 |
Eb/N0 (received) |
|
18.2 |
dB |
| 19 |
Required Eb/N0 (GMSK, BER=1e-5) |
|
9.6 |
dB |
| 20 |
Coding Gain (conv. r=1/2, K=7) |
G_code |
5.2 |
dB |
| 21 |
Required Eb/N0 (with coding) |
|
4.4 |
dB |
| 22 |
Link Margin |
|
13.8 |
dB |
3.2 UHF Uplink (437 MHz)
| Parameter |
Value |
Unit |
| GS TX Power |
36.0 |
dBm (4 W) |
| GS Antenna Gain |
14.0 |
dBi |
| GS Cable Loss |
-1.0 |
dB |
| EIRP |
49.0 |
dBm |
| Path Loss (total) |
-154.55 |
dB |
| Sat RX Antenna Gain |
0.0 |
dBi |
| Sat RX Cable Loss |
-0.5 |
dB |
| Received Power |
-106.05 |
dBm |
| Noise Temp (800 K, Earth-facing) |
800 |
K |
| Eb/N0 (received) |
12.1 |
dB |
| Required Eb/N0 (with coding) |
4.4 |
dB |
| Link Margin |
7.7 |
dB |
4. S-band Link Budget (2.4 GHz Downlink)
4.1 Detailed Budget
| # |
Parameter |
Symbol |
Value |
Unit |
| 1 |
TX Power |
P_tx |
33.0 |
dBm |
| 2 |
TX Cable + Connector Loss |
L_tx |
-1.0 |
dB |
| 3 |
TX Antenna Gain (patch) |
G_tx |
6.0 |
dBi |
| 4 |
TX Pointing Loss (5 deg error) |
L_point_tx |
-1.5 |
dB |
| 5 |
EIRP |
|
36.5 |
dBm |
| 6 |
Free Space Path Loss (10 deg el.) |
L_fs |
-163.6 |
dB |
| 7 |
Atmospheric Loss |
L_atm |
-0.55 |
dB |
| 8 |
Polarization Loss |
L_pol |
-0.5 |
dB |
| 9 |
Total Path Loss |
|
-164.65 |
dB |
| 10 |
RX Antenna Gain (2.4m dish) |
G_rx |
30.0 |
dBi |
| 11 |
RX Cable + Connector Loss |
L_rx |
-1.5 |
dB |
| 12 |
RX Pointing Loss |
L_point_rx |
-0.3 |
dB |
| 13 |
Received Power |
P_rx |
-99.95 |
dBm |
| 14 |
System Noise Temperature |
T_sys |
200 |
K |
| 15 |
Noise Spectral Density |
N_0 |
-205.6 |
dBW/Hz |
| 16 |
Data Rate (256 kbps) |
R |
54.1 |
dB-Hz |
| 17 |
Eb/N0 (received) |
|
21.5 |
dB |
| 18 |
Required Eb/N0 (QPSK, BER=1e-5) |
|
9.6 |
dB |
| 19 |
Coding Gain (LDPC r=1/2) |
G_code |
7.5 |
dB |
| 20 |
Required Eb/N0 (with coding) |
|
2.1 |
dB |
| 21 |
Link Margin |
|
19.4 |
dB |
Note: The original S-band budget showed ~1 dB margin using a 20 dBi ground antenna. Upgrading to a
2.4m dish (30 dBi) and adding LDPC coding resolves the margin issue with substantial reserve.
5. Modulation and Coding Comparison
5.1 Modulation Schemes
| Modulation |
Spectral Eff. (bps/Hz) |
Req. Eb/N0 @ BER=1e-5 |
Complexity |
Selected For |
| BPSK |
1.0 |
9.6 dB |
Low |
- |
| GMSK (BT=0.5) |
1.0 |
9.6 dB |
Low |
UHF |
| QPSK |
2.0 |
9.6 dB |
Medium |
S-band |
| 8PSK |
3.0 |
13.0 dB |
High |
- |
| 16QAM |
4.0 |
13.4 dB |
High |
- |
| MSK |
1.0 |
9.6 dB |
Low |
- |
5.2 Forward Error Correction (FEC)
| Code |
Rate |
Coding Gain (dB) |
Complexity |
Standard |
| None (uncoded) |
1.0 |
0.0 |
None |
- |
| Conv. r=1/2, K=7 |
0.5 |
5.2 |
Low |
CCSDS 131.0-B-3 |
| Reed-Solomon (255,223) |
0.87 |
3.0 |
Medium |
CCSDS 131.0-B-3 |
| Conv + RS (concatenated) |
0.44 |
7.4 |
Medium |
CCSDS 131.0-B-3 |
| Turbo r=1/2 |
0.5 |
8.5 |
High |
CCSDS 131.0-B-3 |
| LDPC r=1/2 |
0.5 |
7.5 |
Medium |
CCSDS 131.1-O-2 |
| LDPC r=7/8 |
0.875 |
4.5 |
Medium |
CCSDS 131.1-O-2 |
Selected: Convolutional r=1/2, K=7 for UHF (low complexity); LDPC r=1/2 for S-band (best gain-to-complexity ratio)
6. Link Margin Sensitivity Analysis
6.1 Sensitivity to Elevation Angle
| Elevation |
UHF Margin (dB) |
S-band Margin (dB) |
Contact Fraction |
| 5 deg |
13.8 |
19.4 |
100% of passes |
| 10 deg |
16.0 |
21.6 |
85% of pass time |
| 20 deg |
19.4 |
25.0 |
60% of pass time |
| 45 deg |
23.7 |
29.3 |
25% of pass time |
| 90 deg |
24.8 |
30.4 |
< 5% of pass time |
6.2 Sensitivity to Key Parameters
Impact of +/- 3 dB change in each parameter on UHF link margin:
| Parameter |
Nominal |
-3 dB effect |
+3 dB effect |
| TX Power |
30 dBm |
Margin = 10.8 dB |
Margin = 16.8 dB |
| TX Antenna Gain |
0 dBi |
Margin = 10.8 dB |
Margin = 16.8 dB |
| RX Antenna Gain |
14 dBi |
Margin = 10.8 dB |
Margin = 16.8 dB |
| System Noise Temp |
500 K |
Margin = 16.8 dB |
Margin = 10.8 dB |
| Data Rate |
9.6 kbps |
Margin = 16.8 dB |
Margin = 10.8 dB |
6.3 Rain Fade Analysis (S-band)
Per ITU-R P.618, rain attenuation at 2.4 GHz for Tashkent (climate zone K):
| Availability |
Rain Rate (mm/hr) |
Attenuation (dB) |
S-band Margin Remaining |
| 99.0% |
12 |
0.15 |
19.3 dB |
| 99.9% |
32 |
0.30 |
19.1 dB |
| 99.99% |
65 |
0.55 |
18.9 dB |
Rain fade is not a significant concern at 2.4 GHz. Impact becomes meaningful only above 10 GHz.
7. Data Throughput Analysis
7.1 Effective Data Rate
| Parameter |
UHF |
S-band |
| Raw bit rate |
9,600 bps |
256,000 bps |
| FEC overhead (rate) |
0.5 |
0.5 |
| AX.25/CCSDS framing overhead |
15% |
8% |
| Effective data rate |
4,080 bps |
117,760 bps |
| Per pass (8 min avg) |
240 KB |
6.9 MB |
| Per pass (12 min best) |
360 KB |
10.4 MB |
| Daily (6 passes, UHF+S) |
1.44 MB UHF + 41.4 MB S |
42.8 MB total |
7.2 Image Downlink Time
| Image Type |
Size |
S-band Passes Needed |
UHF Passes Needed |
| Thumbnail (320x240, JPEG) |
50 KB |
< 1 |
< 1 |
| Preview (1280x960, JPEG) |
500 KB |
< 1 |
2 |
| Full frame (2592x1944, JPEG) |
3 MB |
< 1 |
8 |
| Full frame (RAW) |
10 MB |
1-2 |
28 |
| Multispectral set (3 bands) |
30 MB |
3-5 |
83 |
8. Ground Station Configuration
8.1 Tashkent Primary Station
| Parameter |
UHF System |
S-band System |
| Antenna |
9-element cross Yagi |
2.4m parabolic dish |
| Gain |
14.0 dBi |
30.0 dBi |
| Polarization |
RHCP |
RHCP |
| Feed |
Crossed dipole |
Scalar horn |
| LNA |
NF = 0.5 dB, Gain = 20 dB |
NF = 0.7 dB, Gain = 25 dB |
| Tracking |
Az/El rotator, auto-track |
Az/El rotator, program track |
| TX Power |
4 W (uplink) |
N/A (downlink only) |
| T_sys |
500 K |
200 K |
9. References
- CCSDS 401.0-B-30: Radio Frequency and Modulation Systems, 2020
- CCSDS 131.0-B-3: TM Synchronization and Channel Coding, 2017
- CCSDS 131.1-O-2: LDPC Coding for Near-Earth Applications, 2015
- ITU-R P.618-13: Propagation Data for Design of Earth-Space Systems
- ITU-R P.838-3: Specific Attenuation Model for Rain
- Wertz, “Space Mission Engineering: The New SMAD”, Chapter 16
- ECSS-E-ST-50-05C: Radio Frequency and Modulation, 2008