Ka-band downlink margin with and without coding
A LEO satellite downlinks at 20 GHz. The satellite EIRP is 30 dBW and the slant range at the worst elevation is 1200 km. The ground station uses a 1.2 m dish with 55% aperture efficiency and a receiver with 2 dB noise figure in a 20 MHz channel. Atmospheric absorption is 0.5 dB and pointing loss is 1 dB; rain attenuation at the 0.1% availability target is 6 dB. The modem uses QPSK with a 2 dB implementation margin, and the required Eb/N0 for BER 10^-6 is 10.5 dB. The operator wants 20 Mbit/s of user data and is considering a rate-1/2 convolutional code with 5 dB coding gain, which would halve the information rate within the same 20 MHz channel. The link budget appears to close, but only by a few dB, and the availability target may be tightened.
1. Compute the received C/N0, the Eb/N0 for 20 Mbit/s QPSK, and the margin against the required Eb/N0. Does the link close at 0.1% availability?
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Free-space loss FSPL = 92.45 + 20log10(20 GHz) + 20log10(1200 km) = 92.45 + 26.02 + 61.58 = 180.05 dB.
Receive antenna gain λ = 0.015 m, D = 1.2 m, πD/λ = 251.3. G = 10log10(0.55 × 251.3²) = 10log10(34740) ≈ 45.4 dBi.
Received power Pr = 30 − 180.05 + 45.4 − 0.5 − 1.0 − 6.0 = −112.15 dBW.
Noise density N0 = −228.6 + NF + 10log10(290) = −228.6 + 2 + 24.6 = −202.0 dBW/Hz.
Carrier-to-noise density C/N0 = −112.15 − (−202.0) = 89.85 dB-Hz.
Eb/N0 For 20 Mbit/s, 10log10(20×10^6) = 73.0 dB-Hz. Eb/N0 = 89.85 − 73.0 = 16.85 dB. Required = 10.5 + 2 = 12.5 dB. Margin = 4.35 dB.
The link closes at 0.1% availability, but 4.35 dB must also absorb scintillation, polarization mismatch and ageing. Any additional fade above about 4.3 dB causes outage, so the design is thin rather than comfortable.
2. Compare keeping 20 Mbit/s uncoded with dropping to 10 Mbit/s and using the rate-1/2 code. Show the resulting margins and state which choice you would make.
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Uncoded, 20 Mbit/s
- Eb/N0 = 16.85 dB, margin = 4.35 dB.
- Meets the 20 Mbit/s requirement but has little protection against a deeper fade.
Coded, 10 Mbit/s information rate
- The channel and C/N0 are unchanged: 89.85 dB-Hz.
- Information bit rate is halved, so 10log10(10×10^6) = 70.0 dB-Hz.
- Uncoded Eb/N0 = 89.85 − 70.0 = 19.85 dB.
- Adding 5 dB coding gain gives an effective 24.85 dB.
- Margin against 12.5 dB = 12.35 dB.
The coded option buys about 8 dB of additional margin but halves throughput. If the requirement is strictly 20 Mbit/s, the choice is to keep uncoded QPSK and accept a 4.35 dB margin, or improve the RF chain instead: increasing dish diameter to 1.7 m adds roughly 3 dB, and reducing pointing loss adds up to 1 dB.
Decision For a 0.1% availability target with 20 Mbit/s mandatory, keep uncoded QPSK and tighten pointing and antenna efficiency. If availability is tightened to 0.01%, rain attenuation rises by several dB and the uncoded link fails; then the coded 10 Mbit/s mode, a larger dish, or both are required.
3. Identify the largest uncertainty in this budget and describe how you would verify it before committing to the modem configuration.
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Largest uncertainty The rain attenuation statistic at the specific site dominates. A 6 dB value at 0.1% is a model output, not a measurement, and it changes strongly with rain climate, elevation angle and drop-size distribution. Antenna efficiency and actual implementation loss are secondary but still worth 1–2 dB.
Verification approach
- Recompute rain attenuation with the ITU-R P.618 model using the actual site latitude, altitude, rain rate and elevation angle, and check sensitivity at 0.1% and 0.01%.
- Measure the antenna gain or efficiency rather than relying on the 55% assumption.
- Measure implementation loss on the actual modem at the target BER, since the 2 dB figure may be optimistic at 20 Mbit/s.
- Include scintillation and polarization loss explicitly; at 20 GHz these are not negligible.
Decision rule If the recomputed 0.1% fade exceeds about 10 dB, the uncoded 20 Mbit/s link cannot close and the coded mode or a larger aperture is mandatory. Freezing the modem configuration before this check risks a link that meets specification on paper but fails in heavy rain.