S-Band Telemetry Link: Predicted Margin Versus Measured Eb/N0
A 2.2 GHz S-band telemetry downlink from a 2500 km circular orbit carries 2.0 Mbit/s BPSK data. The transmitter delivers 4 W to the antenna; the transmit antenna gain is 3 dBi and the feed loss is 0.5 dB. The ground station antenna gain is 32 dBi and the receiver system noise temperature is 250 K. The required Eb/N0 for BER 10^-6 with the selected modem is 10.5 dB, and 2.0 dB implementation loss is allocated. During the first pass, the measured Eb/N0 is 11.1 dB and the BER is about 2×10^-5, although the pre-launch budget predicted adequate margin. Telemetry shows the antenna pointing error is 0.35° (0.9 dB loss at the edge of coverage), the measured feed and cable loss is 1.3 dB rather than 0.5 dB, and a neighbouring emitter raises the noise floor by 1.0 dB. The spacecraft cannot increase transmit power without a thermal redesign; the ground station can change modulation/coding and antenna tracking.
1. Compute the pre-launch predicted Eb/N0 and the available margin against the required value. State any assumptions.
Read the worked answer
Assume free-space loss, no atmospheric loss at the assumed elevation, and that the 2.0 Mbit/s is the information rate.
Transmit power: 4 W = 10 log10(4) = 6.02 dBW. EIRP = 6.02 + 3.0 − 0.5 = 8.52 dBW.
Free-space loss at 2.2 GHz and 2500 km: FSPL = 92.45 + 20 log10(2.2) + 20 log10(2500) = 92.45 + 6.85 + 67.96 = 167.26 dB.
Received power: Pr = 8.52 − 167.26 + 32 = −126.74 dBW.
Noise spectral density for T = 250 K: N0 = −228.6 + 10 log10(250) = −204.62 dBW/Hz.
Eb/N0 = Pr − N0 − 10 log10(Rb) = −126.74 + 204.62 − 10 log10(2×10^6) = −126.74 + 204.62 − 63.01 = 14.87 dB.
Required Eb/N0 = 10.5 + 2.0 = 12.5 dB. Predicted margin = 14.87 − 12.5 = 2.37 dB. That is a thin but positive margin, so the pre-launch conclusion of adequacy depended on all losses staying near their allocations.
2. Reconcile the measured 11.1 dB with the prediction. Which impairments explain the difference, and what is the residual unexplained loss?
Read the worked answer
The measured value is 14.87 − 11.1 = 3.77 dB below prediction.
List the identified impairments:
- Pointing loss: 0.9 dB.
- Excess feed/cable loss: 1.3 − 0.5 = 0.8 dB.
- Interference raising the noise floor: 1.0 dB.
These sum to 2.7 dB. The residual is 3.77 − 2.7 = 1.07 dB. That residual is plausibly polarization mismatch, antenna gain not being at the predicted peak, atmospheric or rain loss at the actual elevation, or a transmit power lower than 4 W at the antenna. It should not be ignored or absorbed into a generic margin.
With the measured impairments, the link is below the required 12.5 dB by 1.4 dB, which is consistent with the observed BER of about 2×10^-5 rather than 10^-6. The fact that the raw prediction had only 2.37 dB margin means that a 3.77 dB implementation shortfall is enough to break the link. The correct conclusion is that the modem is not necessarily at fault; the RF chain and interference environment are.
3. Recommend a recovery plan without a spacecraft thermal redesign. Prioritize the actions and quantify the expected recovery.
Read the worked answer
First recover the ground-station and interference losses, because they are available without touching the spacecraft. Restoring the feed/cable loss to 0.5 dB recovers 0.8 dB. Improving tracking or using a better pointing model recovers up to 0.9 dB. Filtering or retuning away from the neighbouring emitter recovers about 1.0 dB. Together these recover 2.7 dB, moving Eb/N0 from 11.1 to about 13.8 dB, which gives 1.3 dB margin against 12.5 dB. That is workable but still thin for a BER 10^-6 service.
If more margin is needed, reduce the information rate from 2.0 Mbit/s to 1.0 Mbit/s for a 3.0 dB improvement, at the cost of halving payload data. Alternatively, add coding: a rate-1/2 convolutional or LDPC code can provide several dB of coding gain at the same information rate, but the occupied bandwidth and modem configuration must be checked. Changing modulation alone, for example BPSK to QPSK, does not improve Eb/N0 at fixed power and rate; it changes bandwidth efficiency.
Do not simply add 1.5 dB of transmit power unless the thermal design is reopened. The prioritized plan is: fix feed and tracking, filter the interference, then use rate reduction or coding if the measured margin after those fixes is still below about 3 dB.