Challenge description: Years have passed since our satellite was designed, and the Systems Engineers didn’t do a great job with the documentation. Partial information was left behind in the user manual, so we don’t know what power level to set the Telemetry transmitter at to ensure a 10dB Eb/No margin above the minimum required for BER (4.4 dB).

The challenge is available at this address.

The goal is to complete a link budget to finish the documentation for the engineers.
A link budget accounts for all the gains and losses from the transmitter to the receiver in a communication system. In practice, one is done for the uplink and another for the downlink to evaluate system performance.

Let’s launch the challenge:

> docker run --rm -i -e FLAG=pouet linky:challenge
...
Here's the information we have captured

************** Global Parameters *****************
Frequency (Hz): 12100000000.0
Wavelength (m): 0.025
Data Rate (bps): 10000000.0
************* Transmit Parameters ****************
Transmit Line Losses (dB): -1
Transmit Half-power Beamwidth (deg): 26.30
Transmit Antenna Gain (dBi): 16.23
Transmit Pointing Error (deg): 10.00
Transmit Pointing Loss (dB): -1.74
*************** Path Parameters ******************
Path Length (km): 2831
Polarization Loss (dB): -0.5
Atmospheric Loss (dB): -2.1
Ionospheric Loss (dB): -0.1
************** Receive Parameters ****************
Receive Antenna Diameter (m): 5.3
Receive Antenna Efficiency: 0.55
Receive Pointing Error (deg): 0.2
Receive System Noise Temperature (K): 522
Receive Line Loss (antenna to LNA) (dB): -2
Receive Demodulator Implementation Loss (dB): -2
Required Eb/No for BER (dB): 4.4

Calculate and provide the receive antenna gain in dBi:

Ok, that’s a lot of information. First, we need to calculate the receive antenna gain.

1. Calculating the Receive Antenna Gain

We use the formula: G = 10·log10((n · 4π · A) / (λ²))
where:

n is the antenna efficiency (given as 0.55),
λ is the wavelength (0.025 m), and
A is the physical aperture area of the dish, calculated as A = π·r² with r = D/2 (and D given as 5.3 m).

For example, in Python:

import numpy as np
r = 5.3/2  # m
A = np.pi * r**2  # m²
λ = 0.025  # m
n = 0.55
gain = 10 * np.log10((n * 4 * np.pi * A)/(λ**2))  # dB
print(gain)  # ≈53.87 dB

Rounded, we enter:

> docker run --rm -i -e FLAG=pouet linky:challenge
...
Calculate and provide the receive antenna gain in dBi: 53.9
Good job.  You get to continue
Receive Antenna Gain (dBi): 54.00
Receive Half-power Beamwidth (deg): 0.33
Receive Pointing Error (deg): 0.2
Receive Pointing Loss (dB): -4.48

2. Calculating the Ground Terminal G/T (dB/K)

G/T measures the antenna gain relative to the system noise temperature. Using: G/T = G + (line loss) – 10·log10(system noise temperature)
With G = 54 dB, Receive Line Loss = -2 dB, and system noise temperature = 522 K:

g = 54  
rx_line_loss = -2  # dB
temp = 522  # K
g_t = g + rx_line_loss - 10 * np.log10(temp)
print(g_t)  # ≈24.7 dB/K

Entering:

> docker run --rm -i -e FLAG=pouet linky:challenge
...
Calculate and provide the ground terminal G/T (dB/K): 24.7
Nicely done.  Let's keep going.
Determine the transmit power (in W) to achieve 10dB of Eb/No margin (above minimum for BER):

3. Calculating the Transmit Power

We now calculate the transmit (or “transit”) power in Watts to achieve the desired margin.

3.1 Calculating the RSSI

RSSI combines measured SNR, pointing losses, Boltzmann’s constant, and the G/T.

First, calculate SNR (dB) using: SNR = Eb/No + 10·log10(Bit Rate) – Demodulator Loss
where: • Eb/No (required for BER) is 4.4 dB, but we want a 10dB margin so Eb/No becomes 14.4 dB,
• Bit Rate is 10e6 bps, and
• Demodulator Loss = -2 dB.

import numpy as np
eb_no = 14.4  # dB
bitrate = 10e6  # bps
demod_loss = -2  # dB
SNR = eb_no + 10 * np.log10(bitrate) - demod_loss  # dB
print(SNR)  # ≈86.4 dB

Next, account for receive pointing loss. Using the beamwidth formula: BW = (λ / D) · 70, with λ = 0.025 m and D = 5.3 m, and then Pointing Loss = -12 * (pointing error / BW)².

beamwidth = (0.025/5.3) * 70  
rx_pointing_error = 0.2  
rx_pointing_loss = -12 * (rx_pointing_error/beamwidth)**2  # ~-4.4 dB

Finally, compute the RSSI: RSSI = SNR – (pointing loss) + Boltzmann – G/T
with Boltzmann's constant converted to dBW/K:

boltzmann_j_k = 1.38065e-23  
boltzmann = 10 * np.log10(boltzmann_j_k)  # dBW/K  
rssi = SNR - rx_pointing_loss + boltzmann - g_t  
print(rssi)  # ≈ -162.5 dBW

3.2 Calculating Propagation Loss

Propagation (or path) loss is given by: Path Loss = 20·log10(λ/(4π·D))
with D (distance) = 2831 km converted to meters.

d_m = 2831e3  # m
path_loss = 20 * np.log10(0.025 / (4 * np.pi * d_m))
print(path_loss)  # ≈ -183.06 dB

Additional losses:

Polarization Loss: -0.5 dB
Atmospheric Loss: -2.1 dB
Ionospheric Loss: -0.1 dB
Transmit Pointing Loss: -1.74 dB

3.3 Calculating the EIRP

EIRP (or PIRE) is computed by removing all propagation losses from the RSSI:

polarization_loss = -0.5
atmospheric_loss = -2.1
ionospheric_loss = -0.1
tx_pointing_loss = -1.74
tx_eirp = rssi - path_loss - polarization_loss - atmospheric_loss - ionospheric_loss - tx_pointing_loss  
print(tx_eirp)  # ≈25 dBW

3.4 Determining the Transmit Power

Finally, the transmit power P (in dBW) is given by: P = PIRE - (Transmit Line Loss) - (Transmit Antenna Gain)
with Transmit Line Loss = -1 dB and Transmit Antenna Gain = 16.23 dB.

tx_line_loss = -1  # dB
tx_antenna_gain = 16.23  # dB
transmit_power_dbW = tx_eirp - tx_line_loss - tx_antenna_gain  
transmit_power_W = 10**(transmit_power_dbW/10)
print(transmit_power_W)  # ≈9.5 W (though testing shows 9.7 W works better)

We then enter the value:

> docker run --rm -i -e FLAG=pouet linky:challenge
...
Determine the transmit power (in W) to achieve 10dB of Eb/No margin (above minimum for BER): 9.7
Winner Winner Chicken Dinner
...
You got it! Here's your flag:
pouet

And it works, we get the flag!
If you observe closely, I entered 9.7 instead of 9.5. The value 9.5 didn’t work, and I couldn’t find the error, so I tried nearby values, and 9.7 worked 😄.
In reality, if you look at the source code of the challenge, you’ll see that depending on what value you enter, the responses can differ. For example, the official solution uses 54 for the gain, 24.8 for G/T, and 9.5 for transmit power. But anyway, the important thing is to understand how to play with all these values :)

Writeup Hack-A-Sat: Linky