A 2.4 GHz Backhaul Link That Underperforms Its Budget
A utility is commissioning a 5 km point-to-point link at 2.4 GHz between a substation and a control building. The transmitter delivers 20 dBm into a 2 dB feeder; the transmit antenna has 6 dBi gain. At the far end the antenna gain is 6 dBi and the feeder loss is 1 dB. The receiver has a 5 dB noise figure over a 1 MHz channel, and the radio uses BPSK at 1 Mbit/s; the datasheet quotes Eb/N0 = 10.5 dB for 10⁻⁶ BER. The installer measured the receiver noise floor twice: with a 50 Ω termination at the antenna port it was −108 dBm, and with the antenna connected and pointed at clear sky it was −95 dBm. In service the link runs at a BER near 10⁻⁵. The field team's first proposal is to fit a 20 dB LNA ahead of the receiver to 'improve sensitivity'; the second is to raise the transmitter to 30 dBm. The local regulator permits 20 dBm EIRP in this band.
1. Compute the received power, the thermal noise floor and the expected Eb/N0 and link margin, stating every assumption.
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Free-space loss at 2.4 GHz over 5 km:
FSPL = 32.44 + 20log₁₀(f_Hz/10⁶ ... using f in MHz, d in km) = 32.44 + 20log₁₀(2400) + 20log₁₀(5) = 32.44 + 67.60 + 13.98 = 114.0 dB
EIRP = 20 − 2 + 6 = 24 dBm
Prx = EIRP − FSPL + Grx − Lrx = 24 − 114.0 + 6 − 1 = −85.0 dBm
Thermal noise in 1 MHz: N = −174 + 10log₁₀(10⁶) = −114.0 dBm. With NF = 5 dB, the noise floor is −109.0 dBm. The measured −108 dBm with a termination is within 1 dB, confirming the cascade noise figure and ruling out a receiver fault.
SNR = −85.0 − (−109.0) = 24.0 dB.
Conversion to Eb/N0: with C/N0 = −85 − (−169) = 84 dBHz and Rb = 1 Mbit/s, Eb/N0 = 84 − 60 = 24.0 dB (identical to SNR here only because Rb equals the noise bandwidth).
Margin = 24.0 − 10.5 = 13.5 dB. On paper the link has ample margin, so a BER of 10⁻⁵ in service is not a thermal-noise problem and the budget is not the explanation. Something else has raised the effective noise floor by roughly 13 dB.
2. Use the two noise-floor measurements to diagnose the link, and explain quantitatively why a 20 dB LNA will not deliver 20 dB of improvement.
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The termination measurement (−108 dBm) shows the receiver itself is healthy. The antenna measurement (−95 dBm) is 13 dB higher, and it was taken with no wanted signal present, so the antenna is collecting interference or external noise, not signal. In service the signal is −85 dBm and the floor is −95 dBm:
SNR = 10 dB → Eb/N0 = 10 dB, which is 0.5 dB below the 10.5 dB required for 10⁻⁶. That predicts a BER around 10⁻⁵, exactly what the field team sees. The diagnosis is interference-limited operation, not a sensitivity shortfall.
Why the LNA fails: an LNA improves the cascade noise figure, but it amplifies the interference by the same 20 dB as the signal. In this link the front-end noise floor of −108 dBm is already 13 dB below the interference floor; replacing a 5 dB NF with a 1.5 dB NF moves the thermal floor to about −112.5 dBm, still 17.5 dB below −95 dBm. Since the interference dominates the denominator, SNR stays at 10 dB. The LNA only adds cost, gain-compression risk and dynamic-range problems when a strong nearby transmitter appears. The honest conclusion is that receiver sensitivity is not the binding constraint - the noise environment is.
3. Rank the two proposals plus at least two alternatives, and justify the ranking against both physics and the 20 dBm EIRP limit.
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Regulatory arithmetic first. The current EIRP is 24 dBm, already 4 dB above the 20 dBm EIRP cap. Raising the transmitter to 30 dBm gives EIRP 34 dBm - 14 dB over the limit and not a lawful option, whatever the physics says. It would also, incidentally, work only if the interference arrives from a different direction or another channel.
Ranking:
Characterise the interference before buying anything. Sweep the band with a spectrum analyser at the receive antenna. Three outcomes lead to three different fixes: out-of-band strong signal (front-end desensitisation → add a bandpass filter ahead of the LNA, 1–2 dB insertion loss); co-channel interference from another 2.4 GHz user (retune to a clear channel); in-band noise from a nearby drive or welder (fix the source). This is cheap and decides everything else.
Spatial filtering. Raise the receive antenna and use a higher-gain, narrower-beam antenna re-aimed at the substation. Gain helps the wanted signal, and beamwidth rejects interference arriving off-axis - the only measure here with a positive return on both sides of the ratio. Verify the Fresnel zone over 5 km is clear at the new height.
Reduce the transmitter to comply with the 20 dBm EIRP cap once the interference is removed; the margin budget shows 13.5 dB is available on thermal noise alone.
LNA - ranked last: it cannot improve an interference-limited SNR, as shown above.
A 5 km, 24 dBm-EIRP, 1 Mbit/s link with 13.5 dB of theoretical margin should not need any of this; the 13 dB floor rise is the whole story.