One thing you don’t often see is a link budget for ADS-B links. But, you can show via a simple link budget that with a good setup you can receive ADS-B over 400nm.
For example start with the following:
Aircraft transponder EIRP: 51 dBm (125.8 Watts)
Free Space Loss (FSL):
For distance in kilometers (dkm):
FSL = 32.4 + 20log(dkm) +20log(FMHz)
For distance in nautical miles (dnm):
FSL = 37.8 + 20log(dnm) +20log(FMHz)
where FMHz = frequency in MHz
For nominal range of 200 nm and 1090 MHz:
FSL = 144.6 dB
Signal at receive antenna:
51 -144.6 = -93.6 dBm
Assume antenna gain = 0dBi
So, signal at receiver input = -93.6 dBm
Thermal noise (kTB) at 290 K:
-174 dBm/Hz
Noise figure:
Assume rtl-sdr dongle : 4 dB
Receiver noise:
-174 + 4 = -170 dBm/Hz
Received C/No:
-93.6 - -170 = 76.4 dB-Hz
Data rate (DR):
1 Mbps
Received Eb/No:
Eb/No = C/No - 10log(DR) = 76.4 - 10log(10^6) = 16.4 dB
Required Eb/No = 14 dB for On-Off-Keying (OOK) at 10^-3 BER
So even a minimal system works at 200 nm with a slight margin of 2.4 dB.
But suppose you have a 6dBi antenna, you could receive 400 nm with the same margin. Also, throw in an LNA with a 1 dB noise figure and you have another 3 dB of margin. So, receiving at 400 nm seems reasonable with troposcatter.