I'm thinking about studying wireless communications to see if I can implement wifi or bluetooth for long ranges, around 50 to 100 miles. Is this even theoretically possible?
Given the 1 watt FCC power limit and the wide receiver bandwidth (17 MHz for 802.11b if I remember correctly) 50 miles is impractical.
Given enough transmit (ERP) effective radiated power (think transmitter power and antenna gain) and a receive antenna having gain it is theoretically possible. An example is analog UHF television. With an ERP of 1 MW, a receiver bandwidth of 6 MHz, and a good receive antenna a range of 50 miles is practical. This gives us a rough idea of what it would take to achieve 50 miles with 2450 MHz WiFi.
Let's be more rigorous in our analysis. This is not an exact analysis but it's much better than the previous one. Fig. 1 in the paper (link below) shows that at a distance of 50 miles (80 km), with the RX and TX antennas 20 meters above ground, and 1 kW ERP the field strength at the RX location is 15 dBuV/m. Note that this graph is for 600 MHz but we'll use it anyway at 2450 MHz.
The AF (Antenna Factor) of a dipole receive RX at 2450 MHz (Wi Fi band) is 38 dB. That means that its output into 50 ohms is -38 dB relative to the field strength. For 15 dBuV/m the dipole output is 15 - 38 -23 dBuV. Converting to dBm (for a 50 ohm system) and we have -23 - 107 = -130 dBm. Let's use a RX antenna having a gain of 20 dBd. The signal we have to work with is now -110 dBm in the TX. But to comply with FCC regulations we can't have an ERP of 1 kW, it can be only 1 watt. So, our -110 dBm is not -140 dBm.
Is -140 dBm enough for a WiFi link? The thermal noise floor at room temperature is -174 dBm. The noise power in the 17 MHz RX bandwidth is 72 dB more, giving noise of -102 dBm. Add to this a 3 dB RX noise figure and a requirement of 12 dB S/N ratio and the signal required to complete the link is -87 dBm.
We need -87 dBm but we have only -140 dBm. We are 53 dB short. The antenna gain is already 20 dBd and an antenna with a gain of 73 dBd at 2450 MHz is not practical. Raising the antennas to 1200 meters gains about 30 dB and now the required RX antenna gain is a doable 43 dBd.