> And if a transmitter isn't pointed at you, then it isn't an interfering transmitter. This is a crucial factor in the math.
This does not really matter, because in the dense wireless networks that are typical for the unlicensed bands, due to the ubiquitous WiFi and Bluetooth devices, there is always a transmitter pointed at you. Typically there are many transmitters pointed at you.
So any argument based on this idea that there are no transmitters pointed at you would fail badly in practice.
Moreover, the interference in digital communications is not something that grows linearly. It grows in jumps, when some thresholds are exceeded and the error correction used by transmitters fails to work. So at certain thresholds the interference would force your device to reduce the bit rate, until a certain threshold where communication would become impossible until the interfering transmitter stops transmitting.
Also, 6 neighbors do not provide 6 units of interference. The amount of interference depends on many factors. The neighbors that use the same communication channels will attempt to not transmit simultaneously, to avoid collisions.
When a neighbor transmits on the same channel, then it is guaranteed that the interference is so high as to prevent other simultaneous communications. So the interference that we discuss is from transmitters that use other channels than yours.
Besides the fact that the neighbors are partitioned in groups within which only one transmits (but almost all the time there is an active transmitter), the interference depends greatly on the distance to the transmitters.
So to estimate the change in interference when all replace their omnidirectional antennas with directive antennas, increasing the radiant intensity, is far more complex than your simple arithmetic.
The worst case, which can never be excluded, is that there will be at least one transmitter pointed at you and its higher radiant intensity will be enough to cross the threshold at which communication becomes impossible for yourself. In this case it is completely irrelevant if you no longer have interference from other transmitters that are not pointed at you.
Planning wireless networks cannot be done based on hopes that you will be the luckiest in the universe and Murphy's law will not apply to you.
A transmitter, sure. If you go from having 40 transmitters pointing at you, to now having 6 transmitters pointing at you, that makes a big difference. Even if they're running at twice the EIRP now, that's a big improvement.
> So any argument based on this idea that there are no transmitters pointed at you would fail badly in practice.
My argument doesn't depend on that.
> The amount of interference depends on many factors. [...] So to estimate the change in interference when all replace their omnidirectional antennas with directive antennas, increasing the radiant intensity, is far more complex than your simple arithmetic.
Yes I simplified. But does that completely upend the result? If so, show me the math that makes it happen.
> groups within which only one transmits (but almost all the time there is an active transmitter)
> cross the threshold at which communication becomes impossible for yourself
And guess what? If everyone doubles their EIRP but transmits in a much narrower beam, the area in which that happens becomes smaller. The number of transmitter pairs that need to time-share decreases.
> Planning wireless networks cannot be done based on hopes that you will be the luckiest in the universe and Murphy's law will not apply to you.
I think your argument depends on me being lucky in the omnidirectional case but unlucky in the directed transmit case. That's not a reasonable way to assess alternatives.
For every percent chance that higher-EIRP directional transmit causes me problems, there's a bigger chance that higher-total-power omnidirectional transmit causes me problems.
This does not really matter, because in the dense wireless networks that are typical for the unlicensed bands, due to the ubiquitous WiFi and Bluetooth devices, there is always a transmitter pointed at you. Typically there are many transmitters pointed at you.
So any argument based on this idea that there are no transmitters pointed at you would fail badly in practice.
Moreover, the interference in digital communications is not something that grows linearly. It grows in jumps, when some thresholds are exceeded and the error correction used by transmitters fails to work. So at certain thresholds the interference would force your device to reduce the bit rate, until a certain threshold where communication would become impossible until the interfering transmitter stops transmitting.
Also, 6 neighbors do not provide 6 units of interference. The amount of interference depends on many factors. The neighbors that use the same communication channels will attempt to not transmit simultaneously, to avoid collisions.
When a neighbor transmits on the same channel, then it is guaranteed that the interference is so high as to prevent other simultaneous communications. So the interference that we discuss is from transmitters that use other channels than yours.
Besides the fact that the neighbors are partitioned in groups within which only one transmits (but almost all the time there is an active transmitter), the interference depends greatly on the distance to the transmitters.
So to estimate the change in interference when all replace their omnidirectional antennas with directive antennas, increasing the radiant intensity, is far more complex than your simple arithmetic.
The worst case, which can never be excluded, is that there will be at least one transmitter pointed at you and its higher radiant intensity will be enough to cross the threshold at which communication becomes impossible for yourself. In this case it is completely irrelevant if you no longer have interference from other transmitters that are not pointed at you.
Planning wireless networks cannot be done based on hopes that you will be the luckiest in the universe and Murphy's law will not apply to you.