

Wifi and the square of the radius - zdw
http://apenwarr.ca/log/?m=201407#14

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ghshephard
The theory (a 1/2 impact doesn't make any real difference when you are dealing
with 1/10th drops based on distance) - doesn't match up with reality.

As one who has run a 1-Watt 900 Mhz Wireless Mesh omnidirectional network over
distances of about 8km, I can tell you that the splitter that drops your power
in half on the transmission/receive side, has a _huge_ impact on networks that
are close to the edge of your receive sensitivity. Enough so that we took some
equipment that incorporated such a split in the signal strength, and sent it
back to engineering for a 9 month spin to remove such a splitter. 1/2 drop =
3dB loss.

If you have a receive sensitivity of about -102 dBm, and your signal is just
on the edge at -100 dBm, and you inject a splitter (a 3dB loss) - you lose a
good chunk of your transmitters. It's the difference between being able to run
a 4km hop and an 8km hop.

Here is my favorite tutorial on "how far" \- it walks the right line between
theory and practice.

[http://www.afar.net/tutorials/how-far/](http://www.afar.net/tutorials/how-
far/)

~~~
Retric
Power drops as R^2, coverage area is R^2 so cutting output by N reduces your
coverage area by N.

~~~
colanderman
To reiterate (because although I had the same thought as you it took me a
moment to realize what you meant), OP is measuring the wrong thing for multi-
user scenarios. Losing 10 ft from 1000 ft radius due to a 20% power loss might
sound inconsequential (only 1%, right?), until you realize that's ~31,000 ft².
That's ¾ acre, or 20% of your users. Nothing to sneeze at.

~~~
mungoman2
How do you get 20%? The area difference between a circle with a radius of 1000
vs 990 is 2%.

~~~
colanderman
Oh shit, you're right. I used 900 instead of 990. That's what I get for doing
math at midnight. Too late to edit it now.

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zb
Incidentally, GPS receivers are typically sensitive down to around -160dBm, or
0.1aW.

~~~
mikeash
A really fun GPS fact is that the signal is so weak by the time it reaches the
surface of the Earth that it's about 1000x, or 30dB, quieter than thermal
noise. Receivers still extract usable data through long-term correlation, and
the fact that GPS is designed so you don't need to reliably recover every bit,
or anywhere close.

This, in turn, means that you can realistically use a one-bit ADC in your
receiver, because that only amounts to a few more dB of loss. You're already
dealing with a system built to overcome massive loss and it can tolerate a
little more.

~~~
sbierwagen
Additional fun fact: "[GPS receivers] being specially designed to employ anti-
jam features (e.g. null steering antenna or electronically steerable antenna)
to function in an environment of active or passive countermeasures" are MTCR
category II dual-use missile related export-restricted components.

[http://www.mtcr.info/english/MTCR-April2011-Technical-
Annex....](http://www.mtcr.info/english/MTCR-April2011-Technical-Annex.pdf)

MTCR is also why GPS receivers will refuse to provide navigation information
if you're flying too high or moving too fast.

~~~
gpvos
MTCR = Missile Technology Control Regime, an informal and voluntary
partnership between 34 countries to prevent the proliferation of missile and
unmanned aerial vehicle technology capable of carrying a 500 kg payload at
least 300 km.
[https://en.wikipedia.org/wiki/Missile_Technology_Control_Reg...](https://en.wikipedia.org/wiki/Missile_Technology_Control_Regime)

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TorKlingberg
Isn't it a little strange to explain a square function by analogy to O(n^2)
algorithms? As in, if you understand big-O notation you should already know
how powers work.

~~~
walshemj
Yes sounds like a hard-core CS guy who's not done any traditional engineering
class's inverse square law was covered at my high school physics class at
15-16.

If you want to grok wifi get the Cisco press books.

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skierscott
And optimazation is critical. Most routers have omnidirectional antennas that
send the signal in the most useful places[0] and there even are routers that
use some fancy aiming algorithm[1].

[0]:[http://superuser.com/questions/99082/direction-of-wifi-
anten...](http://superuser.com/questions/99082/direction-of-wifi-antenna)

[1]:on mobile so no link and I've only heard about it from my dad.

~~~
sbierwagen
I assume you're talking about 802.11n MIMO beamforming

[http://en.wikipedia.org/wiki/Beamforming](http://en.wikipedia.org/wiki/Beamforming)

~~~
gonzo
or even the simple analog beam forming we did at Vivato.

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anonymousDan
I always thought that in theory this is a good argument for dense multihop
wireless networks - the potential energy savings from forwarding over multiple
shorter hops instead of one long range transmission. I guess in practice there
are additional losses at each step that outweigh the potential gains.

~~~
ghshephard
The nice advantage you get with Multi-Hop wireless networks is Link Layer
retry. So not only can you hop 50+ miles, you also are able to retry in the
face of RF noise at some of your hops.

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gonzo
the path loss exponent is 2 in _line of sight_ conditions.

These are relatively rare in typical WiFi deployments.

~~~
lnteveryday
Agreed. There are some things that you wouldn't expect to attenuate signals
(that much) as well, such as glass, that can have a significant effect. Tinted
glass can cause a 12-20db drop. In an outdoor environment you also should keep
60% of the fresnel zone clear. This has to be taken into account when thinking
of line of sight.

