Wifi and the square of the radius

http://apenwarr.ca/log/?m=201407#14

by zdw • 12 years ago

64 26 12 years ago

ghshephard3• 12 years ago

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/

Retric• 12 years ago

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

colanderman2• 12 years ago

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.

zb2• 12 years ago

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

mikeash2• 12 years ago

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.

sbierwagen2• 12 years ago

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....

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

shubhamjain• 12 years ago

I don't have lot of knowledge of Signal processing but how is that possible? Isn't it like detecting sound of a pin drop against massive noise of loud speakers?

zb2• 12 years ago

That's absolutely true of the sidebands (which contain the modulated data), but it's probably worth noting that the carrier still needs to be above the noise floor by at least around 30dBHz in order to decode anything.

skierscott• 12 years ago

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...

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

sbierwagen2• 12 years ago

I assume you're talking about 802.11n MIMO beamforming

http://en.wikipedia.org/wiki/Beamforming

gonzo3• 12 years ago

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

gonzo3• 12 years ago

the path loss exponent is 2 in line of sight conditions.

These are relatively rare in typical WiFi deployments.

lnteveryday2• 12 years ago

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.

anonymousDan• 12 years ago

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.

ghshephard3• 12 years ago

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.

lnteveryday2• 12 years ago

Another issue to consider is that the maximum bandwidth halves with each hop on a normal mesh.

walshemj2• 12 years ago

After you have boosted the power got some decent yagi or parabolic antennas.

one neat hack for PTP is run two bonded wifi links with directional antennas out of phase with each other.

TorKlingberg• 12 years ago

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.

walshemj2• 12 years ago

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.

Wifi and the square of the radius

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