Wifi and the square of the radius | Hacker News Reader

Wifi and the square of the radius

apenwarr.ca

64 pointszdw26 comments

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/

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

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.

In my scenario, I'm saying the addition of a diplexor (in this case, a single antenna port to serve both 900 MHz, and 2.5Ghz, so the signal was split to two RF chips - about 3 dB of loss) - the typical distance at 0.1% BER, with the exact same antenna gain, Free Space Loss, LMR400 loss, etc.. dropped from 8 km radius in all directions down to a little over 4 km radius.

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

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.

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

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.

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.

is also why commercial GPS receivers will refuse.

One can, of course, out-design all of this with software and a decent front-end.

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...

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?

http://www.aholme.co.uk/GPS/Main.htm

Basically, if you are sampling the thermal noise with a 1-bit ADC, you are measuring the times of the zero crossings. The GPS signal will affect the times of those zero crossings. The thermal noise will be random, and therefore over the long term will even out. The GPS signal is a very low bit rate (50 bits per second), so you can gather enough statistics to identify each bit.

The 50bps signal is a side channel that tells the receiver where the satellites are. The main signal is actually slightly over 1Mbps. Decoding that one is really interesting. I won't claim to fully understand it, but my weak understanding is that it's not really 1Mbps of unique data, but rather a long-term pattern that's known to all parties. All the receiver needs to know is the time offset of the pattern, which it can do by listening for a long time and seeing where the small biases line up with the known pattern. In terms of listening to a pin drop against loud speakers, imagine that the pin is being played by a drummer and you know what beat he's playing, and your job is just to figure out what part of the song he's playing at the moment. If you listen long enough, the very small bias he applies to the extremely loud noise can be teased out, because you know what you're listening for, you just don't know exactly how it lines up in time. Do this with several drummers playing the same beat, and you'll get different time offsets for different drummers. Given at least four drummers (satellites), and you can take those differences and the known locations of the drummers (satellites) and figure out where you are.

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.

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.

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.

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.

I assume you're talking about 802.11n MIMO beamforming

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

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

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.

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.

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

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.

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

These are relatively rare in typical WiFi deployments.

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.

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