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Helmhurts: Placing a WiFi router with the Helmholtz equation (jasmcole.com)
145 points by signa11 on Aug 26, 2014 | hide | past | favorite | 19 comments

Good fun here, and a neat exercise! However, a few comments for people looking to do the same:

- Ignoring the 3D nature of antenna placement, you need to model the concrete walls properly to get an answer that is semi reliable. All materials have frequency dependent reflection and transmission (attentuation) coefficients. Its pretty easy to extend a toy FDTD sim to include these.

- For the reasons above, inferring 2.4Ghz behaviour from ~1GHz (30cm) signal isn't really a good thing to do (even in a "hand waving" manner).

- When displaying E-fields, you usually want to plot the ||E||^2 averaged over one complete wave cycle -- the nodes shouldn't jump around. If they do, it means the simulation hasn't reached a steady state.


Given a 2.4Ghz pure sine wave and a couple signal strength detectors couldn't one iteratively modify the frequency dependent values for the various walls?

Not for any practical measurements. This would work in say an anechoic environment – save for the wall under test – but you'd end up sampling multipath constructive/destrictuve interference instead of the wall reflections.

> - Ignoring the 3D nature of antenna placement ...

A real antenna won't be an isotropic radiator, either. Got any antenna-pattern plots?

Did you solve that system by inverting the helmholtz matrix? Your steady state time independent solution looks like it's suffering from major numeric instability. If you didn't already, you should solve the system with linsolve() and see if your results stay the same.

Reading between the lines I wonder if he's just using the backslash operator when he says 'inverse'.

Someone should build a web app that lets you upload a floor sketch to run these calcs on :-)

At least if the solution of this is not normally "place the router in the middle of the flat", as this is the standard advice.

Got me thinking...could you integrate a wireless AP into a light fixture without fear of interference, either EM or physical? I'm sure there is a clever solution for something like a hanging chandelier.

Maybe there are products out there already that allow people to hide their networking hardware in plain sight?

Aruba Networks used to make a model called the AP-65WB. The WB means "wall box" -- it basically fits in a standard wall-box, the same kind of fixture that could also hold a couple of outlets or light switches (or a combination thereof). Not sure if that unit's been replaced or retired, though. Also, it's not exactly targeted at home users.

Many of the enterprise APs with integrated antennas are designed for ceiling installation. They often have an antenna that's intended to radiate its best coverage down from the ceiling in a cone.

It doesn't seem necessary to hide it to me. All the bigger deployments I've seen just put APs on the ceiling. There are enough things on there (smoke detectors, lights, sprinklers) that adding another box probably wouldn't make much aesthetic difference unless you went out of your way to hide all the other things.

That was my first thought, too - but you'd probably have to specify things like wall materials and thicknesses to get decent results.

I'm hoping for precise indoor navigation, Google and Apple are currently working on that. All you'd have to do is walk around with your phone, measuring signal strength and then visualize that.

>I'm hoping for precise indoor navigation, Google and Apple are currently working on that. All you'd have to do is walk around with your phone, measuring signal strength and then visualize that.

I'd wager there are _a lot_ more folks that that looking the problem. Its difficult to just use signal strength as this is heavily multi path dependent and time-varying as anything (e.g., moving your phone and hand around) within the environment changes.

There are results in the literature floating around that show some basic success, but nothing at all like the dreams of indoor GPS we're all hoping for. It's a fun problem space, but still in its infancy.

Now it would be a nice next step if he uses his wifi card's RSSI + Helmholtz reciprocity to verify the theory.

Which would work if zero of his neighbors had wifi routers too, which isn't true in 2014.

It isn't science until you close the feedback loop.

More precisely, if the time-dependence of an electromagnetic wave can be assumed to be of the form sin(\omega t)...

It's not quite true. It assumes that the electric field oscillates with the same phase at every point. Normally the Helmholtz equation is solved assuming that the time dependence is exp(I\omega t), where I is the imaginary unit, and we search for a complex E(x) solution. arg(E(x)) deals with the phase factor, abs(E(x)) is the amplitude. Re( E(x)exp(I\omega t) ) is a solution to the Maxwell equations.

Isn't it kind of obvious that the best coverage will be when the emitter is in the middle of the area to cover? ;-)

for a uniform sphere maybe

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