Signal, Interrupted

Dear Tom,

I hope this finds you well! We moved into our house last spring and love it, except for one thing — the wifi barely reaches the back bedroom we use as a home office. The little bars on my laptop go down to one, sometimes zero, and video calls freeze right when I'm talking. My husband says we just need a "booster" but I don't really understand what that means or why the wifi doesn't just, you know, go everywhere the way the electricity does. Can you explain what's actually happening back there?

— Gary, Boise, Idaho

A lovely question, Gary. It reminds me of the very first thing every student of domestic radio propagation must learn, which is that wifi does not travel through your house so much as *negotiate* with it, room by room, the way a diplomat negotiates a hostile border crossing — and your back bedroom, I regret to inform you, is currently losing that negotiation badly.

Let's start from first principles, which is always the correct place to start, of course. Your router is not, as most people assume, a box that "sends out wifi." It is a stateful non-deterministic packet oracle, humming away in its little cabinet, converting your household's data needs into a modulated electromagnetic waveform — specifically, assuming standard 2.4 and 5 gigahertz dual-band emission, which I will assume for you here since your letter did not specify and there is really no other reasonable assumption to make about a house built after, let's say, 2011. This waveform propagates outward from the router in a shape mathematically known as a lobe pattern, which is decidedly not a sphere, whatever the marketing on the box implies. It is closer to the silhouette of a slightly deflated pumpkin, and your back bedroom, statistically speaking, is sitting exactly in the pumpkin's least generous corner.

Now, here is where most homeowners stop thinking, and where the real story begins. Every wall between your router and your laptop is not simply "in the way" — it is performing what we call attenuation, a term borrowed, interestingly, from acoustics before radio engineers appropriated it in the 1920s, back when the whole discipline was still called "wireless telegraphy" and men wore hats indoors as a matter of professional seriousness. Drywall alone will cost you perhaps three decibels, which sounds trivial until you recall that the decibel scale is logarithmic, meaning each additional wall doesn't add to your losses, it multiplies them — a fact which, once internalized, changes how you look at your own floor plan forever. A stud wall with plumbing in it, of course, behaves altogether differently, since copper pipe is functionally a wave-guide and will actually channel some of your signal in exactly the wrong direction, off toward, say, the water heater, where it does nobody any good at all.

But we haven't even gotten to the interesting part, Gary, which is the 2.4 gigahertz band's unfortunate cohabitation with your microwave oven. This is not a coincidence of engineering, but a genuine historical accident: the 2.4 gigahertz slice of spectrum was set aside as an unlicensed "junk band" back in 1985, precisely because nobody important wanted it, since it happens to sit right on the resonant absorption frequency of the water molecule — which is, incidentally, the entire principle by which your microwave heats a burrito. So every time your spouse reheats coffee, you are, in the most literal sense, in electromagnetic competition with lunch. I find this delightful. Most people find it merely inconvenient, which I attribute to a failure of perspective rather than a failure of the science.

Naturally, this raises the question of multipath interference, which I would be remiss not to address, given that it is almost certainly the dominant term in your back bedroom's signal budget. As the waveform leaves the router, it does not travel to your laptop by one path — it travels by dozens, simultaneously, bouncing off the refrigerator, the bathroom mirror, the metal ductwork above the kitchen, and the decorative tin ceiling tiles I am simply going to assume, for the sake of a clean derivation, that your 1920s Boise craftsman home possesses. Each of these reflected copies arrives at your laptop's antenna at a very slightly different time, and depending on the phase relationship between them — governed, as you'd expect, by the standard interference equations first formalized for double-slit optics and later, somewhat awkwardly, retrofitted onto radio — these copies either add constructively, giving you a lovely strong signal, or destructively, cancelling each other out into what propagation engineers rather poetically call a "fade null." Your back bedroom, Gary, is very likely sitting in a fade null. This is not a design flaw in your home. It is simply where the wave math landed, the way a puddle forms wherever the yard happens to be lowest, and there is a strange comfort, I think, in knowing your discomfort is not your fault but merely geometry's.

I should mention, too, the thermal noise floor, since no complete treatment of your situation would be honest without it. Every conductor in your house — the wiring, the pipes, even, at a small enough scale, the water in your own bloodstream as you sit at your desk — is in a state of continuous thermal agitation, emitting a faint hiss of electromagnetic noise as an unavoidable consequence of having a temperature above absolute zero. Your wifi signal must exceed this noise floor by a healthy margin to be decoded at all, and by the time your signal has been attenuated by drywall, split three ways by multipath, and partially cancelled by destructive interference, it is arriving at your laptop's antenna none too far above that ambient hiss — which is precisely the moment your video call chooses to freeze on an unflattering frame of your face mid-sentence. The full derivation of the signal-to-noise threshold at which a modern 802.11ac decoder gives up entirely is worked out, for the curious, in Appendix B, along with a very satisfying worked example involving a hypothetical two-story colonial.

I want to be clear, Gary, that none of this is really about your booster, which your husband is, in a folk sense, not wrong about, though the term itself flattens a genuinely rich piece of applied electromagnetics into something that sounds like a vitamin. What matters is that you now understand *why* the back bedroom struggles — not merely that it does. Understanding the pumpkin-shaped lobe, the water-molecule coincidence, the fade nulls, and the noise floor gives you, I think, a far richer relationship with your own house than any homeowner has a right to expect. You will never again glance down a hallway and see mere drywall. You will see attenuation. You will see a wave doing its best.

I trust this has settled the matter entirely, and that the back bedroom will, from here on, simply make more sense to you, even if the bars on your laptop remain stubbornly unmoved by any of it. Glad I could clear that up!

— Tom