Chapter 24 showed you two ways to stop standing still: hop between lanes, or smear yourself so thin you sink beneath the hiss. There is a third, and it is the prettiest of the family, because it needs no secret at all. Instead of stirring a message with a scrambled rhythm, you slide it. One long whistle, climbing steadily from the bottom of the lane to the top. That slide is called a chirp , and it is how a sensor in a field talks to a rooftop miles away on a battery meant to outlast the sensor.
Ten years on a coin cell#
Picture the job. A soil-moisture probe stands in a vineyard. Twice an hour it has something to say, and what it has to say is tiny: a number, a battery level, a name. Nobody will visit it. Its battery is a coin the size of your thumbnail, and it must last a decade.
Every radio you have met so far is the wrong shape for this. Wi-Fi is a fire hose that drinks like one and gives up at the far side of a house. A phone radio can reach the vineyard's edge, but it spends its life in conversation with the tower, and conversation costs current. Both are built to move a lot of data quickly, and the probe wants the exact opposite: almost no data, extremely far, almost no power.
When a problem is the mirror image of the usual one, the usual answers invert too. And the law that decides how they invert is the one from chapter 22.
Spend the thing you have plenty of#
Shannon's law says a link's speed is the width of its lane times a bonus that grows with headroom above the hiss. Everyone you have met so far reads that as a recipe for going faster. Read it backward instead: if you are willing to go slower, you can get by with less headroom. And "less headroom" eventually passes zero and keeps going, into the strange country where the signal is quieter than the hiss it arrives in and a receiver can still read it.
The vineyard probe has almost nothing except one currency, and it has that in absurd abundance: time. A twelve-byte reading has no deadline. If sending it slowly is what buys the distance, then send it slowly. Take a whole second over it, if that is the price. The probe was going to sit there doing nothing anyway.
That is the whole design. Everything else on this page is the machinery for spending time gracefully.
The sliding whistle#
Here is the slide itself. Instead of parking on one frequency, the transmitter starts somewhere in its lane and walks smoothly upward, and when it runs off the top it reappears at the bottom and keeps climbing, the way a slide whistle does when someone pulls the plunger all the way out and starts again. One symbol is one full lap of the lane.
Because the whistle visits every frequency in the lane and lingers at none, its energy ends up smeared across the whole width, exactly as in chapter 24: the same fixed helping of energy, spread thin enough to lie under the grass. The picture below is the way radio people actually look at this, a waterfall: frequency across, time flowing downward, brightness for energy. Turn the slides down and watch them sink into the speckle.
A bold staircase of slides: anyone sweeping the dial trips over this.
The slopes cancel#
Now the beautiful part. The receiver makes a slide of its own, running the other way: a mirror falling as fast as the arriving whistle climbs. Then it multiplies the two together.
Appendix C told you what multiplying two waves does: two brand-new waves appear, one at the sum of the originals' speeds and one at the difference. Take the one at the sum. The arriving whistle's speed is climbing at some steady rate, the mirror's is falling at exactly that rate, and a rise added to an equal fall is no movement at all. The sliding cancels, and what is left is a single, flat, steady tone. (The other new wave slides twice as fast as either parent, and the receiver simply throws it away.)
Look at what that does to the energy. It arrived smeared across the entire lane, lying under the grass, invisible. After the stir, every scrap of it is stacked at one pitch. Same energy, a fraction of the width, so it stands up tall: a spike where a moment ago there was a mattress. Then appendix B's un-adding machine reads which pitch it is, and the message is out.
Give the mirror the wrong tilt and none of it happens. The slopes fail to cancel, the tone keeps sliding, the energy stays smeared, and the spike never forms. Try both below.
The slopes cancel exactly. Everything the slide smeared across the lane arrives at one pitch, and where that pitch sits is where the slide began.
Where the slide begins is the message#
So the stir hands you a pitch. Which pitch? That depends on one thing only: where in the lane the whistle started. Start at the bottom and the flat tone lands low. Start a third of the way up and it lands a third of the way up. The slide's starting place survives the whole journey, smeared across the lane and buried under the hiss, and arrives as a position on a dial.
That is where the bits live. Chop the lane into places a slide could start, and each place is a different symbol. Chop it into 128 places and one slide carries seven bits; chop it into 4,096 and it carries twelve. The number of chops has a name you will see on every LoRa datasheet, the spreading factor , and it is the only dial that really matters.
Here is the catch that makes it interesting. Finer chops mean the receiver must tell nearer pitches apart, and telling nearer pitches apart takes longer listening. So each step up the spreading factor doubles how long a slide lasts while adding just one bit to it. Traffic roughly halves. In exchange, the receiver gets twice as long to add the slide up, and can haul it out from about 2.5 dB deeper under the hiss.
- bits in one slide
- 7
- one slide takes
- 1.0 ms
- bits per second
- 6,836
- digs out from
- 7.5 dB under the hiss
The fastest setting: nearly seven thousand bits a second, and the shortest reach of the six.
At the slowest setting the numbers get genuinely strange. The message arrives about twenty decibels below the noise floor: a hundred times fainter than the hiss it is buried in. A spectrum analyzer pointed straight at it shows nothing but grass. And a chip costing a couple of dollars pulls it out anyway.
Why it forgives everything#
GPS also hides beneath the grass, and chapter 24 showed you how: a long scrambled rhythm that the receiver must know by heart and line up almost perfectly. Lining it up is the hard part. It is why GPS satellites carry atomic clocks and why a cold receiver can spend half a minute hunting.
A slide asks for none of that. There is no secret pattern to know, because a slide is just a slide, the same one every time. And it forgives error in a way a scrambled code never does. If the receiver's clock runs slightly early, the stir still cancels the slopes, and the flat tone simply lands at a slightly different pitch. If the transmitter's cheap crystal sits a little off frequency, same story. If the sensor is on a moving truck and Doppler nudges the whole signal, same story again. Timing errors and frequency errors both come out as small shifts of one tone, and a receiver can measure a shift and correct for it far more easily than it can hunt for a needle.
That forgiveness is the practical reason this scheme won its corner of the world. LoRa radios need no network timing, no handshake, no atomic anything. A sensor wakes, whistles for a fraction of a second, and goes back to sleep without ever learning whether anyone was listening. Gateways on rooftops hear whoever they hear. It is the politest possible radio: it never asks a question.
What it costs#
Shannon does not hand out favors, and the bill arrives on time. At the slowest setting a link carries about 366 bits per second, which is slower than a modem from 1980. Sending a single photograph would take a day and a half. There will never be video on this, or voice, or anything that streams. It is a radio for sips: a temperature, a water level, a meter reading, a button press.
There is a second bill, and it is a legal one. These radios live in the small shared bands where nobody needs a license, and the rules there cap how much of the hour any one device may spend talking. A slow radio hits that cap easily, so a sensor that whistles for a third of a second may be required to stay silent for the next minute. The design and the law point the same way: say very little, very rarely, and be heard a long way off.
Within those limits, people have done lovely things with it. Trackers on livestock and beehives. City parking sensors and water meters that report from basements through a foot of concrete, because a signal this patient handles the toll of chapter 11 better than a fast one can. Hikers carrying little relay boxes that pass short text messages between each other with no tower and no network at all, over ridges where phones show nothing.
The same slide, in a radar#
One last echo, and it runs backward through the book. Radar in chapter 28 wants a very short pulse, because a short pulse times an echo sharply. But a short pulse holds very little energy, and a faint echo is a lost echo. Radar engineers hit that wall in the 1950s and escaped it with exactly this trick: send a long pulse that slides in frequency, then stir the returning echo against a mirror slide. The long, weak echo collapses into a short, tall spike, and you get a faint pulse's gentleness with a sharp pulse's timing.
They call it pulse compression, and it is in the weather radar drawing the rain map on your phone. Which is the quiet joke at the heart of this appendix: the trick that lets a coin cell be heard across a valley, and the trick that lets a radar see a raindrop, are the same slide, stirred the same way. Radio does not have many ideas. It just keeps finding new places to put them.