Every wireless thing you own - Wi-Fi, your phone, a car key fob, GPS, a Flipper Zero - does the same two things underneath: it impresses information onto a radio wave, and it picks a place in the spectrum to do it. Get those two ideas and most of radio stops being magic. This is the foundation piece for the signals-intelligence cluster, built from the ground up, with the waveforms drawn live from the actual equations rather than shown as stock pictures.
//The Carrier and the Message
A radio starts with a carrier: a pure sine wave at some frequency, say 100 MHz, that carries no information at all. On its own it is a dead tone. To send something, you vary one of the carrier's three properties in step with your message - its amplitude, its frequency, or its phase. That variation is the information. Everything else is detail.
Amplitude. Make the carrier taller and shorter in time with the message and you have AM - the oldest scheme, and the one behind AM radio. It is simple to build and simple to receive, which is exactly why it is noisy: most natural interference is amplitude noise, and AM cannot tell your message from a lightning crackle.
Frequency. Leave the height alone and wobble the carrier's frequency instead and you have FM. Because the information now lives in frequency, amplitude noise mostly washes off, which is why FM radio sounds clean and why it won the broadcast-quality argument. The demo's modulation-index slider is the knob that trades bandwidth for noise immunity.
Phase. Shift where the wave is in its cycle and you have phase modulation, the basis of almost all modern digital radio. You cannot see phase the way you see height, which is what the constellation diagram in the demo is for.
//Going Digital
Digital radio is the same three knobs, used in discrete steps instead of continuously. Keying is the word for it.
FSK - frequency-shift keying - sends one frequency for a 0 and another for a 1. It is FM's digital cousin, and it is everywhere: pagers, old modems, plenty of telemetry. Rugged and cheap.
BPSK - binary phase-shift keying - flips the carrier's phase by 180 degrees to mark a bit. In the constellation that is two dots on opposite sides of a circle: as far apart as two points can be, which makes BPSK maximally robust and a natural fit for weak, long-distance links. One bit per symbol.
QPSK - quadrature phase-shift keying - uses four phases, so each symbol carries two bits instead of one. Same bandwidth, double the data rate. That is the workhorse behind satellite TV, a lot of cellular, and Wi-Fi's lower rates. Push further - 16-QAM, 64-QAM, 256-QAM - and you pack more dots into the constellation for more bits per symbol, at the cost of needing a cleaner signal to tell the dots apart. That trade, dots-versus-cleanliness, is the whole story of why your Wi-Fi rate drops as you walk away from the router.
Why the constellation matters
A constellation diagram plots each symbol as a point: how far it is from centre is amplitude, what angle it sits at is phase. A receiver demodulates by measuring where each incoming symbol lands and snapping it to the nearest legal point. Noise smears each point into a fuzzy blob; when the blobs overlap, the receiver guesses wrong and you get bit errors. Everything about a digital link - its rate, its range, its resilience - is visible as how many points there are and how much room noise has to push them around.
//The Spectrum Is Real Estate
The second idea is where you transmit. The radio spectrum runs, by convention, from about 3 kHz to 300 GHz, carved into bands by the ITU. The second tab of the demo walks them, but the governing trade is one sentence: higher frequency buys more bandwidth, and costs you range and penetration.
Low frequencies - the HF band at 3 to 30 MHz - bounce off the ionosphere and can cross oceans on a few watts, which is why shortwave and amateur radio live there. They also carry very little data and need big antennas. Climb to UHF - 300 MHz to 3 GHz - and antennas shrink to pocket size, bandwidth opens up enough for TV, cellular, Wi-Fi and GPS, but you are now essentially line of sight. Climb again to the millimetre-wave bands that 5G reaches into and you get enormous bandwidth and almost no range, blocked by a wall or a hand. Nobody picks a band because it is better; they pick the one whose trade fits the job.
//Why This Is the Foundation
These two ideas are load-bearing for everything in the rest of this cluster. Intercepting a signal means reversing the modulation to get the bits back - demodulation is just the receiver measuring the same waveform you drew in the demo. Locating a transmitter depends on which band it is in, because that sets how far away a listener can be. And frequency hopping is just a transmitter changing its place in the spectrum many times a second. If modulation is how information rides the wave, the spectrum is the map it rides across.
FSPL = 20·log10(d) + 20·log10(f) + 32.44, with distance d in kilometres and frequency f in MHz. Two things fall out of it: loss grows with the square of both distance and frequency, so doubling either adds 6 dB; and it is why a higher band is intrinsically shorter-ranged for the same power. This is the formula the link-budget thinking in the rest of the cluster rests on.//Sourcing and Framing
The modulation schemes, the constellation idea and the band plan are standard radio engineering, drawn from amateur-radio and signals textbooks and the ITU band designations. The free-space path loss constant (32.44 for kilometres and megahertz) was checked against reference sources. The demo computes each waveform from its equation rather than displaying a stored image, so the shapes are correct by construction rather than by my drawing.
This cluster stays on the physics and the published fundamentals of how radio and signals intelligence work. It does not touch operational military communications or any specific system - the textbook layer is more than enough to make the mechanisms clear, and it is the layer that explains the tools the site already covers, from the HackRF to the Flipper.