Before this:What is a radio wave?
Digital modulation & constellations
Key takeaways Digital modulation sends data by switching a carrier between a fixed set of states called symbols, each carrying one or more bits. The three families are FSK (switch the frequency), PSK (switch the phase), and QAM (switch both phase and amplitude). A constellation diagram plots those symbols on a 2-D plane so you can see signal quality: tight, separated dots mean a clean signal; smeared dots mean errors are coming. P25 and DMR use four-level FSK (C4FM), which GopherTrunk visualises live in its constellation, symbol-scope, and eye-diagram panels.
In lesson 1 you saw that information rides on a wave by changing its amplitude, frequency, or phase. Analog modes vary those smoothly. Digital modes do something cleaner: they snap the carrier to a few predefined states, so the receiver only has to decide which state arrived — far more robust against noise. This lesson is where the scopes in GopherTrunk finally make sense.
What is a symbol, and how is it different from a bit?
A bit is a single 0 or 1. A symbol is one state the transmitter actually puts on the air, and a symbol can stand for more than one bit at a time.
If a scheme has only two states, each symbol carries one bit. If it has four states, each symbol carries two bits (00, 01, 10, 11). Eight states → three bits, and so on. This is why the symbol rate (symbols per second, called baud) and the bit rate (bits per second) are different numbers:
bit rate = symbol rate × bits per symbol
P25 Phase 1 runs at 4800 baud with 4 states (2 bits each), giving 9600 bits per second. That distinction — explored further in Symbols, baud & bitrate — matters when you size capture buffers and reason about how much SNR a mode needs.
What are the three families of digital modulation?
Every digital mode you’ll meet varies one of the wave’s three properties — exactly the three from lesson 1.
FSK — frequency-shift keying
The carrier jumps between a set of frequencies, one per symbol. Two frequencies gives 2FSK; four gives 4FSK. This is the workhorse of land-mobile digital voice: P25 Phase 1 (C4FM) and DMR both use 4FSK, where the carrier sits at one of four small frequency offsets (deviations) for each symbol. FSK is popular because it tolerates the cheap, efficient amplifiers used in handhelds.
Concretely, C4FM’s four symbols are four exact frequency deviations from the channel centre — and each maps to a fixed 2-bit pair (a dibit):
| Deviation | Symbol level | Bits (dibit) |
|---|---|---|
| +1800 Hz | +3 | 01 |
| +600 Hz | +1 | 00 |
| −600 Hz | −1 | 10 |
| −1800 Hz | −3 | 11 |
When you watch the symbol scope, those four levels are literally these deviations; on the constellation they’re four points. A clean signal lands every symbol on one of the four — anything in between is the receiver guessing.
PSK — phase-shift keying
The carrier’s phase (its timing offset) jumps between fixed angles while amplitude stays constant. Two phases is BPSK; four is QPSK (2 bits/symbol). P25 Phase 2 uses a PSK variant. PSK is spectrally efficient and shows up everywhere from satellites to digital broadcast.
QAM — quadrature amplitude modulation
QAM varies both phase and amplitude, packing many states into the plane — 16-QAM (4 bits/symbol), 64-QAM, and higher. More bits per symbol means more data in the same bandwidth, but the states sit closer together, so QAM needs a higher SNR to decode. You’ll meet it in Wi-Fi, cable, and LTE rather than scanner traffic, but the same constellation idea applies.
What is a constellation diagram, and how do I read one?
A constellation diagram is the single most useful picture in digital radio. It plots each received symbol as a point on a 2-D plane built from the SDR’s IQ data: the horizontal axis (I) and vertical axis (Q) together encode the carrier’s phase as the point’s angle and its amplitude as the point’s distance from the centre.
A perfect signal places every symbol exactly on its ideal spot, so you see a few tight clusters. Real signals scatter around those spots, and how much they scatter is a direct read on quality:
In GopherTrunk, the Constellation panel draws this live. When you’re chasing a marginal signal, a constellation that’s collapsing toward the centre or rotating tells you exactly what’s wrong — too little SNR, a tuning error, or a clock problem — long before you’d guess it from the audio.
What is an eye diagram, and what does it tell me?
Where the constellation shows symbols in the IQ plane, an eye diagram shows them against time. It overlays many short snippets of the recovered signal so they stack up, and the result has open “eye” shapes between the symbol levels. The wider and taller the eye opening, the more margin the decoder has to sample each symbol correctly. A closing eye means noise or timing jitter is eating that margin.
For the 4-level FSK in P25 and DMR you’ll see three stacked eyes (four levels → three gaps). GopherTrunk’s Eye diagram and Symbol scope panels let you watch this directly — together with the constellation, they’re your toolkit for tuning a clean lock later in the path.
Quick check: a 4-level (4FSK) signal at 4800 baud carries how many bits per second?
Recap
- Digital modulation switches the carrier between fixed symbols; each symbol carries one or more bits.
- FSK switches frequency (P25 C4FM, DMR), PSK switches phase (P25 Phase 2), QAM switches both for higher data rates.
- A constellation plots symbols in the IQ plane — tight clusters = clean, smeared = errors.
- An eye diagram plots them against time — a wide-open eye means healthy margin.
- GopherTrunk shows all three views live, which is how you diagnose a shaky signal.
Next in this module: how symbol rate and bit rate relate, and why it matters for capture. Or jump ahead to what software-defined radio actually is to see where these symbols come from.
Frequently asked questions
What is digital modulation?
Digital modulation is the process of putting digital data — ones and zeros — onto a radio carrier by switching the carrier between a fixed set of states. Each state, called a symbol, stands for one or more bits. The receiver measures which state arrived and maps it back to bits. Common families are FSK (switching frequency), PSK (switching phase), and QAM (switching both amplitude and phase).
What is a constellation diagram?
A constellation diagram is a plot of a digital signal’s symbols on a 2-D plane, where each point’s position encodes the carrier’s phase (angle) and amplitude (distance from centre). A clean signal shows tight, well-separated dots at the expected symbol positions; noise, mistuning, or distortion smears the dots, and when they blur together the decoder starts making errors.
What is the difference between a symbol and a bit?
A bit is a single 0 or 1. A symbol is one transmitted state of the carrier, which can carry several bits at once. For example, 4-level FSK (used by P25 and DMR) has four symbols, so each symbol carries 2 bits. That’s why a 4800-symbol-per-second signal moves 9600 bits per second.
What modulation do P25 and DMR use?
P25 Phase 1 uses C4FM, a four-level frequency-shift keying (4FSK) where the carrier sits at one of four frequency deviations per symbol. DMR uses 4FSK as well. P25 Phase 2 uses H-DQPSK, a phase-shift variant. GopherTrunk’s constellation, symbol-scope, and eye-diagram panels let you see these symbols directly.