A constellation shows every allowed phase and amplitude
QAM (quadrature amplitude modulation) varies the amplitude of two carriers of the same frequency, 90° out of phase. A constellation diagram plots the possible phase and amplitude states for each symbol: one dot per symbol. More dots means more bits per symbol, but they sit closer, so noise causes errors sooner.
Each point is one allowed symbol: a phase and an amplitude. Noise smears the dots.
Bits per symbol2
Misread dots0%
Gray code counts so only one bit changes between neighbours: 00, 01, 11, 10. Label the dots this way and a symbol misread as its neighbour costs one bit error, not two.
RememberConstellation = the allowed phase and amplitude states. Gray code = one bit per step.
Bit rate = symbol rate × bits per symbol
The symbol rate is how fast the waveform changes to convey information. It equals the baud rate. Bits per second is higher when each symbol carries more bits.
The waveform changes once per symbol. How many bits ride on each change is up to the code.
Bit rate2000 bit/s
A more efficient digital code packs more bits into each symbol, so the data rate rises without a faster waveform or more bandwidth.
RememberSymbol rate = baud. Better code = more bits per symbol, same bandwidth.
Smooth changes make narrow signals
Sudden changes splatter across the spectrum. A PSK signal should change phase at the zero crossing to minimize bandwidth. PSK31 uses sinusoidal data pulses for the same reason. CW works the same way: its bandwidth depends on keying speed and shape (rise and fall time).
Smooth changes make narrow signals. Abrupt changes make wide ones.
RememberGentle edges keep a signal narrow. Sharp edges widen it.
Digital modes can be as narrow as CW, or far wider
CW is about 4 × WPM wide (a rule of thumb): 13 WPM is 52 Hz. FT8 is 50 Hz. For FSK, bandwidth ≈ baud + 1.2 × shift, so a 4.8 kHz-shift, 9600-baud FM signal is 15.36 kHz: 9.6 + 1.2 × 4.8.
Log scale: each tick is ten times the last. Data modes can be as narrow as CW.
Remember13 WPM CW: 52 Hz. FT8: 50 Hz. 9600-baud, 4.8 kHz-shift FM: 15.36 kHz.
ARQ asks for a resend when it detects an error
ARQ (automatic repeat request) is a detect-and-ask method: if errors are detected, a retransmission is requested. Forward error correction (FEC) is different: it sends extra bits up front so the receiver can fix errors itself.
ARQ asks again. FEC repairs it on the spot.
RememberARQ: detect, then retransmit. FEC: redundancy repairs it.
Mesh nodes have IP addresses and discover each other
In a mesh network, every node has an Internet Protocol (IP) address. Nodes form the mesh using discovery and link establishment protocols, then pass traffic along multi-hop paths.
Nodes find each other, link up, and relay traffic by IP address.
RememberMesh: IP addresses, discovery, link establishment.