Also known as: symbol rate, baud
Symbol rate (baud) is the number of modulation symbols transmitted per second.1 A symbol is one distinct state of the carrier — a phase, a frequency, an amplitude, or a combination — held for one signalling interval, and the symbol rate counts how many of those intervals fit into a second. It differs from the bit rate whenever each symbol carries more than one bit, so conflating the two is one of the most common mistakes when describing a digital radio.
How it works
The governing identity is bit rate = symbol rate × bits-per-symbol, where bits-per-symbol is log₂ of the number of distinct symbol states (an alphabet of M symbols carries log₂M bits each). A two-level scheme carries one bit per symbol, so its bit rate and baud are equal; a four-level scheme carries two bits per symbol (a dibit), doubling the bit rate for the same baud. P25 Phase 1 and DMR both run at 4800 baud with four-level modulation (C4FM / 4FSK), giving 9600 bps. TETRA runs at 18 000 baud with π/4-DQPSK — two bits per symbol — for 36 kbit/s gross.
The symbol rate, not the bit rate, sets the signal’s occupied bandwidth. The Nyquist relation says a symbol rate of Rs baud needs at minimum Rs/2 Hz of baseband bandwidth (about Rs Hz after passband double-sidebanding), before any pulse shaping roll-off widens it. Packing more bits into each symbol — going from four levels to sixteen with QAM — raises the bit rate without widening the channel, at the cost of shrinking the spacing between symbol states and so demanding a higher signal-to-noise ratio to keep them apart.
In practice
Because bandwidth follows baud, spectrum regulators effectively cap the symbol rate a channel may use, and system designers then choose the modulation order to hit their target throughput. Once a radio is on the air the symbol rate is fixed and known, which the receiver exploits: it is the exact rhythm the clock-recovery loop must track, the spacing the eye diagram opens at, and the interval the matched filter is built around. A small error between the transmitter’s and receiver’s notion of the symbol rate accumulates as timing drift and eventually slides the sampling instant off the eye centre.
Relevance to SDR
Knowing a protocol’s symbol rate is the starting point for decoding it: it sets the minimum capture bandwidth for a clean copy, the resampling ratio from the SDR’s raw sample rate down to an integer number of samples per symbol, and the frequency the symbol-timing recovery must lock to. GopherTrunk resamples each protocol’s channel to a fixed samples-per-symbol rate (for example the 4800-baud C4FM family is handled at 48 kHz, ten samples per symbol) so the timing recovery and slicer see a consistent geometry regardless of the front-end sample rate.
Sources
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Symbol rate — Wikipedia, for the baud definition and the bit-rate relationship. ↩