Also known as: crest factor, PAPR, peak-to-average power ratio, peak-to-average ratio
Crest factor is the ratio of a waveform’s peak amplitude to its RMS value, and peak-to-average power ratio (PAPR) is the same idea in power terms — how far the instantaneous peaks rise above the average.1 PAPR is normally quoted in dB as 10·log₁₀(P_peak / P_avg), and it matters because a power amplifier must stay linear all the way up to the peaks, forcing it to run “backed off” from its most efficient operating point.
How it works
A constant-envelope signal — an FM carrier, or a GMSK waveform — has a PAPR near 0 dB: its amplitude never changes, so an amplifier can be run right up into saturation for maximum efficiency without distorting it. As soon as a modulation varies its amplitude, peaks appear. Filtered QAM and root-raised-cosine pulse shaping add a few dB of PAPR because the filter overshoots between symbols.
The extreme case is OFDM, where many subcarriers are summed. When a large number of independent subcarriers happen to align in phase, their voltages add coherently and produce a brief peak far above the average — PAPR of 10–13 dB is typical for a wideband OFDM signal. Statistically these alignments are rare, but the amplifier must handle them without clipping, or the resulting distortion regrows spurious energy into adjacent channels and raises the error vector magnitude.
In practice
The design response is backoff: operate the amplifier several dB below its 1-dB compression point so even the peaks stay linear. Backoff wastes efficiency — a power amplifier backed off 8 dB for an OFDM signal may run at well under 20 % efficiency, draining batteries and generating heat. Several techniques fight back: clipping and filtering shaves the rare peaks at a small cost in distortion; tone reservation and selective mapping reshape the OFDM symbol to lower its peaks; and DPD (digital predistortion) inverts the amplifier’s curve so it can run closer to saturation. The choice trades power efficiency against complexity and signal cleanliness.
Crest factor is distinct from duty cycle: PAPR describes the amplitude spread while transmitting, whereas duty cycle describes the fraction of time transmitting at all.
Relevance to SDR
PAPR shapes real air interfaces. Single-carrier land-mobile systems (P25 C4FM, DMR four-FSK) deliberately use near-constant-envelope modulation so portable radios can use efficient saturated amplifiers and preserve battery life. The high-PAPR penalty of OFDM is exactly why LTE uses OFDM on the downlink (base stations can afford linear, backed-off amplifiers) but switches to lower-PAPR SC-FDMA on the uplink to spare the handset. TETRA’s π/4-DQPSK is chosen partly to keep its envelope variation modest.
GopherTrunk is a receiver, so it never amplifies a transmit signal and has no PAPR budget of its own. On the receive side the same statistics still matter: a high-PAPR signal needs adequate ADC headroom so its peaks are not clipped, which is why dBFS gain staging and avoiding front-end overload are part of getting a clean decode.
Sources
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Crest factor — Wikipedia, definition of peak-to-RMS ratio and its power form. ↩