Crest factor


Crest factor is a parameter of a waveform, such as alternating current or sound, showing the ratio of peak values to the effective value. In other words, crest factor indicates how extreme the peaks are in a waveform. Crest factor 1 indicates no peaks, such as direct current or a square wave. Higher crest factors indicate peaks, for example sound waves tend to have high crest factors.
Crest factor is the peak amplitude of the waveform divided by the RMS value of the waveform.
The peak-to-average power ratio is the peak amplitude squared divided by the RMS value squared. It is the square of the crest factor.
When expressed in decibels, crest factor and PAPR are equivalent, due to the way decibels are calculated for power ratios vs amplitude ratios.
Crest factor and PAPR are therefore dimensionless quantities. While the crest factor is defined as a positive real number, in commercial products it is also commonly stated as the ratio of two whole numbers, e.g., 2:1. The PAPR is most used in signal processing applications. As it is a power ratio, it is normally expressed in decibels (dB). The crest factor of the test signal is a fairly important issue in loudspeaker testing standards; in this context it is usually expressed in dB.
The minimum possible crest factor is 1, 1:1 or 0 dB.

Examples

This table provides values for some normalized waveforms. All peak magnitudes have been normalized to 1.
Wave typeWaveformRMS valueCrest factorPAPR
DC110.0 dB
Sine wave100px3.01 dB
Full-wave rectified sine100px3.01 dB
Half-wave rectified sine100px6.02 dB
Triangle wave100px4.77 dB
Square wave100px110 dB
PWM signal
V ≥ 0.0 V		100px
dB
QPSK111.761 dB
8PSK3.3 dB
-DQPSK3.0 dB
OQPSK3.3 dB
8VSB6.5–8.1 dB
64QAM3.7 dB
-QAM4.8 dB
WCDMA downlink carrier10.6 dB
OFDM4~12 dB
GMSK110 dB
Gaussian noise[standard deviation|]dB
Periodic chirp3.01 dB

Notes:
  1. Crest factors specified for QPSK, QAM, WCDMA are typical factors needed for reliable communication, not the theoretical crest factors which can be larger.

Crest factor reduction

Many modulation techniques have been specifically designed to have constant envelope modulation, i.e., the minimum possible crest factor of 1:1.
In general, modulation techniques that have smaller crest factors usually transmit more bits per second than modulation techniques that have higher crest factors. This is because:
  1. any given linear amplifier has some "peak output power"—some maximum possible instantaneous peak amplitude it can support and still stay in the linear range;
  2. the average power of the signal is the peak output power divided by the crest factor;
  3. the number of bits per second transmitted is proportional to the average power transmitted.
Orthogonal frequency-division multiplexing is a very promising modulation technique; perhaps its biggest problem is its high crest factor. Many crest factor reduction techniques have been proposed for OFDM. The reduction in crest factor results in a system that can either transmit more bits per second with the same hardware, or transmit the same bits per second with lower-power hardware, or both.
Over the years, numerous model-driven approaches have been proposed to reduce the PAPR in communication systems. In recent years, there has been a growing interest in exploring data-driven models for PAPR reduction as part of ongoing research in end-to-end communication networks. These data-driven models offer innovative solutions and new avenues of exploration to address the challenges posed by high PAPR effectively. By leveraging data-driven techniques, researchers aim to enhance the performance and efficiency of communication networks by optimizing power utilization.

Crest factor reduction methods

Various methods for crest factor reduction exist, such as peak windowing, noise shaping, pulse injection and peak cancellation.

Applications