peaktoaverage

Peak-to-average ratio (PAPR) is a measure used to describe the variation of power in a signal by comparing its peak power to its average power. It is defined as PAPR = P_peak / P_avg, where P_peak is the maximum instantaneous power and P_avg is the time-average power over a specified interval. For a complex baseband signal x[n], PAPR = max_n |x[n]|^2 / E[|x[n]|^2], with E denoting expectation and the average taken over time. In decibels, PAPR_dB = 10 log10(PAPR).

Significance: high PAPR indicates that the signal can reach large amplitudes relative to its average energy, which stresses a nonlinear power amplifier and can reduce efficiency if the amplifier must operate with a wide linear region. It also affects spectral regrowth and out-of-band emissions.

Context: PAPR is particularly relevant in multicarrier modulation schemes such as OFDM, where the coherent addition of subcarriers can produce high peaks. In single-carrier systems PAPR is typically lower but still a consideration.

Related terms: crest factor is the ratio of peak amplitude to RMS value, not to average power; while PAPR uses average power. They are related but not interchangeable.

Reduction techniques: PAPR reduction methods include clipping and filtering, companding, tone reservation, selective mapping, and active constellation extension; each involves trade-offs among distortion, bandwidth, and data rate.

Measurement considerations: the choice of averaging interval, sampling rate, and waveform type affects PAPR estimation.