PAPR

Peak-to-Average Power Ratio (PAPR) is a measure used in communications to describe the dynamic range of a signal. It is defined as the ratio of the peak instantaneous power to the average power of the signal. In decibels, PAPR equals 10 log10(Ppeak / Pavg). For multicarrier schemes such as orthogonal frequency-division multiplexing (OFDM), PAPR can be large because the subcarrier signals add coherently at certain times.

Mathematically, for a baseband discrete-time OFDM signal x[n], PAPR = max_n |x[n]|^2 / E{|x[n]|^2}, where E denotes expectation. Since OFDM signals are formed by summing N modulated subcarriers, the peak can be much larger than the average, depending on the subcarrier realization.

High PAPR has practical consequences. To operate a non-linear power amplifier with acceptable distortion, the transmitter must back off from the saturation region, reducing efficiency and increasing cost. In mobile and fixed wireless systems, this is a key design constraint.

PAPR reduction techniques include: distortionless methods such as Selected Mapping (SLM) and Partial Transmit Sequences (PTS), which generate alternative signal representations with lower PAPR; Tone Reservation and Tone Injection; coding schemes that constrain sequences; and clipping with filtering, which reduces PAPR at the expense of in-band and out-of-band distortion. Other approaches include Active Constellation Extension (ACE) and companding. The choice of method depends on acceptable distortion, complexity, and bandwidth.

Typical OFDM systems exhibit PAPR in the 10–12 dB range without reduction; with reduction techniques, several decibels of improvement are often achievable, depending on system constraints.