# What is Peak-To-Average Power Ratio?

What is PAPR or Peak-To-Average Power Ratio?

Peak-to-Average Power Ratio (PAPR) is defined as the ratio of peak power to the average power of a signal and is expressed in decibels (dB). It is typically measured for a transmitted signal in an Orthogonal Frequency-Division Multiplexing (OFDM) system. A lower PAPR is desired for efficient performance of a system. Considering the mathematical equation of PAPR, it is defined as the square of peak amplitude divided by the RMS value. OFDM is a multicarrier modulation technique where the available spectrum is separated into subcarriers, with each subcarrier containing a low-rate data stream. Signals transmitted through an OFDM system typically possess high peak values in the time domain and all the sub-carriers are out of phase with each other in an OFDM system.

At each phase value, the signals are different from each other, however, if at a given instance all data points simultaneously achieve the maximum value, it causes the output to suddenly shoot up. This causes a ‘peak’ in the output envelope. Since in an OFDM system, there are independently modulated subcarriers, the peak value of the system can be very high compared to the average of the whole system. This ratio of the peak to average power value is termed as Peak-to-Average Power Ratio.

This occasional surge (which results in a high PAPR) is one of the biggest disadvantages of an OFDM system as it degrades the efficiency of the power amplifier in the transmitter. High PAPR can also cause problems such as out of band and in-band distortion. In-band distortions further includes, high error vector magnitude (EVM), and also degrades the receiver performance. Out-band distortions include increased adjacent channel leakage ratio, and also degrades performance of users in adjacent channels.

Crest Factor Reduction (CFR)

Crest Factor Reduction, or CFR is a technique adapted to reduce Peak to Average Power Ratio (PAPR) of transmitted signals for efficient operation of power amplifiers. Crest factor is a parameter of a waveform, that evaluates the ratio of peak values to the effective value. In simple words, crest factor denotes the extreme peaks in a waveform.