What is PAPR?

The peak to average power ratio (PAPR) of a transmitted signal is one of main challenges in wideband multi-carrier systems that use orthogonal frequency division multiplexing (OFDM) or multiple-input multiple-output (MIMO) OFDM. Understanding the effects of PAPR on OFDM and MIMO-OFDM systems is critical when determining what techniques to use improve system performance. For the purposes of this blog post, we can use the terms OFDM and MIMO-OFDM interchangeably without affecting the meaning of PAPR.

The use of a large number of subcarriers introduces a high PAPR in OFDM systems. PAPR can be defined as the relationship between the maximum power of a sample in a transmit OFDM symbol and its average power

The same definition of PAPR is applied to MIMO-OFDM systems. A high PAPR appears when a number of subcarriers of a given OFDM symbol are out of phase with each other. Figure 1 shows the time domain representation of the 3 subcarriers of an OFDM symbol. The right column indicates that the subcarriers are out of phase, which causes an increase in PAPR of about 2.5 dB compared to the subcarriers in the left column. Depending on the out-of-phase amount per subcarrier, the PAPR can vary up to its theoretically maximum of 10log_{10 }(N)(dB) , where N is the number of subcarriers. In Figure 1, the 3 subcarriers reach their minimum amplitude at a same time, causing a large negative overshoot in the resulting composite OFDM signal.

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