PAPRn

PAPRn is a generalized concept used in signal processing and communications to describe a multi-channel extension of peak-to-average power ratio (PAPR). It captures how the instantaneous power across a set of n components—such as antennas, subcarriers, or parallel streams—deviates from its average power. In a time-varying, n-dimensional signal x(t) = [x1(t), …, xn(t)], the instantaneous power is p(t) = ||x(t)||^2 = ∑i |xi(t)|^2, and the average power Pavg is the time or ensemble average of p(t). A common definition for PAPRn is the ratio max_t p(t) / Pavg. When used over a finite observation window, a windowed version of PAPRn is computed by taking the maximum p(t) within the window and dividing by the average power inside that same window.

In practice, PAPRn often appears in contexts such as multi-antenna (MIMO) systems and multicarrier setups like OFDM, where the total radiated power is the sum across channels or subcarriers. The metric helps characterize the dynamic range requirements of power amplifiers and the potential efficiency loss due to nonlinearities. Different formulations may arise depending on the chosen norm, whether the measure is taken across time, across subsystems, or across frequency components, and whether normalization is performed per channel or for the aggregate signal.

Applications and research on PAPRn focus on understanding how multi-channel configurations influence peak powers and on developing reduction techniques, such as clipping, tone reservation, or waveform shaping, tailored to multi-channel scenarios. The term PAPRn has appeared in various publications as a generalized or context-dependent extension of the classic PAPR, with no single universally standardized definition. See also PAPR, OFDM, MIMO, and power amplifier efficiency.