Derivation of PAPR Distribution for OFDM Wireless Systems Based on Extreme Value Theory

• Published in: IEEE transactions on wireless communications Vol. 7; no. 4; pp. 1298 - 1305
• Main Authors: Tao Jiang, Guizani, M., Hsiao-Hwa Chen, Weidong Xiang, Yiyan Wu
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.04.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Allocations; Applied sciences; Bandwidth; Bit error rate; Constellation diagram; Degradation; Derivation; Distribution functions; Exact sciences and technology; Extreme value theory; Information, signal and communications theory; Mathematical analysis; Multiplexing; OFDM; Orthogonal Frequency Division Multiplexing; Peak to average power ratio; Power distribution; Signal and communications theory; Signal to noise ratio; Strategy; Studies; Subcarriers; Telecommunications and information theory; Wideband; Performance evaluation; Design criterion; OFDM; peak-to-average power ratio; Wireless telecommunication; Peak to average power ratio; complementary cumulative distribution function; Subcarrier; Power allocation; Simulation; Extreme value; Power distribution; Analytical method; Distribution function; Orthogonal frequency division multiplexing; extreme value theory; Signal to noise ratio
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2008.060862

It has been widely known that one of the key design parameters in orthogonal frequency division multiplexing (OFDM) systems is the distribution of peak-to-average power ratio (PAPR). Recently some theoretical approaches to determine the PAPR distribution have been proposed based on the assumption that all subcarriers are allocated with equal power. However, this assumption may not be valid due to the following facts. First, in all realistic OFDM systems, usually only a subset: of subcarriers are used to carry information (active subcarriers) and the rest (inactive subcarriers) are set to zero. Second, due to the efficiency concerns transmission power should be allocated to active subcarriers. Third, power allocation may vary depending on different constellations used by different active subcarriers and their signal-to-noise-ratios. In this paper, we propose a general approach to identify PAPR distribution in OFDM systems. Specifically, a more accurate analytical expression of the PAPR distribution is derived with the help of Extreme Value Theory for Chi-squared-2 process in OFDM systems with unequal power distribution strategy. To validate the analytical results, extensive simulations have been conducted, showing a very good match between the identified PAPR distribution and that of real OFDM systems.