On the distribution of the peak-to-average power ratio in OFDM signals

The distribution of the peak-to-average power ratio (PAPR) in strictly band-limited orthogonal frequency-division multiplexing (OFDM) signals is studied. Assuming that the base-band OFDM signal is characterized as a band-limited complex Gaussian process, we first attempt to derive the exact distribution of the PAPR in the band-limited OFDM signals. Since this distribution cannot be expressed in a closed form, we further develop a simple closed-form approximation, based on the level-crossing rate analysis. Comparisons of the proposed distributions with those obtained by computer simulations show good agreement and convergence with an increase in the number of subcarriers.

[1]  Maria Huhtala,et al.  Random Variables and Stochastic Processes , 2021, Matrix and Tensor Decompositions in Signal Processing.

[2]  Alan Powell,et al.  On the Fatigue Failure of Structures due to Vibrations Excited by Random Pressure Fields , 1958 .

[3]  Attilio J. Rainal,et al.  First and second passage times of Rayleigh processes , 1987, IEEE Trans. Inf. Theory.

[4]  Stephen H. Crandall.  Zero Crossings, Peaks, and Other Statistical Measures of Random Responses , 1962 .

[5]  Robert F. H. Fischer,et al.  OFDM with reduced peak-to-average power ratio by multiple signal representation , 1997, Ann. des Télécommunications.

[6]  S. Rice.  Mathematical analysis of random noise , 1944 .

[7]  R. V. Nee,et al.  Reducing the peak-to-average power ratio of OFDM , 1998, VTC '98. 48th IEEE Vehicular Technology Conference. Pathway to Global Wireless Revolution (Cat. No.98CH36151).

[8]  Nelson M. Blachman.  The distributions of local extrema of Gaussian noise and of its envelope , 1999, IEEE Trans. Inf. Theory.

[9]  Hikmet Sari,et al.  Transmission techniques for digital terrestrial TV broadcasting , 1995, IEEE Commun. Mag..

[10]  Yiyan Wu,et al.  COFDM: an overview , 1995, IEEE Trans. Broadcast..

[11]  M. Longuet-Higgins,et al.  The statistical distribution of the maxima of a random function , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  H. Imai,et al.  Block Coding Scheme Based on Complementary Sequences for Multicarrier Signals , 1997 .

[13]  Simon J. Shepherd,et al.  Asymptotic limits in peak envelope power reduction by redundant coding in orthogonal frequency-division multiplex modulation , 1998, IEEE Trans. Commun..

[14]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[15]  S. O. Rice,et al.  Statistical properties of a sine wave plus random noise , 1948, Bell Syst. Tech. J..