A modern extreme value theory approach to calculating the distribution of the peak-to-average power ratio in OFDM systems

Orthogonal frequency division multiplexing (OFDM) is a promising framework for future wireless communication systems. One of the main impediments that has limited the applicability of OFDM systems in low-power wireless communication systems is the highly variable amplitude of the baseband transmitted signal; thus, a number of previous analyses have characterized this variation. These analyses have generally employed the following two components: (1) the assumption that the complex envelope of the OFDM signal converges to a Gaussian random process in some sense as the number of subcarriers becomes large, and (2) Rice's (1945) classical results on level-crossing rates for the envelope of Gaussian random processes. In this work, we improve on both of these components to arrive at a simple, accurate, and rigorously-established expression for the peak distribution of the OFDM envelope. In particular, using a rigorous (and non-trivial) proof establishing the convergence in (1) above as justification, the modern extreme value theory for chi-squared processes is applied to the problem. Numerical results for both uncoded and coded systems establish that the simple expression obtained for the distribution of the peaks of the envelope process is extremely accurate, even for a modest number of subcarriers.