Optimality Condition for Selected Mapping in OFDM

Abstract

It is well known that orthogonal-frequency-division-multiplexing (OFDM) transmission is spectrally efficient but power inefficient due to the large peak-to-average power ratio (PAR) of the OFDM signal. Selected mapping (SLM) is a promising PAR reduction technique that is distortionless and has good PAR reducing capability. In SLM, the phases of the frequency domain OFDM subsymbols are first rotated before the inverse Fourier transform is applied; thus, an equivalent representation of the OFDM signal can be obtained. The one with the lowest PAR from among <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> such representations is retained and transmitted in place of the original OFDM signal. In this paper, we investigate the optimum design of the phase rotation table so that the complementary cumulative distribution function (CCDF) of the PAR of the SLM OFDM signal is minimized for any given <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> . We prove that if the phases (denoted by random variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$phi$</tex> ) are independently and identically distributed (i.i.d.) with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$E[e^jphi]=0$</tex> , then optimum SLM performance can be achieved.