  The effective PAPR of the transmit signal is the standard metric to capture
the effect of nonlinear distortion in OFDM transmission. A common rule of thumb
is the log$(N)$ barrier where $N$ is the number of subcarriers which has been
theoretically analyzed by many authors. Recently, new alternative metrics have
been proposed in practice leading potentially to different system design rules
which are theoretically analyzed in this paper. One of the main findings is
that, most surprisingly, the log$(N)$ barrier turns out to be much too
conservative: e.g. for the so-called amplifier-oriented metric the scaling is
rather $\log[ \log(N)]$. To prove this result, new upper bounds on the PAPR
distribution for coded systems are presented as well as a theorem relating PAPR
results to these alternative metrics.
