New Exact Higher Order Moment Expressions for the PAPR of Complex Gaussian Variables

New analytical expressions for the moment of the peak to average power ratio (PAPR) of
${n}$
independent and identically distributed (i.i.d.) zero-mean complex circular Gaussian random variables (r.v.s) are derived. These expressions give the higher order moments. For an orthogonal frequency division multiplexing (OFDM) system with
${n}$
subcarriers, the
${n}$
samples in each OFDM symbol are taken as i.i.d. with each following a zero-mean complex circular Gaussian distribution. The PAPR statistics of these samples play an important role as performance metrics. An exact closed form expression for the
$\ell $
th moment of the PAPR obtained in earlier work is used to derive a compact expression and a simple expression in terms of a function
$H_{n}(-\ell)$
; an alternative expression for
$H_{n}(-\ell)$
is also presented. The variance obtained from the
$\ell $
th moment is shown to be asymptotically equal to a previous result for a large number of r.v.s.