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.