The Probability Density Function for a sum of N linearly polarized time-harmonic plane waves

It is known that under the assumption that N phasors are statistically independent and stationary (which assumption leads to the Probability Density Function (PDF) for the phase of each phasor to be uniform over an interval of length 2π), the Blanc-Lapierre transformation gives the expression for the PDF of the magnitude of the sum of N phasors as a function of the PDF of the magnitude of each phasor. This expression, however, does not take into account the polarization, only the phase and magnitude of the field. This paper includes the polarization as well.