Statistical distribution of the amplitude and phase of a multiply scattered field

Abstract

The probability dist ribu Lion of the ampli tude and phase o f the sum of a large num ber of random two-di mensional vectors is derived under t he fo llowing general condit ions : Both t he ampli tudes a nd th e phases of the component vectors a re random, t he di sLribu tions b eing a rbitrary within the vali dit.\7 of the Central Lim it Theorem ; in part icular, the d ist r ibutions of t he individual veetors need not be identical , the amplitude and phase of each component vec tor need not be independent a nd the di tribu tions Ileed not be symmel ri cal. T he disLributions formerly derived by R ayleigh , nice, H oy t, a nd Heckmanll are shown lo be special cases of this di sLribut ion .