Simultaneous variation of amplitude and phase of Gaussian noise, with applications to ionospheric forward-scatter signals

The conditional probability density p(¿/A) is obtained for Gaussian noise, where ¿ = ¿2¿¿1 is the difference in phase as observed at the two times t and t + ¿ and A the envelope at either t or t + ¿. The mean of |¿| subject to the condition of a particular value of A is evaluated using numerical methods, and the variation of ¿A with A is discussed. A simple relation is obtained for the limiting case when ¿¿0. The noise character of the signal in an ionospheric scatter circuit has been tested. It is concluded that the simultaneous variations of signal amplitude and phase are in good agreement with those to be expected for Gaussian noise, and also that the assumption of a randomly phased angular spectrum appears to be justified.