Statistics of a space-time random pulse train.

ABSTRACT

A general approach for obtaining the statistics of a pulse train is developed, where the pulses are space and time dependent, and where the initial distribution of the pulses may be non-uniform. Explicit expressions for the moments up to fourth order, in terms of the moments of the elementary signals constituting the pulse train, are obtained. This is done for elementary signals that are waves. The expressions obtained are totally general as long as the elementary signals are not correlated. In contrast to the standard scintillation index, it may be space and time dependent, in which case it is called the dynamical scintillation index. This allows one to understand how a space-time pulse train approaches stationarity at different positions and times. The scintillation index using both the raw and central moments is defined. For the raw moments, both exact expressions and expansions in 1/N, where N is the number of elementary signals are obtained. For central moments, particularly simple exact expressions are given.