Question

Suppose a stationary radar illuminates a complex, but stationary, target with a series of pulses.
Which probability density function is an appropriate choice to represent the series of echo
power measurements? Why?

Answer 1

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If the echoing process of the radar is considered to be a stochastic process, the echo signal and the associated power measurements can be considered a random variable. If x and y are the in-phase and quadrature components of the echo signals, then x and y could be assumed to satisfy the Central Limit Theorem, and hence the joint pdf of x and y can be considered a bi-variable Gaussian Distribution. After some complicated algebra, it can be shown that the distribution of the power of the echo signals models the Hoyt, Rayleigh and the Rice distributions.

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