A detailed investigation of the quotient of two independent complex random
variables is presented. The numerator has a zero mean, and the denominator has a
non-zero mean. A normalization step is taken prior to the theoretical developments in
order to simplify the formulation. Next, an indirect approach is taken to derive the
statistics of the modulus and phase angle of the quotient. That in turn enables a
straightforward extension of the statistical results to real and imaginary parts. After
the normalization procedure, the probability density function of the quotient is found
as a function of only the mean of the random variable that corresponds to the
denominator term. Asymptotic analysis shows that the quotient closely resembles a
normally-distributed complex random variable as the mean becomes large. In addition, the
first and second moments, as well as the approximate of the second moment of the clipped
random variable, are derived, which are closely related to practical applications in
complex-signal processing such as microwave metrology of scattering-parameters.
Tolerance intervals associated with the ratio of complex random variables are
presented.
On The Quotient of a Centralized and a Non-centralized Complex Gaussian
Random Variable
