Suppose Z = X + jY is a circular Gaussian random variable whose PDF is described by
Question:
(a) Find the PDF of the magnitude, R = |Z|, and phase angle, θ =ˆ Z, for the special case when μZ = 0.
(b) Find the PDF of the magnitude, R = |Z|, and phase angle, θ =ˆ Z, for the general case when μZ ‰ 0. Hint: In this case, you will have to leave the PDF of the phase angle in terms of a Q- function.
(c) For the case when μZ » σ, show that the PDF of the phase angle is well approximated by a Gaussian PDF. What is the variance of the Gaussian PDF that approximates the PDF of the phase angle?
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expl- 2σ
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a For the special case when x y 0 then b For the general case write z z ejso that ...View the full answer
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Related Book For
Probability and Random Processes With Applications to Signal Processing and Communications
ISBN: 978-0123869814
2nd edition
Authors: Scott Miller, Donald Childers
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