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  1. assume $w_0$, $w_1$, $w_2$, $w_3$ are circular symmetric complex Gaussian distributions, and the composite of $$ h = e^{j\theta_0}w_0 + e^{j\theta_3}w_3 - e^{j\theta_1}w_1 -e^{j\theta_2}w_2 $$

    so what's the distribution of $h$ and $|h|$ given that the $\theta_i$ is determinate random variable, for example : $\theta_0+\theta_3 = \theta_1 + \theta_2$ ?

  2. given $$ w = w_0w_3 - w_1w_2 $$ what's the distribution of $w$ and $|w|$?

  3. given $$ h = Ae^{j(a_1+b_1)} + Ae^{j(a_2+b_2)} - Ae^{j(a_2+b_1)} -Ae^{j(a_1+b_2)} $$ if $a_i\sim \mathcal{U}(0,2\pi)$, $b_i\sim \mathcal{U}(0,2\pi)$, and A is a Rayleigh distribution Amplitude. can the probability distribution of $h$ and $|h|$ be calculated?

Thanks in advance! any hint and suggestion is helpful!

Best Regards!

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