This question is in continuation of the one asked here.
Let's say that the measurement noise $w$ or any random variable is circularly Gaussian complex.
If the imaginary and real components each has a variance of 0.5, then what would be the total variance? Should I write: $w \sim CN(0,\sigma^2_w)$?
If on the other hand, if $w \sim CN(0,2\sigma^2_w)$ then does it mean that the real and imaginary components each have variance 1, so the total variance is 2. Is my understanding correct?
Is there a rule of thumb whether the variance should be 0.5 for each component or can it be anything?