How can we calculate parameter sigma \sigma for rayleigh distribution? What does it actually means in Layman's terms? (Actually, does sigma matters when calculating power?)
If X = x +iy; where x, y are Independent and Normally distributed variables.
For a Rayleigh distributed channel, does abs(X)^2 represent the power of signal?
If X and Y are i.i.d. normally distributed random variables with mean $0$ and variance $\sigma^2$ (i.e. with standard deviation $\sigma$) then $R= \sqrt{X^2+Y^2}$ has a Rayleigh distribution with probability density function $f(r)= \frac{r}{\sigma^2}e^{-r^2/(2\sigma^2)}$ and cumulative distribution function $F(r)=1-e^{-r^2/(2\sigma^2)}$ for $r \ge 0$
$E[R]=\sigma\sqrt{\frac{\pi}2}$ and $\text{Var}(R)=\sigma^2\left(2- \frac{\pi}{2}\right)$. So taking the mean of observations and then multiplying by $\sqrt{\frac2{\pi}}$ would give an unbiased estimate of $\sigma$
$\dfrac{R^2}{\sigma^2}$ has a chi-squared distribution with $\nu=2$ degrees of freedom. Whether this is related to power depends on what you are modelling with your Rayleigh distribution, but it would seem that $\sigma$ matters