How can I approximate the Rician Distribution through the Gaussian Distribution? Which are the techniques used to approximate a distribution into another? I know that I can model a Gaussian Distribution through the parameters of mean and variance. However how can I approximate Rice Distribution through the Gaussian Distribution? There is some good reference covering that? 
 A: Center $(\mu_x, \mu_y) =(1,2)$ and standard deviation $\sigma=2.$
If you can generate univariate normal random variables $X \sim \mathsf{Norm}(1,2)$
and  $Y \sim \mathsf{Norm}(1,2),$ then you have an uncorrelated bi-variate normal
distribution. Similarly, according to the Wikipedia article referenced by @JeanMarie, you can make various kinds of Rice distributions. Here is a plot using R.
x = rnorm(50000, 1, 2);  y = rnorm(50000, 2, 2)
plot(x, y, pch=".")
  abline(v=-10:10, col="lightblue")
  abline(h=-10:10, col="lightblue")
  abline(v=0, lwd=2, col="green2")
  abline(h=0, lwd=2, col="green2")


In order to get normal distributions from randomly generated
points in $(0,1)$ you can use the Box-Muller transform.
(See Wikipedia.)
Below a histogram suggests the shape of the density function of the distance of points from the origin, and a plot of
the corresponding empirical distribution function (ECDF) which approximates
the CDF. (Note: The ECDF sorts the $n$ points on the horizontal axis and 
increments by $1/n$ at corresponding points on the vertical axis)
d = sqrt(s^2 + y^2)
par(mfrow=c(1,2))
  hist(d, prob=T, col="skyblue2")
  plot(ecdf(d))
par(mfrow=c(1,1))


With this introduction in R and reference to the Wikipedia pages, you should be able to figure out how to do this
assignment using most any statistical or mathematical software.
A: You can generate a Rayleigh distribution simply as: 
    x_rayleigh = ( randn(1, 1e6) + 1i*randn(1, 1e6) ) / sqrt(2);

This is a complex normal distribution with zero mean and variance 1/2 per dimension. So the amplitude of x_rayleigh follows a Rayleigh distribution. The phase of x_rayleigh will be uniform. 
Now if you add a line-of-sight component in the above random variable, the amplitude will be Rice distributed. 
    x_rice = 1 + ( randn(1, 1e6) + 1i*randn(1, 1e6) ) / sqrt(2);

The histogram of the absolute value of the generated random variable is shown in the figure. 
