In mobile radio channel, the Rayleigh distribution is

In mobile radio channel, the Rayleigh distribution is commonly used to describe the statistical time-varying nature of the received envelope of a flat fading signal with no line of sight, or the envelope of an individual multipath component.

Prove that the distribution of the sum of the two quadrature Gaussian noise signals in a common quadrature receiver is Rayleigh.

Using the same setting for the generated signal in the previous section, use MATLAB to simulate and construct the PDF (Probability Distribution function) of each of two Gaussian noise signals and their resulting Rayleigh sum and then provide an elaborated discussion on the obtained results.