What Is the Role of Rayleigh Distribution in Wireless Communication?

  • #1
EngWiPy
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Dear all,

I am wondering what is the meaning of Rayleigh distribution? I mean in wireless communication channels we often come to a phenomenon called multipath fading, which is complex Gaussian process in nature. When this Guassian process is zero mean, then the envelope (amplitude) of the channel is Rayleigh distributed. Then the received signal can be expressed as:

[tex]r(t)=\alpha\,s(t)+n(t)[/tex]

where [tex]r(t)[/tex] is the received signal, [tex]\alpha[/tex] is a Rayleigh distributed RV, [tex]s(t)[/tex] is the transmitted signal, and [tex]n(t)[/tex] is the AWGN. Now in communications we need to maximize the ratio [tex]\alpha^2\,E_s/N_0[/tex] where [tex]E_s[/tex] is the signal energy, and [tex]N_0[/tex] is the power spectrum density of the noise.

Now, if we draw the Rayleigh distribution function with different [tex]\sigma[/tex], where [tex]\sigma[/tex] is the standard deviation of the real Gaussian RVs that constitute the complex Gaussian RV, then we note that as we increase [tex]\sigma[/tex] the amplitude of the distribution is decreased, and the tail decays slower. Is this a good thing to our system or bad?

Thanks in advance,

Regards
 

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