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Rafael C Lavrado
Fading Channels Alternative
Representation PAM Analysis QAM Analysis Conclusion
h(t)x(t)
n(t)
y(t)
y(t)= x(t) + n(t)
h(t)x(t)
n(t)
y(t)
y(t)= αx(t) + n(t)
Is a Random Variable
Mean Square Value Ω =
PDF dependent on the nature of the radio propagation environment
As the carrier is attenuated by α, the signal power is attenuated by
And then we will define the instantaneous SNR per bit by
And the average SNR by
Expected value of the probability of error taken over the RV α
Rayleigh◦ Mobile Systems with no LOS path between the
transmitter and receiver
Nakagami-m(Rice)◦ Propagation path consist of one strong direct LOS
Nakagami-q(Hoyt)◦ Satellite Link subject to strong ionospheric
scintillation
Log Normal◦ Caused by trees, buildings- Urban
Nakagami-m◦ Best fit to indoor mobile
In terms of SNR
MGF
General Expression
For M=2
Substituting for
If we use the classical representation of the Q function we going to face some difficulties.
Classical representation
Alternative Representation
Infinite Limit
Variable in the Limit
Remember
:
For the Rayleigh Fading channel
General Expression
For 4-QAM
Substituting for
So now, we need to calculate the integral for Q square
Alternative representation for Q square
So,
=
And,
=
Thus for
The alternative form of Q-Function can help evaluate the error probability in Fading channels.
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