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

PDF

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.