1. Rafael C Lavrado

2.  Fading Channels  Alternative Representation  PAM Analysis  QAM Analysis  Conclusion

3. h(t) x(t) n(t) y(t) y(t)= x(t) + n(t)

4. h(t) x(t) n(t) y(t) y(t)= αx(t) + n(t)

5.  Is a Random Variable  Mean Square Value Ω =  PDF dependent on the nature of the radio propagation environment

6.  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

7.  Expected value of the probability of error taken over the RV α

8.  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

9.  Log Normal ◦ Caused by trees, buildings- Urban  Nakagami-m ◦ Best fit to indoor mobile

10.  PDF  In terms of SNR  MGF

11.  General Expression  For M=2

12.  Substituting for  If we use the classical representation of the Q function we going to face some difficulties.

13.  Classical representation  Alternative Representation Infinite Limit Variable in the Limit

14. Remember

15. : For the Rayleigh Fading channel

16.  General Expression  For 4-QAM

17.  Substituting for  So now, we need to calculate the integral for Q square

18. Alternative representation for Q square

19. So, = And, = Thus for

20.  The alternative form of Q-Function can help evaluate the error probability in Fading channels.