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.