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Performance Analysis Over Fading Channels. Rafael C Lavrado. Agenda. Fading Channels Alternative Representation PAM Analysis QAM Analysis Conclusion. AWGN Channels. h(t). x(t). y(t). n(t). y(t)= x(t) + n(t). Fading Channels. h(t). x(t). y(t). n(t). y(t)= α x(t) + n(t). - PowerPoint PPT Presentation

### Transcript of Performance Analysis Over Fading Channels

• 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)= x(t) + n(t)

• Is a Random Variable

Mean Square Value =

PDF dependent on the nature of the radio propagation environment

• As the carrier is attenuated by , 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

• 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 NormalCaused by trees, buildings- Urban

Nakagami-mBest 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 LimitVariable 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.