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Performance Analysis Over Fading Channels

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).

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Performance Analysis Over Fading Channels

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  1. Performance Analysis Over Fading Channels Rafael C Lavrado

  2. Agenda • Fading Channels • Alternative Representation • PAM Analysis • QAM Analysis • Conclusion

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

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

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

  6. Fading Channels- Probability of Error • 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. Fading Channels- Probability of Error • Expected value of the probability of error taken over the RV α

  8. Fading channel models • 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. Fading channel models • Log Normal • Caused by trees, buildings- Urban • Nakagami-m • Best fit to indoor mobile

  10. Rayleigh Fading • PDF • In terms of SNR • MGF

  11. PAM Modulation • General Expression • For M=2

  12. PAM on a Fading Channel • Substituting for • If we use the classical representation of the Q function we going to face some difficulties.

  13. Gaussian-Q Function • Classical representation • Alternative Representation Infinite Limit Variable in the Limit

  14. Remember

  15. : For the Rayleigh Fading channel

  16. QAM Modulatiom • General Expression • For 4-QAM

  17. QAM on a Fading Channel • 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. Conclusion • The alternative form of Q-Function can help evaluate the error probability in Fading channels.

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