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Kanal Modelleme

Kanal Modelleme. 3. Small Scale Fading due to Multipath . a. Spreading in Time : different paths have different lengths;. Receive. Transmit. time. Example for 100m path difference we have a time delay. Typical values channel time spread:. channel.

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Kanal Modelleme

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  1. Kanal Modelleme

  2. 3. Small Scale Fading due to Multipath. a. Spreading in Time: different paths have different lengths; Receive Transmit time Example for 100m path difference we have a time delay

  3. Typical values channel time spread: channel

  4. b. Spreading in Frequency: motion causes frequency shift (Doppler) Receive Transmit time time for each path Doppler Shift Frequency (Hz)

  5. Put everything together Transmit Receive time time

  6. Re{.} LPF LPF channel Each path has … …shift in time … … attenuation… paths …shift in frequency … (this causes small scale time variations)

  7. 2.1 Statistical Models of Fading Channels Several Reflectors: Transmit

  8. average time delay • each time delay • each doppler shift For each path with NO Line Of Sight (NOLOS):

  9. Some mathematical manipulation … Assume: bandwidth of signal << … leading to this: with random, time varying

  10. Statistical Model for the time varying coefficients random By the CLT is gaussian, zero mean, with: with the Doppler frequency shift.

  11. Each coefficient is complex, gaussian, WSS with autocorrelation and PSD with maximum Doppler frequency. This is called Jakes spectrum.

  12. Bottom Line. This: time time time … can be modeled as: time time delays

  13. For each path • unit power • time varying (from autocorrelation) • time invariant • from power distribution

  14. Parameters for a Multipath Channel (No Line of Sight): Time delays: sec dB Power Attenuations: Hz Doppler Shift: Summary of Channel Model: WSS with Jakes PSD

  15. Non Line of Sight (NOLOS) and Line of Sight (LOS) Fading Channels • Rayleigh (No Line of Sight). • Specified by: Time delays Power distribution Maximum Doppler 2. Ricean (Line of Sight) Same as Rayleigh, plus Ricean Factor Power through LOS Power through NOLOS

  16. Simulink Example M-QAM Modulation Rayleigh Fading Channel Parameters Bit Rate

  17. Set Numerical Values: modulation power channel velocity carrier freq. Recall the Doppler Frequency: Easy to show that:

  18. Channel Parameterization • Time Spread and Frequency Coherence Bandwidth • Flat Fading vs Frequency Selective Fading • Doppler Frequency Spread and Time Coherence • Slow Fading vs Fast Fading

  19. transmitted 1. Time Spread and Frequency Coherence Bandwidth Try a number ofexperiments transmitting a narrow pulse at different random times We obtain a number of received pulses

  20. Received Power time Take theaverage received powerat time More realistically:

  21. This defines the Coherence Bandwidth. Take a complex exponential signal with frequency . The response of the channel is: If then i.e. the attenuation is not frequency dependent Define the Frequency Coherence Bandwidth as

  22. This means that the frequency response of the channel is “flat” within the coherence bandwidth: Channel “Flat” up to the Coherence Bandwidth frequency Coherence Bandwidth Flat Fading Just attenuation, no distortion < Signal Bandwidth Frequency Coherence > Frequency Selective Fading Distortion!!!

  23. Example: Flat Fading Channel : Delays T=[0 10e-6 15e-6] sec Power P=[0, -3, -8] dB Symbol Rate Fs=10kHz Doppler Fd=0.1Hz Modulation QPSK Very low Inter Symbol Interference (ISI) Spectrum: fairly uniform

  24. Example: Frequency Selective Fading Channel : Delays T=[0 10e-6 15e-6] sec Power P=[0, -3, -8] dB Symbol Rate Fs=1MHz Doppler Fd=0.1Hz Modulation QPSK Very high ISI Spectrum with deep variations

  25. transmitted 3. Doppler Frequency Spread and Time Coherence Back to the experiment of sending pulses. Take autocorrelations: Where:

  26. Take the FT of each one: This shows how the multipath characteristics change with time. It defines the Time Coherence: Within the Time Coherence the channel can be considered Time Invariant.

  27. Summary of Time/Frequency spread of the channel Frequency Spread Time Coherence Time Spread Frequency Coherence

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