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Jakes’ Fading Channel Simulator

Jakes’ Fading Channel Simulator. 指導教授：黃文傑 老師 學　　生：曾凱霖 學　　號： M9121014. Outline. Introduction & Problems Background Clarke’s Mathematical Reference Model Jakes’ Simulation Model Time-Average Analyses Statistics of the Reference Model and Jakes’ Fading Channel Simulator

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Jakes’ Fading Channel Simulator

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  1. Jakes’ Fading Channel Simulator 指導教授：黃文傑 老師 學　　生：曾凱霖 學　　號：M9121014

  2. Outline • Introduction & Problems • Background • Clarke’s Mathematical Reference Model • Jakes’ Simulation Model • Time-Average Analyses • Statistics of the Reference Model and Jakes’ Fading Channel Simulator • Conclusion

  3. Introduction & Problems 1、Clarke’s Mathematical Model 2、Jakes’ Simulator Family

  4. Background

  5. Clarke’s Mathematical Reference Model (1/3) Received signal RD(t) is a superposition of waves Normalize RD(t) to have unit power as

  6. Clarke’s Mathematical Reference Model (2/3)

  7. Clarke’s Mathematical Reference Model (3/3)

  8. Rayleigh flat fading narow-band signal • Properties of Rayleigh flat fading narow-band signal • The envelope pdf without LOS is • Phase pdf given by the uniform distribution • Autocorrelation function of the received signal of 2-D isotropic scattering and an omnidirectional receiving antenna

  9. Jakes’ Simulation Model (1/2)

  10. Jakes’ Simulation Model (2/2)

  11. Time-Average Analyses (1/2) • Single sinusoid whit fixed amplitude and random phase is both ergodic and stationary. But, sums of fixed amplitude, random-phase sinusoids are not egodic and stationary. • Cn ,An ,n are RVs in the physical model but are fixed constants in the simulators.

  12. Time-Average Analyses (2/2) • In Jakes’ simulator, in-phase and quadrature share common frequencies as seen in Fig. 1. • But, in fact, the in-phase and quadrature components share no common Doppler frequency shifts.

  13. Statistics of the Reference Model and Jakes’ Fading Channel Simulator (1/2) • Autocorrelation of Reference model, • When N, autocorrelation of low frequency terms, shown in fig.3 becomes Bessel function. • Removing the constraint of (6a), the Anbecomes uniform I.I.d over [0,2), and

  14. Statistics of the Reference Model and Jakes’ Fading Channel Simulator (2/2) • From fig.4, the statistical variance of the simulator fading process is time variant. This means Jakes’ model does not present WSS. • Stochastic autocorrelation of the signal of Jakes’ simulator is time dependent with .

  15. Conclusion • Jakes’ Simulation Model is nonstationary and difficult to generate multiple uncorrelated fading waveforms. • Some model can improved Jakes’ Simulation Model.

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