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

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

10. Jakes’ Simulation Model (1/2)

11. Jakes’ Simulation Model (2/2)

13. 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.

14. 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.

15. 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 An becomes uniform I.I.d over [0,2), and

19. 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

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