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 Conclusion

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

Background

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

Clarke’s Mathematical Reference Model (2/3)

Clarke’s Mathematical Reference Model (3/3)

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

Jakes’ Simulation Model (1/2)

Jakes’ Simulation Model (2/2)

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.

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.

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

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 .

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