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Recently, a novel improved Jakes' fading channel simulator was proposed by Y. Li and X. Huang, which can generate multiple independent Rayleigh faders. In this paper, some important statistical properties of this improved Jakes' simulator are analyzed and compared with those of the classical Jakes' simulator. It is proved that it can generate multiple independent Rayleigh faders easily. The further simulation results also show that it is a good method to reproduce the important proprieties of the real world. Simulating a mobile multipath fading channel often requires multiple independent Rayleigh generator, each of which can generate correlated Rayleigh fading samples. A sum-of-sinusoids (SOS)-based fading channel simulation method has been proposed by Jakes. His simulator may be an efficient way to implement a hardware or software simulation of the Rayleigh fading multipath channel. But it has some undesirable properties, e.g. for any pair of the faders, they are not independent; for a single fader, the correlation function of the in-phase and quadrature components of the signal is not always zero, et al. Recently, another improved simulation method has been proposed by Y. Li and X. Huang. In this paper, its statistical properties are analyzed and compared with those of the classical Jakes' simulation method. The theoretical analysis and simulation results show that it is superior to the other methods.