Introduction to Rayleigh and Rice Fading

This webdemo is a simulation and visualization of Rayleigh and Rice fading. Fading is a phenomenon that occurs in wireless communication and is one of the key differences between systems that rely on a cable to transmit the signal and systems that transmit the signal over a radio channel [1].

Fading occurs due to the physical environment of radio channels. The transmitter and receiver may be surrounded by all manner of objects, both stationary and in motion. Because of this, the transmitted signal will be reflected, diffracted, and scattered [1]. At the receiver, parts of the signal will arrive from different angles, with different strengths, and at different times. The multipath propagation causes parts of the signal to arrive at different times leading to interference. This interference can give rise to a strong frequency-selective behavior. Additionally, the transmitter and receiver, as well as their environment, may be in motion. This motion causes the Doppler effect to occur. The resulting shift in frequency as well as the potential changes in the receiver's and transmitter's relative position cause the channel to vary over time. Because of this the signal may experience strong attenuation in the time domain [1][2]. These types of fading are referred to as small-scale fading and are also the types of fading this webdemo will focus on.

The phase at which the signal arrives at the receiver is random. Therefore, the amplitude of each signal part will also be random. The sum of a significant amount of random variables is Gaussian distributed, and its absolute value is Rayleigh distributed. Because of this, the absolute value of impulse and frequency response are Rayleigh distributed and we speak of "Rayleigh fading". If there is a line of sight (LoS) path, then one path has significantly more power and the distribution changes. The absolute value of impulse and frequency response are Rice distributed and as such "Rice fading" occurs. Rice fading can be modeled by an additional component with power $K$ in the first path [1][2].

For this simulation, it is assumed that there are a number of $N_\mathrm{Delays}$ different time delays. The value of $N_\mathrm{Delays}$ may be configured by the user. Each of those delays reach the receiver from $L=20$ different angles $\alpha_l$ which have a Doppler shift equal to $f_{\mathrm{D,max}} \cdot \cos(\alpha_l)$. The maximum Doppler frequency $f_{\mathrm{D,max}}$ can be configured by the user by modifying the speed $v$.

This simulation implements a model described in a paper by Beaulieu, Xiao, and Zheng [3]. For use in this webdemo, the simulator has been combined with a tapped-delay-line model.

[1] D. Tse and P. Viswanath, Fundamentals of Wireless Communication. Cambridge: Cambridge University Press, 2005.

[2] T. S. Rappaport, Wireless Communications: Principles and Practice. Prentice Hall PTR, 2002.

[3] N. C. Beaulieu, Chengshan Xiao and Yahong Rosa Zheng, “Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician fading Channels,” IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, vol. 5, no. 12, pp. 3667–3679, 2006.