| Communications Blockset | |
Simulate a multipath Rayleigh fading propagation channel
Library
Description 
The Multipath Rayleigh Fading Channel block implements a baseband simulation of a multipath Rayleigh fading propagation channel. This block is useful for modeling mobile wireless communication systems. For details about fading channels, see the works listed in References.
The input can be either a scalar or a frame-based column vector. The input is a complex signal.
Relative motion between the transmitter and receiver causes Doppler shifts in the signal frequency. The Jakes PSD (power spectral density) determines the spectrum of the Rayleigh process.
Since a multipath channel reflects signals at multiple places, a transmitted signal travels to the receiver along several paths that may have different lengths and hence different associated time delays. Fading occurs when signals traveling along different paths interfere with each other. In the block's parameter mask, the Delay vector specifies the time delay for each path. If the Normalize gain vector to 0 dB overall gain box is unchecked, then the Gain vector specifies the gain for each path. If the box is checked, then the block uses a multiple of Gain vector instead of the Gain vector itself, choosing the scaling factor so that the channel's effective gain considering all paths is 0 dB.
The number of paths is the length of Delay vector or Gain vector, whichever is larger. If both of these parameters are vectors, then they must have the same length; if exactly one of these parameters is a scalar, then the block expands it into a vector whose size matches that of the other vector parameter.
The Sample time parameter is the time between successive elements of the input signal. Note that if the input is a frame-based column vector of length n, then the frame period (as Simulink's Probe block reports, for example) is n*Sample time.
The block multiplies the input signal by samples of a Rayleigh-distributed complex random process. The scalar Initial seed parameter seeds the random number generator.
Dialog Box
Algorithm
This implementation is based on the direct form simulator described in Reference [1] below.
Some wireless applications, such as standard GSM (Global System for Mobile Communication) systems, prefer to specify Doppler shifts in terms of the speed of the mobile. If the mobile moves at speed v making an angle of 
with the direction of wave motion, then the Doppler shift is
where f is the transmission carrier frequency and c is the speed of light. The Doppler frequency is the maximum Doppler shift arising from motion of the mobile.
See Also
Rayleigh Noise Generator, Rician Fading Channel
References
[1] Jeruchim, Michel C., Balaban, Philip, and Shanmugan, K. Sam, Simulation of Communication Systems, Second edition, New York, Kluwer Academic/Plenum, 2000.
[2] Jakes, William C., ed. Microwave Mobile Communications, New York, IEEE Press, 1974.
[3] Lee, William C. Y., Mobile Communications Design Fundamentals, 2nd Ed. New York, Wiley, 1993.
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