# Documentation

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Simulate multipath Rician fading propagation channel

Channels

## Description

The Multipath Rician Fading Channel block implements a baseband simulation of a multipath Rician fading propagation channel. You can use this block to model mobile wireless communication systems when the transmitted signal can travel to the receiver along a dominant line-of-sight or direct path. For more details, see Fading Channels.

This block accepts a scalar value or column vector input signal. The block inherits sample time from the input signal. The input signal must have a discrete sample time greater than 0.

Relative motion between the transmitter and receiver causes Doppler shifts in the signal frequency. You can specify the Doppler spectrum of the Rician process using the Doppler spectrum type pop-up menu. For channels with multiple paths, you can assign each path a different Doppler spectrum, by entering a vector of doppler objects in the Doppler spectrum field.

Because a multipath channel reflects signals at multiple places, a transmitted signal travels to the receiver along several paths, each of which may have differing lengths and associated time delays. In the block's parameter dialog box, the Discrete path delay vector specifies the time delay for each path. If you do not check the Normalize gain vector to 0 dB overall gain box, then the Average path gain vector specifies the gain for each path. When you check the box, the block uses a multiple of Average path gain vector instead of the Average path gain vector itself, choosing the scaling factor so that the channel's effective gain considering all paths is 0 dB.

The number of paths indicates the length of Discrete path delay vector or Average path gain vector, whichever is larger. If both of these parameters are vectors, they must have the same length; if exactly one of these parameters contains a scalar value, the block expands it into a vector whose size matches that of the other vector parameter.

Fading causes the signal to become diffuse. The K-factor parameter, which is part of the statistical description of the Rician distribution, represents the ratio between the power in the line-of-sight component and the power in the diffuse component. The ratio is expressed linearly, not in decibels. While the Average path gain vector parameter controls the overall gain through the channel, the K-factor parameter controls the gain's partition into line-of-sight and diffuse components.

You can specify the K-factor parameter as a scalar or a vector. If the K-factor parameter is a scalar, then the first discrete path of the channel is a Rician fading process (it contains a line-of-sight component) with the specified K-factor, while the remaining discrete paths indicate independent Rayleigh fading processes (with no line-of-sight component). If the K-factor parameter is a vector of the same size as Discrete path delay vector, then each discrete path is a Rician fading process with a K-factor given by the corresponding element of the vector. You can attribute the line-of-sight component a Doppler shift, through the Doppler shift(s) of line-of-sight component(s) parameter, and an initial phase, through the Initial phase(s) of line-of-sight component(s). The Doppler shift(s) of line-of-sight component(s) and Initial phase(s) of line-of-sight component(s) parameters must be of the same size as the K-factor parameter.

The block multiplies the input signal by samples of a Rician-distributed complex random process. The scalar Initial seed parameter seeds the random number generator and the block generates random numbers using the Ziggurat method.

Double-clicking this block during simulation or selecting the block dialog's check box labeled Open channel visualization at start of simulation plots the channel characteristics using the channel visualization tool. See Channel Visualization in Communications System Toolbox User's Guide for details.

## Parameters

K-factor

The ratio of power in the line-of-sight component to the power in the diffuse component. The ratio is expressed linearly, not in decibels. If K-factor is a scalar value, then the first discrete path is a Rician fading process (it contains a line-of-sight component) with the specified K-factor, while the remaining discrete paths are independent Rayleigh fading processes (with no line-of-sight component). If K-factor is a vector of the same size as Discrete path delay vector, then each discrete path is a Rician fading process with a K-factor given by the corresponding element of the vector.

Doppler shift(s) of line-of-sight components(s) (Hz)

The Doppler shift of the line-of-sight component. It must be a scalar (if K-factor is a scalar) or a vector of the same size as K-factor. If this parameter contains a scalar value, then the line-of-sight component of the first discrete path has the specified Doppler shift, while the remaining discrete paths become independent Rayleigh fading processes. If the parameter contains a vector, then the line-of-sight component of each discrete path has a Doppler shift given by the corresponding element of the vector.

Initial phase(s) of line-of-sight component(s) (rad)

The initial phase of the line-of-sight component. It must be either a scalar (if K-factor is a scalar value) or a vector of the same size as K-factor.

Maximum diffuse Doppler shift (Hz)

A positive scalar value that indicates the maximum diffuse Doppler shift.

Doppler spectrum type

Specifies the Doppler spectrum of the Rician process.

This parameter defaults to `Jakes` Doppler spectrum. Alternately, you can choose any of the following types:

For all Doppler spectrum types except `Jakes` and `Flat`, You can use one or more parameters to control the shape of the spectrum.

You can also select `Specify as dialog parameter` for the Doppler spectrum type. Specify the Doppler spectrum by entering an object in the Doppler spectrum field. See the `doppler` function reference in Communications System Toolbox User's Guide for details on how to construct doppler objects, and for the meaning of the parameters associated with the various Doppler spectrum types.

Discrete delay vector(s)

A vector that specifies the propagation delay for each path.

Average path gain vector (dB)

A vector that specifies the gain for each path.

Initial seed

The scalar seed for the Gaussian noise generator.

Open channel visualization at start of simulation

Select this check box to open the channel visualization tool when a simulation begins. This block supports channel visualization for a column vector input signal.

Complex path gains port

Select this check box to create a port that outputs the values of the complex path gains for each path. In this N-by-M multichannel output, N represents the number of samples the input contains and M represents the number of discrete paths (number of delays).

Channel filter delay port

Select this check box to create a port that outputs the value of the delay (in samples) that results from the filtering operation of this block. This delay is zero if only one path is simulated, but can be greater than zero if more than one path is present. See Methodology for Simulating Multipath Fading Channels: in Communications System Toolbox User's Guide for a definition of this delay, where it is denoted as ${N}_{1}$.

## Algorithm

This implementation is based on the direct form simulator described in Reference [1]. A detailed explanation of the implementation, including a review of the different Doppler spectra, can be found in [4].

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 θ with the direction of wave motion, the Doppler shift is

fd = (vf/c)cos θ

where f is the transmission carrier frequency and c is the speed of light. The Doppler frequency is the maximum Doppler shift arising from the motion of the mobile.

## References

[1] Jeruchim, Michel C., Balaban, P., 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, John Wiley & Sons, Inc., 1993.

[4] Iskander, Cyril-Daniel, A MATLAB-based Object-Oriented Approach to Multipath Fading Channel Simulation, a MATLAB Central submission available from www.mathworks.com.