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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 with **Inline
parameters** off 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.

**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 .

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

*f*_{d} = (*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.

[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.

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