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# ricianchan

## Syntax

chan = ricianchan(ts,fd,k)
chan = ricianchan(ts,fd,k,tau,pdb)
chan = ricianchan(ts,fd,k,tau,pdb,fdLOS)
chan = ricianchan

## Description

chan = ricianchan(ts,fd,k) constructs a frequency-flat (single path) Rician fading-channel object. ts is the sample time of the input signal, in seconds. fd is the maximum Doppler shift, in hertz. k is the Rician K-factor in linear scale. You can model the effect of the channel chan on a signal x by using the syntax y = filter(chan,x). See filter for more information.

chan = ricianchan(ts,fd,k,tau,pdb) constructs a frequency-selective (multiple paths) fading-channel object. If k is a scalar, then the first discrete path is a Rician fading process (it contains a line-of-sight component) with a K-factor of k, while the remaining discrete paths are independent Rayleigh fading processes (no line-of-sight component). If k is a vector of the same size as tau, then each discrete path is a Rician fading process with a K-factor given by the corresponding element of the vector k. tau is a vector of path delays, each specified in seconds. pdb is a vector of average path gains, each specified in dB.

chan = ricianchan(ts,fd,k,tau,pdb,fdLOS) specifies fdlos as the Doppler shift(s) of the line-of-sight component(s) of the discrete path(s), in hertz. fdlos must be the same size as k. If k and fdlos are scalars, the line-of-sight component of the first discrete path has a Doppler shift of fdlos, while the remaining discrete paths are independent Rayleigh fading processes. If fdlos is a vector of the same size as k, the line-of-sight component of each discrete path has a Doppler shift given by the corresponding element of the vector fdlos. By default, fdlos is 0. The initial phase(s) of the line-of-sight component(s) can be set through the property DirectPathInitPhase.

chan = ricianchan sets the maximum Doppler shift to 0, the Rician K-factor to 1, and the Doppler shift and initial phase of the line-of-sight component to 0. This syntax models a static frequency-flat channel, and, in this trivial case, the sample time of the signal is unimportant.

### Properties

The following tables describe the properties of the channel object, chan, that you can set and that MATLAB® technical computing software sets automatically. To learn how to view or change the values of a channel object, see Display Object Properties or Change Object Properties.

Writeable Properties

PropertyDescription
InputSamplePeriodSample period of the signal on which the channel acts, measured in seconds.
DopplerSpectrumDoppler spectrum object(s). The default is a Jakes doppler object.
MaxDopplerShiftMaximum Doppler shift of the channel, in hertz (applies to all paths of a channel).
KFactorRician K-factor (scalar or vector). The default value is 1 (line-of-sight component on the first path only).
PathDelaysVector listing the delays of the discrete paths, in seconds.
AvgPathGaindBVector listing the average gain of the discrete paths, in decibels.
DirectPathDopplerShiftDoppler shift(s) of the line-of-sight component(s) in hertz. The default value is 0.
DirectPathInitPhaseInitial phase(s) of line-of-sight component(s) in radians. The default value is 0.
NormalizePathGainsIf this value is 1, the Rayleigh fading process is normalized such that the expected value of the path gains' total power is 1.
StoreHistoryIf this value is 1, channel state information needed by the channel visualization tool is stored as the channel filter function processes the signal. The default value is 0.
StorePathGainsIf this value is 1, the complex path gain vector is stored as the channel filter function processes the signal. The default value is 0.
ResetBeforeFilteringIf this value is 1, each call to filter resets the state of chan before filtering. If it is 0, the fading process maintains continuity from one call to the next.

PropertyDescriptionWhen MATLAB Sets or Updates Value
ChannelTypeFixed value, 'Rician'.When you create object.
PathGainsComplex vector listing the current gains of the discrete paths. When you create or reset chan, PathGains is a random vector influenced by AvgPathGaindB and NormalizePathGains.When you create object, reset object, or use it to filter a signal.
ChannelFilterDelayDelay of the channel filter, measured in samples.
The ChannelFilterDelay property returns a delay value that is valid only if the first value of the PathGain is the biggest path gain. In other words, main channel energy is in the first path.
When you create object or change ratio of InputSamplePeriod to PathDelays.
NumSamplesProcessedNumber of samples the channel processed since the last reset. When you create or reset chan, this property value is 0.When you create object, reset object, or use it to filter a signal.

### Relationships Among Properties

Changing the length of PathDelays also changes the length of AvgPathGaindB, the length of KFactor if KFactor is a vector (no change if it is a scalar), and the length of DopplerSpectrum if DopplerSpectrum is a vector (no change if it is a single object).

DirectPathDopplerShift and DirectPathInitPhase both follow changes in KFactor.

The PathDelays and AvgPathGaindB properties of the channel object must always have the same vector length, because this length equals the number of discrete paths of the channel. The DopplerSpectrum property must either be a single Doppler object or a vector of Doppler objects with the same length as PathDelays.

If you change the length of PathDelays, MATLAB truncates or zero-pads the value of AvgPathGaindB if necessary to adjust its vector length (MATLAB may also change the values of read-only properties such as PathGains and ChannelFilterDelay). If DopplerSpectrum is a vector of Doppler objects, and you increase or decrease the length of PathDelays, MATLAB will add Jakes Doppler objects or remove elements from DopplerSpectrum, respectively, to make it the same length as PathDelays.

If StoreHistory is set to 1 (the default is 0), the object stores channel state information as the channel filter function processes the signal. You can then visualize this state information through a GUI using the plot (channel) method.

 Note:   Setting StoreHistory to 1 will result in a slower simulation. If you do not want to visualize channel state information using plot (channel), but want to access the complex path gains, then set StorePathGains to 1, while keeping StoreHistory as 0.

### Reset Method

If MaxDopplerShift is set to 0 (the default), the channel object, chan, models a static channel.

Use the syntax reset(chan) to generate a new channel realization.

### Algorithm

The methodology used to simulate fading channels is described in Methodology for Simulating Multipath Fading Channels:, where the properties specific to the Rician channel object are related to the quantities of this section as follows (see the rayleighchan reference page for properties common to both Rayleigh and Rician channel objects):

• The Kfactor property contains the value of ${K}_{r}$ (if it's a scalar) or $\left\{{K}_{r,k}\right\}$, $1\le k\le K$ (if it's a vector).

• The DirectPathDopplerShift property contains the value of ${f}_{d,LOS}$ (if it's a scalar) or $\left\{{f}_{d,LOS,k}\right\}$, $1\le k\le K$ (if it's a vector).

• The DirectPathInitPhase property contains the value of ${\theta }_{LOS}$ (if it's a scalar) or $\left\{{\theta }_{LOS,k}\right\}$, $1\le k\le K$ (if it's a vector).

## Channel Visualization

The characteristics of a channel can be plotted using the channel visualization tool. You can use the channel visualization tool in Normal mode and Accelerator mode. For more information, see Channel Visualization.

## Examples

The example in Quasi-Static Channel Modeling uses this function.