Filter input signal through SISO multipath fading channel

• Library:
• Communications Toolbox / Channels

## Description

The SISO Fading Channel block filters an input signal using a single-input/single-output (SISO) multipath fading channel. This block models both Rayleigh and Rician fading. For processing details, see the Algorithms section.

## Ports

### Input

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Input data signal, specified as an NS-by-1 vector. NS represents the number of samples in the input signal.

Data Types: `double` | `single`
Complex Number Support: Yes

### Output

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Output data signal for the fading channel, returned as an NS-by-1 vector. NS represents the number of samples in the input signal.

Discrete path gains of the underlying fading process, returned as an NS-by-NP matrix.

• NS represents the number of samples in the input signal.

• NP represents the number of channel paths.

#### Dependencies

To enable this port, on the Main tab, select Output channel path gains.

Channel filter delay, returned as a scalar.

#### Dependencies

To enable this port, on the Main tab, select Output channel filter delay.

## Parameters

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### Main Tab

Multipath parameters (frequency selectivity)

Select this parameter to use the sample rate of the input signal when processing. When `Inherit sample rate from input` is selected, the sample rate is NS/TS, where NS is the number of input samples, and TS is the model sample time.

Input signal sample rate in hertz, specified as a positive scalar. To match the model settings, set the sample rate to NS/TS, where NS is the number of input samples, and TS is the model sample time.

#### Dependencies

This parameter appears when Inherit sample rate from input is not selected.

Data Types: `double`

Delays for each discrete path in seconds, specified as a nonnegative scalar or row vector.

• When you set Discrete path delays (s) to a scalar, the SISO channel is frequency flat.

• When you set Discrete path delays (s) to a vector, the SISO channel is frequency selective.

Data Types: `double`

Average gain for each discrete path in decibels, specified as a scalar or row vector. Average path gains (dB) must have the same size as Discrete path delays (s).

Data Types: `double`

Select this parameter to normalize the fading processes so that the total power of the path gains, averaged over time, is 0 dB.

Select the fading distribution of the channel, either `Rayleigh` or `Rician`.

K-factor of a Rician fading channel, specified as a positive scalar or a 1-by-NP vector of nonnegative values. NP equals the value of the Discrete path delays (s) parameter.

• If you set K-factors to a scalar, the first discrete path is a Rician fading process with a Rician K-factor of K-factors. Any remaining discrete paths are independent Rayleigh fading processes.

• If you set K-factors to a row vector, the discrete path corresponding to a positive element of the K-factors vector is a Rician fading process with a Rician K-factor specified by that element. The discrete path corresponding to any zero-valued elements of the K-factors vector are Rayleigh fading processes. At least one element value must be nonzero.

#### Dependencies

This parameter appears when Fading distribution is `Rician`.

Data Types: `double`

Doppler shifts for the line-of-sight components of the Rician fading channel in hertz, specified as a scalar or row vector. This parameter must have the same size as K-factors.

• If you set LOS path Doppler shifts (Hz) to a scalar, it represents the line-of-sight component Doppler shift of the first discrete path that is a Rician fading process.

• If you set LOS path Doppler shifts (Hz) to a row vector, the discrete path that is a Rician fading process has its line-of-sight component Doppler shift specified by the elements of LOS path Doppler shifts (Hz) that correspond to positive elements in the K-factors vector.

#### Dependencies

This parameter appears when Fading distribution is `Rician`.

Data Types: `double`

Initial phases for the line-of-sight component of the Rician fading channel in radians, specified as a scalar or row vector. This parameter must have the same size as K-factors.

• If you set LOS path initial phases (rad) to a scalar, it is the line-of-sight component initial phase of the first discrete path that is a Rician fading process.

• If you set LOS path initial phases (rad) to a row vector, the discrete path that is a Rician fading process has its line-of-sight component initial phase specified by the elements of LOS path initial phases (rad) that correspond to positive elements in the K-factors vector.

#### Dependencies

This parameter appears when Fading distribution is `Rician`.

Data Types: `double`

Doppler parameters (time dispersion)

Maximum Doppler shift for all channel paths in hertz, specified as a nonnegative scalar.

Maximum Doppler shift (Hz) must be smaller than (fs/10)/fc for each path. fs is the sampling rate at the input to the SISO Fading Channel block. fc is the cutoff frequency factor of the path. For more information, see Cutoff Frequency Factor.

Data Types: `double`

Doppler spectrum shape for all channel paths, specified as a single Doppler spectrum structure returned from the `doppler` function or a 1-by-NP cell array of such structures. The default value of this parameter is the Jakes Doppler spectrum (`doppler('Jakes')`).

• If you assign a single call to `doppler`, all paths have the same specified Doppler spectrum.

• If you assign a 1-by-NP cell array of calls to `doppler` using any of the specified syntaxes, each path has the Doppler spectrum specified by the corresponding Doppler spectrum structure in the array. In this case, NP equals the value of the Discrete path delays (s) parameter.

#### Dependencies

This parameter applies when Maximum Doppler shift (Hz) is greater than zero.

Other parameters

Random number generator initial seed for this block, specified as a nonnegative integer.

Select this parameter to add the Gain output port to the block and output the channel path gains of the underlying fading process.

Select this parameter to add the Delay output port to the block and output the channel filter delay of the underlying fading process.

Compilation type, specified as `Interpreted execution` or `Code generation`.

• `Interpreted execution` — Simulate model using the MATLAB® interpreter. This option shortens startup time but has slower simulation speed than `Code generation`.

• `Code generation` — Simulate model using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but provides faster simulation speed than ```Interpreted execution```.

### Visualization Tab

Select the channel visualization: `Off`, ```Impulse response```, `Frequency response`, ```Doppler spectrum```, or `Impulse and frequency responses`. When visualization is on, the selected channel characteristics, such as impulse response or Doppler spectrum, display in a separate window. For more information, see Channel Visualization.

Select the percentage of samples to display: `10%`, `25%`, `50%`, or `100%`. Increasing the percentage improves display accuracy at the expense of simulation speed.

#### Dependencies

This parameter appears when Channel visualization is `Impulse response`, `Frequency response`, or ```Impulse and frequency responses```.

Path for which the Doppler spectrum is displayed, specified as a positive integer from 1 to NP, where NP equals the value of the Discrete path delays (s) parameter.

#### Dependencies

This parameter appears when Channel visualization is `Doppler spectrum`.

## Block Characteristics

 Data Types `double` | `single` Multidimensional Signals `yes` Variable-Size Signals `yes`

## Algorithms

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The fading process for the SISO channel is described in Methodology for Simulating Multipath Fading Channels.

## References

[1] Oestges, C., and B. Clerckx. MIMO Wireless Communications: From Real-World Propagation to Space-Time Code Design. Academic Press, 2007.

[2] Correira, L. M. Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G. Academic Press, 2006.

[3] Kermoal, J. P., L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen. "A stochastic MIMO radio channel model with experimental validation." IEEE Journal on Selected Areas of Communications. Vol. 20, Number 6, 2002, pp. 1211–1226.

[4] Jeruchim, M., P. Balaban, and K. S. Shanmugan. Simulation of Communication Systems. Second Edition. New York: Kluwer Academic/Plenum, 2000.

[5] Pätzold, Matthias, Cheng-Xiang Wang, and Bjorn Olav Hogstand. "Two New Sum-of-Sinusoids-Based Methods for the Efficient Generation of Multiple Uncorrelated Rayleigh Fading Waveforms." IEEE Transactions on Wireless Communications. Vol. 8, Number 6, 2009, pp. 3122–3131.

## Extended Capabilities

### Topics

Introduced in R2017b