Accelerating the pace of engineering and science

# comm.LTEMIMOChannel System object

Package: comm

Filter input signal through LTE MIMO multipath fading channel

## Description

The comm.LTEMIMOChannel System object™ filters an input signal through an LTE multiple-input multiple-output (MIMO) multipath fading channel.

A specialization of the comm.MIMOChannel System object, the comm.LTEMIMOChannel System objects offers pre-set configurations for use with LTE link level simulations. In addition to the comm.MIMOChannel System object, the comm.LTEMIMOChannel System object also corrects the correlation matrix to be positive semi-definite, after rounding to 4-digit precision. This System object models Rayleigh fading for each of its links.

To filter an input signal using an LTE MIMO multipath fading channel:

1. Define and set up your LTE MIMO multipath fading channel object. See Construction.

2. Call step to filter the input signal using an LTE MIMO multipath fading channel according to the properties of comm.LTEMIMOChannel. The behavior of step is specific to each object in the toolbox.

## Construction

H = comm.LTEMIMOChannel creates a 3GPP Long Term Evolution (LTE) Release 10 specified multiple-input multiple-output (MIMO) multipath fading channel System object, H. This object filters a real or complex input signal through the multipath LTE MIMO channel to obtain the channel impaired signal.

H = comm.LTEMIMOChannel(Name,Value) creates an LTE MIMO multipath fading channel object, H, with the specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

## Properties

 SampleRate Input signal sample rate (Hertz) Specify the sample rate of the input signal in hertz as a double-precision, real, positive scalar. The default value of this property is 30.72 MHz, as defined in the LTE specification. Profile Channel propagation profile Specify the propagation conditions of the LTE multipath fading channel as one of EPA 5Hz | EVA 5Hz | EVA 70Hz | ETU 70Hz | ETU 300Hz, which are supported in the LTE specification Release 10. The default value of this property is EPA 5Hz. This property defines the delay profile of the channel to be one of EPA, EVA, and ETU. This property also defines the maximum Doppler shift of the channel to be 5 Hz, 70 Hz, or 300 Hz. The Doppler spectrum always has a Jakes shape in the LTE specification. The EPA profile has seven paths. The EVA and ETU profiles have nine paths. The following tables list the delay and relative power per path associated with each profile. AntennaConfiguration Antenna configuration Specify the antenna configuration of the LTE MIMO channel as one of 1x2 | 2x2 | 4x2 | 4x4. These configurations are supported in the LTE specification Release 10. The default value of this property is 2x2. The property value is in the format of Nt-by-Nr. Nt represents the number of transmit antennas and Nr represents the number of receive antennas. CorrelationLevel Spatial correlation strength Specify the spatial correlation strength of the LTE MIMO channel as one of Low | Medium | High. The default value of this property is Low. When you set this property to Low, the MIMO channel is spatially uncorrelated. The transmit and receive spatial correlation matrices are defined from this property according to the LTE specification Release 10. See the Algorithms section for more information. AntennaSelection Antenna selection Specify the antenna selection scheme as one of Off | Tx | Rx | Tx and Rx, where Tx represents transmit antennas and Rx represents receive antennas. When you select Tx and/or Rx, additional input(s) are required to specify which antennas are selected for signal transmission. The default value of this property is Off. RandomStream Source of random number stream Specify the source of random number stream as one of Global stream | mt19937ar with seed. The default value of this property is Global stream. When you set this property to Global stream, the current global random number stream is used for normally distributed random number generation. In this case, the reset method only resets the filters. If you set RandomStream to mt19937ar with seed, the object uses the mt19937ar algorithm for normally distributed random number generation. In this case, the reset method resets the filters and reinitializes the random number stream to the value of the Seed property. Seed Initial seed of mt19937ar random number stream Specify the initial seed of an mt19937ar random number generator algorithm as a double-precision, real, nonnegative integer scalar. The default value of this property is 73. This property applies when you set the RandomStream property to mt19937ar with seed. The Seed reinitializes the mt19937ar random number stream in the reset method. NormalizePathGains Normalize path gains (logical) Set this property to true to normalize the fading processes so that the total power of the path gains, averaged over time, is 0 dB. The default value of this property is true. When you set this property to false, there is no normalization for path gains. NormalizeChannelOutputs Normalize channel outputs (logical) Set this property to true to normalize the channel outputs by the number of receive antennas. The default value of this property is true. When you set this property to false, there is no normalization for channel outputs. PathGainsOutputPort Enable path gain output (logical) Set this property to true to output the channel path gains of the underlying fading process. The default value of this property is false.

## Methods

 clone Create LTEMIMOChannel object with same property values getNumInputs Number of expected inputs to step method getNumOutputs Number of outputs from step method isLocked Locked status for input attributes and nontunable properties release Allow property value and input characteristics changes reset Reset states of the LTEMIMOChannel object step Filter input signal through LTE MIMO multipath fading channel

## Examples

expand all

### Configure Equivalent MIMO Channel System Object Using an LTE MIMO Channel System Object

Configure an equivalent MIMOChannel System Object using the LTEMIMOChannel System Object. Then, verify that the channel output and the path gain output from the two objects are the same.

Create a PSK Modulator System object to modulate randomly generated data.

```hMod = comm.PSKModulator;
modData = step(hMod, randi([0 hMod.ModulationOrder-1],2e3,1));```

Split modulated data into two spatial streams.

`channelInput = reshape(modData, [2, 1e3]).';`

Create an LTEMIMOChannel System object with a 2-by-2 antenna configuration and a medium correlation level.

```hLTEChan = comm.LTEMIMOChannel(...
'Profile',              'EVA 5Hz',...
'AntennaConfiguration', '2x2',...
'CorrelationLevel',     'Medium',...
'AntennaSelection',     'Off',...
'RandomStream',         'mt19937ar with seed',...
'Seed',                 99,...
'PathGainsOutputPort',  true);```

Filter the modulated data using the LTEMIMOChannel System object, hLTEChan.

`[LTEChanOut, LTEPathGains] = step(hLTEChan,  channelInput);`

Create an equivalent MIMOChannel System object, hMIMOChan, using the properties of the LTEMIMOChannel System object, hLTEChan.

The KFactor, DirectPathDopplerShift and DirectPathInitialPhase properties only exist for the MIMOChannel System object. All other MIMOChannel System object properties also exist for the LTEMIMOChannel System object; however, some properties are hidden and read-only.

```hMIMOChan = comm.MIMOChannel(...
'SampleRate',                hLTEChan.SampleRate,...
'PathDelays',                hLTEChan.PathDelays,...
'AveragePathGains',          hLTEChan.AveragePathGains,...
'NormalizePathGains',        hLTEChan.NormalizePathGains,...
'MaximumDopplerShift',       hLTEChan.MaximumDopplerShift,...
'DopplerSpectrum',           hLTEChan.DopplerSpectrum,...
'SpatialCorrelation',        hLTEChan.SpatialCorrelation,...
'TransmitCorrelationMatrix', hLTEChan.TransmitCorrelationMatrix,...
'AntennaSelection',          hLTEChan.AntennaSelection,...
'NormalizeChannelOutputs',   hLTEChan.NormalizeChannelOutputs,...
'RandomStream',              hLTEChan.RandomStream,...
'Seed',                      hLTEChan.Seed,...
'PathGainsOutputPort',       hLTEChan.PathGainsOutputPort);
```

Filter the modulated data using the equivalent hMIMOChan and use the step method to process data.

```[MIMOChanOut, MIMOPathGains] = step(hMIMOChan, channelInput);
```

Verify that the channel output and the path gain output from the two objects are the same.

```display(isequal(LTEChanOut, MIMOChanOut));
display(isequal(LTEPathGains, MIMOPathGains));```

You can repeat the preceding process with AntennaConfiguration set to 4x2 or 4x4 and CorrelationLevel set to Medium or High for hLTEChan. If you do so, the resulting channel output and path gain output from the two objects are slightly different. This difference occurs because an LTE channel with such configurations has its spatial correlation matrix rounded to 4-digit precision. See the LTE specification Release 10 for more details.

## Algorithms

This System object is a specialized implementation of the comm.MIMOChannel System object. For additional algorithm information, see the comm.MIMOChannel System object help page.

### Spatial Correlation Matrices

The following table defines the transmitter eNodeB correlation matrix.

One AntennaTwo AntennasFour Antennas
eNodeB Correlation

ReNB = 1

${R}_{eNB}=\left(\begin{array}{cccc}1& {\alpha }^{1}{9}}& {\alpha }^{4}{9}}& \alpha \\ {\alpha }^{1}{9}}{}^{*}& 1& {\alpha }^{1}{9}}& {\alpha }^{4}{9}}\\ {\alpha }^{4}{9}}{}^{*}& {\alpha }^{1}{9}}{}^{*}& 1& {\alpha }^{1}{9}}\\ {\alpha }^{*}& {\alpha }^{4}{9}}{}^{*}& {\alpha }^{1}{9}}{}^{*}& 1\end{array}\right)$

The following table defines the receiver UE correlation matrix.

One AntennaTwo AntennasFour Antennas
UE Correlation

RUE = 1

${R}_{UE}=\left(\begin{array}{cccc}1& {\beta }^{1}{9}}& {\beta }^{4}{9}}& \beta \\ {\beta }^{1}{9}}{}^{*}& 1& {\beta }^{1}{9}}& {\beta }^{4}{9}}\\ {\beta }^{4}{9}}{}^{*}& {\beta }^{1}{9}}{}^{*}& 1& {\beta }^{1}{9}}\\ {\beta }^{*}& {\beta }^{4}{9}}{}^{*}& {\beta }^{1}{9}}{}^{*}& 1\end{array}\right)$

The following table describes the Rspat channel spatial correlation matrix between the transmitter and receiver antennas.

Tx-by-Rx ConfigurationCorrelation Matrix
1-by-2

${R}_{spat}={R}_{UE}=\left[\begin{array}{cc}1& \beta \\ {\beta }^{*}& 1\end{array}\right]$

2-by-2

${R}_{spat}={R}_{eNB}\otimes {R}_{UE}=\left[\begin{array}{cc}1& \alpha \\ {\alpha }^{*}& 1\end{array}\right]\otimes \left[\begin{array}{cc}1& \beta \\ {\beta }^{*}& 1\end{array}\right]=\left[\begin{array}{cccc}1& \beta & \alpha & \alpha \beta \\ {\beta }^{*}& 1& \alpha {\beta }^{*}& \alpha \\ {\alpha }^{*}& {\alpha }^{*}\beta & 1& \beta \\ {\alpha }^{*}{\beta }^{*}& {\alpha }^{*}& {\beta }^{*}& 1\end{array}\right]$

4-by-2

${R}_{spat}={R}_{eNB}\otimes {R}_{UE}=\left[\begin{array}{cccc}1& {\alpha }^{1}{9}}& {\alpha }^{4}{9}}& \alpha \\ {\alpha }^{{1}{9}}^{*}}& 1& {\alpha }^{1}{9}}& {\alpha }^{4}{9}}\\ {\alpha }^{{4}{9}}^{*}}& {\alpha }^{{1}{9}}^{*}}& 1& {\alpha }^{1}{9}}\\ {\alpha }^{*}& {\alpha }^{{4}{9}}^{*}}& {\alpha }^{{1}{9}}^{*}}& 1\end{array}\right]\otimes \left[\begin{array}{cc}1& \beta \\ {\beta }^{*}& 1\end{array}\right]$

4-by-4

${R}_{spat}={R}_{eNB}\otimes {R}_{UE}=\left[\begin{array}{cccc}1& {\alpha }^{1}{9}}& {\alpha }^{4}{9}}& \alpha \\ {\alpha }^{{1}{9}}^{*}}& 1& {\alpha }^{1}{9}}& {\alpha }^{4}{9}}\\ {\alpha }^{{4}{9}}^{*}}& {\alpha }^{{1}{9}}^{*}}& 1& {\alpha }^{1}{9}}\\ {\alpha }^{*}& {\alpha }^{{4}{9}}^{*}}& {\alpha }^{{1}{9}}^{*}}& 1\end{array}\right]\otimes \left(\begin{array}{cccc}1& {\beta }^{1}{9}}& {\beta }^{4}{9}}& \beta \\ {\beta }^{1}{9}}{}^{*}& 1& {\beta }^{1}{9}}& {\beta }^{4}{9}}\\ {\beta }^{4}{9}}{}^{*}& {\beta }^{1}{9}}{}^{*}& 1& {\beta }^{1}{9}}\\ {\beta }^{*}& {\beta }^{4}{9}}{}^{*}& {\beta }^{1}{9}}{}^{*}& 1\end{array}\right)$

### Spatial Correlation Correction

Low CorrelationMedium CorrelationHigh Correlation
αβαβαβ
000.30.90.90.9

To insure the correlation matrix is positive semi-definite after round-off to 4 digit precision, this System object uses the following equation:

${R}_{high}=\left[{R}_{spatial}+a{I}_{n}\right]/\left(1+a\right)$

Where

α represents the scaling factor such that the smallest value is used to obtain a positive semi-definite result.

For the 4-by-2 high correlation case, α=0.00010.

For the 4-by-4 high correlation case, α=0.00012.

The object uses the same method to adjust the 4-by-4 medium correlation matrix to insure the correlation matrix is positive semi-definite after rounding to 4 digit precision with α = 0.00012.

## Selected Bibliography

[1] 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA), Base Station (BS) radio transmission and reception, Release 10, 2009–2010, 3GPP TS 36.104, Vol. 10.0.0.

[2] 3rd Generation Partnership Project, Technical Specification Group Radio Access Network, Evolved Universal Terrestrial Radio Access (E-UTRA), User Equipment (UE) radio transmission and reception, Release 10, 2010, 3GPP TS 36.101, Vol. 10.0.0.

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

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

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