# comm.LTEMIMOChannel

(To be removed) Filter input signal through LTE MIMO multipath fading channel

`comm.LTEMIMOChannel` will be removed in a future release. Use `comm.MIMOChannel` instead.

## 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.

Note

Starting in R2016b, instead of using the `step` method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, `y = step(obj,x)` and `y = obj(x)` perform equivalent operations.

## 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

 reset (To be removed) Reset states of the `LTEMIMOChannel` object step (To be removed) Filter input signal through LTE MIMO multipath fading channel
Common to All System Objects
`release`

Allow System object property value changes

## Examples

collapse all

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.

```pskModulator = comm.PSKModulator; modData = pskModulator(randi([0 pskModulator.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.

```lteChan = comm.LTEMIMOChannel(... 'Profile', 'EVA 5Hz',... 'AntennaConfiguration', '2x2',... 'CorrelationLevel', 'Medium',... 'AntennaSelection', 'Off',... 'RandomStream', 'mt19937ar with seed',... 'Seed', 99,... 'PathGainsOutputPort', true);```
```Warning: COMM.LTEMIMOCHANNEL will be removed in a future release. Use COMM.MIMOCHANNEL or LTEFADINGCHANNEL instead. See <a href="matlab:helpview('comm', 'REMOVE_LTEMIMOChannel')">this release note</a> for more information. ```

Filter the modulated data using the `LTEMIMOChannel` System object, `lteChan`.

`[LTEChanOut,LTEPathGains] = lteChan(channelInput);`

Create an equivalent `MIMOChannel` System object, `mimoChannel`, using the properties of the `LTEMIMOChannel` System object, `lteChan`.

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.

```mimoChannel = comm.MIMOChannel( ... 'SampleRate',lteChan.SampleRate, ... 'PathDelays',lteChan.PathDelays, ... 'AveragePathGains',lteChan.AveragePathGains, ... 'NormalizePathGains',lteChan.NormalizePathGains, ... 'FadingDistribution',lteChan.FadingDistribution, ... 'MaximumDopplerShift',lteChan.MaximumDopplerShift, ... 'DopplerSpectrum',lteChan.DopplerSpectrum, ... 'SpatialCorrelationSpecification', ... lteChan.SpatialCorrelationSpecification, ... 'SpatialCorrelationMatrix',lteChan.SpatialCorrelationMatrix, ... 'AntennaSelection',lteChan.AntennaSelection, ... 'NormalizeChannelOutputs',lteChan.NormalizeChannelOutputs, ... 'RandomStream',lteChan.RandomStream, ... 'Seed',lteChan.Seed, ... 'PathGainsOutputPort',lteChan.PathGainsOutputPort);```

Filter the modulated data using the equivalent `mimoChannel` object.

`[MIMOChanOut, MIMOPathGains] = mimoChannel(channelInput);`

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

`sameChOutput = isequal(LTEChanOut,MIMOChanOut)`
```sameChOutput = logical 1 ```
`samePathGains = isequal(LTEPathGains,MIMOPathGains)`
```samePathGains = logical 1 ```

You can repeat the preceding process with `AntennaConfiguration` set to `4x2` or `4x4` and `CorrelationLevel` set to `Medium` or `High` for `lteChan`.

## 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.