# lteEqualizeMMSE

MMSE equalization

## Description

`[`

returns
equalized data in multidimensional array, `out`

,`csi`

]
= lteEqualizeMMSE(`rxgrid`

,`channelest`

,`noiseest`

)`out`

.
MMSE equalization is applied to the received data resource grid in
the matrix, `rxgrid`

, using the channel information
in the `channelest`

matrix. `noiseest`

is
an estimate of the received noise power spectral density.

Alternatively, the input `channelest`

can
be provided as a 3-D array of size *NRE*-by-`NRxAnts`

-by-*P*,
and the input `rxgrid`

can be provided as a matrix
of size *NRE*-by-`NRxAnts`

. In this
case, the first two dimensions have been reduced to one dimension
by appropriate indexing through the frequency and time locations of
the resource elements of interest, typically for a single physical
channel. The outputs, `out`

and `csi`

,
are of size (*N*×*M*)-by-*P*.

## Examples

### Equalize MMSE for RMC R.4

Equalize the received signal for RMC R.4 after channel estimation. Use the MMSE equalizer.

Create cell-wide configuration structure and generate transmit signal. Configure propagation channel.

enb = lteRMCDL('R.4'); [txSignal,~,info] = lteRMCDLTool(enb,[1;0;0;1]); chcfg.DelayProfile = 'EPA'; chcfg.NRxAnts = 1; chcfg.DopplerFreq = 70; chcfg.MIMOCorrelation = 'Low'; chcfg.SamplingRate = info.SamplingRate; chcfg.Seed = 1; chcfg.InitPhase = 'Random'; chcfg.InitTime = 0; txSignal = [txSignal; zeros(15,1)]; N = length(txSignal); noise = 1e-3*complex(randn(N,chcfg.NRxAnts),randn(N,chcfg.NRxAnts)); rxSignal = lteFadingChannel(chcfg,txSignal)+noise;

Perform synchronization and OFDM demodulation.

offset = lteDLFrameOffset(enb,rxSignal); rxGrid = lteOFDMDemodulate(enb,rxSignal(1+offset:end,:));

Create channel estimation configuration structure and perform channel estimation.

cec.FreqWindow = 9; cec.TimeWindow = 9; cec.InterpType = 'Cubic'; cec.PilotAverage = 'UserDefined'; cec.InterpWinSize = 3; cec.InterpWindow = 'Causal'; [hest,noiseEst] = lteDLChannelEstimate(enb, cec, rxGrid);

Equalize and plot received and equalized grids.

eqGrid = lteEqualizeMMSE(rxGrid, hest, noiseEst); subplot(2,1,1) surf(abs(rxGrid)) title('Received grid') xlabel('OFDM symbol') ylabel('Subcarrier') subplot(2,1,2) surf(abs(eqGrid)) title('Equalized grid') xlabel('OFDM symbol') ylabel('Subcarrier')

### Equalize MMSE for RMC R.5

This example applies MMSE equalization on the received signal for reference measurement channel (RMC) R.5, after channel estimation.

Set the DL reference measurement channel to R.5

`enb = lteRMCDL('R.5');`

Set channel estimator configuration `PilotAverage`

field to `UserDefined`

. as follows: averaging window of 9 resource elements in both frequency and time domain, cubic interpolation with a casual window.

cec = struct('FreqWindow',9,'TimeWindow',9,'InterpType','cubic'); cec.PilotAverage = 'UserDefined'; cec.InterpWinSize = 1; cec.InterpWindow = 'Causal';

Generate the `txWaveform`

.

txWaveform = lteRMCDLTool(enb,[1;0;0;1]); n = length(txWaveform);

Apply some random noise to the transmitted signal and save as the `rxWaveform`

.

rxWaveform = repmat(txWaveform,1,2)+complex(randn(n,2),randn(n,2))*1e-3;

Next, demodulate the received data.

rxGrid = lteOFDMDemodulate(enb,rxWaveform);

Then, perform channel estimation.

[hest,n0] = lteDLChannelEstimate(enb,cec,rxGrid);

Finally, apply the MMSE equalization.

out = lteEqualizeMMSE(rxGrid,hest,n0);

Show scatter plot of one component carrier.

scatterplot(out(:,1))

## Input Arguments

`rxgrid`

— Received data resource grid

3-D numeric array | 2-D numeric matrix

Received data resource grid, specified as a 3-D numeric array
or a 2-D numeric matrix. As a 3-D numeric array, it has size *N*-by-*M*-by-`NRxAnts`

,
where *N* is the number of subcarriers, *M* is
the number of OFDM symbols, and `NRxAnts`

is the
number of receive antennas.

Alternatively, as a 2-D numeric matrix, it has size *NRE*-by-`NRxAnts`

.
In this case, the first two dimensions have been reduced to one dimension
by appropriate indexing through the frequency and time locations of
the resource elements of interest, typically for a single physical
channel.

**Data Types: **`double`

**Complex Number Support: **Yes

`channelest`

— Channel information

4-D numeric array | 3-D numeric array

Channel information, specified as a 4-D numeric array or a 3-D
numeric array. As a 4-D numeric array, it has size *N*-by-*M*-by-`NRxAnts`

-by-*P*. *N* is
the number of subcarriers, *M* is the number of OFDM
symbols, `NRxAnts`

is the number of receive antennas,
and *P* is the number of transmit antennas. Each
element is a complex number representing the narrowband channel for
each resource element and for each link between transmit and receive
antennas. This matrix can be obtained using the channel estimation
command `lteDLChannelEstimate`

.

Alternatively, as a 3-D numeric array, it has size *NRE*-by-`NRxAnts`

-by-*P*.
In this case, the first two dimensions have been reduced to one dimension
by appropriate indexing through the frequency and time locations of
the resource elements of interest, typically for a single physical
channel.

**Data Types: **`double`

**Complex Number Support: **Yes

`noiseest`

— Noise power estimate

numeric scalar

Noise power estimate, specified as a numeric scalar. It is an
estimate of the received noise power spectral density per RE on `rxgrid`

.

**Data Types: **`double`

## Output Arguments

`out`

— Equalized output data

3-D numeric array | 2-D numeric matrix

Equalized output data, returned as a 3-D numeric array or a
2-D numeric matrix. As a 3-D numeric array, it has size *N*-by-*M*-by-*P*,
where *N* is the number of subcarriers, *M* is
the number of OFDM symbols, and *P* is the number
of transmit antennas.

Alternatively, if `channelest`

is provided
as a 3-D array, `out`

is a 2-D numeric matrix of
size (*N*×*M*)-by-*P*.
In this case, the first two dimensions have been reduced to one dimension
by appropriate indexing through the frequency and time locations of
the resource elements of interest, typically for a single physical
channel.

**Data Types: **`double`

**Complex Number Support: **Yes

`csi`

— Soft channel state information

3-D numeric array | 2-D numeric matrix

Soft channel state information, returned as a 3-D numeric array
of the same size as `out`

. As a 3-D numeric array,
it has size *N*-by-*M*-by-*P*,
where *N* is the number of subcarriers, *M* is
the number of OFDM symbols, and *P* is the number
of transmit antennas. `csi`

provides an estimate
(via MMSE) of the received RE gain for each received RE.

Alternatively, if `channelest`

is provided
as a 3-D array, `csi`

is a 2-D numeric matrix of
size (*N*×*M*)-by-*P*.
In this case, the first two dimensions have been reduced to one dimension
by appropriate indexing through the frequency and time locations of
the resource elements of interest, typically for a single physical
channel.

**Data Types: **`double`

## See Also

`lteDLChannelEstimate`

| `lteEqualizeZF`

| `lteEqualizeMIMO`

| `lteEqualizeULMIMO`

| `lteOFDMDemodulate`

| `lteSCFDMADemodulate`

| `lteULChannelEstimate`

**Introduced in R2014a**

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