pre6GEqualizeMMSE

Pre-6G MMSE equalization

Since R2026a

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    Syntax

    [eqSym,csi] = pre6GEqualizeMMSE(rxSym,Hest,nVar)

    Description

    Add-On Required: This feature requires the 6G Exploration Library for 5G Toolbox add-on.

    [eqSym,csi] = pre6GEqualizeMMSE(rxSym,Hest,nVar) performs minimum mean squared error (MMSE) equalization on received symbols rxSym for 6G research and prototyping. The function uses the channel estimate Hest and noise variance estimate nVar to recover the transmitted symbols eqSym and returns soft channel state information csi.

    Examples

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    This example uses:

    Open Live Script

    Create carrier, reference signal, and physical channel configuration objects.

    carrier = pre6GCarrierConfig;
carrier.NSizeGrid = 52;
carrier.SubcarrierSpacing = 30;

rs = pre6GReferenceSignalConfig;
rs.PRBSet = 0:carrier.NSizeGrid-1;
rs.SubcarrierLocations = 0:2:11;
rs.SymbolLocations = [0 7];

ch = pre6GPhysicalChannelConfig;
ch.PRBSet = 0:carrier.NSizeGrid-1;

    Get reference signal indices for the configurations and specify that the physical channel does not use those indices.

    rsInd = pre6GReferenceSignalIndices(carrier,rs);
ch.ReservedRE = rsInd-1;

    Get physical channel indices and resource information. Generate a random codeword and create physical channel symbols.

    [chInd,chInfo] = pre6GPhysicalChannelIndices(carrier,ch);
cw = randi([0 1],chInfo.G,1,"int8");
sym = pre6GPhysicalChannel(carrier,ch,cw);

    Create an empty resource grid. Map the physical channel and reference signal symbols onto the grid.

    rsSym = pre6GReferenceSignal(carrier,rs);
txGrid = pre6GResourceGrid(carrier,1);
txGrid(rsInd) = rsSym;
txGrid(chInd) = sym;

    OFDM-modulate the resource grid. Pass the time-domain waveform through a channel that adds AWGN with a signal-to-noise ratio of 25 dB and applies a 60° phase rotation.

    txWaveform = pre6GOFDMModulate(carrier,txGrid);
snr = 25;
H = exp(1i*pi/3);
rxWaveform = awgn(H*txWaveform,snr,"measured");

    OFDM-demodulate the waveform. Perform practical channel estimation using the reference signal configuration.

    rxGrid = pre6GOFDMDemodulate(carrier,rxWaveform);
[H,nVar] = pre6GChannelEstimate(carrier,rs,rxGrid);

    Prepare the channel estimate for use in equalization by reshaping it to a column vector with length equal to the number of resource elements and extracting the indices that correspond to data symbols. Extract the data symbols from the received resource grid.

    hestVector = reshape(H,[numel(H) 1]);
Hest = hestVector(chInd(:,1));
rxSym = rxGrid(chInd);

    Equalize the received symbols. Plot the received constellation before and after equalization.

    [eqSym,csi] = pre6GEqualizeMMSE(rxSym,Hest,nVar);

refConst = qammod(0:3,4,UnitAveragePower=true);
scatterplot(rxSym,1,0);
hold on;
plot(real(refConst),imag(refConst),"r*",MarkerSize=10);
hold off;
title("Received Constellation");

    Figure Scatter Plot contains an axes object. The axes object with title Received Constellation, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

    scatterplot(eqSym,1,0);
hold on;
plot(real(refConst),imag(refConst),"r*",MarkerSize=10);
hold off;
title("Equalized Constellation");

    Figure Scatter Plot contains an axes object. The axes object with title Equalized Constellation, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

    Input Arguments

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    Received symbols, specified as an NRE-by-R-by-B complex array, where:

    • NRE is the number of resource elements extracted from the received resource grid.

    • R is the number of receive antennas.

    • B is the batch size.

    The number of resource elements and receive antennas must match the first and second dimensions of Hest.

    Data Types: single | double
    Complex Number Support: Yes

    Channel estimate, specified as an NRE-by-R-by-P-by-B complex array, where:

    • NRE is the number of resource elements.

    • R is the number of receive antennas.

    • P is the number of layers (transmit streams).

    • B is the batch size.

    The channel estimate contains the estimated channel frequency response at the resource element locations corresponding to rxSym. Obtain the channel estimate by using the pre6GChannelEstimate or pre6GPerfectChannelEstimate function.

    Data Types: single | double
    Complex Number Support: Yes

    Noise variance estimate, specified as one of these values:

    • Nonnegative scalar — The function applies the same noise variance to all batch elements.

    • 1-by-B nonnegative row vector — The function applies a separate noise variance to each batch element, where B is the batch size.

    Obtain the noise variance estimate from the second output of the pre6GChannelEstimate function.

    Data Types: single | double

    Output Arguments

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    Equalized symbols, returned as an NRE-by-P-by-B complex array, where NRE is the number of resource elements, P is the number of layers, and B is the batch size.

    The MMSE equalizer estimates the transmitted symbols by minimizing the mean squared error between the estimated and actual transmitted signals.

    Data Types: single | double
    Complex Number Support: Yes

    Soft channel state information, returned as an NRE-by-P-by-B real-valued array. Each element quantifies the reliability of the corresponding equalized symbol in eqSym. Use csi to compute soft bits for channel decoding by scaling log-likelihood ratios.

    Data Types: single | double

    Extended Capabilities

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    Version History

    Introduced in R2026a

    See Also

    Functions

    Objects