nrPhaseNoiseCompensate

R2026b

Compensate phase-noise-induced CPE

Since R2026b

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    Syntax

    dataOut = nrPhaseNoiseCompensate(carrier,dataSym,dataInd,cpe)

    Description

    dataOut = nrPhaseNoiseCompensate(carrier,dataSym,dataInd,cpe) compensates for phase‑noise‑induced common phase error (CPE) on the equalized data symbols dataSym. To compensate for the CPE, the function maps the equalized data symbols dataSym to their resource element locations dataInd within a resource grid defined by the carrier configuration carrier. Then, it uses the estimated CPE cpe to correct symbol‑wise phase distortion.

    example

    Examples

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    Open Live Script

    Estimate and compensate for the CPE of a physical downlink shared channel (PDSCH) transmission, in the presence of phase noise, by using equalized PT‑RS symbols.

    To ensure simulation results are repeatable, initialize the random number generator with a fixed seed. For greater statistical accuracy, run the simulation multiple times with different seeds and compute the average results.

    rng("default")

    Configure the carrier using an nrCarrierConfig object. Specify a subcarrier spacing of 60 kHz with a transmission bandwidth of 50 MHz operating in frequency range 2 (FR2).

    carrier = nrCarrierConfig;
carrier.NSizeGrid = 66;
carrier.SubcarrierSpacing = 60;

    Configure the PDSCH that occupies the complete carrier and enable PT-RS.

    pdsch = nrPDSCHConfig(PRBSet=0:carrier.NSizeGrid-1, ...
    Modulation="64QAM", ...
    EnablePTRS=true, ...
    DMRS=nrPDSCHDMRSConfig( ...
    NumCDMGroupsWithoutData=1, ...
    NIDNSCID=1));

    Enable PT‑RS for the PDSCH, and configure the PT‑RS time and frequency density. Set a time density of 1 to place a PT‑RS in every OFDM symbol within the PDSCH allocation, which enables per‑OFDM‑symbol CPE estimation.

    pdsch.EnablePTRS = true;
pdsch.PTRS.TimeDensity = 1;

    Generate DM-RS symbols and indices.

    dmrsInd = nrPDSCHDMRSIndices(carrier,pdsch);
dmrsSym = nrPDSCHDMRS(carrier,pdsch);

    Generate the PT-RS indices and symbols according to the PDSCH configuration.

    ptrsInd = nrPDSCHPTRSIndices(carrier,pdsch);
ptrsSym = nrPDSCHPTRS(carrier,pdsch);

    Generate coded bits and PDSCH symbols using the nrPDSCH function.

    [dataInd,pdschInfo] = nrPDSCHIndices(carrier,pdsch);
codedBits = randi([0 1],pdschInfo.G,1);
pdschSym = nrPDSCH(carrier,pdsch,codedBits);

    Create and populate resource grid with DM-RS, PT-RS, and PDSCH data symbols.

    txGrid = nrResourceGrid(carrier,pdsch.NumLayers);
txGrid(dmrsInd) = dmrsSym;
txGrid(ptrsInd) = ptrsSym;
txGrid(dataInd) = pdschSym;

    Apply OFDM modulation to the transmitted waveform using the nrOFDMModulate function.

    [txWaveform,ofdmInfo] = nrOFDMModulate(carrier,txGrid);

    Model oscillator phase noise using the nrPhaseNoise System object™. Set the carrier frequency to 30 GHz corresponding to FR2.

    Fc = 30e9;   
sr = ofdmInfo.SampleRate;

pnoise = nrPhaseNoise(CarrierFrequency=Fc, ...
    SampleRate=sr,...
    RandomStream="mt19937ar");

    Apply oscillator phase noise to the modulated OFDM waveform.

    rxWaveform = pnoise(txWaveform);

    Demodulate the received waveform using the nrOFDMDemodulate function.

    rxGrid = nrOFDMDemodulate(carrier,rxWaveform);

    Estimate the channel using the nrChannelEstimate function.

    [estChannelGrid,noiseEst] = nrChannelEstimate(carrier,rxGrid,dmrsInd,dmrsSym,CDMLengths=[2 1]);

    Extract and equalize PT‑RS resource elements and obtain PT‑RS symbols.

    [ptrsRx,ptrsHest] = nrExtractResources(ptrsInd,rxGrid,estChannelGrid);
ptrsEqualized = nrEqualizeMMSE(ptrsRx,ptrsHest,noiseEst);

    Estimate the CPE per OFDM symbol using the nrPhaseNoiseEstimate function.

    cpe = nrPhaseNoiseEstimate(carrier,ptrsEqualized,ptrsInd,ptrsSym);
disp(cpe)
        0.0012    0.0151    0.0056   -0.0039    0.0233    0.0018   -0.0087   -0.0055   -0.0025    0.0152    0.0118    0.0053    0.0193    0.0363

    Extract and equalize the PDSCH data symbols from the received grid for CPE compensation.

    [dataRx,dataHest] = nrExtractResources(dataInd,rxGrid,estChannelGrid);
dataEqualized = nrEqualizeMMSE(dataRx,dataHest,noiseEst);

    Calculate the error vector magnitude (EVM) for equalized symbols before CPE compensation using the nrEVM function.

    evm_Before_CPE = nrEVM(pdschSym,dataEqualized)
    evm_Before_CPE = 
0.0426

    Compensate the data symbols for CPE using the nrPhaseNoiseCompensate function.

    dataOut = nrPhaseNoiseCompensate(carrier,dataRx,dataInd,cpe);

    Calculate the EVM for the symbols after CPE compensation, and display the relative EVM improvement.

    evm_After_CPE = nrEVM(pdschSym,dataOut)
    evm_After_CPE = 
0.0369

    relative_EVM_Improvement = 100*(evm_Before_CPE - evm_After_CPE)/evm_Before_CPE
    relative_EVM_Improvement = 
13.4564

    Plot the constellation before CPE compensation. The received symbols show phase rotation because of the phase noise.

    figure
plot(dataEqualized,".",MarkerSize=8)
hold on
plot(pdschSym,"+",MarkerSize=10,LineWidth=1.5)
grid on
title("Equalized Symbols Before CPE Compensation")
xlabel("In-Phase")
ylabel("Quadrature")
legend("Equalized","Transmitted")

    Figure contains an axes object. The axes object with title Equalized Symbols Before CPE Compensation, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Equalized, Transmitted.

    Plot constellation after CPE compensation.

    figure
plot(dataOut,".",MarkerSize=8)
hold on
plot(pdschSym,"+",MarkerSize=10,LineWidth=1.5)
grid on
title("Equalized Symbols After CPE Compensation")
xlabel("In-Phase")
ylabel("Quadrature")
legend("Compensated","Transmitted")

    Figure contains an axes object. The axes object with title Equalized Symbols After CPE Compensation, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Compensated, Transmitted.

    Open Live Script

    Estimate and compensate for CPE in a DFT-s-OFDM physical uplink shared channel (PUSCH) transmission in the presence of phase noise.

    To ensure simulation results are repeatable, initialize the random number generator with a fixed seed. For greater statistical accuracy, run the simulation for multiple times with different seeds and compute the average results.

    rng(1)

    Configure the carrier using an nrCarrierConfig object. Specify a subcarrier spacing of 60 kHz with a transmission bandwidth of 50 MHz operating in frequency range 2 (FR2).

    carrier = nrCarrierConfig(NSizeGrid=66,SubcarrierSpacing=60);

    Configure a transform-precoded PUSCH that occupies the complete carrier and enable PT-RS.

    pusch = nrPUSCHConfig( ...
    PRBSet=0:carrier.NSizeGrid-1, ...
    SymbolAllocation=[0 carrier.SymbolsPerSlot], ...
    TransformPrecoding=true, ...
    Modulation="16QAM", ...
    EnablePTRS=true);
pusch.PTRS = nrPUSCHPTRSConfig(NumPTRSSamples=4,NumPTRSGroups=8);

    Generate the PUSCH resource element indices and PT-RS reference indices, and generate the DM-RS and PT-RS reference symbols.

    [puschInd,puschInfo,ptrsRefInd] = nrPUSCHIndices(carrier,pusch);
dmrsInd = nrPUSCHDMRSIndices(carrier,pusch);
dmrsSym = nrPUSCHDMRS(carrier,pusch);
ptrsRefSym = nrPUSCHPTRS(carrier,pusch);

    Generate the coded bits and PUSCH symbols using the nrPUSCH function. When transform precoding is enabled, nrPUSCH multiplexes the data and PT-RS symbols before transform precoding to form the PUSCH symbol sequence.

    cw = randi([0 1],puschInfo.G,1);
puschSym = nrPUSCH(carrier,pusch,cw);

    Create and populate the resource grid with PUSCH and DM-RS symbols. When transform precoding is enabled, the PUSCH symbols include PT-RS information in addition to data symbols.

    txGrid = nrResourceGrid(carrier);
txGrid(puschInd) = puschSym;
txGrid(dmrsInd) = dmrsSym;

    Perform OFDM modulation on the transmitted waveform.

    [txWaveform,ofdmInfo] = nrOFDMModulate(carrier,txGrid);

    Model oscillator phase noise using the nrPhaseNoise System object™.

    pnoise = nrPhaseNoise( ...
    CarrierFrequency=30e9, ...
    SampleRate=ofdmInfo.SampleRate, ...
    RandomStream="mt19937ar");

    Apply oscillator phase noise to the transmit waveform and demodulate the received waveform.

    rxGrid = nrOFDMDemodulate(carrier,pnoise(txWaveform));

    Estimate the channel using the nrChannelEstimate function.

    [estChannelGrid,noiseEst] = nrChannelEstimate(carrier,rxGrid,dmrsInd,dmrsSym,CDMLengths=pusch.DMRS.CDMLengths);

    Extract and equalize the received PUSCH resource elements.

    [puschRx,puschHest] = nrExtractResources(puschInd,rxGrid,estChannelGrid);
puschEq = nrEqualizeMMSE(puschRx,puschHest,noiseEst);

    Perform transform de-precoding on the equalized PUSCH symbols and extract the PT-RS symbols.

    numPRB = numel(puschInfo.PRBSet);
puschEqDeprecode = nrTransformDeprecode(puschEq,numPRB);
ptrsIndInPUSCH = nrPUSCHPTRSIndices(carrier,pusch);
ptrsEq = puschEqDeprecode(ptrsIndInPUSCH);

    Estimate the CPE per OFDM symbol using the nrPhaseNoiseEstimate function.

    cpe = nrPhaseNoiseEstimate(carrier,ptrsEq,ptrsRefInd,ptrsRefSym)
    cpe = 1×14

    0.0047    0.0152    0.0043   -0.0066    0.0222    0.0003   -0.0285   -0.0128   -0.0100    0.0133    0.0246    0.0119    0.0246    0.0353

    Compensate the data symbols using the nrPhaseNoiseCompensate function.

    dataOut = nrPhaseNoiseCompensate(carrier,puschEq,puschInd,cpe);

    Perform transform de-precoding on the compensated and reference PUSCH symbols. Then, remove the PT-RS locations from the equalized, compensated, and reference PUSCH symbols and use the remaining data symbols for EVM measurement.

    puschEqCompDeprecode = nrTransformDeprecode(dataOut,numPRB);
puschRefDeprecode = nrTransformDeprecode(puschSym,numPRB);

dataEq = puschEqDeprecode;
dataEq(ptrsIndInPUSCH) = [];

dataComp = puschEqCompDeprecode;
dataComp(ptrsIndInPUSCH) = [];

dataRef = puschRefDeprecode;
dataRef(ptrsIndInPUSCH) = [];

    Calculate the EVM for symbols after CPE compensation and display the relative EVM improvement.

    evm_Before_CPE = nrEVM(dataEq,dataRef)
    evm_Before_CPE = 
0.0422

    evm_After_CPE = nrEVM(dataComp,dataRef)
    evm_After_CPE = 
0.0390

    relative_EVM_Improvement = 100*(evm_Before_CPE-evm_After_CPE)/evm_Before_CPE
    relative_EVM_Improvement = 
7.6200

    Input Arguments

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    Carrier configuration parameters for a specific OFDM numerology, specified as an nrCarrierConfig object. This function uses only these object properties of the object:

    Equalized data symbols requiring CPE compensation, specified as an N-by-1 complex-valued vector or an N-by-P complex-valued matrix. N is the number of resource elements carrying data in a slot. P is the number of layers. Layers are independent parallel data streams created by multiple-input multiple-output (MIMO) spatial multiplexing at the physical layer.

    Data Types: double | single
    Complex Number Support: Yes

    Resource‑element indices corresponding to the data symbols in dataSym, specified as an N-by-1 or N-by-P matrix of positive integers. The values of dataInd represent linear indices in the resource grid where the function applies phase correction. The dimensions of dataInd and dataSym must be the same.

    Data Types: double | uint32

    Estimated CPE, specified as a 1-by-L real-valued vector, in radians. L is the number of OFDM symbols in a slot. Each element represents the phase error for the corresponding OFDM symbol, estimated from equalized phase tracking-reference signal (PT-RS) symbols.

    Data Types: double | single

    Output Arguments

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    Phase-compensated data symbols, returned as an N-by-1 complex-valued vector or N-by-P complex-valued matrix. The dimensions of dataOut match the dimensions of dataSym.

    When the data type of dataSym or cpe is single, the data type of dataOut is also single. Otherwise, the data type of dataOut is double.

    Data Types: double | single

    Extended Capabilities

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    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    GPU Code Generation
    Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

    Version History

    Introduced in R2026b

    See Also

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