nrPhaseNoiseEstimate

R2026b

Estimate phase-noise-induced CPE

Since R2026b

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    Syntax

    cpe = nrPhaseNoiseEstimate(carrier,eqSym,refInd,refSym)

    Description

    cpe = nrPhaseNoiseEstimate(carrier,eqSym,refInd,refSym) estimates the phase-noise-induced common phase error (CPE) cpe from equalized symbols. To estimate CPE, the function compares the equalized phase tracking reference signal (PT-RS) symbols eqSym to the known PT-RS symbols refSym at the specified resource element locations refInd within a resource grid defined by the carrier parameters carrier.

    For more information about how the function computes CPE from the equalized PT-RS symbols, see Algorithms.

    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 orthogonal frequency division multiplexing (OFDM) numerology, specified as an nrCarrierConfig object. This function uses only these object properties of the object:

    Equalized PT‑RS symbols, 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 a PT-RS in a slot, and P is the number of reference signal ports.

    Data Types: double | single
    Complex Number Support: Yes

    PT-RS symbol indices, specified as an N-by-1 vector or N-by-P matrix of positive integers. These indices represent PT-RS resource element locations within the resource grid. Each value must be unique. The dimensions of refInd and refSym must be the same.

    Data Types: double | uint32

    Known PT-RS symbols, specified as an N-by-1 complex-valued vector or an N-by-P complex-valued matrix. The dimensions of refInd and refSym must be the same.

    Data Types: double | single
    Complex Number Support: Yes

    Output Arguments

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    Estimated CPE, returned as one of these values. Units are in radians.

    • 1-by-L real-valued vector (Returned when eqSym is of size N-by-1) — Each element represents the phase error for the corresponding OFDM symbol. L is the number of OFDM symbols.

    • 1-by-L-by-P real-valued array (Returned when eqSym is of size N-by-P) — The array contains the CPE for each of the L OFDM symbols in a slot across each of the P PT-RS ports, where cpe(1,i, P) represents the phase error for the ith OFDM symbol on port P.

    When the data type of eqSym or refSym is single, the data type of cpe is also single. Otherwise, the data type of cpe is double.

    Data Types: double | single

    Algorithms

    To estimate CPE, the function executes these steps:

    1. Estimate CPE per OFDM symbol per port:

      1. Compute the complex correlation value for each PT‑RS subcarrier by multiplying the corresponding equalized PT‑RS symbol with the complex conjugate of the known PT‑RS symbol.

      2. Average the complex correlation value across all PT‑RS subcarriers within the OFDM symbol.

      3. Extract the phase of the averaged result to obtain a single CPE estimate for the OFDM symbol.

    2. Determine CPE for OFDM symbols that do not contain PT‑RS based on the available PT‑RS symbol locations. If at least two OFDM symbols contain a PT‑RS, the function computes CPE at the missing OFDM symbol locations by interpolating between adjacent PT‑RS OFDM symbols. The function sets CPE to zero for OFDM symbols that lie outside the PT‑RS symbol range.

    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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