nrSpectralFlatness

R2026b

Measure EVM equalizer spectral flatness for 5G NR waveform

Since R2026b

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Syntax

[metrics,info] = nrSpectralFlatness(carrier,channel,eqGrid,refGrid,Hest)

[metrics,info] = nrSpectralFlatness(carrier,channel,rxGrid)

[metrics,info] = nrSpectralFlatness(___,Name=Value)

Description

[metrics,info] = nrSpectralFlatness(carrier,channel,eqGrid,refGrid,Hest) measures the error vector magnitude (EVM) equalizer spectral flatness for uplink allocations according to 3GPP TS 38.101-1 and TS 38.101-2.

The function evaluates the peak-to-peak ripple of the equalizer coefficients independently across Range 1 and Range 2 frequency regions defined by carrier and channel. It derives EVM equalizer coefficients using least squares (LS) estimation from the equalized symbols grid eqGrid and reference symbols grid refGrid. Then, the function scales these derived coefficients by zero-forcing (ZF) equalizer weights, computed from the channel estimate Hest to account for channel-dependent layer gain.

The function returns the ripple values and pass or fail status in metrics. It returns the equalizer coefficients and range indices in info. To use this syntax you must have equalized symbols, reference symbols, and a channel estimate.

example

[metrics,info] = nrSpectralFlatness(carrier,channel,rxGrid) measures EVM equalizer spectral flatness for uplink allocations from the received grid rxGrid. The function performs channel estimation, using demodulation reference signal (DM-RS) symbols from rxGrid, and constructs equalized symbols using ZF equalization. It reconstructs the transmitted data symbols from the equalized data symbols. The function uses the reconstructed symbols as reference symbols. Then, it derives EVM equalizer coefficients using LS estimation from the equalized and reference symbols.

example

[metrics,info] = nrSpectralFlatness(___,Name=Value) specifies options using one or more name-value arguments in addition to any combination of input arguments from the previous syntaxes.

example

Examples

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Measure EVM and Spectral Flatness for Multislot 5G NR PUSCH Waveform

Open Live Script

Calculate spectral flatness metrics from an equalized grid, reference grid, and channel estimate. You generate a 5G NR physical uplink shared channel (PUSCH) waveform and add noise to the waveform, performs OFDM demodulation and estimate the channel using demodulation reference signal (DM-RS) symbols. To equalize the received grid and reconstruct reference symbols, you use hard decisions.

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

rng(1);

Specify the subcarrier spacing using an nrSCSCarrierConfig object with a resource grid size of 200 resource blocks.

carrierObj = nrSCSCarrierConfig;
carrierObj.NSizeGrid = 200;

Specify the bandwidth part configuration with a 20-RB offset from the carrier grid start and a size of 30 resource blocks.

bwpObj = nrWavegenBWPConfig;
bwpObj.SubcarrierSpacing = 15;
bwpObj.NStartBWP = carrierObj.NStartGrid+20;
bwpObj.NSizeBWP = 30;

Create a PUSCH configuration for 5G uplink waveform generation that allocates all 30 PRBs in the bandwidth part.

puschObj = nrWavegenPUSCHConfig;
puschObj.PRBSet = 0:29;
puschObj.NumLayers = 2;

Configure an uplink carrier for FR1 with a 40 MHz channel bandwidth. Specify 20 subframes to generate a multi-slot waveform for evaluation across multiple measurement intervals.

ChannelBW = 40;
NSFrames = 20;
cfgUL = nrULCarrierConfig( ...
    FrequencyRange="FR1", ...
    ChannelBandwidth=ChannelBW, ...
    NumSubframes=NSFrames, ...
    SCSCarriers={carrierObj}, ...
    BandwidthParts={bwpObj}, ...
    PUSCH={puschObj});

Generate the uplink waveform using the nrWaveformGenerator function.

[waveform,waveInfo] = nrWaveformGenerator(cfgUL);

Add additive white Gaussian noise (AWGN) to the transmitted waveform to simulate channel noise.

SNRdB = 40;
SNR = 10^(SNRdB/10);
R = size(waveform,2);
N0 = 1/sqrt(2*R*double(waveInfo.ResourceGrids.Info.Nfft)*SNR);
noise = N0*complex(randn(size(waveform)),randn(size(waveform)));
waveform = waveform + noise;

Create a configuration for a PUSCH for receiver processing using parameters from the PUSCH configuration for waveform generation.

pusch = nrPUSCHConfig;
pusch.NSizeBWP = bwpObj.NSizeBWP;
pusch.NStartBWP = bwpObj.NStartBWP;
pusch.Modulation = puschObj.Modulation;
pusch.NumLayers = puschObj.NumLayers;
pusch.MappingType = puschObj.MappingType;
pusch.SymbolAllocation = puschObj.SymbolAllocation;
pusch.PRBSet = puschObj.PRBSet;
pusch.NumAntennaPorts = puschObj.NumAntennaPorts;
pusch.DMRS = puschObj.DMRS;

Create a carrier configuration for OFDM demodulation and channel estimation using the same carrier and BWP settings used to generate the uplink waveform.

carrier = nrCarrierConfig;
carrier.NCellID = cfgUL.NCellID;
carrier.NSizeGrid = carrierObj.NSizeGrid;
carrier.NStartGrid = carrierObj.NStartGrid;
carrier.SubcarrierSpacing = carrierObj.SubcarrierSpacing;
carrier.CyclicPrefix = bwpObj.CyclicPrefix;
carrier.NSlot = 0;

Perform OFDM demodulation on the received waveform using the nrOFDMDemodulate function. Set the cyclic prefix fraction to 0.5 to align FFT timing to the middle of the cyclic prefix.

samplerate = waveInfo.ResourceGrids.Info.SampleRate;
carrierFreq = cfgUL.CarrierFrequency;

rxGrid = nrOFDMDemodulate(carrier,waveform, ...
    CyclicPrefixFraction=0.5, ...
    SampleRate=samplerate, ...
    CarrierFrequency=carrierFreq);

Calculate the number of subcarriers, OFDM symbols per slot, and transmission layers from the carrier and channel configuration.

K = carrier.NSizeGrid*12;
L = carrier.SymbolsPerSlot;
P = pusch.NumLayers;
numSlots = NSFrames*carrier.SlotsPerSubframe;

Create the DM-RS reference grid for channel estimation. Extract the DM-RS symbols and DM-RS indices using the nrPUSCHDMRS and nrPUSCHDMRSIndices function respectively.

refGridDMRS = zeros(K,L*numSlots,P);

for nSlot = 0:numSlots-1
    carrier.NSlot = nSlot;
    dmrsInd = nrPUSCHDMRSIndices(carrier,pusch);
    dmrsSym = nrPUSCHDMRS(carrier,pusch);
    slotGrid = nrResourceGrid(carrier,P);
    slotGrid(dmrsInd) = dmrsSym;
    refGridDMRS(:,nSlot*L+(1:L),:) = slotGrid;
end

Perform channel estimation using the received grid and DM-RS reference grid.

[H,nVar] = nrChannelEstimate(rxGrid,refGridDMRS);

Perform equalization on the received grid using nrEqualizeMMSE.

H1 = reshape(H,[K*L*numSlots, R, P]);
rxFlat = reshape(rxGrid,[K*L*numSlots, R]);
eqFlat = nrEqualizeMMSE(rxFlat, H1, nVar);
eqGrid = reshape(eqFlat,[K,L*numSlots, P]);

Construct the reference grid by performing hard slicing on the equalized symbols. Demodulate and remodulate the equalized PUSCH symbols to obtain reference symbols for each slot.

refGrid = zeros(K,L*numSlots,P);

for nSlot = 0:numSlots-1
    carrier.NSlot = nSlot;
    slotSymbols = nSlot*L + (1:L);

    dataInd = nrPUSCHIndices(carrier,pusch);
    dmrsInd = nrPUSCHDMRSIndices(carrier,pusch);
    dmrsSym = nrPUSCHDMRS(carrier,pusch);

    eqSlot = eqGrid(:,slotSymbols,:);
    refSlot = nrResourceGrid(carrier,P);

    dataSymbols = eqSlot(dataInd);
    refBits = nrSymbolDemodulate(dataSymbols(:),pusch.Modulation,DecisionType="hard");
    ref = nrSymbolModulate(refBits,pusch.Modulation);
    refSlot(dataInd) = ref;
    refSlot(dmrsInd) = dmrsSym;
    refGrid(:,slotSymbols,:) = refSlot;
end

Measure EVM and spectral flatness for each slot. Extract the symbols corresponding to each slot, and then compute the EVM and spectral flatness for that slot using the nrEVM and nrSpectralFlatness function, respectively.

evmArray = zeros(numSlots,1);
metricsArray = cell(numSlots,1);
infoArray = cell(numSlots,1);

for nSlot = 0:numSlots-1
    carrier.NSlot = nSlot;
    slotSymbols = nSlot*L + (1:L);
    EVM = nrEVM(eqGrid(:,slotSymbols,:),refGrid(:,slotSymbols,:));
    evmArray(nSlot+1) = EVM;
    [metrics,info] = nrSpectralFlatness(carrier,pusch, ...
        eqGrid(:,slotSymbols,:), ...
        refGrid(:,slotSymbols,:), ...
        H(:,slotSymbols,:,:), ...
        k0=0,FrequencyRange=cfgUL.FrequencyRange, ...
        CarrierFrequency=cfgUL.CarrierFrequency, ...
        ChannelBandwidth=cfgUL.ChannelBandwidth);

    metricsArray{nSlot+1} = metrics;
    infoArray{nSlot+1} = info;
end

Display the EVM and spectral flatness results for first slot.

EVM = evmArray(1)

EVM = 
0.4237

metrics = metricsArray{1}

metrics = struct with fields:
     RP1: [0.2868 0.3616]
     RP2: [0×2 double]
    RP12: [0×2 double]
    RP21: [0×2 double]
    Pass: 1

info = infoArray{1}

info = struct with fields:
    EqualizerCoefficients: [2400×2 double]
            Range1Indices: [360×1 uint32]
            Range2Indices: [0×1 uint32]

Measure Spectral Flatness from Received Grid for PUSCH Waveform

Open Live Script

rng(1);

Specify the subcarrier spacing configuration with 30 kHz and a resource grid size of 51 resource blocks.

carrierObj = nrSCSCarrierConfig;
carrierObj.NSizeGrid = 51;
carrierObj.SubcarrierSpacing = 30;

Specify a bandwidth part configuration that spans the full carrier grid with 30 kHz subcarrier spacing.

bwpObj = nrWavegenBWPConfig;
bwpObj.SubcarrierSpacing = 30;
bwpObj.NStartBWP = carrierObj.NStartGrid;
bwpObj.NSizeBWP = carrierObj.NSizeGrid;

Create a PUSCH configuration for 5G uplink waveform generation with 16-QAM modulation that allocates all 51 PRBs on a single spatial layer.

puschObj = nrWavegenPUSCHConfig;
puschObj.PRBSet = 0:50;
puschObj.NumLayers = 1;
puschObj.Modulation = "16QAM";

Create an uplink carrier configuration for FR1 with a 20 MHz channel bandwidth. Specify 10 subframes to generate a multi-slot waveform.

ChannelBW = 20;
NSFrames = 10;
cfgUL = nrULCarrierConfig( ...
    FrequencyRange="FR1", ...
    ChannelBandwidth=ChannelBW, ...
    NumSubframes=NSFrames, ...
    SCSCarriers={carrierObj}, ...
    BandwidthParts={bwpObj}, ...
    PUSCH={puschObj});

Generate the uplink waveform using nrWaveformGenerator.

[waveform,waveInfo] = nrWaveformGenerator(cfgUL);

Add AWGN to the transmitted waveform to simulate channel noise.

SNRdB = 40;
SNR = 10^(SNRdB/10);
R = size(waveform,2);
N0 = 1/sqrt(2.0*R*double(waveInfo.ResourceGrids.Info.Nfft)*SNR);
noise = N0*complex(randn(size(waveform)),randn(size(waveform)));
waveform = waveform + noise;

Create a configuration for a PUSCH for receiver processing using parameters from the PUSCH configuration for waveform generation. The nrSpectralFlatness function uses these PUSCH properties to generate DM-RS symbols for channel estimation and determine the allocated resource elements on which it performs equalization.

pusch = nrPUSCHConfig;
pusch.NSizeBWP = bwpObj.NSizeBWP;
pusch.NStartBWP = bwpObj.NStartBWP;
pusch.Modulation = puschObj.Modulation;
pusch.NumLayers = puschObj.NumLayers;
pusch.MappingType = puschObj.MappingType;
pusch.SymbolAllocation = puschObj.SymbolAllocation;
pusch.PRBSet = puschObj.PRBSet;
pusch.NumAntennaPorts = puschObj.NumAntennaPorts;
pusch.DMRS = puschObj.DMRS;

Create a carrier configuration.

carrier = nrCarrierConfig;
carrier.NCellID = cfgUL.NCellID;
carrier.NSizeGrid = carrierObj.NSizeGrid;
carrier.NStartGrid = carrierObj.NStartGrid;
carrier.SubcarrierSpacing = carrierObj.SubcarrierSpacing;
carrier.CyclicPrefix = bwpObj.CyclicPrefix;
carrier.NSlot = 0;

Perform OFDM demodulation with FFT timing aligned to the middle of the cyclic prefix.

rxGrid = nrOFDMDemodulate(carrier,waveform, ...
    CyclicPrefixFraction=0.5, ...
    SampleRate=waveInfo.ResourceGrids.Info.SampleRate, ...
    CarrierFrequency=cfgUL.CarrierFrequency);

Calculate the total number of slots in the received grid.

numSlots = NSFrames*carrier.SlotsPerSubframe;

Measure spectral flatness for each slot using the nrSpectralFlatness function.

metricsArray = cell(numSlots,1);
infoArray = cell(numSlots,1);

for nSlot = 0:numSlots-1
    carrier.NSlot = nSlot;
    slotSymbols = nSlot*carrier.SymbolsPerSlot + (1:carrier.SymbolsPerSlot);
    [metrics,info] = nrSpectralFlatness(carrier,pusch, ...
        rxGrid(:,slotSymbols,:), ...
        FrequencyRange=cfgUL.FrequencyRange, ...
        ChannelBandwidth=cfgUL.ChannelBandwidth);
    metricsArray{nSlot+1} = metrics;
    infoArray{nSlot+1} = info;
end

Display the spectral flatness results for the first slot.

metrics = metricsArray{1}

metrics = struct with fields:
     RP1: 0.1047
     RP2: 0.1031
    RP12: 0.0969
    RP21: 0.1109
    Pass: 1

info = infoArray{1}

info = struct with fields:
    EqualizerCoefficients: [612×1 double]
            Range1Indices: [467×1 uint32]
            Range2Indices: [145×1 uint32]

Measure Spectral Flatness for pi/2-BPSK PUSCH Waveform

Open Live Script

Measure EVM equalizer spectral flatness for a pi/2-BPSK PUSCH waveform. Derive the impulse response from the equalizer coefficients according to TS 38.521-1 Annex E.4.4.2. Then, verify the requirements specified in TS 38.101-1 Section 6.4.2.4.

Note: The example does not model or apply an additional transmitter spectral shaping filter.

rng(1);

Specify a subcarrier spacing configuration with 15 kHz and a resource grid size of 200 resource blocks.

carrier = nrCarrierConfig;
carrier.NSizeGrid = 200;
carrier.NStartGrid = 0;
carrier.SubcarrierSpacing = 15;

Create a configuration for a PUSCH that uses pi/2-BPSK modulation. Enable transform precoding for DFT-s-OFDM.

pusch = nrPUSCHConfig;
pusch.NSizeBWP = 30;
pusch.NStartBWP = 20;
pusch.Modulation = "pi/2-BPSK";
pusch.PRBSet = 0:pusch.NSizeBWP-1;
pusch.TransformPrecoding = true;

Calculate the PUSCH data indices.

[puschIndices,puschInfo] = nrPUSCHIndices(carrier,pusch);

Define a random codeword using the bit capacity of the PUSCH configuration.

cw = randi([0 1],puschInfo.G,1);

Calculate, data symbols, DM-RS indices, and DM-RS symbols for your PUSCH configuration.

puschSym = nrPUSCH(carrier,pusch,cw);
puschDMRSInd = nrPUSCHDMRSIndices(carrier,pusch);
puschDMRSSym = nrPUSCHDMRS(carrier,pusch);

Construct the transmitted grid.

txGrid = nrResourceGrid(carrier);
txGrid(puschIndices) = puschSym;
txGrid(puschDMRSInd) = puschDMRSSym;

OFDM modulate the grid to generate the time-domain waveform.

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

Add noise to the transmit waveform.

evmPercent = 2.0;
noise = evmPercent/(100*sqrt(winfo.Nfft))*randn(size(txWaveform),like=1i);
rxWaveform = txWaveform + noise;

Perform OFDM demodulation with FFT timing aligned to the middle of the cyclic prefix.

rxGrid = nrOFDMDemodulate(carrier,rxWaveform);

Use the DM-RS symbols to create a reference grid to use for channel estimation.

refGrid = zeros(size(rxGrid));
refGrid(puschDMRSInd) = puschDMRSSym;

Calculate the channel estimate using the received grid and reference grid.

[H,nVar] = nrChannelEstimate(rxGrid,refGrid,CyclicPrefix = carrier.CyclicPrefix,CDMLengths = pusch.DMRS.CDMLengths);
[rxGrid,refGrid,H] = nrExtractResources(1:numel(rxGrid),rxGrid,refGrid,H);

Perform channel equalization on the extracted PUSCH resource grids.

eqGrid = nrEqualizeMMSE(rxGrid,H,nVar);

Perform hard-decision on the equalized PUSCH symbols to generate the reference symbols.

refBits = nrSymbolDemodulate(eqGrid(puschIndices),pusch.Modulation,DecisionType="hard");
ref = nrSymbolModulate(refBits,pusch.Modulation);

Create the reference grid by placing the reference data symbols on the allocated PUSCH resource elements.

refGrid(puschIndices) = ref;

Calculate the spectral flatness metric using the nrSpectralFlatness function, additionally returning the equalizer coefficients.

[metrics,info] = nrSpectralFlatness(carrier,pusch,eqGrid,refGrid,H);

For pi/2-BPSK, the equalizer coefficients capture the combined frequency response of the transmitter, including the spectral shaping filter. Following TS 38.521-1 Annex E.4.4.2, derive the spectral shaping filter impulse response from the equalizer coefficients. Extract the equalizer coefficients over the allocated bandwidth part and compute the inverse frequency response. Apply an inverse FFT to obtain the corresponding impulse response.

M = pusch.NSizeBWP*12; 
bwpSCs = (pusch.NStartBWP)*12 + (1:M);
EC_f = info.EqualizerCoefficients;
EC_alloc = EC_f(bwpSCs,:);
H_inv = 1./EC_alloc;
a_tau = ifft(H_inv,M);

Normalize the impulse response with respect to its zero-delay tap.

a_tilde = a_tau/a_tau(1);

Verify that the normalized impulse response satisfies the spectral shaping filter requirements defined in TS 38.101-1 Section 6.4.2.4. The peak magnitude must occur at the zero-delay tap. The magnitude of each remaining tap must be at least 15 dB below the peak.

peakAtZero = all(abs(a_tilde(1)) >= abs(a_tilde(2:end)))

peakAtZero = logical
   1

a_tilde_dB = 20*log10(abs(a_tilde));
sidelobeLevels = a_tilde_dB(2:end-1); 
below15dB = all(sidelobeLevels < -15)

below15dB = logical
   1

Input Arguments

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`carrier` — Carrier configuration parameters
`nrCarrierConfig` object

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

`channel` — Physical uplink shared channel configuration
`nrPUSCHConfig` object

Physical uplink shared channel configuration, specified as an nrPUSCHConfig object. This function uses only these properties of the object:

`rxGrid` — Received OFDM symbols grid
K-by-L-by-R complex-valued array

Received OFDM symbols grid, specified as a K-by-L-by-R complex-valued array.

K is the number of subcarriers, equal to carrier.NSizeGrid*12.
L is the number of OFDM symbols per slot.
R is the number of receive antennas.

Data Types: double | single
Complex Number Support: Yes

`Hest` — Estimated channel information
K-by-L-by-R-by-P complex-valued array | N_RE-by-R-by-P complex-valued array

Estimated channel information, specified as a K-by-L-by-R-by-P complex-valued array or N_RE-by-R-by-P complex-valued array.

K is the number of subcarriers, equal to carrier.NSizeGrid*12.
L is the number of OFDM symbols per slot.
N_RE is the number of resource elements, equal to K × L.
R is the number of receive antennas.
P is the number of transmitted layers.

Data Types: double | single
Complex Number Support: Yes

`refGrid` — Reference symbols grid
K-by-L-by-P complex-valued array | N_RE-by-P complex-valued matrix

Reference symbols grid, specified as a K-by-L-by-P complex-valued array or an N_RE-by-P complex-valued matrix. The grid must not exceed one slot duration.

K is the number of subcarriers, equal to carrier.NSizeGrid*12.
L is the number of OFDM symbols per slot.
N_RE is the number of resource elements, equal to K × L.
P is the number of transmitted layers.

Note

The dimensions of the eqGrid and refGrid arguments must be the same.

Data Types: double | single
Complex Number Support: Yes

`eqGrid` — Equalized OFDM symbols grid
K-by-L-by-P complex-valued array | N_RE-by-P complex-valued matrix

Equalized OFDM symbols grid, specified as a K-by-L-by-P complex-valued array or an N_RE-by-P complex-valued matrix.

K is the number of subcarriers, equal to carrier.NSizeGrid*12.
L is the number of OFDM symbols per slot.
N_RE is the number of resource elements, equal to K × L.
P is the number of transmitted layers.

Note

The dimensions of the eqGrid and refGrid arguments must be the same.

Data Types: double | single
Complex Number Support: Yes

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: nrSpectralFlatness(carrier,channel,rxGrid,FrequencyRange="FR1",ChannelBandwidth=10) specifies to use NR frequency range 1 and a channel bandwidth of 10 MHz.

`FrequencyRange` — NR frequency range
`"FR1"` (default) | `"FR2"`

NR frequency range, specified as one of these values.

"FR1" — Frequency range 1 (FR1) that corresponds to frequencies from 410 MHz to 7.125 GHz.
"FR2" — Frequency range 2 (FR2) that corresponds to frequencies from 24.25 GHz to 52.6 GHz (FR2-1) and from 52.6 GHz to 71 GHz (FR2-2).

Data Types: char | string

`k0` — Frequency offset index in subcarriers relative to Point A
`0` (default) | nonnegative integer

Frequency offset index in subcarriers relative to Point A, specified as a nonnegative integer. Point A defines the common reference point for resource block grids. The function defines carrier positions relative to Point A. The function uses this offset to determine absolute frequency positions for Range 1 and Range 2 boundaries.

Example: k0=10, specifies a frequency offset of 10 subcarriers from Point A.

Data Types: double | single

`ChannelBandwidth` — Channel bandwidth in MHz
`[]` (default) | positive scalar

Channel bandwidth in MHz, specified as a positive scalar. Standard channel bandwidths defined in TS 38.101-1 and TS 38.101-2 are:

FR1 — 3, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, or 100
FR2 — 50, 100, 200, 400, 800, 1600, or 2000

The function accepts any positive channel bandwidth value.

When you set this argument to [], the function derives the channel bandwidth from carrier.NSizeGrid and carrier.SubcarrierSpacing.

Data Types: double | single

`BandEdges` — Frequencies of lower and upper edges of operating band in MHz
`[]` (default) | two-element vector

Frequencies of lower and upper edge of operating band in MHz, specified as a two-element vector of the form [F_{UL_Low} F_{UL_High}], as defined in Table 5.5-1 of TS 38.101-1.

When you specify band edges, the function calculates the ChannelBandwidth as F_{UL_High} – F_{UL_Low} and ignores the ChannelBandwidth argument. If you specify this argument, you must also specify the CarrierFrequency argument.

Dependencies

To use this name-value argument, you must specify the FrequencyRange argument as "FR1".

Data Types: double | single

`CarrierFrequency` — Carrier frequency
`0` (default) | nonnegative scalar

Carrier frequency, specified as a nonnegative scalar. For FR1, when you specify BandEdges, the CarrierFrequency value determines the location of the carrier within the operating band. When you specify BandEdges, you must also specify CarrierFrequency as a frequency within the bounds specified by BandEdges. Units are in Hz.

Data Types: double | single

`TxDirectCurrentLocation` — DC subcarrier location for carrier
`[]` (default) | nonnegative integer

DC subcarrier location for the carrier, specified as one of these values:

[] — The function includes all subcarriers in the measurement.
Nonnegative integer — The function excludes the subcarrier at the specified location from the spectral flatness measurement.

You can use this argument when the transmitter has a DC offset that affects the measurement.

Example: TxDirectCurrentLocation=312 excludes subcarrier 312 from the measurement.

Dependencies

To use this name-value argument, you must specify the rxGrid argument.

Data Types: double | single

`TestTolerance` — Tolerance limit for ripple measurements
`0` (default) | nonnegative scalar

Tolerance limit for the ripple measurements in dB, specified as a nonnegative scalar. This value defines how much the measured ripple can exceed the limit defined by TS 38.101-1 and 38.101-2 before the function reports a failure. The function reports a failure only when the measured ripple exceeds the defined limit by more than this value. Units are in dB.

Example: TestTolerance=0.5 adds 0.5 dB margin to all ripple limits.

Data Types: double | single

`IsExtremeCondition` — Flag for extreme measurement conditions
`false` or `0` (default) | `true` or `1`

Flag for extreme measurement conditions, specified as a numeric or logical 1 (true) or 0 (false).

false — Normal measurement conditions. The function applies the standard ripple limits for normal conditions as defined in TS 38.521-1 and TS 38.521-2.
true — Extreme measurement conditions. The function applies the relaxed ripple limits for extreme conditions as defined in TS 38.521-1 and TS 38.521-2.

Data Types: logical

`X` — Frequency regions that belong to Range 1 and Range 2
`[]` (default) | positive scalar

Frequency regions that belong to Range 1 and Range 2, specified as a positive scalar. This argument partitions the carrier bandwidth into Range 1 and Range 2. Units are in MHz.

For FR1 — Range 1 consists of subcarriers that are at least X MHz away from both band edges. Range 2 consists of subcarriers within X MHz of either band edge.
For FR2 — Range 1 consists of subcarriers within X MHz of the channel center. Range 2 consists of subcarriers outside this region.
For pi/2‑BPSK modulation — Range 1 consists of subcarriers within X MHz of the bandwidth part (BWP) center. Range 2 consists of subcarriers outside this region.

When you set this argument to [], the function determines X from the specified frequency range and modulation scheme:

FR1 — The function sets X to 3 MHz. When IsExtremeCondition is true, the function sets X to 5 MHz.
FR2 — The function sets X to 30% of the ChannelBandwidth value, measured from the channel center.
pi/2-BPSK — The function sets X to 25% of the BWP bandwidth, measured from the BWP center.

Example: nrSpectralFlatness(carrier,channel,rxGrid,FrequencyRange="FR1",X=5) specifies that subcarriers within 5 MHz of either band edge belong to Range 2, and the remaining subcarriers belong to Range 1.

Data Types: double | single

Output Arguments

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`metrics` — Spectral flatness metrics
structure

Spectral flatness metrics, returned as a structure containing these fields:

Field	Value	Description
`RP1`	Numeric vector of size 1-by-P	Maximum peak-to-peak ripple of equalizer coefficients in Range 1, in dB.
`RP2`	Numeric vector of size 1-by-P	Maximum peak-to-peak ripple of equalizer coefficients in Range 2, in dB.
`RP12`	Numeric vector of size 1-by-P	Relative difference between the maximum equalizer coefficient in Range 1 and the minimum equalizer coefficient in Range 2, in dB.
`RP21`	Numeric vector of size 1-by-P	Relative difference between the maximum equalizer coefficient in Range 2 and the minimum equalizer coefficient in Range 1, in dB.
`Pass`	Logical scalar	Logical output that indicates whether the spectral flatness requirements are satisfied across all layers.

The function returns Pass as true when all ripple values satisfy specification limits, including TestTolerance.

Data Types: Struct

`info` — Spectral flatness processing information
structure

Spectral flatness processing information, returned as a structure containing these fields:

Field	Value	Description
`EqualizerCoefficients`	Complex-valued matrix of size K-by-P	Equalizer coefficients per subcarrier per layer. For `pi/2`-BPSK modulation, use these coefficients to evaluate the shaping filter response.
`Range1Indices`	Column vector	Indices of subcarriers that fall into Range 1.
`Range2Indices`	Column vector	Indices of subcarriers that fall into Range 2.

Data Types: struct

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EVM Equalizer Spectral Flatness

EVM equalizer spectral flatness quantifies the frequency response variation of a UE transmitter across its allocated uplink bandwidth. An ideal transmitter produces equalizer coefficients of equal magnitude at every subcarrier. In practice, transmitters introduce variation due to analog filter passband ripple, DAC sinc roll-off, power amplifier gain slope, and I/Q imbalance, causing the equalizer coefficient magnitude to vary across subcarriers. The EVM equalizer spectral flatness measures this variation as the maximum peak-to-peak ripple of the equalizer coefficients (in dB) across the allocated uplink block.

The nrSpectralFlatness function derives equalizer coefficients using least squares (LS) estimation over the allocated uplink bandwidth for each subcarrier k and layer p independently using this equation:

$E C_{p} (f) = \frac{\sum_{t = 0}^{13} N S_{p} (f, t) * N S_{p} (f, t)}{\sum_{t = 0}^{13} M S_{p} (f, t) * N S_{p} (f, t)}$

where MS is the measured symbols from the equalized grid, NS is the nominal symbols from the reference grid, and "*" denotes complex conjugation. f denotes the subcarrier index and t denotes the OFDM symbol index.

The function partitions the allocated bandwidth into Range 1 and Range 2, then evaluates ripple independently in each range.

The partitioning depends on frequency range and modulation:

FR1 — Range 2 consists of subcarriers within X MHz of either operating-band edge, F_{UL_Low} or F_{UL_High}. Range 1 consists of subcarriers between F_{UL_Low} + X and F_{UL_High} – X. The default value of X is 3 MHz for normal conditions and 5 MHz for extreme conditions.
For the FR1 limits shown in the figure, ripple limit values outside the parentheses apply under normal conditions and values inside the parentheses apply under extreme conditions. For example, 8(12) dB_p-p indicates an RP2 limit of 8 dB peak-to-peak under normal conditions and 12 dB peak-to-peak under extreme conditions.
The figure shows only one side of the operating band. The spectral flatness distribution on the opposite side of the operating band is symmetric about the operating-band center frequency.
FR2 — The frequency axis folds about the carrier center frequency. Each subcarrier maps to the axis by its absolute distance from the center, |F_{UL_Meas} — F_center|. Range 1 contains subcarriers within X MHz of the carrier center frequency, including X MHz. Range 2 contains the remaining subcarriers up to the band edges. By default, X is 30% of the channel bandwidth.
The figure shows only one side of the carrier. The spectral flatness distribution on the opposite side of the carrier is symmetric about the carrier center frequency.
pi/2-BPSK — The frequency axis folds about the BWP center frequency. Each subcarrier maps to the axis by its absolute distance from the BWP center frequency. Range 1 consists of subcarriers within X MHz of the BWP center frequency. Range 2 consists of the remaining subcarriers up to the BWP edges. By default, X is 25% of the BWP bandwidth. According to TS 38.101‑1 Table 6.4.2.4.1‑1, the peak-to-peak limit is 6 dB for Range 1 and 14 dB for Range 2.
The figure shows only one side of the BWP. The spectral flatness distribution on the opposite side of the BWP is symmetric about the BWP center frequency.

Spectral Flatness for Multiple Layers

For single-layer transmission, the spectral flatness is the peak-to-peak ripple of |EC_p(f)|, in dB. For uplink MIMO transmission, ZF equalization separates the layers using the pseudo inverse of the effective channel matrix:

$G_{Z F} (f) = \tilde{H} {(f)}^{- 1}$

where $\tilde{H} {(f)}^{- 1}$ is the P-by-R effective channel matrix at subcarrier f, averaged over OFDM symbols. The p^th row of G_ZF(f) specifies how the R received antenna signals are combined to recover layer p. Because the channel is frequency-selective, this row has different magnitudes at different subcarriers. The LS coefficient EC_p(f) therefore reflects both the transmitter frequency response and the frequency-dependent ZF gain. To extract only the transmitter contribution, the function multiplies |EC_p(f)| by the Euclidean norm of the pth row of G_ZF(f), producing the spectral flatness coefficient c_p:

For 2-Layer uplink MIMO — $c_{p} = | E C_{p} (f) | \times \sqrt{{| g_{p, 0} |}^{2} + {| g_{p, 1} |}^{2}}$
For 4-Layer uplink MIMO — $c_{p} = | E C_{p} (f) | \times \sqrt{{| g_{p, 0} |}^{2} + {| g_{p, 1} |}^{2} + {| g_{p, 2} |}^{2} + {| g_{p, 3} |}^{2}}$

where g_p,r are elements of the pth row of G_ZF, and r is the receive antenna index.

3GPP TS 38.101-1 Annex F.10 defines this ZF scaling procedure for uplink MIMO. For single-layer transmission, Annex F.4 defines the spectral flatness without separate ZF scaling. This function applies G_ZF uniformly to both cases, treating single-layer as a 1-by-1 MIMO configuration. The results are equivalent because G_ZF reduces to a scalar inverse for a single receive antenna and a single transmitted layer.

References

[1] 3GPP TS 38.101-1. “NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

[2] 3GPP TS 38.101-2. “NR; User Equipment (UE) radio transmission and reception; Part 2: Range 2 Standalone.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

[3] 3GPP TS 38.521-1. “NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

[4] 3GPP TS 38.521-2. “NR; User Equipment (UE) radio transmission and reception; Part 2: Range 2 Standalone.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

nrSpectralFlatness

Syntax

Description

Examples

Measure EVM and Spectral Flatness for Multislot 5G NR PUSCH Waveform

Measure Spectral Flatness from Received Grid for PUSCH Waveform

Measure Spectral Flatness for pi/2-BPSK PUSCH Waveform

Input Arguments

carrier — Carrier configuration parameters nrCarrierConfig object

channel — Physical uplink shared channel configuration nrPUSCHConfig object

rxGrid — Received OFDM symbols grid K-by-L-by-R complex-valued array

Hest — Estimated channel information K-by-L-by-R-by-P complex-valued array | NRE-by-R-by-P complex-valued array

refGrid — Reference symbols grid K-by-L-by-P complex-valued array | NRE-by-P complex-valued matrix

eqGrid — Equalized OFDM symbols grid K-by-L-by-P complex-valued array | NRE-by-P complex-valued matrix

Name-Value Arguments

FrequencyRange — NR frequency range "FR1" (default) | "FR2"

k0 — Frequency offset index in subcarriers relative to Point A 0 (default) | nonnegative integer

ChannelBandwidth — Channel bandwidth in MHz [] (default) | positive scalar

BandEdges — Frequencies of lower and upper edges of operating band in MHz [] (default) | two-element vector

Dependencies

CarrierFrequency — Carrier frequency 0 (default) | nonnegative scalar

TxDirectCurrentLocation — DC subcarrier location for carrier [] (default) | nonnegative integer

Dependencies

TestTolerance — Tolerance limit for ripple measurements 0 (default) | nonnegative scalar

IsExtremeCondition — Flag for extreme measurement conditions false or 0 (default) | true or 1

X — Frequency regions that belong to Range 1 and Range 2 [] (default) | positive scalar

Output Arguments

metrics — Spectral flatness metrics structure

info — Spectral flatness processing information structure

More About

EVM Equalizer Spectral Flatness

Spectral Flatness for Multiple Layers

References

Extended Capabilities

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

See Also

Functions

Objects

Topics

`carrier` — Carrier configuration parameters
`nrCarrierConfig` object

`channel` — Physical uplink shared channel configuration
`nrPUSCHConfig` object

`rxGrid` — Received OFDM symbols grid
K-by-L-by-R complex-valued array

`Hest` — Estimated channel information
K-by-L-by-R-by-P complex-valued array | N_RE-by-R-by-P complex-valued array

`refGrid` — Reference symbols grid
K-by-L-by-P complex-valued array | N_RE-by-P complex-valued matrix

`eqGrid` — Equalized OFDM symbols grid
K-by-L-by-P complex-valued array | N_RE-by-P complex-valued matrix

`FrequencyRange` — NR frequency range
`"FR1"` (default) | `"FR2"`

`k0` — Frequency offset index in subcarriers relative to Point A
`0` (default) | nonnegative integer

`ChannelBandwidth` — Channel bandwidth in MHz
`[]` (default) | positive scalar

`BandEdges` — Frequencies of lower and upper edges of operating band in MHz
`[]` (default) | two-element vector

`CarrierFrequency` — Carrier frequency
`0` (default) | nonnegative scalar

`TxDirectCurrentLocation` — DC subcarrier location for carrier
`[]` (default) | nonnegative integer

`TestTolerance` — Tolerance limit for ripple measurements
`0` (default) | nonnegative scalar

`IsExtremeCondition` — Flag for extreme measurement conditions
`false` or `0` (default) | `true` or `1`

`X` — Frequency regions that belong to Range 1 and Range 2
`[]` (default) | positive scalar

`metrics` — Spectral flatness metrics
structure

`info` — Spectral flatness processing information
structure

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

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