nrChannelEstimate

Practical channel estimation

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Syntax

[h,nVar,info] = nrChannelEstimate(rxGrid,refInd,refSym)
[h,nVar,info] = nrChannelEstimate(rxGrid,refGrid)
[h,nVar,info] = nrChannelEstimate(carrier,___)
[h,nVar,info] = nrChannelEstimate(___,Name=Value)

Description

[h,nVar,info] = nrChannelEstimate(rxGrid,refInd,refSym) performs practical channel estimation on the received resource grid rxGrid by using a reference resource grid containing reference symbols refSym at locations refInd. The function returns the channel estimate h, noise variance estimate nVar, and additional information info.

example

[h,nVar,info] = nrChannelEstimate(rxGrid,refGrid) specifies a predefined reference resource grid refGrid.

[h,nVar,info] = nrChannelEstimate(carrier,___) specifies carrier configuration parameters for a specific orthogonal frequency-division multiplexing (OFDM) numerology, in addition to the input arguments from any of the previous syntaxes. The function uses only the CyclicPrefix property of the carrier input.

[h,nVar,info] = nrChannelEstimate(___,Name=Value) specifies options by using one or more name-value arguments in addition to the input arguments in any of the previous syntaxes.

Examples

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Open Live Script

Generate physical broadcast channel (PBCH) demodulation reference signal (DM-RS) symbols for physical layer cell identity number 42. The time-dependent part of the DM-RS scrambling initialization is 0.

ncellid = 42;
ibar_SSB = 0;
dmrsSym = nrPBCHDMRS(ncellid,ibar_SSB);

Obtain resource element indices for the PBCH DM-RS.

dmrsInd = nrPBCHDMRSIndices(ncellid);

Create a resource grid containing the generated DM-RS symbols.

nrb = 20;
scs = 15;
carrier = nrCarrierConfig('NSizeGrid',nrb,'SubcarrierSpacing',scs);
nTxAnts = 1;
txGrid = nrResourceGrid(carrier,nTxAnts);
txGrid(dmrsInd) = dmrsSym;

Modulate the resource grid using the specified FFT length and cyclic prefix length. 

ofdmInfo = nrOFDMInfo(carrier);
txWaveform = nrOFDMModulate(carrier,txGrid);

Create a TDL-C channel model with the specified properties. 

channel = nrTDLChannel;
channel.NumReceiveAntennas = 1;
channel.SampleRate = ofdmInfo.SampleRate;
channel.DelayProfile = 'TDL-C';
channel.DelaySpread = 100e-9;
channel.MaximumDopplerShift = 20;

Get the maximum channel delay.

chInfo = info(channel);
maxChDelay = chInfo.MaximumChannelDelay;

To flush delayed samples from the channel, append zeros at the end of the transmitted waveform corresponding to the maximum number of delayed samples and the number of transmit antennas. Transmit the padded waveform through the TDL-C channel model. 

[rxWaveform,pathGains] = channel([txWaveform; zeros(maxChDelay,nTxAnts)]);

Estimate timing offset for the transmission using the DM-RS symbols as reference symbols. The OFDM modulation of the reference symbols uses an initial slot number of 0. 

initialSlot = 0;
offset = nrTimingEstimate(carrier,rxWaveform,txGrid);

Synchronize the received waveform according to the estimated timing offset. 

rxWaveform = rxWaveform(1+offset:end,:);

Create a received resource grid containing the demodulated and synchronized received waveform.

cpFraction = 0.55;
rxGrid = nrOFDMDemodulate(carrier,rxWaveform,'CyclicPrefixFraction',cpFraction);

Obtain the practical channel estimate.

H = nrChannelEstimate(rxGrid,dmrsInd,dmrsSym);

Obtain the perfect channel estimate.

pathFilters = getPathFilters(channel);
H_ideal = nrPerfectChannelEstimate(carrier,pathGains,pathFilters,offset);

Compare practical and perfect channel estimates. 

figure;
subplot(1,2,1);
imagesc(abs(H));
xlabel('OFDM Symbol');
ylabel('Subcarrier');
title('Practical Estimate Magnitude');
subplot(1,2,2);
imagesc(abs(H_ideal));
xlabel('OFDM Symbol');
ylabel('Subcarrier');
title('Perfect Estimate Magnitude');

Figure contains 2 axes objects. Axes object 1 with title Practical Estimate Magnitude, xlabel OFDM Symbol, ylabel Subcarrier contains an object of type image. Axes object 2 with title Perfect Estimate Magnitude, xlabel OFDM Symbol, ylabel Subcarrier contains an object of type image.

Input Arguments

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Received resource grid, specified as a K-by-L-by-R complex array.

  • K is the number of subcarriers equal to NRB × 12, where NRB is the number of resource blocks in the range from 1 to 275.

  • L is the number of OFDM symbols in a slot or in a reference grid.

    • When you call nrChannelEstimate with reference symbols refSym, L is 12 for extended cyclic prefix and 14 for normal cyclic prefix. Set the cyclic prefix length by using the 'CyclicPrefix' name-value pair argument.

    • When you call nrChannelEstimate with reference resource grid refGrid, L must equal N, the number of OFDM symbols in the reference grid.

  • R is the number of receive antennas.

Data Types: single | double
Complex Number Support: Yes

Reference symbol indices, specified as an integer matrix. The number of rows equals the number of resource elements. You can specify all indices in a single column or spread them across several columns. The number of elements in refInd and refSym must be the same but their dimensionality can differ. The function reshapes refInd and refSym into column vectors before mapping them into a reference grid: refGrid(refInd(:)) = refSym(:).

The elements of refInd are 1-based linear indices addressing a K-by-L-by-P resource array.

  • K is the number of subcarriers equal to NRB × 12, where NRB is the number of resource blocks in the range from 1 to 275. K must be equal to the first dimension of rxGrid.

  • L is the number of OFDM symbols in a slot. L is 12 for extended cyclic prefix and 14 for normal cyclic prefix. Set the cyclic prefix length by using the 'CyclicPrefix' name-value pair argument.

  • P is the number of reference signal ports, inferred from the range of values in refInd.

Data Types: double

Reference symbols, specified as a complex matrix. The number of rows equals the number of resource elements. You can specify all symbols in a single column or distribute them across several columns. The number of elements in refInd and refSym must be the same but their dimensionality can differ. The function reshapes refInd and refSym into column vectors before mapping them into a reference grid: refGrid(refInd(:)) = refSym(:).

Data Types: single | double
Complex Number Support: Yes

Predefined reference grid, specified as a K-by-N-by-P complex array. refGrid can span multiple slots.

  • K is the number of subcarriers equal to NRB × 12, where NRB is the number of resource blocks in the range from 1 to 275.

  • N is the number of OFDM symbols in the reference grid.

  • P is the number of reference signal ports.

Data Types: single | double
Complex Number Support: Yes

Carrier configuration parameters for a specific OFDM numerology, specified as an nrCarrierConfig object. The function uses only the CyclicPrefix property of this input.

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'CyclicPrefix','extended' specifies extended cyclic prefix length.

Cyclic prefix length, specified as one of these values:

  • 'normal' — Use this value to specify normal cyclic prefix. This option corresponds to 14 OFDM symbols in a slot.

  • 'extended' — Use this value to specify extended cyclic prefix. This option corresponds to 12 OFDM symbols in a slot. For the numerologies specified in TS 38.211 Section 4.2, the extended cyclic prefix length only applies to 60 kHz subcarrier spacing.

Note

If you specify the carrier input, use the CyclicPrefix property of the carrier input to specify the cyclic prefix length. You cannot use this name-value pair argument together with the carrier input.

Data Types: char | string

Code domain multiplexing (CDM) arrangement for reference signals, specified as a 1-by-2 array of nonnegative integers [FD TD]. Array elements FD and TD specify the length of CDM despreading in the frequency domain (FD-CDM) and time domain (TD-CDM), respectively. A value of 1 for an element specifies no CDM.

Example: CDMLengths=[2 1] specifies FD-CDM2 and no TD-CDM.

Example: CDMLengths=[1 1] specifies no orthogonal despreading.

Data Types: double

Preinterpolation averaging window, specified as a 1-by-2 array of nonnegative odd integers [F T]. Array elements F and T specify the number of adjacent reference symbols in the frequency domain and time domain, respectively, over which the function performs averaging before interpolation. If F or T is zero, the function determines the averaging value from the estimated signal-to-noise ratio (SNR) based on the noise variance estimate nVar.

Data Types: double

Since R2025a

Precoding resource block group (PRG) bundle size, specified as [], 2, or 4. When you specify a nonempty value, the function returns the nVar and info outputs in terms of the number of the transmitted PRGs.

Note

You can use this name-value argument only with the carrier input.

Since R2025a

Interpolation, specified as one of these values:

  • 'on' — By default, the function interpolates the averaged consecutive estimates across frequency, then interpolates the averaged consecutive estimates across time and frequency.

  • 'off' — The function returns the channel estimates only for the reference symbol locations that are specified by the refInd or refGrid inputs for each receive antenna across all ports. The function returns zero for all other grid locations.

Data Types: string | char

Output Arguments

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Practical channel estimate, returned as a K-by-L-by-R-by-P complex array. K-by-L-by-R is the shape of the received resource grid rxGrid. P is the number of reference signal ports.

h inherits its data type from rxGrid.

Data Types: double | single

Noise variance estimate, returned as a nonnegative scalar or an NPRG-by-1 column vector of nonnegative numbers (when PRGBundleSize is nonempty) (since R2025a). NPRG is the number of the transmitted PRGs based on the PRGBundleSize input.

nVar is the measured variance of additive white Gaussian noise on the received reference symbols.

Data Types: double

Additional information, returned as a structure with the field AveragingWindow.

Parameter FieldValueDescription
AveragingWindow

1-by-2 array,

NPRG-by-2 array (since R2025a)

Preinterpolation averaging window, returned as a 1-by-2 array or an NPRG-by-2 array (when PRGBundleSize is nonempty) (since R2025a). NPRG is the number of the transmitted PRGs based on the PRGBundleSize input.

The array rows are of the form [F T], where F and T indicate the number of adjacent reference symbols in the frequency domain and time domain, respectively, over which the function performed averaging before interpolation.

Extended Capabilities

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

Version History

Introduced in R2019b

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See Also

Functions

Objects