nrChannelEstimate

Practical channel estimation

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 .

[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 pair arguments in addition to the input arguments in any of the previous syntaxes.

Examples

Compare Practical and Perfect Channel Estimates

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);
nulls = [1:136 377:512].';
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;

Obtain the maximum number of delayed samples from the channel path by using the largest delay and the implementation delay of the channel filter.

chInfo = info(channel);
maxChDelay = ceil(max(chInfo.PathDelays*channel.SampleRate)) + chInfo.ChannelFilterDelay;

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');

Input Arguments

rxGrid — Received resource grid

K-by-L-by-R complex array

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

refInd — Reference symbol indices

integer matrix

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 one-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

refSym — Reference symbols

complex matrix

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

refGrid — Predefined reference grid

K-by-N-by-P complex array

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 — Carrier configuration parameters

nrCarrierConfig object

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 Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

'CyclicPrefix' — Cyclic prefix length

'normal' (default) | 'extended'

Cyclic prefix length, specified as the comma-separated pair consisting of 'CyclicPrefix' and one of these options:

• '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.

If you specify the carrier input and this input, the function uses the value specified in the CyclicPrefix property of the carrier input as the cyclic prefix length.

Data Types: char | string

'CDMLengths' — CDM arrangement for reference signals

[1 1] (default) | 1-by-2 array of nonnegative integers

Code domain multiplexing (CDM) arrangement for reference signals, specified as the comma-separated pair consisting of 'CDMLengths' and 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

'AveragingWindow' — Pre-interpolation averaging window

[0 0] (default) | 1-by-2 array of nonnegative odd integers

Pre-interpolation averaging window, specified as the comma-separated pair consisting of 'AveragingWindow' and 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

Output Arguments

h — Practical channel estimate

K-by-L-by-R-by-P complex array

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

nVar — Noise variance estimate

nonnegative scalar

Noise variance estimate, returned as a nonnegative scalar. nVar is the measured variance of additive white Gaussian noise on the received reference symbols.

Data Types: double

info — Additional information

structure

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

Parameter Field	Value	Description
AveragingWindow	1-by-2 array	Pre-interpolation averaging window, returned as a 1-by-2 array [F T]. Array elements 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

C/C++ Code Generation
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