nrPerfectChannelEstimate

Perfect channel estimation

Syntax

h = nrPerfectChannelEstimate(carrier,pathGains,pathFilters)

h = nrPerfectChannelEstimate(pathGains,pathFilters,nrb,scs,initialNSlot)

h = nrPerfectChannelEstimate(___,toffset)

h = nrPerfectChannelEstimate(___,toffset,sampleTimes)

h = nrPerfectChannelEstimate(___,cpl)

h = nrPerfectChannelEstimate(___,Name,Value)

Description

h = nrPerfectChannelEstimate(carrier,pathGains,pathFilters) performs perfect channel estimation. The function first reconstructs the channel impulse response from the channel path gains pathGains and the path filter impulse response pathFilters. The function then performs orthogonal frequency division multiplexing (OFDM) demodulation. carrier specifies the parameters for the OFDM demodulation.

h = nrPerfectChannelEstimate(pathGains,pathFilters,nrb,scs,initialNSlot) performs the OFDM demodulation for nrb number of resource blocks with subcarrier spacing scs and initial slot number initialNSlot.

h = nrPerfectChannelEstimate(___,toffset) specifies the timing offset in addition to the input arguments in any of the previous syntaxes. The timing offset indicates the OFDM demodulation starting point on the reconstructed waveform.

h = nrPerfectChannelEstimate(___,toffset,sampleTimes) specifies the sample times of the channel snapshots in addition to the input arguments in the previous syntax.

h = nrPerfectChannelEstimate(___,cpl) specifies the cyclic prefix (CP) length in addition to the input arguments in any of the previous syntaxes that do not include the carrier input.

h = nrPerfectChannelEstimate(___,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.

Note

The function limits the timing offset to the CP length. To synchronize the channel impulse response to the start of the useful part of the OFDM symbols when the toffset input exceeds the specified CP length (cpl, CyclicPrefix, or carrier.CyclicPrefix), the function shortens the specified path filter impulse response, pathFilters.

Examples

Plot Estimated Channel Magnitude Response for TDL-C Channel Model

Define a channel configuration structure using an nrTDLChannel System object. Use delay profileTDL-C from TR 38.901 Section 7.7.2.

SR = 7.68e6;
tdl = nrTDLChannel;
tdl.DelayProfile = 'TDL-C';
tdl.DelaySpread = 100e-9;
tdl.MaximumDopplerShift = 300;
tdl.SampleRate = SR;

Create a random waveform with a duration of 1 subframe.

T = SR*1e-3;
tdlInfo = info(tdl);
Nt = tdlInfo.NumTransmitAntennas;
in = complex(randn(T,Nt),randn(T,Nt));

Transmit the input waveform through the channel. Obtain the path filters used in channel filtering.

[~,pathGains] = tdl(in);
pathFilters = getPathFilters(tdl);

Perform perfect channel estimation using the specified number of blocks, subcarrier spacing, and slot number.

NRB = 25;
SCS = 15;
nSlot = 0;

hest = nrPerfectChannelEstimate(pathGains,pathFilters,NRB,SCS,nSlot);
size(hest)

ans = 1×3

   300    14     2

Plot the estimated channel magnitude response for the first receive antenna.

figure;
surf(abs(hest(:,:,1)));
shading('flat');
xlabel('OFDM Symbols');
ylabel('Subcarriers');
zlabel('|H|');
title('Channel Magnitude Response');

Repeat the channel estimate for extended cyclic prefix.

hest = nrPerfectChannelEstimate(pathGains,pathFilters,NRB,SCS, ...
    nSlot,'extended');
size(hest)

ans = 1×3

   300    12     2

Plot the updated results.

figure;
surf(abs(hest(:,:,1)));
shading('flat');
xlabel('OFDM Symbols');
ylabel('Subcarriers');
zlabel('|H|');
title('Channel Magnitude Response with Extended Cyclic Prefix');

Plot Estimated Channel Magnitude Response for CDL-D Channel Model

Define a channel configuration structure using an nrCDLChannel System object. Use delay profile CDL-C from TR 38.901 Section 7.7.1.

 cdl = nrCDLChannel;
 cdl.DelayProfile = 'CDL-D';
 cdl.DelaySpread = 30e-9;
 cdl.MaximumDopplerShift = 5;

Create a random waveform with a duration of 1 subframe.

SR = 15.36e6;
T = SR*1e-3;
cdl.SampleRate = SR;
cdlInfo = info(cdl);
Nt = cdlInfo.NumTransmitAntennas;
in = complex(randn(T,Nt),randn(T,Nt));

Transmit the input waveform through the channel. Obtain the path filters used in channel filtering.

[~,pathGains,sampleTimes] = cdl(in);
pathFilters = getPathFilters(cdl);

Perform timing offset estimation using the path filter and path gains.

offset = nrPerfectTimingEstimate(pathGains,pathFilters);

Perform perfect channel estimation. Use the specified number of blocks, subcarrier spacing, slot number, timing offset, and sample times.

NRB = 25;
SCS = 15;
nSlot = 0;
hest = nrPerfectChannelEstimate(pathGains,pathFilters,...
    NRB,SCS,nSlot,offset,sampleTimes);
size(hest)

ans = 1×4

   300    14     2     8

Plot the estimated channel magnitude response for the first receive antenna.

figure;
surf(abs(hest(:,:,1)));
shading('flat');
xlabel('OFDM Symbols');
ylabel('Subcarriers');
zlabel('|H|');
title('Channel Magnitude Response');

Input Arguments

carrier — Carrier configuration parameters

nrCarrierConfig object

Carrier configuration parameters for a specific OFDM numerology, specified as an nrCarrierConfig object. Only these object properties are relevant for this function.

• NSizeGrid

• SubcarrierSpacing

• NSlot

• CyclicPrefix

pathGains — Channel path gains of fading process

N_CS-by-N_P-by-N_T-by-N_R complex matrix

Channel path gains of the fading process, specified as an N_CS-by-N_P-by-N_T-by-N_R complex matrix, where:

• N_CS is the number of channel snapshots.

• N_P is the number of paths.

• N_T is the number of transmit antennas.

• N_R is the number of receive antennas.

Data Types: single | double
Complex Number Support: Yes

pathFilters — Path filter impulse response

N_H-by-N_P real matrix

Path filter impulse response, specified as an N_H-by-N_P real matrix, where:

• N_H is the number of impulse response samples.

• N_P is the number of paths.

Each column of the matrix contains the filter impulse response for each path of the delay profile.

Data Types: double

nrb — Number of resource blocks

integer from 1 to 275

Number of resource blocks, specified as an integer from 1 to 275.

Data Types: double

scs — Subcarrier spacing in kHz

15 | 30 | 60 | 120 | 240 | 480 | 960

Subcarrier spacing in kHz, specified as 15, 30, 60, 120, 240, 480, or 960.

Data Types: double

initialNSlot — Initial slot number

nonnegative integer

Initial slot number, 0-based, specified as a nonnegative integer. The function selects the appropriate cyclic prefix length for the OFDM demodulation based on the value of initialNSlot modulo the number of slots per subframe.

Data Types: double

toffset — Timing offset in samples

nonnegative integer

Timing offset in samples, specified as a nonnegative integer. The timing offset indicates the OFDM demodulation starting point on the reconstructed waveform. The offset accounts for propagation delays, which is essential when obtaining the perfect estimate of the channel seen by a synchronized receiver. toffset defaults to the value nrPerfectTimingEstimate(pathGains,pathFilters) when not specified as an input argument.

Data Types: double

sampleTimes — Sample times of channel snapshots

N_CS-by-1 column vector of nonnegative real numbers

Sample times of channel snapshots, specified as an N_CS-by-1 column vector of nonnegative real numbers. sampleTimes specifies the time of occurrence of each channel snapshot. The number of channel snapshots, N_CS, is identical to the first dimension of pathGains. When not specified, sampleTimes defaults to an N_CS-by-1 vector of times starting at zero with sampling rate used for the OFDM modulation of the number of resource blocks nrb and subcarrier spacing scs. Ensure that the channel snapshots span at least one slot. The function performs channel estimation for each complete slot.

Data Types: double

cpl — Cyclic prefix length

'normal' (default) | 'extended'

Cyclic prefix length, specified as 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.

Note

• If you specify the carrier input, use the CyclicPrefix property of the carrier input to specify the cyclic prefix length. You cannot use the cpl input together with the carrier input.

• If you specify the cyclic prefix length with the 'CyclicPrefix' name-value pair argument, you cannot use the cpl input.

Data Types: char | string

Name-Value Arguments

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: 'CyclicPrefixFraction',0.75 specifies the start location for demodulation relative to the 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 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.

• If you specify the cyclic prefix length with the cpl input, you cannot use this name-value pair argument.

Data Types: char | string

Nfft — Number of FFT points

integer greater than 127 (default depends on other input values) | []

Number of fast Fourier transform (FFT) points, specified as the comma-separated pair consisting of 'Nfft' and a nonnegative integer greater than 127 or []. The value you specify must result in integer-valued cyclic prefix lengths and a maximum occupancy of 100%. The occupancy is defined as the value of (12 × N_RB)/Nfft, where N_RB is the number of resource blocks.

If you do not specify this input, or if you specify 'Nfft',[], the function sets an integer value greater than 127 as a default value for this input. The actual default value depends on other input values.

• If you do not specify the SampleRate input, or if you specify 'SampleRate',[], the function sets Nfft satisfying these conditions.

  • Nfft is an integer power of 2.

  • Nfft results in a maximum occupancy of 85%.

• If you specify the SampleRate input, the function sets Nfft satisfying these conditions.

  • Nfft results in integer-valued cyclic prefix lengths.

  • Nfft maximises the value of gcd (Nfft × SCS, SampleRate), where SCS is specified by the carrier.SubcarrierSpacing property or the scs input.

For more information, see Configure OFDM Sample Rate and FFT Size.

Data Types: double

SampleRate — Waveform sample rate

positive scalar (default depends on other input values) | []

Waveform sample rate, specified as the comma-separated pair consisting of 'SampleRate' and either a positive scalar or [].

If you do not specify this input, or if you specify 'SampleRate',[], then the function sets this input to the value of N_fft × SCS.

• N_fft is the value of the 'Nfft' input.

• SCS is the subcarrier spacing. Depending on the function syntax you use, SCS is specified by the carrier.SubcarrierSpacing property or the scs input.

For more information, see Configure OFDM Sample Rate and FFT Size.

Data Types: double

CyclicPrefixFraction — FFT window position within cyclic prefix

0.5 (default) | scalar in the interval [0, 1]

Fast Fourier transform (FFT) window position within the cyclic prefix, specified as the comma-separated pair consisting of 'CyclicPrefixFraction' and a scalar in the interval [0, 1].

The value that you specify indicates the start location for OFDM demodulation relative to the beginning of the cyclic prefix.

Data Types: double

Output Arguments

h — Perfect channel estimate

N_SC-by-N_SYM-by-N_R-by-N_T complex array

Perfect channel estimate, returned as an N_SC-by-N_SYM-by-N_R-by-N_T complex array, where:

• N_SC is the number of subcarriers.

• N_SYM is the number of OFDM symbols.

• N_R is the number of receive antennas.

• N_T is the number of transmit antennas.

h inherits its data type from pathGains.

Data Types: double | single

References

[1] 3GPP TS 38.211. “NR; Physical channels and modulation.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The 'SampleRate' name-value argument must be compile-time constant for code generation. For example, when you call the function with 'SampleRate',15.36e6, include {coder.Constant('SampleRate'),coder.Constant(15.36e6)} in the -args value of the codegen function. For more information, see the coder.Constant (MATLAB Coder) class.

• If you specify the 'SampleRate' name-value argument, the nrb, scs input arguments and the 'Nfft' name-value argument must also be compile-time constants. For example, include also {coder.Constant(nrb)} and {coder.Constant(scs)} in the -args value of the codegen function.

• The 'SampleRate' name-value pair argument cannot be used together with the carrier input.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™. (since R2024b)

The nrPerfectChannelEstimate function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2018b

R2024b: GPU array support

The nrPerfectChannelEstimate function adds support for GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

R2023a: Subcarrier spacing for FR2-2

The function now supports 480 kHz and 960 kHz subcarrier spacings, as defined in TS 38.211 Sections 4.2 and 4.3.

R2023a: C/C++ code generation updates

For C/C++ code generation, the limitation to specify 'CyclicPrefix', 'CyclicPrefixFraction', or 'Nfft' name-value arguments as compile-time constants has been removed. However, if you specify the 'SampleRate' name-value argument, the 'Nfft' name-value argument must still be compile-time constant for code generation.