nrExtractResources

Extract resource elements from resource array

Syntax

re = nrExtractResources(ind,grid)

[re,reind] = nrExtractResources(ind,grid)

[re1,...,reN,reind1,...,reindN] = nrExtractResources(ind,grid1,grid2,....,gridN)

[___] = nrExtractResources(___,Name,Value)

Description

re = nrExtractResources(ind,grid) returns the resource elements from the resource array grid using resource element indices ind. The function can extract resource elements even if grid has a dimensionality which is different than the dimensionality of the indices ind. In this syntax, the specified indices are one-based using linear indexing form.

Typically, channel or signal specific functions generate resource element indices to map the channel or signal symbols to a resource grid. The indices address resource elements in an M-by-N-by-P array. M is the number of subcarriers, N is the number of OFDM symbols, and P is the number of antenna ports.

For example, the following diagram highlights resource elements of a 4-by-4-by-2 resource array. The resource element indices are in one-based linear indexing form. The number of the antenna ports is two (P = 2).

[re,reind] = nrExtractResources(ind,grid) also returns reind, the indices of the extracted resource elements re within the resource array grid. The array reind is the same size as the extracted resource elements re.

[re1,...,reN,reind1,...,reindN] = nrExtractResources(ind,grid1,grid2,....,gridN) extracts resource elements from multiple resource arrays using the resource element indices ind.

[___] = nrExtractResources(___,Name,Value) specifies optional name-value pair arguments in addition to any of the input argument sets in previous syntaxes. Use these name-value pair arguments to specify the format of the input indices and the extraction method. Unspecified arguments take default values.

Examples

Extract PBCH Symbols and Channel Estimates for Decoding

Extract physical broadcast channel (PBCH) symbols from a received grid and associated channel estimates in preparation for decoding a beamformed PBCH.

PBCH Coding and Beamforming

Create a random sequence of binary values corresponding to a BCH codeword. The length of the codeword is 864, as specified in TS 38.212 Section 7.1.5. Using the codeword, create symbols and indices for a PBCH transmission. Specify the physical layer cell identity number.

E = 864;
cw = randi([0 1],E,1);
ncellid = 17;
v = 0;
pbchTxSym = nrPBCH(cw,ncellid,v);
pbchInd = nrPBCHIndices(ncellid);

Use nrExtractResources to create indices for the two transmit antennas of a beamformed PBCH. Use these indices to map the beamformed PBCH into the transmitter resource array.

P = 2;
txGrid = zeros([240 4 P]);
F = [1 1i];
[~,bfInd] = nrExtractResources(pbchInd,txGrid);
txGrid(bfInd) = pbchTxSym*F;

OFDM modulate the PBCH symbols mapped into the transmitter resource array.

txWaveform = ofdmmod(txGrid,256,[22 18 18 18],[1:8 249:256].');

PBCH Transmission and Decoding

Create and apply a channel matrix to the waveform. Receive the transmitted waveforms.

R = 3;
H = dftmtx(max([P R]));
H = H(1:P,1:R);
H = H/norm(H);
rxWaveform = txWaveform*H;

Create channel estimates including beamforming.

 hEstGrid = repmat(permute(H.'*F.',[3 4 1 2]),[240 4]);
 nEst = 0;

Demodulate the received waveform using orthogonal frequency division multiplexing (OFDM).

 rxGrid = ofdmdemod(rxWaveform,256,[22 18 18 18],0,[1:8 249:256].');

In preparation for PBCH decoding, extract symbols from the received grid and the channel estimate grid.

[pbchRxSym,pbchHestSym] = nrExtractResources(pbchInd,rxGrid,hEstGrid);
figure;
plot(pbchRxSym,'o:');
title('Received PBCH Constellation'); 

Equalize the symbols by performing MMSE equalization on the extracted resources. Plot the results.

pbchEqSym = nrEqualizeMMSE(pbchRxSym,pbchHestSym,nEst);
figure;
plot(pbchEqSym,'o:');
title('Equalized PBCH Constellation');

Retrieve soft bits by performing PBCH decoding on the equalized symbols.

pbchBits = nrPBCHDecode(pbchEqSym,ncellid,v)

pbchBits = 864×1
1010 ×

   -2.0000
   -2.0000
    2.0000
   -2.0000
   -2.0000
    2.0000
    2.0000
   -2.0000
   -2.0000
   -2.0000
      ⋮

Input Arguments

ind — Resource element indices

matrix

Resource element indices, specified as a matrix.

• If 'IndexStyle' is 'index', each column of the matrix contains linear indices for the corresponding antenna.

• If 'IndexStyle' is 'subscript', ind is a three-column matrix. The matrix rows correspond to the [subcarrier, symbol, antenna] subscripts based on the number of subcarriers, OFDM symbols, and antennas, respectively.

The function assumes that the indices are one-based, unless you specify otherwise with the 'IndexBase' argument.

Data Types: double

grid — Resource array

3-D numeric array (default) | 4-D numeric array

Resource array from which to extract resource elements, specified as one of these values:

• 3-D numeric array of size M-by-N-by-R that corresponds to a received grid — M is the number of subcarriers, N is the number of OFDM symbols, and R is the number of receive antennas. The grid is created after OFDM demodulation.

• A 4-D numeric array of size M-by-N-by-R-by-P that corresponds to a channel estimation grid — P is the number of antenna ports. The grid is created after channel estimation.

Data Types: double

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: nrExtractResources(ind,grid,'ExtractionMethod','direct','IndexBase','0based') specifies direct extraction method with zero-based indexing.

'IndexStyle' — Resource element indexing form

'index' (default) | 'subscript'

Resource element indexing form, specified as the comma-separated pair consisting of 'IndexStyle' and one of these values:

• 'index' — The indices are in linear index form.

• 'subscript' — The indices are in [subcarrier, symbol, antenna] subscript row form.

Data Types: char | string

'IndexBase' — Resource element indexing base

'1based' (default) | '0based'

Resource element indexing base, specified as the comma-separated pair consisting of 'IndexBase' and one of these values:

• '1based' — The index counting starts from one.

• '0based' — The index counting starts from zero.

Data Types: char | string

'ExtractionMethod' — Resource element extraction method

'allplanes' (default) | 'direct'

Resource element extraction method, specified as the comma-separated pair consisting of 'ExtractionMethod' and 'allplanes' or 'direct'.

• 'allplanes' — The function extracts resource elements from each M-by-N plane within grid. The function uses indices that address unique subcarrier and symbol locations over all planes of the indexed resource array. See All-Planes Extraction Method (Default).

• 'direct' — The function extracts resource elements from each M-by-N plane (for a 3-D grid) or M-by-N-by-R array (for a 4-D grid). The function uses indices that address the corresponding plane of the indexed resource array directly. See Direct Extraction Method.

Data Types: string | char

Output Arguments

re — Extracted resource elements

column vector | numeric array

Extracted resource elements, returned as a column vector, or a numeric array.

When 'ExtractionMethod' is set to 'allplanes', the size of re is N_RE-by-R-by-P, where:

• N_RE is the number of resource elements extracted from each M-by-N plane of grid.

• R number of receive antennas.

• P is the number of planes.

When 'ExtractionMethod' is set to 'direct', the size of re depends on the number of indices addressing each plane of the indexed resource grid.

• If the number of indices addressing each plane is the same, then re is of size N_RE-by-R-by-P.

• If the number of indices addressing each plane is different, then re is a column vector containing all extracted resource elements.

For more details on the resource extraction methods, see Algorithms.

reind — Indices of extracted resource elements

numeric array

Indices of extracted resource elements within grid, returned as numeric array. reind is the same size as the extracted resource elements array re. The reind output inherits the indexing style and index base from ind.

Algorithms

All-Planes Extraction Method (Default)

To use this method, set 'ExtractionMethod' to 'allplanes'. This method extracts resource elements from each M-by-N plane within grid. The indices address unique subcarrier and symbol locations over all the planes of the indexed resource array. The diagram highlights the indices used to extract resource elements from a resource grid with P = 2.

Extraction Process for a 3-D Received Grid

The following diagrams illustrate the resource element extraction from a 3-D received grid, where the number of receive antennas R = 3. Resource elements are extracted from the grid at the symbol and subcarrier locations.

Extraction Process for a 4-D Channel Estimate Grid

The following diagram shows the extraction process for a 4-D channel estimate grid. The number of receive antennas R = 3 and the number of antenna ports P = 2. The 4-D resource grid consists of P M-by-N-by-R arrays, each associated with an antenna port. Resource elements are extracted from all planes within these arrays.

Direct Extraction Method

To use this method, set 'ExtractionMethod' to 'direct'. This method extracts resource elements from grid assuming that the third and fourth dimensions of the grid represent the same property as the planes of the indexed resource array such as antenna ports, layers, transmit antennas. Therefore the function extracts only the resource elements relevant to each plane of the indexed resource grid.

• For a 3-D grid, the direct method extracts elements from each M-by-N plane of grid using indices addressing the same plane of the indexed resource array. This method is the same as the standard MATLAB^® operation re = grid(ind). Therefore, reind = ind.

• For a 4-D grid, the direct method extracts elements from each M-by-N-by-R array of grid by using indices addressing the same plane of the indexed resource array. The function assumes that the property represented by the planes of the indexed resource array is the same as the fourth dimension of grid.

Extraction Process for a 4-D Channel Estimate Grid

The following diagram shows the extraction process for a 4-D channel estimate grid. The number of receive antennas R = 3 and the number of antenna ports P = 2. The 4-D resource grid consists of P number of M-by-N-by-R arrays, each associated with an antenna port. The indices corresponding to each individual antenna port in the indexed resource array are used to extract resource elements from each of these arrays.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

Names and values in name-value pair arguments must be compile-time constants. For example, to specify linear indexing form, include {coder.Constant('IndexStyle'),coder.Constant('index')} in the -args value of codegen. For more information, see coder.Constant.