# LTE Waveform Modeling Using Downlink Transport and Physical Channels

This example shows how to generate a time domain waveform containing a Physical Downlink Shared Channel (PDSCH), corresponding Physical Downlink Control Channel (PDCCH) transmission and the Physical Control Format Indicator Channel (PCFICH), for one subframe.

### Introduction

This example demonstrates how to generate a complete Downlink Shared Channel (DL-SCH) transmission for 6 resource blocks, 4 antenna transmit diversity using the functions from the LTE Toolbox™. The following physical channels are modeled:

Physical Downlink Shared Channel (PDSCH)

Physical Downlink Control Channel (PDCCH)

Physical Downlink Control Format Indicator Channel (PCFICH)

This example generates a time domain (post OFDM modulation) for all 4 antenna ports. A single subframe (number 0) is considered in this example.

Note: The recommended way to generate RMC waveforms is using `lteRMCDLTool`

, this example shows how a waveform can be built by creating and combining individual physical channels, as happens in an LTE system.

### Cell-Wide Settings

eNodeB settings are configured with a structure.

enb.NDLRB = 6; % No of Downlink Resource Blocks(DL-RB) enb.CyclicPrefix = 'Normal'; % CP length enb.PHICHDuration = 'Normal'; % Normal PHICH duration enb.DuplexMode = 'FDD'; % FDD duplex mode enb.CFI = 3; % 4 PDCCH symbols enb.Ng = 'Sixth'; % HICH groups enb.CellRefP = 4; % 4-antenna ports enb.NCellID = 10; % Cell id enb.NSubframe = 0; % Subframe number 0

### Subframe Resource Grid Generation

A resource grid can easily be created using the `lteDLResourceGrid`

function. This creates an empty resource grid for one subframe. The subframe is a 3 dimensional matrix. The number of rows represents the number of subcarriers available, this is equal to `12*enb.NDLRB`

since there are 12 subcarriers per resource block. The number of columns equals the number of OFDM symbols in a subframe, i.e. 7*2, since we have 7 OFDM symbols per slot for normal cyclic prefix and there are 2 slots in a subframe. The number of planes (3rd dimension) in subframe is 4 corresponding to the 4 antenna ports as specified in `enb.CellRefP`

.

subframe = lteDLResourceGrid(enb);

### DL-SCH and PDSCH Settings

The DL-SCH and PDSCH are configured using a structure `pdsch`

. The settings here configure 4 antenna transmit diversity with QPSK modulation.

pdsch.NLayers = 4; % No of layers pdsch.TxScheme = 'TxDiversity'; % Transmission scheme pdsch.Modulation = 'QPSK'; % Modulation scheme pdsch.RNTI = 1; % 16-bit UE-specific mask pdsch.RV = 0; % Redundancy Version

### PDSCH Mapping Indices Generation

The indices to map the PDSCH complex symbols to the subframe resource grid are generated using `ltePDSCHIndices`

. The parameters required by this function include some of the cell-wide settings in `enb`

, channel transmission configuration `pdsch`

and the physical resource blocks (PRBs). The latter indicates the resource allocation for transmission of the PDSCH. In this example we have assumed all resource blocks are allocated to the PDSCH. This is specified using a column vector as shown below.

These indices are made '1based' for direct mapping on the resource grid as MATLAB® uses 1 based indexing. In this case we have assumed that both slots in the subframe share the same resource allocation. It is possible to have different allocations for each slot by specifying a two column matrix as allocation, where each column will refer to each slot in the subframe.

The resulting matrix `pdschIndices`

has 4 columns, each column contains a set of indices in linear style pointing to the resource elements to be used for the PDSCH in each antenna port. Note that this function returns indices avoiding resource elements allocated to reference signals, the control region, broadcast channels and synchronization signals.

The generated indices are represented in 1-base format as used by MATLAB but can be made standard specific 0-based using the option `'0based'`

instead of `'1based'`

. If this option is not specified the default is 1-based index generation.

The coded block size for DL-SCH transmission can be calculated by the `ltePDSCHIndices`

function. The `ltePDSCHIndices`

function returns an information structure as its second output, which contains the parameter `G`

which specifies the number of coded and rate-matched DL-SCH data bits to satisfy the physical PDSCH capacity. This value will be used subsequently to parameterize the DL-SCH channel coding.

pdsch.PRBSet = (0:enb.NDLRB-1).'; % Subframe resource allocation [pdschIndices,pdschInfo] = ... ltePDSCHIndices(enb, pdsch, pdsch.PRBSet, {'1based'});

### DL-SCH Channel Coding

We now generate the DL-SCH bits and apply channel coding. This includes CRC calculation, code block segmentation and CRC insertion, turbo coding, rate matching and code block concatenation. It can be performed using `lteDLSCH`

.

The DL-SCH transport block size is chosen according to rules in TS36.101, Annex A.2.1.2 [ 1 ] "Determination of payload size" with target code rate and number of bits per subframe given by `codedTrBlkSize`

.

codedTrBlkSize = pdschInfo.G; % Available PDSCH bits transportBlkSize = 152; % Transport block size dlschTransportBlk = randi([0 1], transportBlkSize, 1); % Perform Channel Coding codedTrBlock = lteDLSCH(enb, pdsch, codedTrBlkSize, ... dlschTransportBlk);

### PDSCH Complex Symbols Generation

The following operations are applied to the coded transport block to generate the Physical Downlink Shared Channel complex symbols: scrambling, modulation, layer mapping and precoding. This can be achieved using `ltePDSCH`

. As well as some of the cell-wide settings specified in `enb`

this function also requires other parameters related to the modulation and channel transmission configuration, `pdsch`

. The resulting matrix `pdschSymbols`

has 4 columns. Each column contains the complex symbols to map to each antenna port.

pdschSymbols = ltePDSCH(enb, pdsch, codedTrBlock);

### PDSCH Mapping

The complex PDSCH symbols are then easily mapped to each of the resource grids for each antenna port using a simple assignment operation. The locations of the PDSCH symbols in the resource grids are given by `pdschIndices`

.

```
% Map PDSCH symbols on resource grid
subframe(pdschIndices) = pdschSymbols;
```

### DCI Message Configuration

Downlink Control Information (DCI), conveys information about the DL-SCH resource allocation, transport format, and information related to the DL-SCH hybrid ARQ. `lteDCI`

can be used to generate a DCI message to be mapped to the Physical Downlink Control Channel (PDCCH). These parameters include the number of downlink Resource Blocks (RBs), the DCI format and the Resource Indication Value (RIV). The RIV of 26 correspond to full bandwidth assignment. The `lteDCI`

function returns a structure and a vector containing the DCI message bits. Both contain the same information. The structure is more readable, while the serialized DCI message is a more suitable format to send to the channel coding stages.

dci.DCIFormat = 'Format1A'; % DCI message format dci.Allocation.RIV = 26; % Resource indication value [dciMessage, dciMessageBits] = lteDCI(enb, dci); % DCI message

### DCI Channel Coding

The DCI message bits are channel coded. This includes the following operations: CRC insertion, tail-biting convolutional coding and rate matching. The field `PDCCHFormat`

indicates that one Control Channel Element (CCE) is used for the transmission of PDCCH, where a CCE is composed of 36 useful resource elements.

pdcch.NDLRB = enb.NDLRB; % Number of DL-RB in total BW pdcch.RNTI = pdsch.RNTI; % 16-bit value number pdcch.PDCCHFormat = 0; % 1-CCE of aggregation level 1 % Performing DCI message bits coding to form coded DCI bits codedDciBits = lteDCIEncode(pdcch, dciMessageBits);

### PDCCH Bits Generation

The capacity of the control region depends on the bandwidth, the Control Format Indicator (CFI), the number of antenna ports and the PHICH groups. The total number of resources available for PDCCH can be calculated using `ltePDCCHInfo`

. This returns a structure `pdcchInfo`

where the different fields express the resources available to the PDCCH in different units: bits, CCEs, Resource Elements (REs) and Resource Elements Groups (REGs). The total number of bits available in the PDCCH region can be found in the field `pdcchInfo.MTot`

. This allows us to build a vector with the appropriate number of elements. Not all the available bits in the PDCCH region are necessarily used. Therefore the convention adopted is to set unused bits to -1, while bit locations with values 0 or 1 are used.

Note that we have initialized all elements in `pdcchBits`

to -1, indicating that initially all the bits are unused. The elements of `codedDciBits`

are mapped to the appropriate locations in `pdcchBits`

.

Only a subset of all the bits in `pdcchBits`

may be used, these are called the candidate bits. Indices to these can be calculated using `ltePDCCHSpace`

. This returns a two column matrix. Each row indicates the available candidate locations for the provided cell-wide settings `enb`

and PDCCH configuration structure `pdcch`

. The first and second columns contain the indices of the first and last locations respectively of each group of candidates. In this case these indices are 1-based and refer to bits, hence they can be used to access locations in `pdcchBits`

. The vector `pdcchBits`

has 664 elements. The 72 bits of `codedDciBits`

are mapped to the chosen candidate in `pdcchBits`

. Therefore out of 664 elements, 72 will take 0 and 1 values, while the rest remain set to -1. `ltePDCCH`

will interpret these locations as unused and will only consider those with 1s and 0s.

pdcchInfo = ltePDCCHInfo(enb); % Get the total resources for PDCCH pdcchBits = -1*ones(pdcchInfo.MTot, 1); % Initialized with -1 % Performing search space for UE-specific control channel candidates candidates = ltePDCCHSpace(enb, pdcch, {'bits','1based'}); % Mapping PDCCH payload on available UE-specific candidate. In this example % the first available candidate is used to map the coded DCI bits. pdcchBits( candidates(1, 1) : candidates(1, 2) ) = codedDciBits;

### PDCCH Complex Symbol Generation

From the set of bits used in `pdcchBits`

(values not set to -1) PDCCH complex symbols are generated. The following operations are required: scrambling, QPSK modulation, layer mapping and precoding.

The `ltePDCCH`

function takes a set of PDCCH bits and generates complex-valued PDCCH symbols performing the operations mentioned above. In this case pdcchSymbols is a 4 column matrix, each corresponding to each antenna port.

pdcchSymbols = ltePDCCH(enb, pdcchBits);

### PDCCH Mapping Indices Generation and Resource Grid Mapping

PDCCH indices are generated for symbol mapping on resource grid. `pdcchIndices`

is a matrix with 4 columns, one column per antenna port. The rows contain the indices in linear form for mapping the PDCCH symbols to the subframe resource grid.

pdcchIndices = ltePDCCHIndices(enb, {'1based'}); % The complex PDCCH symbols are easily mapped to each of the resource grids % for each antenna port subframe(pdcchIndices) = pdcchSymbols;

### CFI Channel Coding

The number of OFDM symbols in a subframe is linked to the Control Format Indicator (CFI) value. Cell-wide settings structure `enb`

specifies a CFI value of 3, which means that 4 OFDM symbols are used for the control region in the case of 6 downlink resource blocks. The CFI is channel coded using `lteCFI`

. The resulting set of coded bits is a 32 element vector.

cfiBits = lteCFI(enb);

### PCFICH Complex Symbol Generation

The CFI coded bits are then scrambled, QPSK modulated, mapped to layers and precoded to form the PCFICH complex symbols. The `pcfichSymbols`

is a matrix having 4 columns where each column contains the PCFICH complex symbols that map to each of the antenna ports.

pcfichSymbols = ltePCFICH(enb, cfiBits);

### PCFICH Indices Generation and Resource Grid Mapping

The PCFICH complex symbols are mapped to the subframe resource grid using the appropriate mapping indices. These are generated using `ltePCFICHIndices`

and will be used to map the PCFICH symbol quadruplets to resource element groups in the first OFDM symbol in a subframe. All antenna ports are considered, and resource elements used by Reference Signals (RSs) are avoided. Note that the resulting matrix has 4 columns; each column contains the indices in linear form for each antenna port. These indices are 1-based, however they can also be generated using 0-based. The linear indexing style used makes the resource grid mapping process straight forward. The resulting matrix contains the complex symbols in `pcfichSymbols`

in the locations specified by `pcfichIndices`

.

```
pcfichIndices = ltePCFICHIndices(enb);
% Map PCFICH symbols to resource grid
subframe(pcfichIndices) = pcfichSymbols;
```

### Plot Grid

Plot the resource grid for the first antenna. This includes (in yellow) the physical channels added in the example: PDSCH, PDCCH and PCFICH. Use `surf()`

to avoid aliasing. This plots the values (REs) of the grid and joins them with lines (for 12 subcarriers, `surf()`

plots 12 points and 11 lines; thus, the last subcarrier is not visible). Repeat the last row of the resource grid so that the last subcarrier is visible.

surf(abs([subframe(:,:,1);subframe(end,:,1)])); view(2); h = rotate3d; setAllowAxesRotate(h,gca,false); axis tight; xlabel('OFDM Symbol'); ylabel('Subcarrier'); title('Resource grid');

### OFDM Modulation

Time domain mapping by performing OFDM modulation for downlink symbols. The resulting matrix has 4 columns; each column contains the samples for each antenna port.

[timeDomainMapped, timeDomainInfo] = lteOFDMModulate(enb, subframe);

### Selected Bibliography

3GPP TS 36.101 "User Equipment (UE) radio transmission and reception"