NR PDSCH Throughput

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This reference simulation shows how to measure the physical downlink shared channel (PDSCH) throughput of a 5G New Radio (NR) link, as defined by the 3GPP NR standard. The example implements the PDSCH and downlink shared channel (DL-SCH). The transmitter model includes PDSCH demodulation reference signals (DM-RS) and PDSCH phase tracking reference signals (PT-RS). The example supports both clustered delay line (CDL) and tapped delay line (TDL) propagation channels. You can perform perfect or practical synchronization and channel estimation. To reduce the total simulation time, you can execute the SNR points in the SNR loop in parallel by using the Parallel Computing Toolbox™.

Introduction

This example measures the PDSCH throughput of a 5G link, as defined by the 3GPP NR standard [ 1 ], [ 2 ], [ 3 ], [ 4 ].

The example models these 5G NR features:

DL-SCH transport channel coding
Multiple codewords, dependent on the number of layers
PDSCH, PDSCH DM-RS, and PDSCH PT-RS generation
Variable subcarrier spacing and frame numerologies (2^n * 15 kHz)
Normal and extended cyclic prefix
TDL and CDL propagation channel models

Other features of the simulation are:

PDSCH subband precoding using SVD
CP-OFDM modulation
Slot wise and non slot wise PDSCH and DM-RS mapping
Perfect or practical synchronization and channel estimation
HARQ operation with 16 processes
The example uses a single bandwidth part across the whole carrier

The figure shows the implemented processing chain. For clarity, the DM-RS and PT-RS generation are omitted.

For a more detailed explanation of the steps implemented in this example, see Model 5G NR Communication Links and DL-SCH and PDSCH Transmit and Receive Processing Chain.

This example supports both wideband and subband precoding. The precoding matrix is determined using SVD by averaging the channel estimate across all PDSCH PRBs in the allocation (wideband case) or in the subband.

To reduce the total simulation time, you can use the Parallel Computing Toolbox to execute the SNR points of the SNR loop in parallel.

Simulation Length and SNR Points

Set the length of the simulation in terms of the number of 10ms frames. A large number of NFrames should be used to produce meaningful throughput results. Set the SNR points to simulate. The SNR for each layer is defined per RE, and it includes the effect of signal and noise across all antennas. For an explanation of the SNR definition that this example uses, see SNR Definition Used in Link Simulations.

simParameters = struct();       % Clear simParameters variable to contain all key simulation parameters
simParameters.NFrames = 2;      % Number of 10 ms frames
simParameters.SNRIn = [-5 0 5]; % SNR range (dB)

Channel Estimator Configuration

The logical variable PerfectChannelEstimator controls channel estimation and synchronization behavior. When set to true, perfect channel estimation and synchronization is used. Otherwise, practical channel estimation and synchronization is used, based on the values of the received PDSCH DM-RS.

simParameters.PerfectChannelEstimator = true;

Simulation Diagnostics

The variable DisplaySimulationInformation controls the display of simulation information such as the HARQ process ID used for each subframe. In case of CRC error, the value of the index to the RV sequence is also displayed.

simParameters.DisplaySimulationInformation = true;

% The |DisplayDiagnostics| flag enables the plotting of the EVM per layer.
% This plot monitors the quality of the received signal after equalization.
% The EVM per layer figure shows:
%
% * The EVM per layer per slot, which shows the EVM evolving with time.
% * The EVM per layer per resource block, which shows the EVM in frequency.
%
% This figure evolves with the simulation and is updated with each slot.
% Typically, low SNR or channel fades can result in decreased signal
% quality (high EVM). The channel affects each layer differently,
% therefore, the EVM values may differ across layers.
%
% In some cases, some layers can have a much higher EVM than others. These
% low-quality layers can result in CRC errors. This behavior may be caused
% by low SNR or by using too many layers for the channel conditions. You
% can avoid this situation by a combination of higher SNR, lower number
% of layers, higher number of antennas, and more robust transmission
% (lower modulation scheme and target code rate).

simParameters.DisplayDiagnostics = false;

Carrier and PDSCH Configuration

Set the key parameters of the simulation. These include:

The bandwidth in resource blocks (12 subcarriers per resource block).
Subcarrier spacing: 15, 30, 60, 120 (kHz)
Cyclic prefix length: normal or extended
Cell ID
Number of transmit and receive antennas

A substructure containing the DL-SCH and PDSCH parameters is also specified. This includes:

Target code rate
Allocated resource blocks (PRBSet)
Modulation scheme: 'QPSK', '16QAM', '64QAM', '256QAM'
Number of layers
PDSCH mapping type
DM-RS configuration parameters
PT-RS configuration parameters

Other simulation wide parameters are:

Propagation channel model delay profile (TDL or CDL)

% Set waveform type and PDSCH numerology (SCS and CP type)
simParameters.Carrier = nrCarrierConfig;         % Carrier resource grid configuration
simParameters.Carrier.NSizeGrid = 51;            % Bandwidth in number of resource blocks (51 RBs at 30 kHz SCS for 20 MHz BW)
simParameters.Carrier.SubcarrierSpacing = 30;    % 15, 30, 60, 120 (kHz)
simParameters.Carrier.CyclicPrefix = 'Normal';   % 'Normal' or 'Extended' (Extended CP is relevant for 60 kHz SCS only)
simParameters.Carrier.NCellID = 1;               % Cell identity

% PDSCH/DL-SCH parameters
simParameters.PDSCH = nrPDSCHConfig;      % This PDSCH definition is the basis for all PDSCH transmissions in the BLER simulation
simParameters.PDSCHExtension = struct();  % This structure is to hold additional simulation parameters for the DL-SCH and PDSCH

% Define PDSCH time-frequency resource allocation per slot to be full grid (single full grid BWP)
simParameters.PDSCH.PRBSet = 0:simParameters.Carrier.NSizeGrid-1;                 % PDSCH PRB allocation
simParameters.PDSCH.SymbolAllocation = [0,simParameters.Carrier.SymbolsPerSlot];  % Starting symbol and number of symbols of each PDSCH allocation
simParameters.PDSCH.MappingType = 'A';     % PDSCH mapping type ('A'(slot-wise),'B'(non slot-wise))

% Scrambling identifiers
simParameters.PDSCH.NID = simParameters.Carrier.NCellID;
simParameters.PDSCH.RNTI = 1;

% PDSCH resource block mapping (TS 38.211 Section 7.3.1.6)
simParameters.PDSCH.VRBToPRBInterleaving = 0; % Disable interleaved resource mapping
simParameters.PDSCH.VRBBundleSize = 4;

% Define the number of transmission layers to be used
simParameters.PDSCH.NumLayers = 2;            % Number of PDSCH transmission layers

% Define codeword modulation and target coding rate
% The number of codewords is directly dependent on the number of layers so ensure that
% layers are set first before getting the codeword number
if simParameters.PDSCH.NumCodewords > 1                             % Multicodeword transmission (when number of layers being > 4)
    simParameters.PDSCH.Modulation = {'16QAM','16QAM'};             % 'QPSK', '16QAM', '64QAM', '256QAM'
    simParameters.PDSCHExtension.TargetCodeRate = [490 490]/1024;   % Code rate used to calculate transport block sizes
else
    simParameters.PDSCH.Modulation = '16QAM';                       % 'QPSK', '16QAM', '64QAM', '256QAM'
    simParameters.PDSCHExtension.TargetCodeRate = 490/1024;         % Code rate used to calculate transport block sizes
end

% DM-RS and antenna port configuration (TS 38.211 Section 7.4.1.1)
simParameters.PDSCH.DMRS.DMRSPortSet = 0:simParameters.PDSCH.NumLayers-1; % DM-RS ports to use for the layers
simParameters.PDSCH.DMRS.DMRSTypeAPosition = 2;      % Mapping type A only. First DM-RS symbol position (2,3)
simParameters.PDSCH.DMRS.DMRSLength = 1;             % Number of front-loaded DM-RS symbols (1(single symbol),2(double symbol))
simParameters.PDSCH.DMRS.DMRSAdditionalPosition = 2; % Additional DM-RS symbol positions (max range 0...3)
simParameters.PDSCH.DMRS.DMRSConfigurationType = 2;  % DM-RS configuration type (1,2)
simParameters.PDSCH.DMRS.NumCDMGroupsWithoutData = 1;% Number of CDM groups without data
simParameters.PDSCH.DMRS.NIDNSCID = 1;               % Scrambling identity (0...65535)
simParameters.PDSCH.DMRS.NSCID = 0;                  % Scrambling initialization (0,1)

% PT-RS configuration (TS 38.211 Section 7.4.1.2)
simParameters.PDSCH.EnablePTRS = 0;                  % Enable or disable PT-RS (1 or 0)
simParameters.PDSCH.PTRS.TimeDensity = 1;            % PT-RS time density (L_PT-RS) (1, 2, 4)
simParameters.PDSCH.PTRS.FrequencyDensity = 2;       % PT-RS frequency density (K_PT-RS) (2 or 4)
simParameters.PDSCH.PTRS.REOffset = '00';            % PT-RS resource element offset ('00', '01', '10', '11')
simParameters.PDSCH.PTRS.PTRSPortSet = [];           % PT-RS antenna port, subset of DM-RS port set. Empty corresponds to lower DM-RS port number

% Reserved PRB patterns, if required (for CORESETs, forward compatibility etc)
simParameters.PDSCH.ReservedPRB{1}.SymbolSet = [];   % Reserved PDSCH symbols
simParameters.PDSCH.ReservedPRB{1}.PRBSet = [];      % Reserved PDSCH PRBs
simParameters.PDSCH.ReservedPRB{1}.Period = [];      % Periodicity of reserved resources

% Additional simulation and DL-SCH related parameters
%
% PDSCH PRB bundling (TS 38.214 Section 5.1.2.3)
simParameters.PDSCHExtension.PRGBundleSize = [];     % 2, 4, or [] to signify "wideband"
%
% HARQ process and rate matching/TBS parameters
simParameters.PDSCHExtension.XOverhead = 6*simParameters.PDSCH.EnablePTRS; % Set PDSCH rate matching overhead for TBS (Xoh) to 6 when PT-RS is enabled, otherwise 0
simParameters.PDSCHExtension.NHARQProcesses = 16;    % Number of parallel HARQ processes to use
simParameters.PDSCHExtension.EnableHARQ = true;      % Enable retransmissions for each process, using RV sequence [0,2,3,1]

% LDPC decoder parameters
% Available algorithms: 'Belief propagation', 'Layered belief propagation', 'Normalized min-sum', 'Offset min-sum'
simParameters.PDSCHExtension.LDPCDecodingAlgorithm = 'Normalized min-sum';
simParameters.PDSCHExtension.MaximumLDPCIterationCount = 6;

% Define the overall transmission antenna geometry at end-points
% If using a CDL propagation channel then the integer number of antenna elements is
% turned into an antenna panel configured when the channel model object is created
simParameters.NTxAnts = 8;                        % Number of PDSCH transmission antennas (1,2,4,8,16,32,64,128,256,512,1024) >= NumLayers
if simParameters.PDSCH.NumCodewords > 1           % Multi-codeword transmission
    simParameters.NRxAnts = 8;                    % Number of UE receive antennas (even number >= NumLayers)
else
    simParameters.NRxAnts = 2;                    % Number of UE receive antennas (1 or even number >= NumLayers)
end

% Define the general CDL/TDL propagation channel parameters
simParameters.DelayProfile = 'CDL-C';   % Use CDL-C model (Urban macrocell model)
simParameters.DelaySpread = 300e-9;
simParameters.MaximumDopplerShift = 5;

% Cross-check the PDSCH layering against the channel geometry
validateNumLayers(simParameters);

The simulation relies on various pieces of information about the baseband waveform, such as sample rate.

waveformInfo = nrOFDMInfo(simParameters.Carrier); % Get information about the baseband waveform after OFDM modulation step

Propagation Channel Model Construction

Create the channel model object for the simulation. Both CDL and TDL channel models are supported [ 5 ].

% Constructed the CDL or TDL channel model object
if contains(simParameters.DelayProfile,'CDL','IgnoreCase',true)

    channel = nrCDLChannel; % CDL channel object

    % Turn the overall number of antennas into a specific antenna panel
    % array geometry. The number of antennas configured is updated when
    % nTxAnts is not one of (1,2,4,8,16,32,64,128,256,512,1024) or nRxAnts
    % is not 1 or even.
    [channel.TransmitAntennaArray.Size,channel.ReceiveAntennaArray.Size] = ...
        hArrayGeometry(simParameters.NTxAnts,simParameters.NRxAnts);
    nTxAnts = prod(channel.TransmitAntennaArray.Size);
    nRxAnts = prod(channel.ReceiveAntennaArray.Size);
    simParameters.NTxAnts = nTxAnts;
    simParameters.NRxAnts = nRxAnts;
else
    channel = nrTDLChannel; % TDL channel object

    % Set the channel geometry
    channel.NumTransmitAntennas = simParameters.NTxAnts;
    channel.NumReceiveAntennas = simParameters.NRxAnts;
end

% Assign simulation channel parameters and waveform sample rate to the object
channel.DelayProfile = simParameters.DelayProfile;
channel.DelaySpread = simParameters.DelaySpread;
channel.MaximumDopplerShift = simParameters.MaximumDopplerShift;
channel.SampleRate = waveformInfo.SampleRate;

Get the maximum number of delayed samples by a channel multipath component. This is calculated from the channel path with the largest delay and the implementation delay of the channel filter. This is required later to flush the channel filter to obtain the received signal.

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

Processing Loop

To determine the throughput at each SNR point, analyze the PDSCH data per transmission instance using the following steps:

Update current HARQ process. Check the transmission status for the given HARQ process to determine whether a retransmission is required. If that is not the case then generate new data.
Resource grid generation. Perform channel coding by calling the nrDLSCH System object. The object operates on the input transport block and keeps an internal copy of the transport block in case a retransmission is required. Modulate the coded bits on the PDSCH by using the nrPDSCH function. Then apply precoding to the resulting signal.
Waveform generation. OFDM modulate the generated grid.
Noisy channel modeling. Pass the waveform through a CDL or TDL fading channel. Add AWGN. For an explanation of the SNR definition that this example uses, see SNR Definition Used in Link Simulations.
Perform synchronization and OFDM demodulation. For perfect synchronization, reconstruct the channel impulse response to synchronize the received waveform. For practical synchronization, correlate the received waveform with the PDSCH DM-RS. Then OFDM demodulate the synchronized signal.
Perform channel estimation. For perfect channel estimation, reconstruct the channel impulse response and perform OFDM demodulation. For practical channel estimation, use the PDSCH DM-RS.
Perform equalization and CPE compensation. MMSE equalize the estimated channel. Estimate the common phase error (CPE) by using the PT-RS symbols, then correct the error in each OFDM symbol within the range of reference PT-RS OFDM symbols.
Precoding matrix calculation. Generate the precoding matrix W for the next transmission by using singular value decomposition (SVD).
Decode the PDSCH. To obtain an estimate of the received codewords, demodulate and descramble the recovered PDSCH symbols for all transmit and receive antenna pairs, along with a noise estimate, by using the nrPDSCHDecode function.
Decode the downlink shared channel (DL-SCH) and update HARQ process with the block CRC error. Pass the vector of decoded soft bits to the nrDLSCHDecoder System object. The object decodes the codeword and returns the block CRC error used to determine the throughput of the system.

% Array to store the maximum throughput for all SNR points
maxThroughput = zeros(length(simParameters.SNRIn),1);
% Array to store the simulation throughput for all SNR points
simThroughput = zeros(length(simParameters.SNRIn),1);

% Set up redundancy version (RV) sequence for all HARQ processes
if simParameters.PDSCHExtension.EnableHARQ
    % In the final report of RAN WG1 meeting #91 (R1-1719301), it was
    % observed in R1-1717405 that if performance is the priority, [0 2 3 1]
    % should be used. If self-decodability is the priority, it should be
    % taken into account that the upper limit of the code rate at which
    % each RV is self-decodable is in the following order: 0>3>2>1
    rvSeq = [0 2 3 1];
else
    % HARQ disabled - single transmission with RV=0, no retransmissions
    rvSeq = 0;
end

% Create DL-SCH encoder system object to perform transport channel encoding
encodeDLSCH = nrDLSCH;
encodeDLSCH.MultipleHARQProcesses = true;
encodeDLSCH.TargetCodeRate = simParameters.PDSCHExtension.TargetCodeRate;

% Create DL-SCH decoder system object to perform transport channel decoding
% Use layered belief propagation for LDPC decoding, with half the number of
% iterations as compared to the default for belief propagation decoding
decodeDLSCH = nrDLSCHDecoder;
decodeDLSCH.MultipleHARQProcesses = true;
decodeDLSCH.TargetCodeRate = simParameters.PDSCHExtension.TargetCodeRate;
decodeDLSCH.LDPCDecodingAlgorithm = simParameters.PDSCHExtension.LDPCDecodingAlgorithm;
decodeDLSCH.MaximumLDPCIterationCount = simParameters.PDSCHExtension.MaximumLDPCIterationCount;

for snrIdx = 1:numel(simParameters.SNRIn)      % comment out for parallel computing
% parfor snrIdx = 1:numel(simParameters.SNRIn) % uncomment for parallel computing
% To reduce the total simulation time, you can execute this loop in
% parallel by using the Parallel Computing Toolbox. Comment out the 'for'
% statement and uncomment the 'parfor' statement. If the Parallel Computing
% Toolbox is not installed, 'parfor' defaults to normal 'for' statement.
% Because parfor-loop iterations are executed in parallel in a
% nondeterministic order, the simulation information displayed for each SNR
% point can be intertwined. To switch off simulation information display,
% set the 'displaySimulationInformation' variable above to false

    % Reset the random number generator so that each SNR point will
    % experience the same noise realization
    rng('default');

    % Take full copies of the simulation-level parameter structures so that they are not
    % PCT broadcast variables when using parfor
    simLocal = simParameters;
    waveinfoLocal = waveformInfo;

    % Take copies of channel-level parameters to simplify subsequent parameter referencing
    carrier = simLocal.Carrier;
    pdsch = simLocal.PDSCH;
    pdschextra = simLocal.PDSCHExtension;
    decodeDLSCHLocal = decodeDLSCH;  % Copy of the decoder handle to help PCT classification of variable
    decodeDLSCHLocal.reset();        % Reset decoder at the start of each SNR point
    pathFilters = [];

    % Prepare simulation for new SNR point
    SNRdB = simLocal.SNRIn(snrIdx);
    fprintf('\nSimulating transmission scheme 1 (%dx%d) and SCS=%dkHz with %s channel at %gdB SNR for %d 10ms frame(s)\n', ...
        simLocal.NTxAnts,simLocal.NRxAnts,carrier.SubcarrierSpacing, ...
        simLocal.DelayProfile,SNRdB,simLocal.NFrames);

    % Specify the fixed order in which we cycle through the HARQ process IDs
    harqSequence = 0:pdschextra.NHARQProcesses-1;

    % Initialize the state of all HARQ processes
    harqEntity = HARQEntity(harqSequence,rvSeq,pdsch.NumCodewords);

    % Reset the channel so that each SNR point will experience the same
    % channel realization
    reset(channel);

    % Total number of slots in the simulation period
    NSlots = simLocal.NFrames * carrier.SlotsPerFrame;

    % Obtain a precoding matrix (wtx) to be used in the transmission of the
    % first transport block
    estChannelGrid = getInitialChannelEstimate(carrier,simLocal.NTxAnts,channel);
    newWtx = getPrecodingMatrix(carrier,pdsch,estChannelGrid,pdschextra.PRGBundleSize);

    % Timing offset, updated in every slot for perfect synchronization and
    % when the correlation is strong for practical synchronization
    offset = 0;

    % Loop over the entire waveform length
    for nslot = 0:NSlots-1

        % Update the carrier slot numbers for new slot
        carrier.NSlot = nslot;

        % Calculate the transport block sizes for the transmission in the slot
        [pdschIndices,pdschIndicesInfo] = nrPDSCHIndices(carrier,pdsch);
        trBlkSizes = nrTBS(pdsch.Modulation,pdsch.NumLayers,numel(pdsch.PRBSet),pdschIndicesInfo.NREPerPRB,pdschextra.TargetCodeRate,pdschextra.XOverhead);

        % HARQ processing
        for cwIdx = 1:pdsch.NumCodewords
            % If new data for current process and codeword then create a new DL-SCH transport block
            if harqEntity.NewData(cwIdx)
                trBlk = randi([0 1],trBlkSizes(cwIdx),1);
                setTransportBlock(encodeDLSCH,trBlk,cwIdx-1,harqEntity.HARQProcessID);
                % If new data because of previous RV sequence time out then flush decoder soft buffer explicitly
                if harqEntity.SequenceTimeout(cwIdx)
                    resetSoftBuffer(decodeDLSCHLocal,cwIdx-1,harqEntity.HARQProcessID);
                end
            end
        end

        % Encode the DL-SCH transport blocks
        codedTrBlocks = encodeDLSCH(pdsch.Modulation,pdsch.NumLayers, ...
            pdschIndicesInfo.G,harqEntity.RedundancyVersion,harqEntity.HARQProcessID);

        % Get precoding matrix (wtx) calculated in previous slot
        wtx = newWtx;

        % Create resource grid for a slot
        pdschGrid = nrResourceGrid(carrier,simLocal.NTxAnts);

        % PDSCH modulation and precoding
        pdschSymbols = nrPDSCH(carrier,pdsch,codedTrBlocks);
        [pdschAntSymbols,pdschAntIndices] = hPRGPrecode(size(pdschGrid),carrier.NStartGrid,pdschSymbols,pdschIndices,wtx);

        % PDSCH mapping in grid associated with PDSCH transmission period
        pdschGrid(pdschAntIndices) = pdschAntSymbols;

        % PDSCH DM-RS precoding and mapping
        dmrsSymbols = nrPDSCHDMRS(carrier,pdsch);
        dmrsIndices = nrPDSCHDMRSIndices(carrier,pdsch);
        [dmrsAntSymbols,dmrsAntIndices] = hPRGPrecode(size(pdschGrid),carrier.NStartGrid,dmrsSymbols,dmrsIndices,wtx);
        pdschGrid(dmrsAntIndices) = dmrsAntSymbols;

        % PDSCH PT-RS precoding and mapping
        ptrsSymbols = nrPDSCHPTRS(carrier,pdsch);
        ptrsIndices = nrPDSCHPTRSIndices(carrier,pdsch);
        [ptrsAntSymbols,ptrsAntIndices] = hPRGPrecode(size(pdschGrid),carrier.NStartGrid,ptrsSymbols,ptrsIndices,wtx);
        pdschGrid(ptrsAntIndices) = ptrsAntSymbols;

        % OFDM modulation
        txWaveform = nrOFDMModulate(carrier,pdschGrid);

        % Pass data through channel model. Append zeros at the end of the
        % transmitted waveform to flush channel content. These zeros take
        % into account any delay introduced in the channel. This is a mix
        % of multipath delay and implementation delay. This value may
        % change depending on the sampling rate, delay profile and delay
        % spread
        txWaveform = [txWaveform; zeros(maxChDelay,size(txWaveform,2))]; %#ok<AGROW>
        [rxWaveform,pathGains,sampleTimes] = channel(txWaveform);

        % Add AWGN to the received time domain waveform
        % Normalize noise power by the IFFT size used in OFDM modulation,
        % as the OFDM modulator applies this normalization to the
        % transmitted waveform. Also normalize by the number of receive
        % antennas, as the channel model applies this normalization to the
        % received waveform, by default
        SNR = 10^(SNRdB/10);
        N0 = 1/sqrt(2.0*simLocal.NRxAnts*double(waveinfoLocal.Nfft)*SNR);
        noise = N0*complex(randn(size(rxWaveform)),randn(size(rxWaveform)));
        rxWaveform = rxWaveform + noise;

        if (simLocal.PerfectChannelEstimator)
            % Perfect synchronization. Use information provided by the
            % channel to find the strongest multipath component
            pathFilters = getPathFilters(channel);
            [offset,mag] = nrPerfectTimingEstimate(pathGains,pathFilters);
        else
            % Practical synchronization. Correlate the received waveform
            % with the PDSCH DM-RS to give timing offset estimate 't' and
            % correlation magnitude 'mag'. The function
            % hSkipWeakTimingOffset is used to update the receiver timing
            % offset. If the correlation peak in 'mag' is weak, the current
            % timing estimate 't' is ignored and the previous estimate
            % 'offset' is used
            [t,mag] = nrTimingEstimate(carrier,rxWaveform,dmrsIndices,dmrsSymbols);
            offset = hSkipWeakTimingOffset(offset,t,mag);
            % Display a warning if the estimated timing offset exceeds the
            % maximum channel delay
            if offset > maxChDelay
                warning(['Estimated timing offset (%d) is greater than the maximum channel delay (%d).' ...
                    ' This will result in a decoding failure. This may be caused by low SNR,' ...
                    ' or not enough DM-RS symbols to synchronize successfully.'],offset,maxChDelay);
            end
        end
        rxWaveform = rxWaveform(1+offset:end,:);

        % Perform OFDM demodulation on the received data to recreate the
        % resource grid, including padding in the event that practical
        % synchronization results in an incomplete slot being demodulated
        rxGrid = nrOFDMDemodulate(carrier,rxWaveform);
        [K,L,R] = size(rxGrid);
        if (L < carrier.SymbolsPerSlot)
            rxGrid = cat(2,rxGrid,zeros(K,carrier.SymbolsPerSlot-L,R));
        end

        if (simLocal.PerfectChannelEstimator)
            % Perfect channel estimation, using the value of the path gains
            % provided by the channel. This channel estimate does not
            % include the effect of transmitter precoding
            estChannelGrid = nrPerfectChannelEstimate(carrier,pathGains,pathFilters,offset,sampleTimes);

            % Get perfect noise estimate (from the noise realization)
            noiseGrid = nrOFDMDemodulate(carrier,noise(1+offset:end ,:));
            noiseEst = var(noiseGrid(:));

            % Get precoding matrix for next slot
            newWtx = getPrecodingMatrix(carrier,pdsch,estChannelGrid,pdschextra.PRGBundleSize);

            % Get PDSCH resource elements from the received grid and
            % channel estimate
            [pdschRx,pdschHest,~,pdschHestIndices] = nrExtractResources(pdschIndices,rxGrid,estChannelGrid);

            % Apply precoding to channel estimate
            pdschHest = hPRGPrecode(size(estChannelGrid),carrier.NStartGrid,pdschHest,pdschHestIndices,permute(wtx,[2 1 3]));
        else
            % Practical channel estimation between the received grid and
            % each transmission layer, using the PDSCH DM-RS for each
            % layer. This channel estimate includes the effect of
            % transmitter precoding
            [estChannelGrid,noiseEst] = nrChannelEstimate(carrier,rxGrid,dmrsIndices,dmrsSymbols,'CDMLengths',pdsch.DMRS.CDMLengths);

            % Get PDSCH resource elements from the received grid and
            % channel estimate
            [pdschRx,pdschHest] = nrExtractResources(pdschIndices,rxGrid,estChannelGrid);

            % Remove precoding from estChannelGrid prior to precoding
            % matrix calculation
            estChannelGridPorts = precodeChannelEstimate(carrier,estChannelGrid,conj(wtx));

            % Get precoding matrix for next slot
            newWtx = getPrecodingMatrix(carrier,pdsch,estChannelGridPorts,pdschextra.PRGBundleSize);
        end

        % Equalization
        [pdschEq,csi] = nrEqualizeMMSE(pdschRx,pdschHest,noiseEst);

        % Common phase error (CPE) compensation
        if ~isempty(ptrsIndices)
            % Initialize temporary grid to store equalized symbols
            tempGrid = nrResourceGrid(carrier,pdsch.NumLayers);

            % Extract PT-RS symbols from received grid and estimated
            % channel grid
            [ptrsRx,ptrsHest,~,~,ptrsHestIndices,ptrsLayerIndices] = nrExtractResources(ptrsIndices,rxGrid,estChannelGrid,tempGrid);

            if (simLocal.PerfectChannelEstimator)
                % Apply precoding to channel estimate
                ptrsHest = hPRGPrecode(size(estChannelGrid),carrier.NStartGrid,ptrsHest,ptrsHestIndices,permute(wtx,[2 1 3]));
            end

            % Equalize PT-RS symbols and map them to tempGrid
            ptrsEq = nrEqualizeMMSE(ptrsRx,ptrsHest,noiseEst);
            tempGrid(ptrsLayerIndices) = ptrsEq;

            % Estimate the residual channel at the PT-RS locations in
            % tempGrid
            cpe = nrChannelEstimate(tempGrid,ptrsIndices,ptrsSymbols);

            % Sum estimates across subcarriers, receive antennas, and
            % layers. Then, get the CPE by taking the angle of the
            % resultant sum
            cpe = angle(sum(cpe,[1 3 4]));

            % Map the equalized PDSCH symbols to tempGrid
            tempGrid(pdschIndices) = pdschEq;

            % Correct CPE in each OFDM symbol within the range of reference
            % PT-RS OFDM symbols
            symLoc = pdschIndicesInfo.PTRSSymbolSet(1)+1:pdschIndicesInfo.PTRSSymbolSet(end)+1;
            tempGrid(:,symLoc,:) = tempGrid(:,symLoc,:).*exp(-1i*cpe(symLoc));

            % Extract PDSCH symbols
            pdschEq = tempGrid(pdschIndices);
        end

        % Decode PDSCH physical channel
        [dlschLLRs,rxSymbols] = nrPDSCHDecode(carrier,pdsch,pdschEq,noiseEst);

        % Display EVM per layer, per slot and per RB
        if (simLocal.DisplayDiagnostics)
            plotLayerEVM(NSlots,nslot,pdsch,size(pdschGrid),pdschIndices,pdschSymbols,pdschEq);
        end

        % Scale LLRs by CSI
        csi = nrLayerDemap(csi); % CSI layer demapping
        for cwIdx = 1:pdsch.NumCodewords
            Qm = length(dlschLLRs{cwIdx})/length(rxSymbols{cwIdx}); % bits per symbol
            csi{cwIdx} = repmat(csi{cwIdx}.',Qm,1);                 % expand by each bit per symbol
            dlschLLRs{cwIdx} = dlschLLRs{cwIdx} .* csi{cwIdx}(:);   % scale by CSI
        end

        % Decode the DL-SCH transport channel
        decodeDLSCHLocal.TransportBlockLength = trBlkSizes;
        [decbits,blkerr] = decodeDLSCHLocal(dlschLLRs,pdsch.Modulation,pdsch.NumLayers,harqEntity.RedundancyVersion,harqEntity.HARQProcessID);

        % Store values to calculate throughput
        simThroughput(snrIdx) = simThroughput(snrIdx) + sum(~blkerr .* trBlkSizes);
        maxThroughput(snrIdx) = maxThroughput(snrIdx) + sum(trBlkSizes);

        % Update current process with CRC error and advance to next process
        procstatus = updateAndAdvance(harqEntity,blkerr,trBlkSizes,pdschIndicesInfo.G);
        if (simLocal.DisplaySimulationInformation)
            fprintf('\n(%3.2f%%) NSlot=%d, %s',100*(nslot+1)/NSlots,nslot,procstatus);
        end

     end

    % Display the results dynamically in the command window
    if (simLocal.DisplaySimulationInformation)
        fprintf('\n');
    end
    fprintf('\nThroughput(Mbps) for %d frame(s) = %.4f\n',simLocal.NFrames,1e-6*simThroughput(snrIdx)/(simLocal.NFrames*10e-3));
    fprintf('Throughput(%%) for %d frame(s) = %.4f\n',simLocal.NFrames,simThroughput(snrIdx)*100/maxThroughput(snrIdx));

end

Simulating transmission scheme 1 (8x2) and SCS=30kHz with CDL-C channel at -5dB SNR for 2 10ms frame(s)

(2.50%) NSlot=0, HARQ Proc 0: CW0: Initial transmission failed (RV=0,CR=0.474736).
(5.00%) NSlot=1, HARQ Proc 1: CW0: Initial transmission failed (RV=0,CR=0.474736).
(7.50%) NSlot=2, HARQ Proc 2: CW0: Initial transmission failed (RV=0,CR=0.474736).
(10.00%) NSlot=3, HARQ Proc 3: CW0: Initial transmission failed (RV=0,CR=0.474736).
(12.50%) NSlot=4, HARQ Proc 4: CW0: Initial transmission failed (RV=0,CR=0.474736).
(15.00%) NSlot=5, HARQ Proc 5: CW0: Initial transmission failed (RV=0,CR=0.474736).
(17.50%) NSlot=6, HARQ Proc 6: CW0: Initial transmission failed (RV=0,CR=0.474736).
(20.00%) NSlot=7, HARQ Proc 7: CW0: Initial transmission failed (RV=0,CR=0.474736).
(22.50%) NSlot=8, HARQ Proc 8: CW0: Initial transmission failed (RV=0,CR=0.474736).
(25.00%) NSlot=9, HARQ Proc 9: CW0: Initial transmission failed (RV=0,CR=0.474736).
(27.50%) NSlot=10, HARQ Proc 10: CW0: Initial transmission failed (RV=0,CR=0.474736).
(30.00%) NSlot=11, HARQ Proc 11: CW0: Initial transmission failed (RV=0,CR=0.474736).
(32.50%) NSlot=12, HARQ Proc 12: CW0: Initial transmission failed (RV=0,CR=0.474736).
(35.00%) NSlot=13, HARQ Proc 13: CW0: Initial transmission failed (RV=0,CR=0.474736).
(37.50%) NSlot=14, HARQ Proc 14: CW0: Initial transmission failed (RV=0,CR=0.474736).
(40.00%) NSlot=15, HARQ Proc 15: CW0: Initial transmission failed (RV=0,CR=0.474736).
(42.50%) NSlot=16, HARQ Proc 0: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(45.00%) NSlot=17, HARQ Proc 1: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(47.50%) NSlot=18, HARQ Proc 2: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(50.00%) NSlot=19, HARQ Proc 3: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(52.50%) NSlot=20, HARQ Proc 4: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(55.00%) NSlot=21, HARQ Proc 5: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(57.50%) NSlot=22, HARQ Proc 6: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(60.00%) NSlot=23, HARQ Proc 7: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(62.50%) NSlot=24, HARQ Proc 8: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(65.00%) NSlot=25, HARQ Proc 9: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(67.50%) NSlot=26, HARQ Proc 10: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(70.00%) NSlot=27, HARQ Proc 11: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(72.50%) NSlot=28, HARQ Proc 12: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(75.00%) NSlot=29, HARQ Proc 13: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(77.50%) NSlot=30, HARQ Proc 14: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(80.00%) NSlot=31, HARQ Proc 15: CW0: Retransmission #1 passed (RV=2,CR=0.474736).
(82.50%) NSlot=32, HARQ Proc 0: CW0: Initial transmission failed (RV=0,CR=0.474736).
(85.00%) NSlot=33, HARQ Proc 1: CW0: Initial transmission failed (RV=0,CR=0.474736).
(87.50%) NSlot=34, HARQ Proc 2: CW0: Initial transmission failed (RV=0,CR=0.474736).
(90.00%) NSlot=35, HARQ Proc 3: CW0: Initial transmission failed (RV=0,CR=0.474736).
(92.50%) NSlot=36, HARQ Proc 4: CW0: Initial transmission failed (RV=0,CR=0.474736).
(95.00%) NSlot=37, HARQ Proc 5: CW0: Initial transmission failed (RV=0,CR=0.474736).
(97.50%) NSlot=38, HARQ Proc 6: CW0: Initial transmission failed (RV=0,CR=0.474736).
(100.00%) NSlot=39, HARQ Proc 7: CW0: Initial transmission failed (RV=0,CR=0.474736).

Throughput(Mbps) for 2 frame(s) = 24.1728
Throughput(%) for 2 frame(s) = 40.0000

Simulating transmission scheme 1 (8x2) and SCS=30kHz with CDL-C channel at 0dB SNR for 2 10ms frame(s)

(2.50%) NSlot=0, HARQ Proc 0: CW0: Initial transmission passed (RV=0,CR=0.474736).
(5.00%) NSlot=1, HARQ Proc 1: CW0: Initial transmission passed (RV=0,CR=0.474736).
(7.50%) NSlot=2, HARQ Proc 2: CW0: Initial transmission passed (RV=0,CR=0.474736).
(10.00%) NSlot=3, HARQ Proc 3: CW0: Initial transmission passed (RV=0,CR=0.474736).
(12.50%) NSlot=4, HARQ Proc 4: CW0: Initial transmission passed (RV=0,CR=0.474736).
(15.00%) NSlot=5, HARQ Proc 5: CW0: Initial transmission passed (RV=0,CR=0.474736).
(17.50%) NSlot=6, HARQ Proc 6: CW0: Initial transmission passed (RV=0,CR=0.474736).
(20.00%) NSlot=7, HARQ Proc 7: CW0: Initial transmission passed (RV=0,CR=0.474736).
(22.50%) NSlot=8, HARQ Proc 8: CW0: Initial transmission passed (RV=0,CR=0.474736).
(25.00%) NSlot=9, HARQ Proc 9: CW0: Initial transmission passed (RV=0,CR=0.474736).
(27.50%) NSlot=10, HARQ Proc 10: CW0: Initial transmission passed (RV=0,CR=0.474736).
(30.00%) NSlot=11, HARQ Proc 11: CW0: Initial transmission passed (RV=0,CR=0.474736).
(32.50%) NSlot=12, HARQ Proc 12: CW0: Initial transmission passed (RV=0,CR=0.474736).
(35.00%) NSlot=13, HARQ Proc 13: CW0: Initial transmission passed (RV=0,CR=0.474736).
(37.50%) NSlot=14, HARQ Proc 14: CW0: Initial transmission passed (RV=0,CR=0.474736).
(40.00%) NSlot=15, HARQ Proc 15: CW0: Initial transmission passed (RV=0,CR=0.474736).
(42.50%) NSlot=16, HARQ Proc 0: CW0: Initial transmission passed (RV=0,CR=0.474736).
(45.00%) NSlot=17, HARQ Proc 1: CW0: Initial transmission passed (RV=0,CR=0.474736).
(47.50%) NSlot=18, HARQ Proc 2: CW0: Initial transmission passed (RV=0,CR=0.474736).
(50.00%) NSlot=19, HARQ Proc 3: CW0: Initial transmission passed (RV=0,CR=0.474736).
(52.50%) NSlot=20, HARQ Proc 4: CW0: Initial transmission passed (RV=0,CR=0.474736).
(55.00%) NSlot=21, HARQ Proc 5: CW0: Initial transmission passed (RV=0,CR=0.474736).
(57.50%) NSlot=22, HARQ Proc 6: CW0: Initial transmission passed (RV=0,CR=0.474736).
(60.00%) NSlot=23, HARQ Proc 7: CW0: Initial transmission passed (RV=0,CR=0.474736).
(62.50%) NSlot=24, HARQ Proc 8: CW0: Initial transmission passed (RV=0,CR=0.474736).
(65.00%) NSlot=25, HARQ Proc 9: CW0: Initial transmission passed (RV=0,CR=0.474736).
(67.50%) NSlot=26, HARQ Proc 10: CW0: Initial transmission passed (RV=0,CR=0.474736).
(70.00%) NSlot=27, HARQ Proc 11: CW0: Initial transmission passed (RV=0,CR=0.474736).
(72.50%) NSlot=28, HARQ Proc 12: CW0: Initial transmission passed (RV=0,CR=0.474736).
(75.00%) NSlot=29, HARQ Proc 13: CW0: Initial transmission passed (RV=0,CR=0.474736).
(77.50%) NSlot=30, HARQ Proc 14: CW0: Initial transmission passed (RV=0,CR=0.474736).
(80.00%) NSlot=31, HARQ Proc 15: CW0: Initial transmission passed (RV=0,CR=0.474736).
(82.50%) NSlot=32, HARQ Proc 0: CW0: Initial transmission passed (RV=0,CR=0.474736).
(85.00%) NSlot=33, HARQ Proc 1: CW0: Initial transmission passed (RV=0,CR=0.474736).
(87.50%) NSlot=34, HARQ Proc 2: CW0: Initial transmission passed (RV=0,CR=0.474736).
(90.00%) NSlot=35, HARQ Proc 3: CW0: Initial transmission passed (RV=0,CR=0.474736).
(92.50%) NSlot=36, HARQ Proc 4: CW0: Initial transmission passed (RV=0,CR=0.474736).
(95.00%) NSlot=37, HARQ Proc 5: CW0: Initial transmission passed (RV=0,CR=0.474736).
(97.50%) NSlot=38, HARQ Proc 6: CW0: Initial transmission passed (RV=0,CR=0.474736).
(100.00%) NSlot=39, HARQ Proc 7: CW0: Initial transmission passed (RV=0,CR=0.474736).

Throughput(Mbps) for 2 frame(s) = 60.4320
Throughput(%) for 2 frame(s) = 100.0000

Simulating transmission scheme 1 (8x2) and SCS=30kHz with CDL-C channel at 5dB SNR for 2 10ms frame(s)

(2.50%) NSlot=0, HARQ Proc 0: CW0: Initial transmission passed (RV=0,CR=0.474736).
(5.00%) NSlot=1, HARQ Proc 1: CW0: Initial transmission passed (RV=0,CR=0.474736).
(7.50%) NSlot=2, HARQ Proc 2: CW0: Initial transmission passed (RV=0,CR=0.474736).
(10.00%) NSlot=3, HARQ Proc 3: CW0: Initial transmission passed (RV=0,CR=0.474736).
(12.50%) NSlot=4, HARQ Proc 4: CW0: Initial transmission passed (RV=0,CR=0.474736).
(15.00%) NSlot=5, HARQ Proc 5: CW0: Initial transmission passed (RV=0,CR=0.474736).
(17.50%) NSlot=6, HARQ Proc 6: CW0: Initial transmission passed (RV=0,CR=0.474736).
(20.00%) NSlot=7, HARQ Proc 7: CW0: Initial transmission passed (RV=0,CR=0.474736).
(22.50%) NSlot=8, HARQ Proc 8: CW0: Initial transmission passed (RV=0,CR=0.474736).
(25.00%) NSlot=9, HARQ Proc 9: CW0: Initial transmission passed (RV=0,CR=0.474736).
(27.50%) NSlot=10, HARQ Proc 10: CW0: Initial transmission passed (RV=0,CR=0.474736).
(30.00%) NSlot=11, HARQ Proc 11: CW0: Initial transmission passed (RV=0,CR=0.474736).
(32.50%) NSlot=12, HARQ Proc 12: CW0: Initial transmission passed (RV=0,CR=0.474736).
(35.00%) NSlot=13, HARQ Proc 13: CW0: Initial transmission passed (RV=0,CR=0.474736).
(37.50%) NSlot=14, HARQ Proc 14: CW0: Initial transmission passed (RV=0,CR=0.474736).
(40.00%) NSlot=15, HARQ Proc 15: CW0: Initial transmission passed (RV=0,CR=0.474736).
(42.50%) NSlot=16, HARQ Proc 0: CW0: Initial transmission passed (RV=0,CR=0.474736).
(45.00%) NSlot=17, HARQ Proc 1: CW0: Initial transmission passed (RV=0,CR=0.474736).
(47.50%) NSlot=18, HARQ Proc 2: CW0: Initial transmission passed (RV=0,CR=0.474736).
(50.00%) NSlot=19, HARQ Proc 3: CW0: Initial transmission passed (RV=0,CR=0.474736).
(52.50%) NSlot=20, HARQ Proc 4: CW0: Initial transmission passed (RV=0,CR=0.474736).
(55.00%) NSlot=21, HARQ Proc 5: CW0: Initial transmission passed (RV=0,CR=0.474736).
(57.50%) NSlot=22, HARQ Proc 6: CW0: Initial transmission passed (RV=0,CR=0.474736).
(60.00%) NSlot=23, HARQ Proc 7: CW0: Initial transmission passed (RV=0,CR=0.474736).
(62.50%) NSlot=24, HARQ Proc 8: CW0: Initial transmission passed (RV=0,CR=0.474736).
(65.00%) NSlot=25, HARQ Proc 9: CW0: Initial transmission passed (RV=0,CR=0.474736).
(67.50%) NSlot=26, HARQ Proc 10: CW0: Initial transmission passed (RV=0,CR=0.474736).
(70.00%) NSlot=27, HARQ Proc 11: CW0: Initial transmission passed (RV=0,CR=0.474736).
(72.50%) NSlot=28, HARQ Proc 12: CW0: Initial transmission passed (RV=0,CR=0.474736).
(75.00%) NSlot=29, HARQ Proc 13: CW0: Initial transmission passed (RV=0,CR=0.474736).
(77.50%) NSlot=30, HARQ Proc 14: CW0: Initial transmission passed (RV=0,CR=0.474736).
(80.00%) NSlot=31, HARQ Proc 15: CW0: Initial transmission passed (RV=0,CR=0.474736).
(82.50%) NSlot=32, HARQ Proc 0: CW0: Initial transmission passed (RV=0,CR=0.474736).
(85.00%) NSlot=33, HARQ Proc 1: CW0: Initial transmission passed (RV=0,CR=0.474736).
(87.50%) NSlot=34, HARQ Proc 2: CW0: Initial transmission passed (RV=0,CR=0.474736).
(90.00%) NSlot=35, HARQ Proc 3: CW0: Initial transmission passed (RV=0,CR=0.474736).
(92.50%) NSlot=36, HARQ Proc 4: CW0: Initial transmission passed (RV=0,CR=0.474736).
(95.00%) NSlot=37, HARQ Proc 5: CW0: Initial transmission passed (RV=0,CR=0.474736).
(97.50%) NSlot=38, HARQ Proc 6: CW0: Initial transmission passed (RV=0,CR=0.474736).
(100.00%) NSlot=39, HARQ Proc 7: CW0: Initial transmission passed (RV=0,CR=0.474736).

Throughput(Mbps) for 2 frame(s) = 60.4320
Throughput(%) for 2 frame(s) = 100.0000

Results

Display the measured throughput. This is calculated as the percentage of the maximum possible throughput of the link given the available resources for data transmission.

figure;
plot(simParameters.SNRIn,simThroughput*100./maxThroughput,'o-.')
xlabel('SNR (dB)'); ylabel('Throughput (%)'); grid on;
title(sprintf('%s (%dx%d) / NRB=%d / SCS=%dkHz', ...
              simParameters.DelayProfile,simParameters.NTxAnts,simParameters.NRxAnts, ...
              simParameters.Carrier.NSizeGrid,simParameters.Carrier.SubcarrierSpacing));

% Bundle key parameters and results into a combined structure for recording
simResults.simParameters = simParameters;
simResults.simThroughput = simThroughput;
simResults.maxThroughput = maxThroughput;

The figure below shows throughput results obtained simulating 10000 subframes (NFrames = 1000, SNRIn = -18:2:16).

Selected Bibliography

3GPP TS 38.211. "NR; Physical channels and modulation." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.
3GPP TS 38.212. "NR; Multiplexing and channel coding." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.
3GPP TS 38.213. "NR; Physical layer procedures for control." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.
3GPP TS 38.214. "NR; Physical layer procedures for data." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.
3GPP TR 38.901. "Study on channel model for frequencies from 0.5 to 100 GHz." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

Local Functions

function validateNumLayers(simParameters)
% Validate the number of layers, relative to the antenna geometry

    numlayers = simParameters.PDSCH.NumLayers;
    ntxants = simParameters.NTxAnts;
    nrxants = simParameters.NRxAnts;
    antennaDescription = sprintf('min(NTxAnts,NRxAnts) = min(%d,%d) = %d',ntxants,nrxants,min(ntxants,nrxants));
    if numlayers > min(ntxants,nrxants)
        error('The number of layers (%d) must satisfy NumLayers <= %s', ...
            numlayers,antennaDescription);
    end

    % Display a warning if the maximum possible rank of the channel equals
    % the number of layers
    if (numlayers > 2) && (numlayers == min(ntxants,nrxants))
        warning(['The maximum possible rank of the channel, given by %s, is equal to NumLayers (%d).' ...
            ' This may result in a decoding failure under some channel conditions.' ...
            ' Try decreasing the number of layers or increasing the channel rank' ...
            ' (use more transmit or receive antennas).'],antennaDescription,numlayers); %#ok<SPWRN>
    end

end

function estChannelGrid = getInitialChannelEstimate(carrier,nTxAnts,propchannel)
% Obtain channel estimate before first transmission. This can be used to
% obtain a precoding matrix for the first slot.

    ofdmInfo = nrOFDMInfo(carrier);

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

    % Temporary waveform (only needed for the sizes)
    tmpWaveform = zeros((ofdmInfo.SampleRate/1000/carrier.SlotsPerSubframe)+maxChDelay,nTxAnts);

    % Filter through channel
    [~,pathGains,sampleTimes] = propchannel(tmpWaveform);

    % Perfect timing synch
    pathFilters = getPathFilters(propchannel);
    offset = nrPerfectTimingEstimate(pathGains,pathFilters);

    % Perfect channel estimate
    estChannelGrid = nrPerfectChannelEstimate(carrier,pathGains,pathFilters,offset,sampleTimes);

end

function wtx = getPrecodingMatrix(carrier,pdsch,hestGrid,prgbundlesize)
% Calculate precoding matrices for all PRGs in the carrier that overlap
% with the PDSCH allocation

    % Maximum CRB addressed by carrier grid
    maxCRB = carrier.NStartGrid + carrier.NSizeGrid - 1;

    % PRG size
    if nargin==4 && ~isempty(prgbundlesize)
        Pd_BWP = prgbundlesize;
    else
        Pd_BWP = maxCRB + 1;
    end

    % PRG numbers (1-based) for each RB in the carrier grid
    NPRG = ceil((maxCRB + 1) / Pd_BWP);
    prgset = repmat((1:NPRG),Pd_BWP,1);
    prgset = prgset(carrier.NStartGrid + (1:carrier.NSizeGrid).');

    [~,~,R,P] = size(hestGrid);
    wtx = zeros([pdsch.NumLayers P NPRG]);
    for i = 1:NPRG

        % Subcarrier indices within current PRG and within the PDSCH
        % allocation
        thisPRG = find(prgset==i) - 1;
        thisPRG = intersect(thisPRG,pdsch.PRBSet(:) + carrier.NStartGrid,'rows');
        prgSc = (1:12)' + 12*thisPRG';
        prgSc = prgSc(:);

        if (~isempty(prgSc))

            % Average channel estimate in PRG
            estAllocGrid = hestGrid(prgSc,:,:,:);
            Hest = permute(mean(reshape(estAllocGrid,[],R,P)),[2 3 1]);

            % SVD decomposition
            [~,~,V] = svd(Hest);
            wtx(:,:,i) = V(:,1:pdsch.NumLayers).';

        end

    end

    wtx = wtx / sqrt(pdsch.NumLayers); % Normalize by NumLayers

end

function estChannelGrid = precodeChannelEstimate(carrier,estChannelGrid,W)
% Apply precoding matrix W to the last dimension of the channel estimate

    [K,L,R,P] = size(estChannelGrid);
    estChannelGrid = reshape(estChannelGrid,[K*L R P]);
    estChannelGrid = hPRGPrecode([K L R P],carrier.NStartGrid,estChannelGrid,reshape(1:numel(estChannelGrid),[K*L R P]),W);
    estChannelGrid = reshape(estChannelGrid,K,L,R,[]);

end

function plotLayerEVM(NSlots,nslot,pdsch,siz,pdschIndices,pdschSymbols,pdschEq)
% Plot EVM information

    persistent slotEVM;
    persistent rbEVM
    persistent evmPerSlot;

    if (nslot==0)
        slotEVM = comm.EVM;
        rbEVM = comm.EVM;
        evmPerSlot = NaN(NSlots,pdsch.NumLayers);
        figure;
    end
    evmPerSlot(nslot+1,:) = slotEVM(pdschSymbols,pdschEq);
    subplot(2,1,1);
    plot(0:(NSlots-1),evmPerSlot,'o-');
    xlabel('Slot number');
    ylabel('EVM (%)');
    legend("layer " + (1:pdsch.NumLayers),'Location','EastOutside');
    title('EVM per layer per slot');

    subplot(2,1,2);
    [k,~,p] = ind2sub(siz,pdschIndices);
    rbsubs = floor((k-1) / 12);
    NRB = siz(1) / 12;
    evmPerRB = NaN(NRB,pdsch.NumLayers);
    for nu = 1:pdsch.NumLayers
        for rb = unique(rbsubs).'
            this = (rbsubs==rb & p==nu);
            evmPerRB(rb+1,nu) = rbEVM(pdschSymbols(this),pdschEq(this));
        end
    end
    plot(0:(NRB-1),evmPerRB,'x-');
    xlabel('Resource block');
    ylabel('EVM (%)');
    legend("layer " + (1:pdsch.NumLayers),'Location','EastOutside');
    title(['EVM per layer per resource block, slot #' num2str(nslot)]);

    drawnow;

end