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PUCCH3 ACK Missed Detection Probability Conformance Test

This example measures the ACK missed detection probability using the LTE System Toolbox™ under the single user Physical Uplink Control Channel (PUCCH3) conformance test conditions as defined in TS 36.104 Section [ 1 ].


This example uses a simulation length of 10 subframes. This value has been chosen to speed up the simulation. A larger value should be chosen to obtain more accurate results. The target defined in TS36.104 Section [ 1 ] for 10 MHz bandwidth (50 resource blocks) and a single transmit antenna is an Acknowledgment (ACK) missed detection probability not exceeding 1% at an SNR of -3.7 dB. The test is defined for 1 transmit antenna.

numSubframes = 10;                          % Number of subframes
SNRdB = [-9.7 -7.7 -5.7 -3.7 -1.7];         % SNR range
NTxAnts = 1;                                % Number of transmit antennas

UE Configuration

ue = struct;                                % UE config structure
ue.NULRB = 50;                              % 50 resource blocks (10 MHz)
ue.CyclicPrefixUL = 'Normal';               % Normal cyclic prefix
ue.NTxAnts = NTxAnts;
ue.NCellID = 9;
ue.RNTI = 1;                                % Radio network temporary id
ue.Hopping = 'Off';                         % No frequency hopping
ue.Shortened = 0;                           % No SRS transmission

PUCCH 3 Configuration

% Vector of PUCCH resource indices, one per transmission antenna. This is
% the n3pucch parameter.
pucch = struct;
pucch.ResourceIdx = 0:ue.NTxAnts-1;

Propagation Channel Configuration

Configure the channel model with the parameters specified in the tests described in TS36.104 Section [ 1 ].

channel = struct;                 % Channel config structure
channel.NRxAnts = 2;              % Number of receive antennas
channel.DelayProfile = 'EPA';     % Channel delay profile
channel.DopplerFreq = 5.0;        % Doppler frequency in Hz
channel.MIMOCorrelation = 'Low';  % Low MIMO correlation
channel.NTerms = 16;              % Oscillators used in fading model
channel.ModelType = 'GMEDS';      % Rayleigh fading model type
channel.Seed = 4;                 % Random number generator seed
channel.InitPhase = 'Random';     % Random initial phases
channel.NormalizePathGains = 'On';% Normalize delay profile power
channel.NormalizeTxAnts = 'On';   % Normalize for transmit antennas

% SC-FDMA modulation information: required to get the sampling rate
info = lteSCFDMAInfo(ue);
channel.SamplingRate = info.SamplingRate;

Channel Estimator Configuration

The channel estimator is configured using a structure cec. Here cubic interpolation will be used with an averaging window of 12-by-1 Resource Elements (REs). This configures the channel estimator to use a special mode which ensures the ability to despread and orthogonalize the different overlapping PUCCH transmissions.

cec = struct;                     % Channel estimation config structure
cec.PilotAverage = 'UserDefined'; % Type of pilot averaging
cec.FreqWindow = 12;              % Frequency averaging window in REs (special mode)
cec.TimeWindow = 1;               % Time averaging window in REs (Special mode)
cec.InterpType = 'cubic';         % Cubic interpolation

Simulation Loop for Configured SNR Points

For each SNR point the loop below calculates the probability of successful ACK detection using information obtained from NSubframes consecutive subframes. The following operations are performed for each subframe and SNR values:

  • Create an empty resource grid

  • Generate and map PUCCH 3 and its Demodulation Reference Signal (DRS) to the resource grid

  • Apply SC-FDMA modulation

  • Send the modulated signal through the channel

  • Receiver synchronization

  • Apply SC-FDMA demodulation

  • Estimate the channel

  • Minimum Mean Squared Error (MMSE) equalization

  • PUCCH 3 demodulation/decoding

  • Record decoding failures

% Preallocate memory for missed detection probability vector
PMISS = zeros(size(SNRdB));
for nSNR = 1:length(SNRdB)

    % Detection failures counter
    missCount = 0;
    falseCount = 0;

    % Noise configuration
    SNR = 10^(SNRdB(nSNR)/20);              % Convert dB to linear
    % The noise added before SC-FDMA demodulation will be amplified by the
    % IFFT. The amplification is the square root of the size of the IFFT.
    % To achieve the desired SNR after demodulation the noise power is
    % normalized by this value. In addition, because real and imaginary
    % parts of the noise are created separately before being combined into
    % complex additive white Gaussian noise, the noise amplitude must be
    % scaled by 1/sqrt(2*ue.NTxAnts) so the generated noise power is 1.
    N = 1/(SNR*sqrt(double(info.Nfft)))/sqrt(2.0*ue.NTxAnts);
    % Set the type of random number generator and its seed to the default
    % value

    % Loop for subframes
    offsetused = 0;
    for nsf = 1:numSubframes

        % Create resource grid
        ue.NSubframe = mod(nsf-1,10);       % Subframe number
        reGrid = lteULResourceGrid(ue);       % Resource grid

        % Generate PUCCH 3 and its DRS
        N_ACK = 4;                          % 4 ACK bits
        ACK = randi([0 1], N_ACK, 1);       % Generate N_ACK random bits
        coded = lteUCI3Encode(ACK);         % PUCCH 3 coding
        pucch3Sym = ltePUCCH3(ue, pucch, coded);     % PUCCH 3 modulation
        pucch3DRSSym = ltePUCCH3DRS(ue, pucch, ACK); % PUCCH 3 DRS creation

        % Generate indices for PUCCH 3 and its DRS
        pucch3Indices = ltePUCCH3Indices(ue, pucch);
        pucch3DRSIndices = ltePUCCH3DRSIndices(ue, pucch);

        % Map PUCCH 3 and its DRS to the resource grid
        reGrid(pucch3Indices) = pucch3Sym;
        reGrid(pucch3DRSIndices) = pucch3DRSSym;

        % SC-FDMA modulation
        txwave = lteSCFDMAModulate(ue, reGrid);

        % Channel state information: set the init time to the correct value
        % to guarantee continuity of the fading waveform after each
        % subframe
        channel.InitTime = (nsf-1)/1000;

        % Channel modeling
        % The additional 25 samples added to the end of the waveform
        % are to cover the range of delays expected from the channel
        % modeling (a combination of implementation delay and
        % channel delay spread)
        rxwave = lteFadingChannel(channel, [txwave; zeros(25, ue.NTxAnts)]);

        % Add noise at receiver
        noise = N*complex(randn(size(rxwave)), randn(size(rxwave)));
        rxwave = rxwave + noise;

        % Receiver

        % Synchronization
        % An offset within the range of delays expected from the channel
        % modeling (a combination of implementation delay and channel
        % delay spread) indicates success
        offset = lteULFrameOffsetPUCCH3(ue, pucch, rxwave);
        if (offset<25)
            offsetused = offset;

        % SC-FDMA demodulation
        rxgrid = lteSCFDMADemodulate(ue, rxwave(1+offsetused:end, :));

        % Channel estimation
        [H, n0] = lteULChannelEstimatePUCCH3(ue, pucch, cec, rxgrid);

        % Extract REs corresponding to the PUCCH 3 from the given subframe
        % across all receive antennas and channel estimates
        [pucch3Rx, pucch3H] = lteExtractResources(pucch3Indices, rxgrid, H);

        % PUCCH 3 MMSE Equalization
        eqgrid = lteULResourceGrid(ue);
        eqgrid(pucch3Indices) = lteEqualizeMMSE(pucch3Rx, pucch3H, n0);

        % PUCCH 3 demodulation
        rxBits = ltePUCCH3Decode(ue, pucch, eqgrid(pucch3Indices));

        % PUCCH 3 decoding
        rxACK = lteUCI3Decode(rxBits, N_ACK);

        % Detect missed (empty rxACK) or incorrect Hybrid Automatic Repeat
        % Request (HARQ)-ACK
        % (compare against transmitted ACK)

        if (isempty(rxACK) || any(rxACK ~= ACK))
            missCount = missCount + 1;


    PMISS(nSNR) = missCount/numSubframes;



plot(SNRdB, PMISS, 'b-o', 'MarkerSize', 7, 'LineWidth', 2);
hold on;
plot(-3.7, 0.01, 'rx', 'MarkerSize', 7, 'LineWidth', 2);
xlabel('SNR (dB)');
ylabel('Probability of ACK missed detection');
title(['PUCCH format 3 ACK missed detection test' ...
        ' (TS36.104 Section']);
axis([SNRdB(1)-0.1 SNRdB(end)+0.1 -0.05 0.25]);
legend('simulated performance', 'target');

Selected Bibliography

  1. 3GPP TS 36.104 "Base Station (BS) radio transmission and reception"

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