Main Content

PUCCH1a ACK Missed Detection Probability Conformance Test

This example measures the Acknowledgment (ACK) missed detection probability using the LTE Toolbox™ under the single user Physical Uplink Control Channel (PUCCH1a) conformance test conditions as defined in TS 36.104 Section


This example uses a simulation length of 10 subframes. This value has been chosen to speed up the simulation. A higher value should be chosen to obtain more accurate results. The probability of erroneous ACK detection is calculated for a number of SNR point. The target defined in TS36.104 Section [ 1 ] for 1.4 MHz bandwidth (6 RBs) and a single transmit antenna is an ACK missed detection probability not exceeding 1% at an SNR of -4.2 dB. The test is defined for 1 transmit antenna.

NSubframes = 10;                            % Number of subframes
SNRIn = [-10.2 -8.2 -6.2 -4.2 -2.2];        % SNR range in dB
NTxAnts = 1;                                % Number of transmit antennas

UE Configuration

ue = struct;                                % UE config structure
ue.NULRB = 6;                               % 6 resource blocks (1.4 MHz)
ue.CyclicPrefixUL = 'Extended';             % Extended cyclic prefix
ue.Hopping = 'Off';                         % No frequency hopping
ue.NCellID =  9;
ue.Shortened = 0;                           % No SRS transmission
ue.NTxAnts = NTxAnts;

PUCCH 1a Configuration

% Hybrid ARQ indicator bit set to one. Only one bit is required for PUCCH
% 1a
ACK = 1;
pucch = struct;                         % PUCCH config structure
% Set the size of resources allocated to PUCCH format 2. This affects the
% location of PUCCH 1 transmission
pucch.ResourceSize = 0;
pucch.DeltaShift = 1;                       % Delta shift PUCCH parameter
% Number of cyclic shifts used for PUCCH format 1 in resource blocks with a
% mixture of formats 1 and 2. This is the N1cs parameter
pucch.CyclicShifts = 0;
% Vector of PUCCH resource indices, one per transmission antenna. This is
% the n2pucch parameter
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 = 'ETU';           % Channel delay profile
channel.DopplerFreq = 70.0;             % 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 = 13;                      % Channel 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
scfdmaInfo = lteSCFDMAInfo(ue);
channel.SamplingRate = scfdmaInfo.SamplingRate;   % Channel sampling rate

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 1 and its Demodulation Reference Signal (DRS) to the resource grid

  • Apply SC-FDMA modulation

  • Send the modulated signal through the channel

  • Receiver synchronization

  • SC-FDMA demodulation

  • Channel estimation

  • Minimum Mean Squared Error (MMSE) equalization

  • PUCCH 1 demodulation/decoding

  • Measure missing or incorrect Hybrid Automatic Repeat Request (HARQ)-ACK

% Preallocate memory for probability of detection vector
PMISS = zeros(size(SNRIn));

for nSNR = 1:length(SNRIn)

    % Missed or incorrect ACK detection counter
    missCount = 0;

    % Noise configuration
    SNR = 10^(SNRIn(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(scfdmaInfo.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:NSubframes

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

        % Create PUCCH 1 and its DRS
        pucch1Sym = ltePUCCH1(ue,pucch,ACK);
        pucch1DRSSym = ltePUCCH1DRS(ue,pucch);

        % Generate indices for PUCCH 1 and its DRS
        pucch1Indices = ltePUCCH1Indices(ue,pucch);
        pucch1DRSIndices = ltePUCCH1DRSIndices(ue,pucch);

        % Map PUCCH 1 and PUCCH 1 DRS to the resource grid
        reGrid(pucch1Indices) = pucch1Sym;
        reGrid(pucch1DRSIndices) = pucch1DRSSym;

        % 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
        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 = lteULFrameOffsetPUCCH1(ue,pucch,rxwave);
        if (offset < 25)
            offsetused = offset;

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

        % Channel estimation
        [H,n0] = lteULChannelEstimatePUCCH1(ue,pucch,cec,rxgrid);

        % Extract REs corresponding to the PUCCH 1 from the given subframe
        % across all receive antennas and channel estimates
        [pucch1Rx,pucch1H] = lteExtractResources(pucch1Indices,rxgrid,H);

        % MMSE equalization
        eqgrid = lteULResourceGrid(ue);
        eqgrid(pucch1Indices) = lteEqualizeMMSE(pucch1Rx,pucch1H,n0);

        % PUCCH 1 demodulation/decoding
        rxACK = ltePUCCH1Decode(ue,pucch,length(ACK),eqgrid(pucch1Indices));

        % Detect missed (empty rxACK) or incorrect HARQ-ACK (compare
        % against transmitted ACK
        if (isempty(rxACK) || any(rxACK ~= ACK))
            missCount = missCount + 1;


    PMISS(nSNR) = (missCount/NSubframes);



The graph shows the simulation result for ACK missed detection test

hold on;
xlabel('SNR (dB)');
ylabel('Probability of missed ACK detection');
title('ACK missed detection test (TS36.104 Section');
axis([SNRIn(1)-0.1 SNRIn(end)+0.1 -0.05 .35]);
legend('simulated performance','target');

Selected Bibliography

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