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PUCCH1a Multi User ACK Missed Detection Probability Conformance Test

This example shows how to use the LTE Toolbox™ to measure the probability of Acknowledgment (ACK) missed detection for multiuser Physical Uplink Control Channel (PUCCH) 1a. The test conditions are defined in TS36.104 Section [ 1 ].


In this example, four different UEs are configured, each of which transmits a PUCCH format 1a signal. Appropriate Demodulation Reference Signals (DRS) are also generated. For each considered SNR value, the transmitted signals are fed through different channels and added, together with Gaussian noise. This simulates the reception of the signals from four different UEs at a base station. The receiver decodes the PUCCH1a for the user of interest and the probability of ACK missed detection is measured. 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 1.4 MHz bandwidth (6 Resource Blocks-RBs) and a single transmit antenna is an ACK missed detection probability not exceeding 1% at an SNR of -4.1 dB. The test is defined for 1 transmit antenna.

numSubframes = 10;                          % Number of subframes
SNRdB = [-16.1 -12.1 -8.1 -4.1 -0.1];        % SNR range
NTxAnts = 1;                                % Number of transmit antennas

UE 1 Configuration

Create a User Equipment (UE) configuration structure. These parameters are common for all the users.

ue = struct;                  % UE config structure
ue.NULRB = 6;                 % 6 resource blocks (1.4 MHz)
ue.CyclicPrefixUL = 'Normal'; % Normal cyclic prefix
ue.Hopping = 'Off';         % No frequency hopping
ue.NCellID = 150;           % Cell id as specified in TS36.104 Appendix A9
ue.Shortened = 0;           % No SRS transmission
ue.NTxAnts = NTxAnts;

PUCCH 1a Configuration

We intend to transmit an ACK via a PUCCH of Format 1, so we create an appropriate configuration structure pucch. We give the cell an arbitrary identification number, and set up PUCCH Resource Indices, transmission powers and channel seeds for each user. A different random channel seed for each user ensures that each experiences different channel conditions.

% Hybrid Automatic Repeat Request (HARQ)  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;
% Delta shift PUCCH parameter as specified in TS36.104 Appendix A9 [ <#8 1> ]
pucch.DeltaShift = 2;
% 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 as specified in
% TS36.104 Appendix A9
pucch.CyclicShifts = 0;
% Vector of PUCCH resource indices for all UEs as specified in TS36.104
% Appendix A9
usersPUCCHindices = [2 1 7 14];
% PUCCH power for all UEs as specified in TS36.104 Appendix A9
usersPUCCHpower = [0 0 -3 3];

Propagation Channel Configuration

This section of the code configures the propagation channels for the four UEs. The parameters are specified in the tests described in TS36.104 Section [ 1 ] and are: ETU 70Hz and 2 receive, i.e. base station, antennas is configured to be 2. Each UE will see a different channel, therefore a different seed is used in each case. This is specified in the ueChannelSeed parameter.

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.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 sampling rate

% Channel seeds for each of the 4 UEs (arbitrary)
ueChannelSeed = [11 1 7 14];

Channel Estimator Configuration

The channel estimator is configured using a structure. Here cubic interpolation will be used with an averaging window of 9x9 resource elements.

cec = struct;        % Channel estimation config structure
cec.TimeWindow = 9;  % Time averaging window size in resource elements
cec.FreqWindow = 9;  % Frequency averaging window size in resource elements
cec.InterpType = 'cubic';         % Cubic interpolation
cec.PilotAverage = 'UserDefined'; % Type of pilot averaging

Simulation Loop for Configured SNR Points

A loop is used to run the simulation for a set of SNR points, given by the vector SNRdB. The SNR vector configured here is a range of SNR points including an SNR point at -4.1dB, the SNR at which the test requirement for ACK detection rate (99%) is to be achieved.

% 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

    % Subframe and user loops
    % We now enter two further loops to process multiple subframes and
    % create each of the users' transmissions. The fading process time
    % offset, InitTime, is also generated for the current subframe

    offsetused = 0;
    for nsf = 1:numSubframes

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

        % Loop for each user
        for user = 1:4

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

            % Configure resource index for this user
            pucch.ResourceIdx = usersPUCCHindices(user);

            % ACK bit to transmit for the 1st (target) user, the PUCCH
            % Format 1 carries the Hybrid ARQ (HARQ) indicator ACK and for
            % other users it carries a random HARQ indicator. As there is a
            % single indicator, the transmissions will be of Format 1a. The
            % PUCCH Format 1 DRS carries no data.
            if (user==1)
                txACK = ACK;
                txACK = randi([0 1],1,1);

            % Generate PUCCH 1 and its DRS
            % Different users have different relative powers
            pucch1Sym = ltePUCCH1(ue,pucch,txACK)* ...
            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
            if (~isempty(txACK))
                txgrid(pucch1Indices) = pucch1Sym;
                txgrid(pucch1DRSIndices) = pucch1DRSSym;

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

            % Channel modeling and superposition of received signals.
            % 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). On each iteration of the loop we accumulate
            % the sum of each transmitted signal, simulating the reception
            % of all four users at the base station.
            channel.Seed = ueChannelSeed(user);
            if (user==1)
                rxwave = lteFadingChannel(channel,[txwave; zeros(25,NTxAnts)]);
                rxwave = rxwave + ...
                    lteFadingChannel(channel,[txwave; zeros(25,NTxAnts)]);

        % Receiver

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

        % Use the resource indices for the user of interest
        pucch.ResourceIdx = usersPUCCHindices(1);

        % Synchronization
        % The uplink frame timing estimate for UE1 is calculated using
        % the PUCCH 1 DRS signals and then used to demodulate the
        % SC-FDMA signal.
        % 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
        % The resulting grid (rxgrid) is a 3-dimensional matrix. The number
        % of rows represents the number of subcarriers. The number of
        % columns equals the number of SC-FDMA symbols in a subframe. The
        % number of subcarriers and symbols is the same for the returned
        % grid from lteSCFDMADemodulate as the grid passed into
        % lteSCFDMAModulate. The number of planes (3rd dimension) in the
        % grid corresponds to the number of receive antenna.
        rxgrid = lteSCFDMADemodulate(ue,rxwave(1+offsetused:end,:));

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

        % PUCCH 1 indices for UE of interest
        pucch1Indices = ltePUCCH1Indices(ue,pucch);

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

        % Minimum Mean Squared Error (MMSE) Equalization
        eqgrid = lteULResourceGrid(ue);
        eqgrid(pucch1Indices) = lteEqualizeMMSE(pucch1Rx,pucch1H,n0);

        % PUCCH 1 decoding
        rxACK = ltePUCCH1Decode(ue,pucch,1,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/numSubframes;



Finally we plot the simulated results against the target performance as stipulated in the standard.

grid on;
hold on;
xlabel('SNR (dB)');
ylabel('Probability of ACK missed detection');
title('Multi user PUCCH Format 1a test (TS36.104 Section');
axis([SNRdB(1)-0.1 SNRdB(end)+0.1 -0.05 0.4]);
legend('simulated performance','target');

Selected Bibliography

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