802.11ax Packet Error Rate Simulation for Uplink Trigger-Based Format

This example shows how to measure the packet error rate of an IEEE® 802.11ax™ high efficiency (HE) uplink, trigger-based (TB) format.

Introduction

The 802.11ax [1] HE trigger-based (HE TB) format allows for OFDMA or MU-MIMO transmission in the uplink. An HE TB transmission is controlled entirely by an access point (AP). All the parameters required for the transmission are provided in a trigger frame to all STAs participating in the HE TB transmission. Each station (STA) transmits an HE TB packet simultaneously, when triggered by the AP as shown in the following diagram.

In this example an end-to-end simulation is used to determine the packet error rate of an HE TB link for four STAs in a MU-MIMO configuration. At each SNR point multiple packets are transmitted with no impairments apart from channel and noise. The received packets are demodulated and the PSDUs recovered for each STA. The PSDUs are compared to those transmitted to determine the number of packet errors and hence the packet error rate for all users. Packet detection, timing synchronization and symbol equalization is performed by the receiver. No frequency offset correction is performed in this example. The processing of HE TB processing chain is shown in the following diagram.

The receiver performs a minimum-mean-square-error-based ordered successive interference cancellation (MMSE-SIC) process for data equalization [2]. To avoid error propagation in the cancellation stage, data streams for all STAs are sorted in descending order based on the channel state information and equalized sequentially. This diagram shows the procedure of MMSE-SIC equalization.

Equalization Method

In this example, you can specify the equalization method as 'mmse' or 'mmse-sic'. The default equalizer is 'mmse-sic'.

equalizationMethod = 'mmse-sic';

User Configuration

In this example the allocation information and transmit parameters for multiple uplink STAs are configured using an heTBSystemConfig object.

allocationIndex = 195; % Four uplink users in a MU-MIMO configuration
cfgSys = heTBSystemConfig(allocationIndex);

In a trigger-based transmission some parameters are the same for all uplink users, while some can differ. The User property of cfgSys contains a cell array of user configurations. Each element of the cell array is an object which can be configured to set the parameters of individual users. In this example, all users have the same transmission parameters.

% These parameters are same for all users in the MU-MIMO system
cfgSys.HELTFType = 4;          % HE-LTF compression mode
cfgSys.GuardInterval = 3.2;    % Guard interval type
cfgSys.SingleStreamPilots = 1; % Single stream pilot transmission of HE-LTF
numRx = 8;                     % Number of receive(AP) antennas

% The individual parameters for each user are specified below
allocInfo = ruInfo(cfgSys);
numUsers = allocInfo.NumUsers; % Number of uplink users

for userIdx = 1:numUsers
    cfgSys.User{userIdx}.NumTransmitAntennas = 1;
    cfgSys.User{userIdx}.NumSpaceTimeStreams = 1;
    cfgSys.User{userIdx}.SpatialMapping = 'Direct';
    cfgSys.User{userIdx}.MCS = 7;
    cfgSys.User{userIdx}.APEPLength = 1e3;
    cfgSys.User{userIdx}.ChannelCoding = 'LDPC';
end

A trigger-based transmission for a single user within the system is configured with an wlanHETBConfig object. The transmission configurations for all users are generated using the method getUserConfig. A cell array of four HE TB objects is created to describe the transmission of four users.

cfgTB = getUserConfig(cfgSys);

Simulation Parameters

For each SNR point (dB) in the snr vector a number of packets are generated, passed through a channel and demodulated to determine the packet error rate.

snr = 20:2:24;

% The sample rate and field indices for the HE TB packet is same for all
% users. Here the trigger configuration of the first user is used to get
% the sample rate and field indices of the HE TB PPDU.
fs = wlanSampleRate(cfgTB{1});    % Same for all users
ind = wlanFieldIndices(cfgTB{1}); % Same for all users

Channel Configuration

In this example, a TGax NLOS indoor channel model is used with delay profile Model-B. Model-B is considered NLOS when the distance between the transmitter and receiver is greater than or equal to 5 meters. This is described further in wlanTGaxChannel. In this example all the STAs are assumed to be at the same distance from the AP.

tgaxBase = wlanTGaxChannel;
tgaxBase.SampleRate = fs;
tgaxBase.TransmissionDirection = 'Uplink';
tgaxBase.TransmitReceiveDistance = 10;
chanBW = cfgSys.ChannelBandwidth;
tgaxBase.ChannelBandwidth = chanBW;
tgaxBase.NumReceiveAntennas = numRx;
tgaxBase.NormalizeChannelOutputs = false;

An individual channel is created for each of the four users. Each channel is a clone of tgaxBase, but with a different UserIndex property, and is stored in a cell array tgax. The UserIndex property of each individual channel is set to provide a unique channel for each user. In this example a random channel realization is used for each packet by randomly varying the UserIndex property for each transmitted packet.

% A cell array stores the channel objects, one per user
tgax = cell(1,numUsers);
for userIdx = 1:numUsers
    tgax{userIdx} = clone(tgaxBase);
    tgax{userIdx}.NumTransmitAntennas = cfgSys.User{userIdx}.NumTransmitAntennas;
    tgax{userIdx}.UserIndex = userIdx;
end

Processing SNR Points

For each SNR point a number of packets are tested and the packet error rate is calculated. The pre-HE preamble of 802.11ax is backwards compatible with 802.11ac™, therefore in this example the timing synchronization components for a VHT waveform are used to synchronize the HE waveform at the receiver. For each user, the following processing steps occur to create a waveform at the receiver containing all four users:

1. To create an HE TB waveform, a PSDU is created and encoded for each user based on predefined user parameters.

2. The waveform for each user is passed through an indoor TGax channel model. Different channel realizations are modeled for different users and packets, by randomly varying the UserIndex property of the channel. This results in same spatial correlation properties for all users.

3. The waveforms for all HE TB users are scaled and combined to ensure same SNR for each user after the addition of noise.

4. AWGN is added to the received waveform to create the desired average SNR per active subcarrier after OFDM demodulation.

At the receiver (AP) the following processing steps occur:

1. The packet is detected.

2. Fine timing synchronization is established. The L-STF, L-LTF and L-SIG samples are provided for fine timing to allow for packet detection at the start or end of the L-STF.

3. The HE-LTF and HE-Data fields for all users are extracted from the synchronized received waveform. The HE-LTF and HE-Data fields are OFDM demodulated.

4. The demodulated HE-LTF is extracted for each RU and channel estimation is performed.

5. Noise estimation is performed using the demodulated data field pilots for each RU.

6. The data field is extracted and equalized for all users within an RU, from the demodulated data field.

7. For each RU, and user within the RU, the spatial streams for a user are demodulated and decoded to recover the transmitted PSDU.

A parfor loop can be used to parallelize processing of the SNR points. To enable the use of parallel computing for increased speed comment out the 'for' statement and uncomment the 'parfor' statement below.

ofdmInfo = wlanHEOFDMInfo('HE-Data',cfgSys.ChannelBandwidth,cfgSys.GuardInterval);
numSNR = numel(snr); % Number of SNR points
numPackets = 50; % Number of packets to simulate
packetErrorRate = zeros(numUsers,numSNR);
txPSDU = cell(numUsers);

% parfor isnr = 1:numSNR % Use 'parfor' to speed up the simulation
for isnr = 1:numSNR
    % Create HE TB object for receiver processing
    cfgHETB = wlanHETBConfig;
    cfgHETB.ChannelBandwidth = cfgSys.ChannelBandwidth;
    cfgHETB.HELTFType = cfgSys.HELTFType;
    cfgHETB.SingleStreamPilots = cfgSys.SingleStreamPilots;

    % Set random substream index per iteration to ensure that each
    % iteration uses a repeatable set of random numbers
    stream = RandStream('combRecursive','Seed',0);
    stream.Substream = isnr;
    RandStream.setGlobalStream(stream);

    % RU allocation information
    sysInfo = ruInfo(cfgSys);

    % Simulate multiple packets
    numPacketErrors = zeros(numUsers,1);
    for pktIdx = 1:numPackets

        % Transmit processing
        rxWaveform = 0;
        packetError = zeros(numUsers,1);
        txPSDU = cell(1,numUsers);

        % Generate random channel realization for each packet by varying
        % the UserIndex property of the channel. This assumes all users
        % have the same number of transmit antennas.
        chPermutations = randperm(numUsers);
        for userIdx = 1:numUsers
            % HE TB config object for each user
            cfgUser = cfgTB{userIdx};

            % Generate a packet with random PSDU
            txPSDU{userIdx} = randi([0 1],getPSDULength(cfgUser)*8,1,'int8');

            % Generate HE TB waveform, containing payload for single user
            txTrig = wlanWaveformGenerator(txPSDU{userIdx},cfgUser);

            % Pass waveform through a random TGax Channel
            channelIdx = chPermutations(userIdx);
            reset(tgax{channelIdx}); % New channel realization
            rxTrig = tgax{channelIdx}([txTrig; zeros(15,size(txTrig,2))]);

            % Scale the transmit power of the user within an RU. This is to
            % ensure same SNR for each user after the addition of noise.
            ruNum = cfgSys.User{userIdx}.RUNumber;
            SF = sqrt(1/sysInfo.NumUsersPerRU(ruNum))*sqrt(cfgUser.RUSize/(sum(sysInfo.RUSizes)));

            % Combine uplink users into one waveform
            rxWaveform = rxWaveform+SF*rxTrig;
        end

        % Pass the waveform through AWGN channel. Account for noise
        % energy in nulls so the SNR is defined per active subcarriers.
        packetSNR = convertSNR(snr(isnr),"snrsc","snr",...
            FFTLength=ofdmInfo.FFTLength,...
            NumActiveSubcarriers=sum(sysInfo.RUSizes));
        rxWaveform = awgn(rxWaveform,packetSNR);

        % Receive processing
        % Packet detect and determine coarse packet offset
        coarsePktOffset = wlanPacketDetect(rxWaveform,chanBW,0,0.05);
        if isempty(coarsePktOffset) % If empty no L-STF detected; packet error
            numPacketErrors = numPacketErrors+1;
            continue; % Go to next loop iteration
        end

        % Extract the non-HT fields and determine fine packet offset
        nonhtfields = rxWaveform(coarsePktOffset+(ind.LSTF(1):ind.LSIG(2)),:);
        finePktOffset = wlanSymbolTimingEstimate(nonhtfields,chanBW);

        % Determine final packet offset
        pktOffset = coarsePktOffset+finePktOffset;

        % If packet detected out with the range of expected delays from
        % the channel modeling; packet error
        if pktOffset>50
            numPacketErrors = numPacketErrors+1;
            continue; % Go to next loop iteration
        end

        % Extract HE-LTF and HE-Data fields for all RUs
        rxLTF = rxWaveform(pktOffset+(ind.HELTF(1):ind.HELTF(2)),:);
        rxData = rxWaveform(pktOffset+(ind.HEData(1):ind.HEData(2)),:);

        for ruIdx = 1:allocInfo.NumRUs
            % Demodulate HE-LTF and HE-Data field for the RU of interest
            ru = [allocInfo.RUSizes(ruIdx) allocInfo.RUIndices(ruIdx)];
            demodHELTFRU = wlanHEDemodulate(rxLTF,'HE-LTF',chanBW,cfgSys.GuardInterval,cfgSys.HELTFType,ru);
            demodHEDataRU = wlanHEDemodulate(rxData,'HE-Data',chanBW,cfgSys.GuardInterval,ru);

            % Configure the relevant properties in HE TB object
            cfgHETB.RUSize = allocInfo.RUSizes(ruIdx);
            cfgHETB.RUIndex = allocInfo.RUIndices(ruIdx);
            cfgHETB.NumSpaceTimeStreams = allocInfo.NumSpaceTimeStreamsPerRU(ruIdx);
            cfgHETB.NumHELTFSymbols = numHELTFSymbols(cfgSys);

            % Channel estimate
            [chanEst,ssPilotEst] = wlanHELTFChannelEstimate(demodHELTFRU,cfgHETB);

            % Get indices of data and pilots within RU (without nulls)
            ruOFDMInfo = wlanHEOFDMInfo('HE-Data',cfgSys.ChannelBandwidth,cfgSys.GuardInterval, ...
                                        [allocInfo.RUSizes(ruIdx) allocInfo.RUIndices(ruIdx)]);

            % Estimate noise power in HE fields of each user
            nVarEst = wlanHEDataNoiseEstimate(demodHEDataRU(ruOFDMInfo.PilotIndices,:,:),ssPilotEst,cfgHETB,ruIdx);

            % Discard pilot subcarriers
            demodDataSym = demodHEDataRU(ruOFDMInfo.DataIndices,:,:);
            chanEstData = chanEst(ruOFDMInfo.DataIndices,:,:);

            % Equalize
            if strcmpi(equalizationMethod,'mmse-sic')
                [eqSym,csi] = heSuccessiveEqualize(demodDataSym,chanEstData,nVarEst,cfgSys,ruIdx);
            else
                [eqSym,csi] = wlanHEEqualize(demodDataSym,chanEstData,nVarEst,cfgHETB,'HE-Data'); %#ok<UNRCH>
            end

            for userIdx = 1:allocInfo.NumUsersPerRU(ruIdx)
                % Get TB config object for each user
                userNum = cfgSys.RU{ruIdx}.UserNumbers(userIdx);
                cfgUser = cfgTB{userNum};

                % Get space-time stream indices for the current user
                stsIdx = cfgUser.StartingSpaceTimeStream-1+(1:cfgUser.NumSpaceTimeStreams);

                % Demap and decode bits
                rxPSDU = wlanHEDataBitRecover(eqSym(:,:,stsIdx),nVarEst,csi(:,stsIdx),cfgUser,'LDPCDecodingMethod','norm-min-sum');

                % PER calculation
                packetError(userNum) = any(biterr(txPSDU{userNum},rxPSDU));
            end
        end
        numPacketErrors = numPacketErrors+packetError;
    end

    % Calculate packet error rate (PER) at SNR point
    packetErrorRate(:,isnr)= numPacketErrors/numPackets;
    disp(['SNR ' num2str(snr(isnr)) ...
          ' completed for ' num2str(numUsers) ' users']);

end

SNR 20 completed for 4 users
SNR 22 completed for 4 users
SNR 24 completed for 4 users

Plot Packet Error Rate vs SNR

markers = 'ox*sd^v><ph+ox*sd^v';
color = 'bmcrgbrkymcrgbrkymc';
figure;

for nSTA = 1:numUsers
    semilogy(snr,packetErrorRate(nSTA,:).',['-' markers(nSTA) color(nSTA)]);
    hold on;
end

grid on;
xlabel('SNR (dB)');
ylabel('PER');
dataStr = arrayfun(@(x)sprintf('STA- %d',x),1:numUsers,'UniformOutput',false);
legend(dataStr);
title('PER for uplink 802.11ax link');

The number of packets tested at each SNR point is controlled by numPackets. For meaningful results, this value should be larger than those presented in this example. The figure below was created by running a longer simulation with numPackets:1e4 and snr:20:2:28, which shows the packet error rate of both MMSE equalizer and MMSE-SIC equalizer.

Selected Bibliography

[1] IEEE Std 802.11ax™-2021. IEEE Standard for Information Technology - Telecommunications and Information Exchange between Systems - Local and Metropolitan Area Networks - Specific Requirements - Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications - Amendment 1: Enhancements for High-Efficiency WLAN.

[2] M. Debbah, B. Muquet, M. de Courville, M. Muck, S. Simoens, and P. Loubaton. A MMSE successive interference cancellation scheme for a new adjustable hybrid spread OFDM system. IEEE 51st Vehicular Technology Conference Proceedings, pp. 745-749, vol. 2, 2000.