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802.11ax Compressed Beamforming Packet Error Rate Simulation

This example shows how to measure the packet error rate of a beamformed IEEE® 802.11ax™ high efficiency single user (HE-SU) format link with different beamforming feedback quantization levels.

Introduction

Transmit beamforming focuses energy towards a receiver to improve the SNR of a link. In this scheme, the transmitter is called a beamformer and the receiver is called a beamformee. A steering matrix is used by the beamformer to direct the energy to the beamformee. The steering matrix is calculated using channel state information obtained through channel measurements. These measurements are obtained by sounding the channel between beamformer and beamformee. To sound the channel, the beamformer sends an NDP (Null Data Packet) to the beamformee. The beamformee measures the channel information during sounding to calculate a feedback matrix. This matrix is compressed in the form of quantized angles (phi and psi) and fed back to the beamformer. The beamformer can then calculate the feedback matrix from the quantized angles to create a steering matrix and beamform transmissions to the beamformee. The process of forming steering matrix is shown in 802.11ac Transmit Beamforming.

In this example, a 4x2 MIMO configuration is considered between a transmitter and receiver, with two space-time streams used for each data packet transmission. An end-to-end simulation is used to determine the packet error rate (PER) for an 802.11ax [ 1 ] single user (SU) format link with compressed beamforming feedback quantization for different quantization levels and a selection of SNR points. A plot is generated showing the PER vs SNR curve for each quantization resolution. This example does not consider grouping of sub-carriers (see Section 9.4.1.63 in [ 1 ]).

Waveform Configuration

An HE-SU packet is a full-band transmission to a single user. The transmit parameters for the HE-SU format are configured using a wlanHESUConfig object. The properties of the object contain the configuration. In this example, the object is configured for a 20 MHz channel bandwidth, 4 transmit antennas, 2 space-time streams and 16-QAM rate-1/2 (MCS 3).

NumTxAnts = 4; % Number of transmit antennas
NumSTS = 2;    % Number of space-time streams
NumRxAnts = 2; % Number of receive antennas
cfgHEBase = wlanHESUConfig;
cfgHEBase.ChannelBandwidth = 'CBW20';      % Channel bandwidth
cfgHEBase.NumSpaceTimeStreams = NumSTS;    % Number of space-time streams
cfgHEBase.NumTransmitAntennas = NumTxAnts; % Number of transmit antennas
cfgHEBase.APEPLength = 1e3;                % Payload length in bytes
cfgHEBase.ExtendedRange = false;           % Do not use extended range format
cfgHEBase.Upper106ToneRU = false;          % Do not use upper 106 tone RU
cfgHEBase.PreHESpatialMapping = false;     % Spatial mapping of pre-HE fields
cfgHEBase.GuardInterval = 0.8;             % Guard interval duration
cfgHEBase.HELTFType = 4;                   % HE-LTF compression mode
cfgHEBase.ChannelCoding = 'LDPC';          % Channel coding
cfgHEBase.MCS = 3;                         % Modulation and coding scheme
cfgHEBase.SpatialMapping = 'Custom';       % Custom for beamforming

Null Data Packet (NDP) Configuration

The NDP transmission is configured to have data length of zero. Since the NDP is used to obtain the channel state information, the number of space-time streams is equal to number of transmit antennas. This results in a direct mapping of each space-time stream to a transmit antenna.

cfgNDP = cfgHEBase;
cfgNDP.APEPLength = 0;                  % NDP has no data
cfgNDP.NumSpaceTimeStreams = NumTxAnts; % For feedback matrix calculation
cfgNDP.SpatialMapping = 'Direct';       % Each TxAnt carries a STS

Channel Configuration

In this example, a TGax NLOS indoor channel model is used with delay profile Model-B. The Model-B profile is considered NLOS when the distance between transmitter and receiver is greater than or equal to 5 meters. This is described further in wlanTGaxChannel. A 4x2 MIMO channel is simulated in this example.

% Create and configure the TGax channel
chanBW = cfgHEBase.ChannelBandwidth;
tgaxChannel = wlanTGaxChannel;
tgaxChannel.DelayProfile = 'Model-B';
tgaxChannel.NumTransmitAntennas = NumTxAnts;
tgaxChannel.NumReceiveAntennas = NumRxAnts;
tgaxChannel.TransmitReceiveDistance = 5; % Distance in meters for NLOS
tgaxChannel.ChannelBandwidth = chanBW;
tgaxChannel.LargeScaleFadingEffect = 'None';
fs = wlanSampleRate(cfgHEBase);
tgaxChannel.SampleRate = fs;

Simulation Parameters

This example compares the performance of beamforming with two different resolutions of compression quantization, and without compression. For each quantization resolution, an end to end simulation with various SNR values is run to determine the packet error rate. 802.11ax Draft 3.1 specifies only two sets of quantization resolution for single user beamforming (Table 9-25a in [ 1 ]). The value of codeBookSize determines the number of bits used to quantize the beamforming feedback angles (phi and psi) in this simulation. When codeBookSize is Inf, no compression is performed. The quantization levels selected by codeBookSize are shown in the table below:

codeBookSize            Compression Configuration
--------------------------------------------------------
    0                   NumBitsphi = 4; NumBitspsi = 2
    1                   NumBitsphi = 6; NumBitspsi = 4
   Inf                  No compression
--------------------------------------------------------
codeBookSize = [0 1 Inf];

A number of packets are generated, passed through a channel and demodulated to determine the packet error rate for each compression configuration at each SNR (dB) value in the snr vector.

snr = 10:2:18;

The number of packets tested at each SNR point is limited to a maxNumErrors or maxNumPackets:

  1. maxNumErrors is the maximum number of packet errors simulated at each SNR point. When the number of packet errors reaches this limit, the simulation at this SNR point is complete.

  2. maxNumPackets is the maximum number of packets simulated at each SNR point and limits the length of the simulation if the packet error limit is not reached.

The numbers chosen in this example will lead to a very short simulation. For statistically meaningful results we recommend increasing these numbers.

maxNumErrors = 10;   % The maximum number of packet errors at an SNR point
maxNumPackets = 100; % The maximum number of packets at an SNR point

Processing SNR Points

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

The beamformer obtains the steering matrix by transmitting an NDP which is processed by the beamformee to create a feedback matrix:

  1. An NDP waveform is transmitted through an indoor TGax channel model. Different channel realizations are modeled for different packets.

  2. AWGN is added to the received waveform to create the desired average SNR per subcarrier after OFDM demodulation. The comm.AWGNChannel is configured to provide the correct SNR. The configuration accounts for normalization within the channel by the number of receive antennas, and the noise energy in unused subcarriers which are removed during OFDM demodulation.

  3. The packet is detected at the beamformee.

  4. Coarse carrier frequency offset is estimated and corrected.

  5. 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.

  6. Fine carrier frequency offset is estimated and corrected.

  7. The HE-LTF is extracted from the synchronized received waveform. The HE-LTF is OFDM demodulated and channel estimation is performed.

  8. Singular value decomposition is performed on the estimated channel and the beamforming feedback matrix, V is calculated.

  9. If there is no compression, this feedback matrix, V will be used as the steering matrix by the beamformer.

  10. If compression is used, the feedback matrix, V will be compressed and quantized to create a set of angles as specified in the standard.

The beamformer transmits a data packet using the recovered steering matrix and the beamformee decodes the beamformed data transmission to recover the PSDU:

  1. Since the current example assumes zero delay in getting the beamforming feedback from the beamformee, the quantized angles are converted back to the beamforming feedback matrix, V.

  2. A PSDU is created and encoded to create a single packet waveform with the steering matrix set to the beamforming feedback matrix, V.

  3. The waveform is passed through the same indoor TGax channel realization as the NDP transmission.

  4. AWGN is added to the received waveform.

  5. As with NDP, synchronization and HE channel estimation are performed.

  6. The data field is extracted from the synchronized received waveform and OFDM demodulated.

  7. Common phase error pilot tracking is performed to track any residual carrier frequency offset.

  8. Noise estimation is performed using the demodulated data field pilots and single-stream channel estimate at pilot subcarriers.

  9. The phase corrected OFDM symbols are equalized with the channel estimate.

  10. The equalized symbols are demodulated and decoded to recover the 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.

numQuant = numel(codeBookSize);
numSNR = numel(snr); % Number of SNR points
packetErrorRate = zeros(numQuant,numSNR);

% Get occupied subcarrier indices and OFDM parameters
ofdmInfo = wlanHEOFDMInfo('HE-Data',cfgHEBase);

% Indices to extract fields from the PPDU
ind = wlanFieldIndices(cfgHEBase);
indSound = wlanFieldIndices(cfgNDP);

for ibf = 1:numQuant
    switch codeBookSize(ibf) % See section 9.4.1.62
        case 0
            NumBitsPsi = 2; % Number of bits for psi
            NumBitsPhi = 4; % Number of bits for phi
            disp('End-to-End simulation with compressed beamforming quantization with');
            disp(['Number of Bits for phi = ' num2str(NumBitsPhi) ...
                ' and Number of Bits for psi = ' num2str(NumBitsPsi)]);
        case 1
            NumBitsPsi = 4; % Number of bits for psi
            NumBitsPhi = 6; % Number of bits for phi
            disp('End-to-End simulation with compressed beamforming quantization with');
            disp(['Number of Bits for phi = ' num2str(NumBitsPhi) ...
                ' and Number of Bits for psi = ' num2str(NumBitsPsi)]);
        otherwise
            disp('End-to-End simulation with non-compressed beamforming');
    end

    %parfor isnr = 1:numSNR % Use 'parfor' to speed up the simulation
    for isnr = 1:numSNR
        % Set random substream index per iteration to ensure that each
        % iteration uses a repeatable set of random numbers
        stream = RandStream('combRecursive','Seed',100);
        stream.Substream = isnr;
        RandStream.setGlobalStream(stream);

        % Create an instance of the AWGN channel per SNR point simulated
        awgnChannel = comm.AWGNChannel;
        awgnChannel.NoiseMethod = 'Signal to noise ratio (SNR)';
        awgnChannel.SignalPower = 1/tgaxChannel.NumReceiveAntennas;
        % Account for noise energy in nulls so the SNR is defined per
        % active subcarrier
        awgnChannel.SNR = snr(isnr)-10*log10(ofdmInfo.FFTLength/ofdmInfo.NumTones);

        % Create an instance of the HE configuration object per SNR point
        % simulated. This will enable to use parfor
        cfgHE = cfgHEBase;

        % Loop to simulate multiple packets
        numPacketErrors = 0;
        numPkt = 1; % Index of packet transmitted
        while numPacketErrors<=maxNumErrors && numPkt<=maxNumPackets
            % Null data packet transmission
            tx = wlanWaveformGenerator([],cfgNDP);

            % Add trailing zeros to allow for channel delay
            txPad = [tx; zeros(50,cfgNDP.NumTransmitAntennas)];

            % Pass through a fading indoor TGax channel
            reset(tgaxChannel); % Reset channel for different realization
            rx = tgaxChannel(txPad);

            % Pass the waveform through AWGN channel
            rx = awgnChannel(rx);

            % Calculate the steering matrix at the beamformee
            V = heUserBeamformingFeedback(rx,cfgNDP,true);

            if isempty(V)
                % User feedback failed, packet error
                numPacketErrors = numPacketErrors+1;
                numPkt = numPkt+1;
                continue; % Go to next loop iteration
            end

            if ~isinf(codeBookSize(ibf))
                % Find quantized angles of the beamforming feedback matrix
                angidx = bfCompressQuantize(V(:,1:NumSTS,:),NumBitsPhi,NumBitsPsi);

                % Calculate steering matrix from the quantized angles at
                % beamformer:
                % Assuming zero delay in transmitting the quantized angles
                % from beamformee to beamformer, the steering matrix is
                % calculated from the quantized angles and is used in the
                % data transmission of beamformer.

                [~,Nc,Nr] = size(V(1,1:NumSTS,:));
                V = bfDecompress(angidx,Nr,Nc,NumBitsPhi,NumBitsPsi);
            end

            steeringMat = V(:,1:NumSTS,:);

            % Beamformed data transmission
            psduLength = getPSDULength(cfgHE); % PSDU length in bytes
            txPSDU = randi([0 1],psduLength*8,1); % Generate random PSDU
            cfgHE.SpatialMappingMatrix = steeringMat;
            tx = wlanWaveformGenerator(txPSDU,cfgHE);

            % Add trailing zeros to allow for channel delay
            txPad = [tx; zeros(50,cfgHE.NumTransmitAntennas)];

            % Pass through a fading indoor TGax channel
            rx = tgaxChannel(txPad);

            % Pass the waveform through AWGN channel
            rx = awgnChannel(rx);

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

            % Extract L-STF and perform coarse frequency offset correction
            lstf = rx(coarsePktOffset+(ind.LSTF(1):ind.LSTF(2)),:);
            coarseFreqOff = wlanCoarseCFOEstimate(lstf,chanBW);
            rx = helperFrequencyOffset(rx,fs,-coarseFreqOff);

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

            % Determine final packet offset
            pktOffset = coarsePktOffset+finePktOffset;

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

            % Extract L-LTF and perform fine frequency offset correction
            rxLLTF = rx(pktOffset+(ind.LLTF(1):ind.LLTF(2)),:);
            fineFreqOff = wlanFineCFOEstimate(rxLLTF,chanBW);
            rx = helperFrequencyOffset(rx,fs,-fineFreqOff);

            % HE-LTF demodulation and channel estimation
            rxHELTF = rx(pktOffset+(ind.HELTF(1):ind.HELTF(2)),:);
            heltfDemod = wlanHEDemodulate(rxHELTF,'HE-LTF',cfgHE);
            [chanEst,pilotEst] = heLTFChannelEstimate(heltfDemod,cfgHE);

            % Data demodulate
            rxData = rx(pktOffset+(ind.HEData(1):ind.HEData(2)),:);
            demodSym = wlanHEDemodulate(rxData,'HE-Data',cfgHE);

            % Pilot phase tracking
            % Average single-stream pilot estimates over symbols (2nd dimension)
            pilotEstTrack = mean(pilotEst,2);
            demodSym = heCommonPhaseErrorTracking(demodSym,pilotEstTrack,cfgHE);

            % Estimate noise power in HE fields
            nVarEst = heNoiseEstimate(demodSym(ofdmInfo.PilotIndices,:,:),pilotEstTrack,cfgHE);

            % Extract data subcarriers from demodulated symbols and channel
            % estimate
            demodDataSym = demodSym(ofdmInfo.DataIndices,:,:);
            chanEstData = chanEst(ofdmInfo.DataIndices,:,:);

            % Equalization and STBC combining
            [eqDataSym,csi] = heEqualizeCombine(demodDataSym,chanEstData,nVarEst,cfgHE);

            % Recover data
            rxPSDU = wlanHEDataBitRecover(eqDataSym,nVarEst,csi,cfgHE);

            % Determine if any bits are in error, i.e. a packet error
            packetError = ~isequal(txPSDU,rxPSDU);
            numPacketErrors = numPacketErrors+packetError;
            numPkt = numPkt+1;
        end

        % Calculate packet error rate (PER) at SNR point
        packetErrorRate(ibf,isnr) = numPacketErrors/(numPkt-1);
        disp(['MCS ' num2str(cfgHE.MCS) ','...
            ' SNR ' num2str(snr(isnr)) ...
            ' completed after ' num2str(numPkt-1) ' packets,'...
            ' PER:' num2str(packetErrorRate(ibf,isnr))]);
    end
    disp(newline);
end
End-to-End simulation with compressed beamforming quantization with
Number of Bits for phi = 4 and Number of Bits for psi = 2
MCS 3, SNR 10 completed after 13 packets, PER:0.84615
MCS 3, SNR 12 completed after 30 packets, PER:0.36667
MCS 3, SNR 14 completed after 63 packets, PER:0.1746
MCS 3, SNR 16 completed after 100 packets, PER:0.04
MCS 3, SNR 18 completed after 100 packets, PER:0.01


End-to-End simulation with compressed beamforming quantization with
Number of Bits for phi = 6 and Number of Bits for psi = 4
MCS 3, SNR 10 completed after 13 packets, PER:0.84615
MCS 3, SNR 12 completed after 33 packets, PER:0.33333
MCS 3, SNR 14 completed after 81 packets, PER:0.1358
MCS 3, SNR 16 completed after 100 packets, PER:0.02
MCS 3, SNR 18 completed after 100 packets, PER:0


End-to-End simulation with non-compressed beamforming
MCS 3, SNR 10 completed after 12 packets, PER:0.91667
MCS 3, SNR 12 completed after 31 packets, PER:0.35484
MCS 3, SNR 14 completed after 81 packets, PER:0.1358
MCS 3, SNR 16 completed after 100 packets, PER:0.02
MCS 3, SNR 18 completed after 100 packets, PER:0


Plot Packet Error Rate vs Signal to Noise Ratio

figure;
lineTypes = ["k-o" "b-s" "r-*"];
semilogy(snr,packetErrorRate(1,:),lineTypes(1));
hold on;
grid on;
xlabel('SNR (dB)');
ylabel('PER');
for ibf = 2:numQuant
    semilogy(snr,packetErrorRate(ibf,:),lineTypes(ibf));
end
dataStr = [string(['Compressed Beamforming, ' newline ...
                   'NumBitsPhi = 4, NumBitsPsi = 2' newline])...
           string(['Compressed Beamforming, ' newline ...
                   'NumBitsPhi = 6, NumBitsPsi = 4' newline]) ...
                   "Non-Compressed Beamforming"];
legend(dataStr);
title(sprintf('802.11ax Beamforming PER for Channel %s, %s, %s',tgaxChannel.DelayProfile,cfgHEBase.ChannelBandwidth,cfgHEBase.ChannelCoding));

The number of packets tested at each SNR point is controlled by two parameters: maxNumErrors and maxNumPackets. For meaningful results, these values should be larger than those presented in this example. As an example, the figure below was created by running a longer simulation with maxNumErrors:1e3 and maxNumPackets:1e4.

Appendix

This example uses the following helper functions:

Selected Bibliography

  1. IEEE P802.11ax™/D3.1 Draft 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 6: Enhancements for High Efficiency WLAN.