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802.11ac Transmitter Modulation Accuracy and Spectral Emission Testing

This example shows how to perform transmitter modulation accuracy and spectrum emission mask and flatness measurements on an IEEE® 802.11ac™ waveform.

Introduction

The transmitter modulation accuracy, required spectrum mask and required spectral flatness for given configurations are specified in Section 22.3.18 of the 802.11ac standard [ 1 ]. This example shows how these measurements can be performed on a waveform. The waveform is generated with WLAN System Toolbox™, but a waveform captured with a spectrum analyzer could be used.

A waveform consisting of 20 80 MHz VHT packets each separated by 10 microseconds gaps is generated. Random data is used in each packet and 256QAM modulation is used. The baseband waveform is upsampled and filtered to reduce the out of band emissions to meet the spectral mask requirement. A high power amplifier (HPA) model is used, which introduces inband distortion and spectral regrowth. The spectral emission mask measurement is performed on the upsampled waveform after the high power amplifier modeling. The waveform is downsampled and the error vector magnitude (EVM) of the VHT Data field is measured to determine the modulation accuracy. The spectral flatness is additionally measured. The example is illustrated in the following diagram:

IEEE 802.11ac VHT Packet Configuration

In this example an IEEE 802.11ac waveform consisting of multiple VHT format packets is generated. The format specific configuration of a VHT waveform is described using a VHT format configuration object. The object is created using the wlanVHTConfig function. The properties of the object contain the configuration. In this example the object is configured for a 80 MHz bandwidth. One spatial stream is transmitted per antenna to allow the modulation accuracy to be measured per spatial stream, therefore no space time block coding is used.

cfgVHT = wlanVHTConfig;            % Create packet configuration
cfgVHT.ChannelBandwidth = 'CBW80'; % 80 MHz
cfgVHT.NumTransmitAntennas = 1;    % One transmit antenna
cfgVHT.NumSpaceTimeStreams = 1;    % One space-time stream
cfgVHT.STBC = false;               % No STBC so one spatial stream
cfgVHT.MCS = 8;                    % Modulation: 256 QAM
cfgVHT.APEPLength = 3000;          % A-MPDU length pre-EOF padding in bytes

Baseband Waveform Generation

The waveform generator wlanWaveformGenerator can be configured to generate one or more packets and add an idle time between each packet. In this example 20 packets with 10 microseconds idle periods will be created.

numPackets = 20;  % Generate 20 packets
idleTime = 10e-6; % 10 microseconds idle time between packets

Random bits for all packets, data, are created and passed as an argument to wlanWaveformGenerator along with the VHT packet configuration object cfgVHT. This configures the waveform generator to synthesize an 802.11ac VHT waveform. The waveform generator is additionally configured using name-value pairs to generate multiple packets with a specified idle time between each packet.

% Create random data; PSDULength is in bytes
savedState = rng(0); % Set random state
data = randi([0 1],cfgVHT.PSDULength*8*numPackets,1);

% Generate a multi-packet waveform
txWaveform = wlanWaveformGenerator(data,cfgVHT, ...
    'NumPackets',numPackets,'IdleTime',idleTime);

% Get the sampling rate of the waveform
fs = wlanSampleRate(cfgVHT);
disp(['Baseband sampling rate: ' num2str(fs/1e6) ' Msps']);
Baseband sampling rate: 80 Msps

Oversampling and Filtering

Spectral filtering is used to reduce the out of band spectral emissions owing to the implicit rectangular pulse shaping in the OFDM modulation, and spectral regrowth caused by the high power amplifier model. To model the effect of a high power amplifier on the waveform and view the out of band spectral emissions the waveform must be oversampled. Oversampling requires an interpolation filter to remove spectral images caused by upsampling. In this example the waveform is oversampled with an interpolation filter which also acts as a spectral filter. This allows the waveform to meet spectral mask requirements. The waveform is oversampled and filtered using dsp.FIRInterpolator.

% Oversample the waveform
osf = 3;         % Oversampling factor
filterLen = 120; % Filter length
beta = 0.5;      % Design parameter for Kaiser window

% Generate filter coefficients
coeffs = osf.*firnyquist(filterLen,osf,kaiser(filterLen+1,beta));
coeffs = coeffs(1:end-1); % Remove trailing zero
interpolationFilter = dsp.FIRInterpolator(osf,'Numerator',coeffs);
txWaveform = interpolationFilter(txWaveform);

% Plot the magnitude and phase response of the filter applied after
% oversampling
h = fvtool(interpolationFilter);
h.Analysis = 'freq';           % Plot magnitude and phase responses
h.FS = osf*fs;                 % Set sampling rate
h.NormalizedFrequency = 'off'; % Plot responses against frequency

High Power Amplifier Modeling

The high power amplifier introduces nonlinear behavior in the form of inband distortion and spectral regrowth. The Rapp model is used to simulate power amplifiers in 802.11ac [ 2 ]. The Rapp model causes AM/AM distortion and is modeled with comm.MemorylessNonlinearity. The high power amplifier is backed-off to operate below the saturation point to reduce distortion. The backoff is controlled by the variable hpaBackoff.

hpaBackoff = 8; % dB

% Create and configure a memoryless nonlinearity to model the amplifier
nonLinearity = comm.MemorylessNonlinearity;
nonLinearity.Method = 'Rapp model';
nonLinearity.Smoothness = 3; % p parameter
nonLinearity.LinearGain = -hpaBackoff;

% Apply the model to each transmit antenna
for i=1:cfgVHT.NumTransmitAntennas
    txWaveform(:,i) = nonLinearity(txWaveform(:,i));
end

Thermal noise is added to the waveform with a 6 dB noise figure [ 3 ].

NF = 6;         % Noise figure (dB)
BW = fs*osf;    % Bandwidth (Hz)
k = 1.3806e-23; % Boltzman constant (J/K)
T = 290;        % Ambient temperature (K)
noisePower = 10*log10(k*T*BW)+NF;

awgnChannel = comm.AWGNChannel('NoiseMethod','Variance', ...
    'Variance',10^(noisePower/10));
txWaveform = awgnChannel(txWaveform);

Modulation Accuracy (EVM) and Spectral Flatness Measurements

The oversampled waveform is resampled down to baseband for physical layer processing and EVM and spectral flatness measurements. As part of the resampling a low-pass anti-aliasing filter is applied before downsampling. The impact of the low-pass filter will be visible in the spectral flatness measurement. The waveform is resampled to baseband using dsp.FIRDecimator with the same coefficients used for oversampling earlier in the example.

% Resample to baseband
decimationFilter = dsp.FIRDecimator(osf,'Numerator',coeffs);
rxWaveform = decimationFilter(txWaveform);

Each packet within rxWaveform is detected, synchronized and extracted. The EVM and spectral flatness measurements are made for each packet. The following steps are performed for each packet:

  • The start of the packet is detected

  • The non-HT fields are extracted and coarse carrier frequency offset (CFO) estimation and correction are performed

  • The frequency corrected non-HT fields are used to estimate fine symbol timing

  • The packet is extracted from the waveform using the fine symbol timing offset

  • The extracted packet is corrected with the coarse CFO estimate

  • The L-LTF is extracted and used to estimate the fine CFO. The offset is corrected for the whole packet

  • The L-LTF is used to estimate the noise power

  • The VHT-LTF is extracted and channel estimation is performed for each of the transmit streams

  • The channel estimate is used to measure the spectral flatness

  • The VHT Data field is extracted, OFDM demodulated, phase corrected and equalized using the channel estimate

  • For each data-carrying subcarrier in each spatial stream, the closest constellation point is found and the EVM computed

The processing chain is shown in the diagram below:

Note the VHT-LTF symbols include pilot symbols to allow for phase tracking, but this is not done in this example.

The spectral flatness is tested for each packet by measuring the deviation in the magnitude of individual subcarriers in the channel estimate against the average [ 1 ]. These deviations are plotted for each packet using the helper function vhtTxSpectralFlatnessMeasurement. The average EVM per data-carrying subcarrier, and the equalized symbols are plotted for each packet.

The function wlanVHTDataRecover is used to demodulate, equalize and decode the VHT Data symbols. The equalized symbols are used in this example to measure the modulation accuracy. This function is parameterized using a wlanRecoveryConfig object. The object is parameterized to perform pilot phase tracking and zero forcing equalization as required by the standard.

% Configure VHT Data symbol recovery
cfgRec = wlanRecoveryConfig;
cfgRec.EqualizationMethod = 'ZF';    % Use zero forcing algorithm
cfgRec.PilotPhaseTracking = 'PreEQ'; % Use pilot phase tracking

Two different EVM measurements are made in this example using two instances of comm.EVM. The first measurement is the RMS EVM per packet. For this measurement the EVM is averaged over subcarriers, OFDM symbols and spatial streams.

EVMPerPkt = comm.EVM;
EVMPerPkt.AveragingDimensions = [1 2 3]; % Nst-by-Nsym-by-Nss
EVMPerPkt.Normalization = 'Average constellation power';
EVMPerPkt.ReferenceSignalSource  = 'Estimated from reference constellation';
EVMPerPkt.ReferenceConstellation = helperReferenceSymbols(cfgVHT);

The second measurement is the RMS EVM per subcarrier per spatial stream for a packet. As spatial streams are mapped directly to antennas in this setup, this measurement can help detect frequency dependent impairments which may affect individual RF chains differently. For this measurement the EVM is only averaged over OFDM symbols.

% Measure average EVM over symbols
EVMPerSC = comm.EVM;
EVMPerSC.AveragingDimensions = 2; % Nst-by-Nsym-by-Nss
EVMPerSC.Normalization = 'Average constellation power';
EVMPerSC.ReferenceSignalSource  = 'Estimated from reference constellation';
EVMPerSC.ReferenceConstellation = helperReferenceSymbols(cfgVHT);

The following code configures objects and variables for processing.

% Indices for accessing each field within the time-domain packet
ind = wlanFieldIndices(cfgVHT);

rxWaveformLength = size(rxWaveform,1);
pktLength = double(ind.VHTData(2));

% Minimum length of data we can detect; length of the L-STF in samples
minPktLen = double(ind.LSTF(2)-ind.LSTF(1))+1;

% Setup the measurement plots
[hSF,hCon,hEVM] = vhtTxSetupPlots(cfgVHT);

rmsEVM = zeros(numPackets,1);
pktOffsetStore = zeros(numPackets,1);

rng(savedState); % Restore random state

A while loop is used to detect and process packets within the received waveform. The sample offset searchOffset is used to index into rxWaveform to detect a packet. The first packet within rxWaveform is detected and processed. The sample index offset searchOffset is then incremented to move beyond the processed packet in rxWaveform and the next packet is detected and processed until no further packets are detected.

pktNum = 0;
searchOffset = 0; % Start at first sample (no offset)
while (searchOffset+minPktLen)<=rxWaveformLength
    % Packet detect
    pktOffset = wlanPacketDetect(rxWaveform,cfgVHT.ChannelBandwidth, ...
        searchOffset,0.9);
    % Packet offset from start of waveform
    pktOffset = searchOffset+pktOffset;
    % If no packet detected or offset outwith bounds of waveform then stop
    if isempty(pktOffset) || (pktOffset<0) || ...
            ((pktOffset+ind.LSIG(2))>rxWaveformLength)
        break;
    end

    % Extract non-HT fields and perform coarse frequency offset correction
    % to allow for reliable symbol timing
    nonht = rxWaveform(pktOffset+(ind.LSTF(1):ind.LSIG(2)),:);
    coarsefreqOff = wlanCoarseCFOEstimate(nonht,cfgVHT.ChannelBandwidth);
    nonht = helperFrequencyOffset(nonht,fs,-coarsefreqOff);

    % Determine offset between the expected start of L-LTF and actual start
    % of L-LTF
    lltfOffset = wlanSymbolTimingEstimate(nonht,cfgVHT.ChannelBandwidth);
    % Determine packet offset
    pktOffset = pktOffset+lltfOffset;
    % If offset is without bounds of waveform  skip samples and continue
    % searching within remainder of the waveform
    if (pktOffset<0) || ((pktOffset+pktLength)>rxWaveformLength)
        searchOffset = pktOffset+double(ind.LSTF(2))+1;
        continue;
    end

    % Timing synchronization complete; extract the detected packet
    rxPacket = rxWaveform(pktOffset+(1:pktLength),:);
    pktNum = pktNum+1;
    disp(['  Packet ' num2str(pktNum) ' at index: ' num2str(pktOffset+1)]);

    % Apply coarse frequency correction to the extracted packet
    rxPacket = helperFrequencyOffset(rxPacket,fs,-coarsefreqOff);

    % Perform fine frequency offset correction on the extracted packet
    lltf = rxPacket(ind.LLTF(1):ind.LLTF(2),:); % Extract L-LTF
    fineFreqOff = wlanFineCFOEstimate(lltf,cfgVHT.ChannelBandwidth);
    rxPacket = helperFrequencyOffset(rxPacket,fs,-fineFreqOff);

    % Estimate noise power in VHT fields
    lltf = rxPacket(ind.LLTF(1):ind.LLTF(2),:);
    demodLLTF = wlanLLTFDemodulate(lltf,cfgVHT);
    noiseVarVHT = helperNoiseEstimate(demodLLTF,cfgVHT.ChannelBandwidth, ...
        cfgVHT.NumSpaceTimeStreams);

    % Extract VHT-LTF samples, demodulate and perform channel estimation
    vhtltf = rxPacket(ind.VHTLTF(1):ind.VHTLTF(2),:);
    vhtltfDemod = wlanVHTLTFDemodulate(vhtltf,cfgVHT);
    chanEst = wlanVHTLTFChannelEstimate(vhtltfDemod,cfgVHT);

    % Spectral flatness measurement
    vhtTxSpectralFlatnessMeasurement(chanEst,cfgVHT,pktNum,hSF);

    % Extract VHT Data samples and perform OFDM demodulation, equalization
    % and phase tracking
    vhtdata = rxPacket(ind.VHTData(1):ind.VHTData(2),:);
    [~,~,eqSym] = wlanVHTDataRecover(vhtdata,chanEst,noiseVarVHT, ...
                    cfgVHT,cfgRec);

    % Compute RMS EVM over all spatial streams for packet
    rmsEVM(pktNum) = EVMPerPkt(eqSym);
    fprintf('    RMS EVM: %2.2f%%, %2.2fdB\n', ...
        rmsEVM(pktNum),20*log10(rmsEVM(pktNum)/100));

    % Compute RMS EVM per subcarrier and spatial stream for the packet
    evmPerSC = EVMPerSC(eqSym); % Nst-by-1-by-Nss

    % Plot RMS EVM per subcarrier and equalized constellation
    vhtTxEVMConstellationPlots(eqSym,evmPerSC,cfgVHT,pktNum,hCon,hEVM);

    % Store the offset of each packet within the waveform
    pktOffsetStore(pktNum) = pktOffset;

    % Increment waveform offset and search remaining waveform for a packet
    searchOffset = pktOffset+pktLength+minPktLen;
end

if pktNum>0
fprintf('Average EVM for %d packets: %2.2f%%, %2.2fdB\n', ...
    pktNum,mean(rmsEVM(1:pktNum)),20*log10(mean(rmsEVM(1:pktNum))/100));
else
    disp('No complete packet detected');
end
  Packet 1 at index: 41
    Spectral flatness passed
    RMS EVM: 2.36%, -32.55dB
  Packet 2 at index: 9801
    Spectral flatness passed
    RMS EVM: 2.32%, -32.70dB
  Packet 3 at index: 19561
    Spectral flatness passed
    RMS EVM: 2.16%, -33.29dB
  Packet 4 at index: 29321
    Spectral flatness passed
    RMS EVM: 2.16%, -33.31dB
  Packet 5 at index: 39081
    Spectral flatness passed
    RMS EVM: 2.27%, -32.88dB
  Packet 6 at index: 48841
    Spectral flatness passed
    RMS EVM: 1.93%, -34.29dB
  Packet 7 at index: 58601
    Spectral flatness passed
    RMS EVM: 2.19%, -33.21dB
  Packet 8 at index: 68361
    Spectral flatness passed
    RMS EVM: 2.06%, -33.70dB
  Packet 9 at index: 78121
    Spectral flatness passed
    RMS EVM: 2.12%, -33.47dB
  Packet 10 at index: 87881
    Spectral flatness passed
    RMS EVM: 2.01%, -33.95dB
  Packet 11 at index: 97641
    Spectral flatness passed
    RMS EVM: 2.10%, -33.54dB
  Packet 12 at index: 107401
    Spectral flatness passed
    RMS EVM: 2.20%, -33.14dB
  Packet 13 at index: 117161
    Spectral flatness passed
    RMS EVM: 2.00%, -33.97dB
  Packet 14 at index: 126921
    Spectral flatness passed
    RMS EVM: 2.11%, -33.52dB
  Packet 15 at index: 136681
    Spectral flatness passed
    RMS EVM: 2.19%, -33.21dB
  Packet 16 at index: 146441
    Spectral flatness passed
    RMS EVM: 1.88%, -34.52dB
  Packet 17 at index: 156201
    Spectral flatness passed
    RMS EVM: 2.03%, -33.84dB
  Packet 18 at index: 165961
    Spectral flatness passed
    RMS EVM: 2.43%, -32.28dB
  Packet 19 at index: 175721
    Spectral flatness passed
    RMS EVM: 2.39%, -32.43dB
  Packet 20 at index: 185481
    Spectral flatness passed
    RMS EVM: 2.63%, -31.60dB
Average EVM for 20 packets: 2.18%, -33.24dB

Transmit Spectrum Emission Mask Measurement

In this example the spectrum emission mask of the filtered and impaired waveform after high power amplifier modeling is measured.

A time gated spectral measurement of the VHT Data field is used for the transmitter spectrum emission mask test [ 4 ]. As part of the baseband processing the start index of each packet within the baseband waveform was stored. These indices are used to extract the VHT Data field of each packet from the oversampled txWaveform. Any delay introduced in the baseband processing chain used to determine the packet indices must be accounted for when gating the VHT data field within txWaveform. The extracted VHT Data fields are concatenated in preparation for measurement.

startIdx = osf*(ind.VHTData(1)-1)+1;  % Upsampled start of VHT Data
endIdx = osf*ind.VHTData(2);          % Upsampled end of VHT Data
delay = grpdelay(decimationFilter,1); % Group delay of downsampling filter
idx = zeros(endIdx-startIdx+1,pktNum);
for i = 1:pktNum
    % Start of packet in txWaveform
    pktOffset = osf*pktOffsetStore(i)-delay;
    % Indices of VHT Data in txWaveform
    idx(:,i) = (pktOffset+(startIdx:endIdx));
end
gatedVHTData = txWaveform(idx(:),:);

The spectral mask is specified by the standard relative to the peak power spectral density. The plot generated by the helper function helperSpectralMaskTest overlays the required mask with the measured PSD.

helperSpectralMaskTest(gatedVHTData,fs,osf);
   Spectrum mask passed

Conclusion and Further Exploration

Four results are plotted by this example; spectral flatness, RMS EVM per subcarrier, equalized constellation, and spectral mask.

The high power amplifier model introduces significant inband distortion and spectral regrowth which is visible in the EVM results, noisy constellation and out-of-band emissions in the spectral mask plot. Try increasing the high power amplifier backoff and note the improved EVM, constellation and lower out-of-band emissions.

The spectral filtering and downsampling (to bring the waveform to baseband for processing) stages include filtering. These filter responses affect the spectral flatness measurement. The ripple in the spectral flatness measurement is mainly due to downsampling to baseband. Try using different filters or filter lengths and note the impact on the spectral flatness.

Appendix

This example uses the following helper functions:

Selected Bibliography

  1. IEEE Std 802.11ac™-2013 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 4: Enhancements for Very High Throughput for Operation in Bands below 6 GHz.

  2. Loc and Cheong. IEEE P802.11 Wireless LANs. TGac Functional Requirements and Evaluation Methodology Rev. 16. 2011-01-19.

  3. Perahia, E., and R. Stacey. Next Generation Wireless LANs: 802.11n and 802.11ac. 2nd Edition. United Kingdom: Cambridge University Press, 2013.

  4. Archambault, Jerry, and Shravan Surineni. "IEEE 802.11 spectral measurements using vector signal analyzers." RF Design 27.6 (2004): 38-49.

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