This example shows how to perform transmitter modulation accuracy and spectrum emission mask and flatness measurements on an IEEE® 802.11ac™ waveform.
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 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:
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
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
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
% 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
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 = 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);
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 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 and OFDM demodulated
Noise estimation is performed using the demodulated data field pilots and single-stream channel estimate at pilot subcarriers
The VHT Data field is phase corrected and equalized using the channel and noise estimates
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.
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 to perform pilot phase tracking and zero forcing equalization as required by the standard.
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 = wlanReferenceSymbols(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 = wlanReferenceSymbols(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); % Extract VHT-LTF samples, demodulate and perform channel estimation vhtltf = rxPacket(ind.VHTLTF(1):ind.VHTLTF(2),:); vhtltfDemod = wlanVHTLTFDemodulate(vhtltf,cfgVHT); % Get single stream channel estimate chanEstSSPilots = vhtSingleStreamChannelEstimate(vhtltfDemod,cfgVHT); % Channel estimate chanEst = wlanVHTLTFChannelEstimate(vhtltfDemod,cfgVHT); % Spectral flatness measurement vhtTxSpectralFlatnessMeasurement(chanEst,cfgVHT,pktNum,hSF); % Extract VHT Data samples from the waveform vhtdata = rxPacket(ind.VHTData(1):ind.VHTData(2),:); % Estimate the noise power in VHT data field noiseVarVHT = vhtNoiseEstimate(vhtdata,chanEstSSPilots,cfgVHT); % Extract VHT Data samples and perform OFDM demodulation, equalization % and phase tracking [~,~,eqSym] = wlanVHTDataRecover(vhtdata,chanEst,noiseVarVHT,cfgVHT,... 'EqualizationMethod','ZF','PilotPhaseTracking','PreEQ'); % Use zero forcing algorithm for equalization % 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
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.
Spectrum mask passed
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.
This example uses the following helper functions:
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.
Loc and Cheong. IEEE P802.11 Wireless LANs. TGac Functional Requirements and Evaluation Methodology Rev. 16. 2011-01-19.
Perahia, E., and R. Stacey. Next Generation Wireless LANs: 802.11n and 802.11ac. 2nd Edition. United Kingdom: Cambridge University Press, 2013.
Archambault, Jerry, and Shravan Surineni. "IEEE 802.11 spectral measurements using vector signal analyzers." RF Design 27.6 (2004): 38-49.