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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.

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 ]).

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

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

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 = cfgHE.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(cfgHE); tgaxChannel.SampleRate = fs;

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 2.0 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`

:

`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.`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

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:

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

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.The packet is detected at the beamformee.

Coarse carrier frequency offset is estimated and corrected.

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.

Fine carrier frequency offset is estimated and corrected.

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

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

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

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:

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.

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

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

AWGN is added to the received waveform.

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

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

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

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

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

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

numQuant = numel(codeBookSize); numSNR = numel(snr); % Number of SNR points packetErrorRate = zeros(numQuant,numSNR); % Get occupied subcarrier indices and OFDM parameters scIndices = helperOccupiedSubcarrierIndices('HE-Data',cfgHE); ofdmInfo = helperOFDMInfo('HE-Data',cfgHE); % Indices to extract fields from the PPDU ind = wlanFieldIndices(cfgHE); 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 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); % 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,cfgHE.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 = helperOFDMDemodulate(rxHELTF,'HE-LTF',cfgHE); [chanEst,pilotEst] = heLTFChannelEstimate(heltfDemod,cfgHE); % Data demodulate rxData = rx(pktOffset+(ind.HEData(1):ind.HEData(2)),:); demodSym = helperOFDMDemodulate(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(scIndices.Pilot,:,:),pilotEstTrack,cfgHE); % Extract data subcarriers from demodulated symbols and channel % estimate demodDataSym = demodSym(scIndices.Data,:,:); chanEstData = chanEst(scIndices.Data,:,:); % 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

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,cfgHE.ChannelBandwidth,cfgHE.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.

This example uses the following helper functions:

IEEE P802.11ax™/D2.0 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.