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802.11ah Packet Error Rate Simulation for 2x2 TGah Channel

This example shows how to measure the packet error rate of an IEEE® 802.11ah™ S1G short preamble link using an end-to-end simulation with a fading TGah indoor channel model and additive white Gaussian noise.

Introduction

In this example an end-to-end simulation is used to determine the packet error rate for an 802.11ah [ 1 ] S1G short preamble link with a fading channel at a selection of SNR points. For each SNR point multiple packets are transmitted through a channel, demodulated and the PSDUs recovered. The PSDUs are compared to those transmitted to determine the number of packet errors and hence the packet error rate. The processing for each packet is summarized in the following diagram.

This example simulates the S1G-Short format with no impairment correction apart from channel estimation and equalization. The received signal is synchronized to the start of the packet by compensating for a known delay and the default OFDM demodulation symbol sampling offset. No frequency synchronization is performed. For information on how to automatically detect and synchronize to the received signal, see the following examples for 802.11n™ and 802.11ac™:

This example also demonstrates how a parfor loop can be used instead of the for loop when simulating each SNR point to speed up a simulation. parfor, as part of the Parallel Computing Toolbox™, executes processing for each SNR in parallel to reduce the total simulation time.

Waveform Configuration

A single-user 802.11ah S1G short preamble transmission is simulated in this example. An S1G format configuration object contains the format specific configuration of the transmission. The object is created using the wlanS1GConfig function. The properties of the object contain the configuration. In this example the object is configured for a 2 MHz channel bandwidth, short preamble, 2 transmit antennas, 2 space-time streams, 256 bytes payload, and 64-QAM rate-5/6 (MCS 7).

% Create S1G configuration object for single user S1G short preamble
% transmission with 2 transmit antennas and 2 space-time streams
cfgS1G = wlanS1GConfig;
cfgS1G.ChannelBandwidth = 'CBW2'; % 2 MHz channel bandwidth
cfgS1G.Preamble = 'Short';        % Short preamble
cfgS1G.NumTransmitAntennas = 2;   % 2 transmit antennas
cfgS1G.NumSpaceTimeStreams = 2;   % 2 space-time streams
cfgS1G.APEPLength = 256;          % APEP length in bytes
cfgS1G.MCS = 7;                   % 64-QAM rate-5/6

Channel Configuration

In this example a TGah N-LOS indoor channel model is used with delay profile Model-B. For Model-B, when the distance between transmitter and receiver is greater than or equal to 5 meters, the model is NLOS. This is described further in wlanTGahChannel. A 2x2 MIMO channel is simulated in this example therefore 2 receive antennas are specified.

% Create and configure the TGah channel
tgahChannel = wlanTGahChannel;
tgahChannel.DelayProfile = 'Model-B';
tgahChannel.NumTransmitAntennas = cfgS1G.NumTransmitAntennas;
tgahChannel.NumReceiveAntennas = 2;
tgahChannel.TransmitReceiveDistance = 5; % Distance in meters for NLOS
tgahChannel.ChannelBandwidth = cfgS1G.ChannelBandwidth;
tgahChannel.LargeScaleFadingEffect = 'None';

Simulation Parameters

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

snr = 25:10:45;

The number of packets tested at each SNR point is controlled by two parameters:

  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 meaningful results we recommend increasing the numbers.

maxNumErrors = 1e2;  % The maximum number of packet errors at an SNR point
maxNumPackets = 1e3; % Maximum number of packets at an SNR point

Set the remaining variables for the simulation.

% Indices for accessing each field within the time-domain packet
fieldInd = wlanFieldIndices(cfgS1G);

% OFDM information
ofdmInfo = helperOFDMInfo('S1G-Data',cfgS1G);

% Indices of occupied data and pilot carrying subcarriers
scInd = helperOccupiedSubcarrierIndices('S1G-Data',cfgS1G);

% Set the sampling rate of the channel
tgahChannel.SampleRate = wlanSampleRate(cfgS1G);

if ~strcmp(packetFormat(cfgS1G),'S1G-Short')
    error('This example only supports the S1G-Short packet format');
end

Processing SNR Points

For each SNR point a number of packets are tested and the packet error rate calculated. At each SNR point:

  1. Multiple data packets are transmitted through a 2x2 TGah channel with AWGN.

  2. Each packet is time synchronized given a known delay.

  3. The S1G-LTF1 and S1G-LTF2N fields are demodulated and channel estimation is performed.

  4. The S1G-Data field is extracted from the synchronized received waveform and OFDM demodulated.

  5. The data carrying subcarriers are equalized using the channel estimates.

  6. The PSDU is recovered using the equalized data subcarriers, noise variance estimate, and channel state information (CSI).

  7. The recovered PSDU of each packet is compared to those transmitted to determine the number of packet errors and hence the packet error rate.

A parfor loop can be used to parallelize processing of the SNR points, therefore for each SNR point an AWGN channel is created and configured with comm.AWGNChannel.

packetErrorRate = zeros(numel(snr),1);
%parfor i = 1:numel(snr) % Use 'parfor' to speed up the simulation
for i = 1:numel(snr) % Use 'for' to debug the simulation
    % 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 = i;
    RandStream.setGlobalStream(stream);

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

    % Loop to simulate multiple packets
    numPacketErrors = 0;
    numPkt = 1; % Index of packet transmitted
    while numPacketErrors<=maxNumErrors && numPkt<=maxNumPackets
        % Generate a packet for 802.11ah short preamble
        txPSDU = randi([0 1],cfgS1G.PSDULength*8,1);
        txWaveform = wlanWaveformGenerator(txPSDU,cfgS1G);

        % Add trailing zeros to allow for channel delay
        tx = [txWaveform; zeros(50,cfgS1G.NumTransmitAntennas)];

        % Pass through fading indoor TGah channel
        reset(tgahChannel); % Reset channel for different realization
        rx = tgahChannel(tx);

        % Add noise
        rx = awgnChannel(rx);

        % Synchronize
        % The received signal is synchronized to the start of the packet by
        % compensating for a known delay and the default OFDM demodulation
        % symbol sampling offset.
        delay = 4;
        rxSync = rx(delay+1:end,:);

        % LTF demodulation and channel estimation
        % Demodulate S1G-LTF1
        rxLTF1 = rxSync(fieldInd.S1GLTF1(1):fieldInd.S1GLTF1(2),:);
        demodLTF1 = helperOFDMDemodulate(rxLTF1,'S1G-LTF1',cfgS1G);

        % If required, demodulate S1G-LTF2N, and perform channel estimation
        if cfgS1G.NumSpaceTimeStreams>1
            % Use S1G-LTF1 and S1G-LTF2N for channel estimation
            rxLTF2N = rxSync(fieldInd.S1GLTF2N(1):fieldInd.S1GLTF2N(2),:);
            demodLTF2N = helperOFDMDemodulate(rxLTF2N,'S1G-LTF2N',cfgS1G);
            chanEst = s1gLTFChannelEstimate([demodLTF1 demodLTF2N],cfgS1G);
        else
            % Use only S1G-LTF1 for channel estimation
            chanEst = s1gLTFChannelEstimate(demodLTF1,cfgS1G);
        end

        % Noise variance estimate from S1G-LTF1 demodulated symbols
        noiseVarEst = helperNoiseEstimate(demodLTF1);

        % Extract S1G-Data field
        rxData = rxSync(fieldInd.S1GData(1):fieldInd.S1GData(2),:);

        % OFDM demodulation
        demodSym = helperOFDMDemodulate(rxData,'S1G-Data',cfgS1G);

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

        % MMSE frequency domain equalization
        [eqDataSym,csi] = helperSymbolEqualize(demodDataSym,chanEstData,noiseVarEst);

        % Recover PSDU bits
        rxPSDU = s1gDataBitRecover(eqDataSym,noiseVarEst,csi,cfgS1G);

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

    % Compute PER for this SNR point
    packetErrorRate(i) = numPacketErrors/(numPkt-1);
    disp(['PER = ' num2str(packetErrorRate(i)) ' at SNR = ' num2str(snr(i)) ...
        ' dB. Completed after ' num2str(numPkt-1) ' packets.']);
end
PER = 0.84874 at SNR = 25 dB. Completed after 119 packets.
PER = 0.1051 at SNR = 35 dB. Completed after 961 packets.
PER = 0.01 at SNR = 45 dB. Completed after 1000 packets.

Plot Packet Error Rate vs SNR Results

figure;
semilogy(snr,packetErrorRate,'-ob');
grid on;
xlabel('SNR (dB)');
ylabel('PER');
title(['802.11ah ' cfgS1G.Preamble ', ' num2str(cfgS1G.ChannelBandwidth(4:end)) ...
    'MHz, MCS' num2str(cfgS1G.MCS) ', ' ...
    num2str(tgahChannel.NumTransmitAntennas) 'x' num2str(tgahChannel.NumReceiveAntennas) ...
    ' TGah Channel ' num2str(tgahChannel.DelayProfile)]);

Further Exploration

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, and the SNR range snr = 20:8:60.

Appendix

This example uses the following helper functions:

Selected Bibliography

  1. IEEE P802.11ah™ D5.0 IEEE 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 2: Sub 1 GHz License Exempt Operation.

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