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Parallel BER Simulations of the IEEE 802.11b Physical Layer

This example shows how to use the Communications System Toolbox™ Error Rate Test Console to run parallel BER simulations of a system that implements the physical layer of the IEEE® 802.11b standard.

IEEE 802.11b Communications System

The file IEEE80211b.mIEEE80211b.m contains the definition of a communications system that implements DBPSK modulation, Barker code spreading, and pulse shaping over a flat fading Rayleigh channel with additive white Gaussian noise. This class definition uses the System Basic API (i.e. extends the testconsole.SystemBasicAPI class) and thus, can be attached to an Error Rate Test Console for analysis.

% Instantiate the 802.11b communications system
sys = IEEE80211b
sys = 

            Description: 'IEEE 802.11b physical layer'
                   EsNo: 0
                Doppler: 200
    FilterSpanInSymbols: 5
          RolloffFactor: 0.7000
         SamplesPerChip: 8

We may change the system property values to change the pulse shaping filter order (FilterSpanInSymbols) and rolloff factor (RolloffFactor), the samples per chip (SamplesPerChip), the energy per symbol to noise power spectral density ratio (EsNo), and the maximum Doppler shift (Doppler) of the Rayleigh channel. As will be explained shortly, these last two properties, EsNo and Doppler, are registered by the system as test parameters. Registered test parameters can be controlled by a test console to run parameterized simulations.

Debug Mode

A system that uses the System Basic API can be run by itself (without the need to attach it to a test console), and this scenario is referred to as debug mode. The system does not generate any outputs in debug-mode. This mode is useful to debug the system using break points before running simulations through a test console. We run the system in debug mode and confirm that the system can be run without errors or warnings.

% Setup, reset, and run the system to check for errors or warnings
setup(sys)
reset(sys)
run(sys)

Error Rate Test Console

We use an Error Rate Test Console to run parameterized simulations of the system to obtain error rate performance metrics. The Error Rate Test Console can sweep through a set of test parameter values and collect error rate data. The Error Rate Test Console automatically utilizes a parallel computing environment created by the Parallel Computing Toolbox™. If a Parallel Computing Toolbox license exists, the Error Rate Test Console automatically detects the parallel pool and distributes the simulation among multiple workers. Otherwise, simulations are run on a single core. Simulation duration can be drastically reduced if multiple workers are utilized.

Starting an Error Rate Test Console

Error rate simulations can be run on the 802.11b system by instantiating a commtest.ErrorRate test console and attaching the IEEE80211b communications system to it. When instantiating, we will set the FrameLength property of the test console to 8192 symbols, which corresponds to the packet size of an 802.11b system (ignoring preamble and sync bits). The FrameLength property defines the length of the transmitted frame that will be used at each simulation iteration.

testConsole = commtest.ErrorRate(sys,'FrameLength',8192)
testConsole = 

                   Description: 'Error Rate Test Console'
           SystemUnderTestName: 'IEEE80211b'
                   FrameLength: 8192
                 IterationMode: 'Combinatorial'
               SystemResetMode: 'Reset at new simulation point'
         SimulationLimitOption: 'Number of transmissions'
    TransmissionCountTestPoint: 'Not set'
           MaxNumTransmissions: 1000

Test Console Configuration

We need to configure the test console before running simulations. Configuration involves registering test points, setting test parameter sweep values, specifying the simulation stop and reset criteria, and the way we want the test console to combine the test parameter sweep values. We can get the information needed to configure the test console using the INFO method of the test console.

% Get information about the test console and the attached system
info(testConsole)
Test console name:           commtest.ErrorRate
System under test name:      IEEE80211b
Available test inputs:       NumTransmissions, RandomIntegerSource
Registered test inputs:      RandomIntegerSource
Registered test parameters:  Doppler, EsNo, M
Registered test probes:      RxOutputSymbols, TxInputSymbols
Registered test points:      None
Metric calculator functions: None
Test metrics:                None

Setting Test Parameter Sweep Values

The INFO method shows that there are three registered test parameters, 'EsNo' (energy per symbol to noise power spectral density ratio), 'M' (modulation order), and 'Doppler' (maximum Doppler shift for the Rayleigh channel). Error rate simulations may be obtained for various combinations of values of these parameters.

Sweep values for each parameter can be specified by calling the setTestParameterSweepValues method of the test console. To see the valid ranges for test parameter values we first use the getTestParameterValidRanges method.

% Get test valid ranges for 'EsNo' test parameter
getTestParameterValidRanges(testConsole, 'EsNo')
ans =

     []

We observe that the IEEE80211b system has not set any range limits for the 'EsNo' parameter.

% Get test valid ranges for 'Doppler'
getTestParameterValidRanges(testConsole, 'Doppler')
ans =

     0   500

The IEEE80211b system has set limits on the maximum Doppler shift of the Rayleigh channel 'Doppler' parameter so that it remains inside the [0 500] Hz interval.

% Get test valid ranges for 'M'
getTestParameterValidRanges(testConsole, 'M')
ans =

     2     2

The system has set limits on modulation order 'M' such that it remains constant and equal to 2 since it implements a DBPSK modulation scheme. In this case 'M' has been registered as a test parameter not to enable simulations for different modulation orders but to enable the system to use a 'RandomIntegerSource' source data available at the test console as a test input.

Let us obtain simulation results for a range of EsNo values and for two different Doppler values. To do this, we set the sweep values for each test parameter using the setTestParameterSweepValues method.

% Set EsNo sweep values from -2 to 8 dB
setTestParameterSweepValues(testConsole,'EsNo',-2:2:8)

% Set maximum Doppler shift sweep values to 0 and 200
setTestParameterSweepValues(testConsole,'Doppler',[0 200])

To verify that the sweep values have been set call the getTestParameterSweepValues method of the test console. Observe how 'M' is set to its default value of 2. When we do not specify sweep values for a test parameter, the test console runs simulations using the parameter's registered default value.

% Get sweep values for test parameter 'EsNo'
getTestParameterSweepValues(testConsole,'EsNo')
ans =

    -2     0     2     4     6     8

% Get sweep values for test parameter 'Doppler'
getTestParameterSweepValues(testConsole,'Doppler')
ans =

     0   200

% Get sweep values for test parameter 'M'
getTestParameterSweepValues(testConsole,'M')
ans =

     2

Registering Test Points

Test points are used to pair two data probes that were previously registered to the test console by the communications system. A test point contains two probes, and if desired, a handle to a user-defined error calculator function. The IEEE80211b system registered two test probes named 'TxInputSymbols', and 'RxOutputSymbols' when it was attached to the test console, as can be seen in the information displayed by the INFO method. In this example, a single test point named 'SymbolErrorRate' will be registered and will contain the two aforementioned test probes and a handle to a user-defined error calculator function, errorCalculatorFunction80211b.m, defined specifically for the IEEE80211b system. Error rates will be calculated by comparing data available in the two probes using the user-defined error calculator function. In this example, a user-defined error calculator function is necessary since error calculation needs to account for transmitter and receiver delays caused by the root raised cosine pulse shaping filters and the differential modulation. The default error calculator function available in the Error Rate Test Console performs simple one-to-one comparisons of the data in the probes and does not account for transmitter-receiver delays. Test points will hold error and transmission counts for each sweep point simulation.

registerTestPoint(testConsole,'SymbolErrorRate','TxInputSymbols', ...
    'RxOutputSymbols',@IEEE80211bErrorCalculator)

We can review all the test console simulation settings by calling the INFO method again

info(testConsole)
Test console name:           commtest.ErrorRate
System under test name:      IEEE80211b
Available test inputs:       NumTransmissions, RandomIntegerSource
Registered test inputs:      RandomIntegerSource
Registered test parameters:  Doppler, EsNo, M
Registered test probes:      RxOutputSymbols, TxInputSymbols
Registered test points:      SymbolErrorRate
Metric calculator functions: @IEEE80211bErrorCalculator
Test metrics:                ErrorCount, TransmissionCount, ErrorRate

Setting the Simulation Stop Criteria

The simulation for a particular EsNo value may be stopped in different ways. You can control the stop mechanism using the SimulationLimitOption property of the test console. Simulations may be stopped when a specified number of transmissions, or errors has been reached. In this example simulations will be stopped when at least 100 errors are counted for each EsNo value, or when 5 packets have been transmitted, whichever happens first (we choose only 5 packet transmissions to keep the simulation time short, longer simulation results will be presented shortly). For this purpose the SimulationLimitOption property is set to 'Number of errors or transmissions', the MinNumErrors property is set to 100, and the MaxNumTransmissions property is set to 5*testConsole.FrameLength. The TransmissionCountTestPoint, and ErrorCountTestPoint properties are set to the name of the only available test point 'SymbolErrorRate'. This last property is used to tell the test console at which of the test points to look for the transmission and error counts.

testConsole.SimulationLimitOption = 'Number of errors or transmissions';
testConsole.MaxNumTransmissions = 5*testConsole.FrameLength;
testConsole.MinNumErrors = 100;
testConsole.TransmissionCountTestPoint = 'SymbolErrorRate';
testConsole.ErrorCountTestPoint = 'SymbolErrorRate';
disp(testConsole)
                   Description: 'Error Rate Test Console'
           SystemUnderTestName: 'IEEE80211b'
                   FrameLength: 8192
                 IterationMode: 'Combinatorial'
               SystemResetMode: 'Reset at new simulation point'
         SimulationLimitOption: 'Number of errors or transmissions'
    TransmissionCountTestPoint: 'SymbolErrorRate'
           MaxNumTransmissions: 40960
           ErrorCountTestPoint: 'SymbolErrorRate'
                  MinNumErrors: 100

Setting the Simulation Reset Criteria

The system reset criteria is controlled by the SystemResetMode property of the Error Rate Test Console. When this property is set to 'Reset at new simulation point' the system under test is reset only at the beginning of a new simulation point. When this property is set to 'Reset at every iteration' the system under test will be reset at every iteration. We choose the 'Reset at new simulation point' option.

testConsole.SystemResetMode = 'Reset at new simulation point';

Setting the Iteration Mode Criteria

The iteration mode refers to the way in which the test console combines test parameter sweep values to perform simulations. The IterationMode property of the test console controls this behavior. When this property is set to 'Combinatorial', simulations are performed for all possible combinations of registered test parameter sweep values. When this property is set to 'Indexed', simulations are performed for all indexed sweep value sets. The ith sweep value set consists of the ith element of every sweep value vector of each registered test parameter. In the simulations at hand, we want to obtain results for all the combinations of EsNo and Doppler sweep values so we choose the 'Combinatorial' option.

testConsole.IterationMode = 'Combinatorial';

Running 802.11b Error Rate Simulations

The simulations for the specified EsNo and Doppler sweep values may be run by calling the run method of the Error Rate Test Console.

run(testConsole)
Starting parallel pool (parpool) using the 'local' profile ... connected to 12 workers.
12 workers available for parallel computing. Simulations will be distributed among these workers. 
Running simulations...

Getting and Plotting Results

Results my be obtained by calling the getResults method of the error rate test console,

results80211b = getResults(testConsole);

In order to obtain more accurate results we increased MinNumErrors to 1000, MaxNumTransmissions to 200*testConsole.FrameLength, and ran the simulation again. Since the simulation takes a long time we saved the results object results80211b in IEEE80211bDemoResults.mat.

load IEEE80211bDemoResults.mat
disp(results80211b)
        TestConsoleName: 'commtest.ErrorRate'
    SystemUnderTestName: 'IEEE80211b'
          IterationMode: 'Combinatorial'
              TestPoint: 'SymbolErrorRate'
                 Metric: 'ErrorRate'
         TestParameter1: 'Doppler'
         TestParameter2: 'None'

results80211b is a testconsole.Results object that contains all the results for all the specified test points and sweep values. In the simulation at hand only one test point called 'SymbolErrorRate' was registered. The resulting data and plots for this test point may be obtained by calling the getData and plot or semilogy methods of the results object results80211b.

If we want to obtain error rate results versus EsNo values for Doppler shifts of 0 and 200 Hz we configure the results80211b object to have 'EsNo' as TestParameter1 (parameter in control of the rows of the data matrix and of the x-axis of the plot) and 'Doppler' as TestParameter2 (parameter in control of the columns of the data matrix and of the number of parametric curves in the plot).

results80211b.TestParameter1 = 'EsNo';
results80211b.TestParameter2 = 'Doppler';
% Get results data
data = getData(results80211b)
data =

    0.2737    0.2759
    0.1980    0.2745
    0.0994    0.1893
    0.0420    0.1304
    0.0094    0.0668
    0.0008    0.0484

% Plot results in semi-log scale
semilogy(results80211b,'LineWidth',2)

Exploring Results For Different Metrics

Calling the INFO method allows us to see the test metrics available in the Error Rate Test Console: 'ErrorCount', 'TransmissionCount', 'ErrorRate'. To see the results for these metrics set the Metric property of the results80211b object accordingly and get the results data.

Get the error count from the results object:

results80211b.Metric = 'ErrorCount';
getData(results80211b)
ans =

        2242        2260
        1622        2248
        1628        1550
        1031        1068
        1077        1095
        1011        1190

Get the transmissions count from the results object:

results80211b.Metric = 'TransmissionCount';
getData(results80211b)
ans =

        8190        8190
        8190        8190
       16382        8190
       24574        8190
      114686       16382
     1204222       24574

Recall that since TestParameter1 = 'EsNo', and TestParameter2 = 'Doppler', rows of the results data correspond to different 'EsNo' values while columns correspond to different 'Doppler' values.

Summary

We utilized the Error Rate Test Console to simulate an IEEE 802.11b physical layer system over a flat fading Rayleigh channel. The system was defined using the System Basic API. We specified sweep values for EsNo and maximum Doppler shift to obtain simulation results. We registered a test point to detect and count symbol errors. We obtained plots of symbol error rate versus EsNo for two different Doppler shifts.

Further Exploration

You can modify parts of this example or the system definition, IEEE80211b.

You can add more test parameters by registering these as test parameters in the register method of the IEEE80211b system. For example, you can register the RolloffFactor property as a test parameter to obtain simulations using different pulse shaping rolloff factor values. You can do the same with the FilterSpanInSymbols property.

Selected Bibliography

  1. IEEE Std 802.11, "Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications," 2007.

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