Optimize Eye Height in SerDes System Model

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This example shows how to optimize performance metrics of a Simulink model using an optimization feature called msbOptimizer from the Mixed-Signal Blockset™. msbOptimizer uses a solver called surrogateopt (Global Optimization Toolbox) from Global Optimization Toolbox™ for optimization. Any Simulink model can be optimized for best performance using the steps mentioned here. In this example, you will optimize eye metrics of a SerDes system. Eye metrics are an indication of the signal's quality and reliability and hence important parameters for serial communication.

Open the model eyeMeasurement_1Eye attached to this example. The model comprises a stimulus generator, transmitter (Tx), analog channel and a receiver (Rx). This model will be used to optimize the parameter TapWeights (DFE tap weights) of DFECDR block inside Rx to meet eye performance metrics. It was originally created in the SerDes Designer app and then exported to Simulink®. For more information, see Design SerDes System and Export IBIS-AMI Model (SerDes Toolbox).

model='eyeMeasurement_1Eye';
open_system(model);

Eye Measurement

Run simulation with an initial set of DFE tap weights to obtain the time-domain metrics before optimization. To generate time-domain metrics including the eye measurement summary, double click on the Configuration block and select Plot time domain analysis after simulation.

weights=[0.06 -0.01 -0.04 -0.01];
tapWeights=['[',num2str(weights),']'];
set_param([model '/Rx/DFECDR'],'TapWeights',tapWeights);
sim(model);

Figure Time Domain Analysis Results contains an axes object and another object of type uipanel. The axes object with title Time Domain Eye, xlabel [ps], ylabel [V] contains 6 objects of type image, line.

The eye is almost closed and not optimal. You can also access the eye measurement summary which is exported to the model workspace using following function calls. In the next step, set up prerequisites for msbOptimizer to optimize DFE tap weights for optimal eye height. 

mws=get_param(bdroot,'ModelWorkspace');
results=mws.getVariable('SerDesResults');
metrics=results.TimeDomain.summary
metrics=9×2 cell array
    {'Eye Height (V)' }    {[1.5058e-06]}
    {'Eye Width (ps)' }    {[7.9261e-04]}
    {'Eye Area (V*ps)'}    {[7.3412e-05]}
    {'COM'            }    {[6.8135e-05]}
    {'VEC'            }    {[        60]}
    {'Minimum BER'    }    {[5.2632e-05]}
    {'Ignore Symbols' }    {[      1000]}
    {'Total Symbols'  }    {[     20000]}
    {'SER'            }    {[    0.0034]}

Optimization setup

msbOptimizer supports optimization within the Simulink environment and requires setting up output table, variable table and objective function.

Output Table

Create a table with output parameters and specifications to be met during optimization. The performance specifications considered in this example are Eye Height, Eye Width and Symbol Error Rate (SER).

outputTable=table();
outputTable.Test=["eye1";"eye1";"eye1"];
outputTable.Name={'Eye Height';'Eye Width';'SER'};
outputTable.Weight=[100;90;50];
outputTable.Units={'V';'ps';''};
outputTable.Spec={'> 0.12';'> 82';'< 1e-04'}
outputTable=3×5 table
     Test          Name         Weight      Units          Spec    
    ______    ______________    ______    __________    ___________

    "eye1"    {'Eye Height'}     100      {'V'     }    {'> 0.12' }
    "eye1"    {'Eye Width' }      90      {'ps'    }    {'> 82'   }
    "eye1"    {'SER'       }      50      {0×0 char}    {'< 1e-04'}

Variable Table

Create a table of optimization variables and their ranges. In this example you will be optimizing the DFE tap weights in the Rx block to meet the performance metrics specified in the output table.

variableTable=table();
variableTable.parameters={'w1';'w2';'w3';'w4'};
variableTable.values=["-0.2:0.001:0.2";"-0.1:0.001:0.1";"-0.1:0.001:0.1";"-0.1:0.001:0.1"]
variableTable=4×2 table
    parameters         values     
    __________    ________________

      {'w1'}      "-0.2:0.001:0.2"
      {'w2'}      "-0.1:0.001:0.1"
      {'w3'}      "-0.1:0.001:0.1"
      {'w4'}      "-0.1:0.001:0.1"

Objective Function

The objective function sets values for optimization variables in the model, runs simulations in Simulink and extracts the performance metrics from the simulations. For this example, you need to define an objective function to perform the following steps:

  1. Set the DFE tap weights using set_param()

  2. Run simulations

  3. Create a table of simulation results.

You will pass a handle from this objective function to the msbOptimizer object in the next section. 

function out=getEyeMetrics(x,parameterNames,paramScaleFactor,constraints,designName)
    % Pass the function handle to your custom
    % getMetrics() function as a Name-Value pair argument while instantiating the msbOptimizer.
    % E.g.,designOptimizer=msbOptimizer('simEnvironment','simulink','objectiveFunction',funcHandle),
    % where funcHandle=@(x) getMetrics(x,variableNames,variableScaleFactor,constraintTable,modelName)
    out.Fval =NaN(size(x,1),1);
    out.Ineq =NaN(size(x,1),height(constraints)-1);
    xHeight=size(x,1);
    simIn(1:xHeight)=Simulink.SimulationInput(designName);
    weights=zeros(1,numel(parameterNames));
    resultsTable=table();
    fprintf("\nRunning %d simulations in Simulink...\n",size(x,1));
    for ii=1:xHeight
        ji=1;
        %set variable values in the next for loop
        for variable=parameterNames
            try
                simIn(ii)=setVariable(simIn(ii),variable,paramScaleFactor(ji).*x(ii,ji));
                weights(ji)=paramScaleFactor(ji).*x(ii,ji);
            catch
                error(message('msblks:msblksMessages:optimSimulatorError'));
            end
            ji=ji+1;
        end
        tapWeights=['[',num2str(weights),']'];
        % 1. SET DFE TAP WEIGHTS
        set_param('eyeMeasurement_1Eye/Rx/DFECDR','TapWeights',tapWeights);
        try
            % 2. RUN SIMULATIONS
            sim(simIn(ii));
            save_system('eyeMeasurement_1Eye');
            % 3. EXTRACT METRICS AND CREATE A TABLE OF SIMULAITON RESULTS
            mws=get_param(bdroot,'ModelWorkspace');            
            results=mws.getVariable('SerDesResults');
            metrics=results.TimeDomain.summary;
            eyeTable=cell2table(metrics);
            eyeTable=eyeTable(contains(eyeTable.metrics1, {'Eye Height','Eye Width','SER'}),:);
            resultsTable1=table();
            resultsTable1.Output(1)="Eye Height";
            resultsTable1.Output(2)="Eye Width";      
            resultsTable1.Output(3)="SER";      
            resultsTable1.Point=NaN(height(resultsTable1),1);
            resultsTable1.DataPoint=NaN(height(resultsTable1),1);
            resultsTable1.Result=eyeTable{:,2};
            
        catch
            disp("Error during simulation. Setting results to 0.")
            resultsTable1=table();
            resultsTable1.Output=zeros(3,1);
            resultsTable1.Result=zeros(3,1);            
            resultsTable1.Point=zeros(3,1);
            resultsTable1.DataPoint=zeros(3,1);
        end

        if ~isempty(resultsTable)
            resultsTable=[resultsTable; resultsTable1];
        else
            resultsTable=resultsTable1;
        end
    end
    % Create a struct called out which is required by surrogateopt
    [fval,ineq]=msblks.optimization.surrogateOptHelper.getFvalIneq(size(x,1),resultsTable,constraints, "Nominal");
    out.Fval=fval;
    out.Ineq=ineq;
end

Run Optimization

To run optimization, first instantiate an object of msbOptimizer class with the SimulationEnvironment option set to simulink, and other options set as shown below. 

m=msbOptimizer('SimulationEnvironment','simulink',...
    'DesignName',model,...
    'OutputsSetup',outputTable,...
    'VariableSetup',variableTable);
Number of parameters: 4
Recommended max number of simulations: 200
Recommended min surrogate points: 120

Create the function handle objFunction from the objective function that was defined in the previous section. Pass the objective function handle as an argument to the optimizeDesign method in the next step.

objFunction=@(x) getEyeMetrics(x,m.ParameterNames,m.ParameterScaleFactor,m.Constraints,m.DesignName);

Optimize the DFE tap weights for the specified time-domain metrics using the optimizeDesign method of the msbOptimizer object. You can specify the maximum number of simulations that will be run using MaxNumberSims. You can set the number of simulations per iteration using NumParallelSims. Disable ProgressPlot by setting it to false since there are also plots generated by Time-Domain Analysis. 

[bestSolution1,bestMetrics1]=m.optimizeDesign('ObjectiveFunction',objFunction,'ProgressPlot',false,...
    'NumParallelSims',5,'MinSurrogatePoints',15,'MaxNumberSims',45)
Maximum number of simulations: 45
Number of parallel simulations: 5

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Optimizer was unable to meet some or all the specifications.
You can continue optimization from the current state by using the checkpoint file.
E.g., if your object is called 'optimizer', run the following command:
 [solution, bestMetrics] = optimizer.optimizeDesign('useCheckPoint',true)

Figure Time Domain Analysis Results contains an axes object and another object of type uipanel. The axes object with title Time Domain Eye, xlabel [ps], ylabel [V] contains 6 objects of type image, line.

bestSolution1=4×2 table
    Name    Value 
    ____    ______

    "w1"    -0.027
    "w2"    -0.008
    "w3"    -0.004
    "w4"     0.001


bestMetrics1=3×4 table
        Name        FinalMetrics      Specs      Units
    ____________    ____________    _________    _____

    "Eye Height"      0.10126       "> 0.12"     "V"  
    "Eye Width"        79.694       "> 82"       "ps" 
    "SER"                   0       "< 1e-04"    ""

Using InitialPoints

Observe that the performance metrics are close to but not quite at the target specifications set by the output table. You can continue the optimization process by passing the argument InitialPoints which lets the optimization solver start from a set of initial points defined by the previously run iterations. This information is saved in Trials property of msbOptimizer, which must be passed as a Name-Value pair argument for InitialPoints to the optimizeDesign method as shown below.

[bestSolution2,bestMetrics2]=m.optimizeDesign('InitialPoints',m.Trials,'ObjectiveFunction',objFunction,'ProgressPlot',false,...
    'NumParallelSims',5,'MinSurrogatePoints',15,'MaxNumberSims',45)
Maximum number of simulations: 45
Number of parallel simulations: 5

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Running 5 simulations in Simulink...

Optimizer was able to meet all the specifications.

Figure Time Domain Analysis Results contains an axes object and another object of type uipanel. The axes object with title Time Domain Eye, xlabel [ps], ylabel [V] contains 6 objects of type image, line.

bestSolution2=4×2 table
    Name    Value 
    ____    ______

    "w1"    -0.044
    "w2"     -0.01
    "w3"    -0.006
    "w4"    -0.005


bestMetrics2=3×4 table
        Name        FinalMetrics      Specs      Units
    ____________    ____________    _________    _____

    "Eye Height"      0.12111       "> 0.12"     "V"  
    "Eye Width"        82.428       "> 82"       "ps" 
    "SER"                   0       "< 1e-04"    ""

Verification

You can see that all the performance metrics are met after the second round of optimization run. Although MaxNumberSims was set to 45, optimizer stopped after 15 simulations since all the performance specifications were met. Verify that the tap weights stored in bestSolution provide the required performance by setting the tap weights to the optimized values and observing the eye metrics. You can see that the eye metrics meet the specifications set in the output table. 

weights=bestSolution2.Value';
tapWeights=['[',num2str(weights),']'];
set_param([model '/Rx/DFECDR'],'TapWeights',tapWeights);
sim(model);

Figure Time Domain Analysis Results contains an axes object and another object of type uipanel. The axes object with title Time Domain Eye, xlabel [ps], ylabel [V] contains 6 objects of type image, line.

See Also

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