How to Calculate Normalized MSE in ns3

To calculate the Normalized Mean Squared Error (NMSE) in ns3, this is frequently used to evaluate the performance of techniques that specifically in the signal processing and the simulated scenarios. In the regarding it Normalized Mean Squared Error (NMSE) to the variance of data and offers a scale independent measure of error. For ideal results in Normalized Mean Squared Error (NMSE)  based on your project, please contact ns3simulation.com.

Here, we are going to see how to compute the NMSE in ns3 by the following steps:

  1. Collect the Actual and Predicted Data: Ensure you have two sets of data:
    • The actual data values.
    • The predicted data values from your simulation.
  2. Calculate the Mean Squared Error (MSE): The MSE is the average of the squared differences between the actual and predicted values. In mathematical terms:

MSE=1N∑i=1N(yi−y^i)2\text{MSE} = \frac{1}{N} \sum_{i=1}^{N} (y_i – \hat{y}_i)^2MSE=N1​i=1∑N​(yi​−y^​i​)2

where yiy_iyi​ is the actual value, y^i\hat{y}_iy^​i​ is the predicted value, and NNN is the number of data points.

  1. Calculate the Variance of the Actual Data: The variance measures the spread of the actual data values. It is given by:

Var(y)=1N∑i=1N(yi−yˉ)2\text{Var}(y) = \frac{1}{N} \sum_{i=1}^{N} (y_i – \bar{y})^2Var(y)=N1​i=1∑N​(yi​−yˉ​)2

where yˉ\bar{y}yˉ​ is the mean of the actual values.

  1. Calculate NMSE: The NMSE is the MSE divided by the variance of the actual data:

NMSE=MSEVar(y)\text{NMSE} = \frac{\text{MSE}}{\text{Var}(y)}NMSE=Var(y)MSE​

Example Code in ns3

At this direction, we illustrate the steps to complete the NMSE in ns3:

#include <iostream>

#include <vector>

#include <cmath>

// Function to calculate Mean Squared Error (MSE)

double calculateMSE(const std::vector<double>& actual, const std::vector<double>& predicted) {

double mse = 0.0;

for (size_t i = 0; i < actual.size(); ++i) {

mse += std::pow(actual[i] – predicted[i], 2);

}

mse /= actual.size();

return mse;

}

// Function to calculate variance

double calculateVariance(const std::vector<double>& data) {

double mean = 0.0;

for (double value : data) {

mean += value;

}

mean /= data.size();

double variance = 0.0;

for (double value : data) {

variance += std::pow(value – mean, 2);

}

variance /= data.size();

return variance;

}

// Function to calculate Normalized MSE (NMSE)

double calculateNMSE(const std::vector<double>& actual, const std::vector<double>& predicted) {

double mse = calculateMSE(actual, predicted);

double variance = calculateVariance(actual);

return mse / variance;

}

int main() {

// Example data

std::vector<double> actual = {1.0, 2.0, 3.0, 4.0, 5.0};

std::vector<double> predicted = {0.9, 2.1, 2.9, 4.2, 5.1};

// Calculate NMSE

double nmse = calculateNMSE(actual, predicted);

std::cout << “Normalized MSE: ” << nmse << std::endl;

return 0;

}

Explanation:

  1. calculateMSE: Computes the MSE by iterating over the actual and predicted values, summing the squared differences, and dividing by the number of data points.
  2. calculateVariance: Computes the variance of the actual values by calculating the mean and then summing the squared differences from the mean, dividing by the number of data points.
  3. calculateNMSE: Divides the MSE by the variance to obtain the NMSE.

At the conclusion, the Normalised Mean square Error can computes by the variance of actual values with the help of ns3 simulated tool. If you want further insights that related to NMSE we will support and provide the elaborated details.

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