CCDF Calculator & Formula for PAPR | OFDM Signal Analysis

This CCDF calculator allows you to compute the Complementary Cumulative Distribution Function (CCDF) of an OFDM signal based on input parameters. CCDF is a key performance metric in digital communication systems that quantifies the probability of exceeding a certain Peak to Average Power Ratio (PAPR) threshold.

What is CCDF ?

CCDF is defined as the probability that the PAPR of an OFDM signal exceeds a given threshold. Mathematically, it can be expressed as following.

Following are the relations between PDF, CDF and CCDF:

• PDF (Probability Density Function) represents the probability distribution of PAPR values in the OFDM signal.
• CDF (Cumulative Distribution Function) represents the cumulative probability of PAPR values up to a certain threshold.
• CCDF (Complementary Cumulative Distribution Function) represents the probability of PAPR values exceeding a certain threshold, which is calculated as 1 - CDF.

Why is CCDF Important ?

CCDF is crucial for analyzing the performance of OFDM systems, as it helps engineers understand the likelihood of encountering high PAPR values, which can lead to signal distortion and reduced efficiency in power amplifiers. By calculating CCDF, engineers can optimize their designs to minimize PAPR and improve signal quality.

Which CCDF plot is better than the other one ?

The one with lower CCDF values (CCDF dB = -10 dB) indicates better performance and lower likelihood of encountering high PAPR values, while higher CCDF values (CCDF dB = -5 dB) indicate a higher probability of exceeding the PAPR threshold, which can lead to signal distortion and reduced efficiency in power amplifiers.

CCDF Calculator for OFDM Signal

CCDF OFDM Calculation Example:

• Inputs : Number of Carriers = 64, Number of Symbols = 5000
• Outputs : Plot as shown once user click “Plot Chart” button

Step-wise Calculation of CCDF

1. Generate OFDM Signal: Create an OFDM signal based on the specified number of carriers and symbols.

2. Calculate PAPR: Compute the Peak to Average Power Ratio (PAPR) for the generated OFDM signal having “N” OFDM symbols.

3. Sort PAPR Values: Sort the calculated PAPR values in ascending order to analyze the distribution.

4. Compute CCDF: For each PAPR threshold, calculate the CCDF using the formula:

5. Create CCDF Table: Compile the calculated CCDF values into a table for different PAPR thresholds to visualize the distribution and identify the likelihood of exceeding specific PAPR levels.

Conclusion

The CCDF calculator provides a convenient way to compute the CCDF and PAPR for OFDM signals, which are essential for analyzing the performance of communication systems. By understanding the CCDF formula and using the calculator, engineers can optimize their designs to minimize PAPR and improve signal quality.