PAPR CDF Plot Generation for OFDM BPSK Systems

This documentation presents the methodology for generating Cumulative Distribution Function (CDF) plots of Peak-to-Average Power Ratio (PAPR) for OFDM BPSK transmissions compliant with IEEE 802.11a specifications. The implementation utilizes 52 active subcarriers as mandated by the standard. While the theoretical maximum PAPR reaches 52 (approximately 17 dB), the incorporation of a scrambler in the transmission chain prevents simultaneous equal modulation across all subcarriers within a single OFDM symbol.

The analytical approach employs a custom MATLAB/Python script that processes randomly generated BPSK-modulated OFDM symbols. Key algorithmic steps include: generating BPSK constellation points, applying IFFT transformation to create time-domain signals, calculating instantaneous power peaks and average power values, and computing PAPR statistics across multiple symbol iterations. The script incorporates statistical functions to aggregate PAPR measurements and plot the cumulative distribution using empirical CDF calculation methods. The resulting visualization provides critical insights into PAPR distribution characteristics and occurrence probabilities under realistic transmission conditions.

This PAPR CDF analysis methodology is essential for evaluating wireless communication system performance, particularly for assessing power amplifier requirements and optimizing OFDM system designs. The implemented scripting solution enables efficient characterization of PAPR behavior through systematic subcarrier analysis and probability distribution mapping, providing valuable quantitative data for system optimization and standardization compliance verification.