Revisiting R: Statistical Envelope Analysis for Lightweight RF Modulation Classification

Modulation classification plays a crucial role in wireless communication systems, enabling applications such as cognitive radio, spectrum monitoring, and electronic warfare. Conventional techniques often involve deep learning or complex feature extraction, which, while effective, require substantial computational resources and memory. An early approach by Chan and Gadbois in 1985 introduced a theoretical approach for modulation classification using a mathematically derived parameter called ’R’. The authors proved that the ’R’ value, the ratio of the variance to the square of the mean of the signal envelope, can be a distinguishing feature for classification. In this work, we revisit R and show classification accuracy can be improved further through statistical methods. We extend R-value analysis to demonstrate its effectiveness even after signals are transformed using Hilbert transform followed by the Short-Time Fourier Transform (STFT). Our rigorous analysis includes testing on 300000 signals of AM, DSB and SSB classes with each class having 100000 random variations. On average, we achieve 98.60%, 97.30%, and 97.90% Classification accuracies for AM, DSB, and SSB signals after applying the Hilbert transform are presented. Similar or improved accuracies are observed after applying the Short-Time Fourier Transform (STFT), similar or better accuracies are observed; 98.80%, 99.10%, and 99.00% respectively for AM, DSB and SSB types.