Receiver Operating Characteristic (ROC) Analysis for Energy Detection in AWGN Channels

This paper provides a comprehensive analysis of Receiver Operating Characteristic (ROC) curves for energy detection systems operating under Additive White Gaussian Noise (AWGN) conditions. We examine the fundamental principles underlying ROC curve generation, including detailed methodologies for calculating and analyzing detection performance metrics. The implementation typically involves computing the energy statistic using a summation of squared signal samples over an observation window, followed by threshold comparison for hypothesis testing. We explore how ROC curves serve as critical tools for evaluating energy detection performance through probability of detection (Pd) versus probability of false alarm (Pfa) relationships. Practical applications of these evaluation results for optimizing system design parameters, such as threshold selection and integration time, are discussed with relevant MATLAB or Python code snippets demonstrating threshold optimization algorithms. Furthermore, we extend the analysis to non-ideal scenarios where practical impairments affect detection performance, presenting modified ROC analysis techniques and adaptive threshold adjustment methods that can be implemented using numerical computation approaches to maintain optimal performance under realistic operating conditions.