ROC Simulation for Energy Detection and Double-Threshold Detection in Spectrum Sensing

In the domain of spectrum sensing, energy detection and double-threshold detection represent two prominent signal processing techniques extensively employed for distinguishing between signals and noise in frequency-domain analysis. These methods are fundamental to cognitive radio systems and wireless communication applications.

Energy detection operates by calculating the received signal's energy and comparing it against a predetermined threshold. In MATLAB implementation, this typically involves computing the squared magnitude of FFT results using functions like abs(fft(signal)).^2, followed by threshold comparison using logical operators. When the computed energy exceeds the threshold (implemented via conditional statements like if energy > threshold), the system classifies it as a valid signal; otherwise, it's identified as noise.

Double-threshold detection enhances decision robustness by implementing two distinct thresholds (lower_threshold and upper_threshold). The algorithmic implementation involves sequential checks: if signal energy falls below the lower threshold (energy < lower_threshold), it's classified as noise; if between thresholds (energy >= lower_threshold && energy <= upper_threshold), it's categorized as a weak signal requiring further processing; and if above the upper threshold (energy > upper_threshold), it's identified as a strong signal.

Performance evaluation of these detection schemes utilizes Receiver Operating Characteristic (ROC) curves, which plot detection probability (Pd) against false alarm probability (Pf). Simulation typically involves Monte Carlo methods with nested loops iterating over threshold values and signal-to-noise ratio (SNR) conditions. Key functions include probability calculation using mean(detection_results) for Pd/Pf estimation and plot(Pf, Pd) for curve generation. Parameter sweeps across threshold ranges enable comprehensive analysis of detection trade-offs, with optimization focusing on maximizing Pd while constraining Pf.