ROC of Energy detection under AWGN

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ROC of Energy detection under AWGN

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Energy detection is a fundamental technique in signal processing used to determine the presence or absence of a signal in noisy environments. When operating under Additive White Gaussian Noise (AWGN), the performance of an energy detector is often evaluated using the Receiver Operating Characteristic (ROC) curve, which plots the Probability of Detection (Pd) against the Probability of False Alarm (Pfa).

### Understanding Energy Detection Energy detection works by measuring the energy of the received signal over a specified bandwidth and time period. If the measured energy exceeds a predefined threshold, the detector declares the presence of a signal. The key challenge is setting this threshold to balance detection performance and false alarms.

### ROC Analysis under AWGN In AWGN, noise is Gaussian-distributed, making the analysis tractable. The ROC curve for energy detection depends on: SNR (Signal-to-Noise Ratio): Higher SNR improves detection probability. Threshold Selection: A lower threshold increases detection but also raises false alarms. Sample Size: More samples improve detection accuracy but require additional computational resources.

Theoretical ROC curves can be derived using the distributions of noise and signal-plus-noise scenarios. Under AWGN, the energy of the received signal follows a Chi-square distribution (central for signal+noise, non-central for noise alone).

### Practical Implications Trade-off between Pd and Pfa: Engineers must choose thresholds based on system requirements (e.g., radar systems prioritize high Pd, while communication systems may prioritize low Pfa). Impact of SNR: Low-SNR scenarios require sophisticated detection techniques or longer observation windows to achieve acceptable performance.

Energy detection remains widely used due to its simplicity, making ROC analysis essential for optimizing detection systems under AWGN.