Energy Detection: Threshold Determination Based on False Alarm Probability for Signal Decision

Energy detection is a widely used signal detection method in signal processing, primarily employed to determine the presence of useful signals in specific frequency bands. The core principle involves comparing the energy of received signals against a predetermined threshold to make detection decisions.

In energy detection implementation, the two most critical components are threshold setting and decision execution. The threshold determination directly depends on the false alarm probability, which refers to the probability of incorrectly declaring signal presence when only noise exists. Given specified false alarm probability requirements, we can calculate the corresponding detection threshold through statistical analysis methods typically implemented using inverse cumulative distribution functions.

The decision phase compares the actually measured signal energy with this preset threshold. If the measured energy exceeds the threshold, the system declares signal presence; otherwise, it concludes only noise exists. This method's advantage lies in its simplicity of implementation, as it doesn't require prior knowledge of signal characteristics, making it suitable for scenarios with limited signal prior information.

In practical applications, the threshold accuracy directly impacts detection performance. An excessively high threshold increases missed detection rates, while an overly low threshold raises false alarm rates. Therefore, properly setting the false alarm probability and precisely calculating the threshold value based on it are crucial for ensuring energy detection reliability. Typical implementation involves calculating thresholds using statistical distributions like Chi-square or Gaussian approximations based on noise characteristics.