Computation of Classical CFAR Binary Detection Threshold for Radar Detection

This problem involves computing the classical CFAR (Constant False Alarm Rate) binary detection threshold for radar detection under additive white Gaussian noise conditions with a specified false alarm probability. This represents a fundamental challenge in radar signal processing that requires consideration of multiple factors including noise level, signal-to-noise ratio, and statistical characteristics of target signals. In practical implementation, CFAR algorithms typically operate by estimating background noise statistics from reference cells surrounding the cell under test. Common approaches include cell-averaging CFAR (CA-CFAR) where the threshold is calculated using mean values from adjacent cells, or more robust variants like greatest-of CFAR (GO-CFAR) that handle clutter edges more effectively. The key computational steps involve: establishing reference windows around the test cell, calculating noise statistics from these reference samples, applying scaling factors based on the desired false alarm probability, and dynamically adjusting the detection threshold. The scaling factor is typically derived from statistical distributions (often Rayleigh or Gaussian) and can be precomputed using numerical methods or lookup tables for efficiency. Proper implementation requires handling edge cases, managing window sizes to balance estimation accuracy and resolution, and potentially incorporating clutter map techniques for non-homogeneous environments. The algorithm aims to maintain constant false alarm probability while minimizing missed detections through adaptive threshold adjustment based on local noise characteristics.