Constant False Alarm Rate (CFAR) Detection for Chi-Square Distribution (Nakagami Distribution)

Constant False Alarm Rate (CFAR) detection based on Chi-square distribution (Nakagami distribution) is a widely used method in radar signal processing that aims to effectively identify target signals while maintaining a constant false alarm probability. This approach employs precomputed lookup tables to optimize parameter estimation and threshold calculation, thereby enhancing detection efficiency. In implementation, developers typically create lookup arrays storing precalculated threshold values for different shape and scale parameters, which can be rapidly accessed using interpolation functions like interp1 in MATLAB.

The Chi-square distribution (or Nakagami distribution) is extensively employed in signal detection to characterize amplitude distribution properties, where the shape parameter (m) and scale parameter (ω) directly influence detection performance. The core principle of CFAR detection involves adaptively adjusting detection thresholds based on background noise statistics to maintain stable false alarm rates in complex environments. Algorithm developers often implement parameter estimation using maximum likelihood estimation (MLE) methods, with key functions including mle() for distribution fitting and nakafit() for Nakagami-specific parameter calculation.

During implementation, the process first rapidly estimates distribution parameters through lookup tables, then computes corresponding detection thresholds. This methodology reduces real-time computational complexity, making it suitable for high-dynamic signal environments. Compared to traditional fixed-threshold detection, the CFAR approach better adapts to varying noise conditions, improves target detection probability, and suppresses false alarms. Code implementation typically involves sliding window techniques where background noise statistics are calculated using cell-averaging or ordered-statistics CFAR variants, with threshold scaling factors determined from the precomputed tables.

This algorithm can be applied to signal detection tasks in radar, sonar, and wireless communication systems, demonstrating particularly robust performance under low signal-to-noise ratio conditions. Practical implementation often includes noise power estimation using moving average filters and threshold adaptation mechanisms that dynamically update based on environmental changes.