CFAR Detection for Chi-squared (Nakagami) Distribution

Chi-squared and Nakagami distributions play significant roles in signal processing and target detection applications, particularly in radar signal analysis where Constant False Alarm Rate (CFAR) detection serves as a crucial adaptive threshold technique.

### Fundamental Concepts Chi-squared Distribution: Commonly used to describe the sum of squares of independent random variables, suitable for statistical modeling of signal power. Nakagami Distribution: A more generalized fading channel model that flexibly describes signal amplitude variations in different scattering environments. Constant False Alarm Rate (CFAR): Dynamically adjusts detection thresholds in noise or clutter environments to maintain a constant false alarm rate, thereby enhancing target identification robustness.

### Implementation Approach Lookup Table Optimization: Pre-computes thresholds for different signal-to-noise ratios and false alarm probabilities to improve real-time detection efficiency. In MATLAB implementation, this can be achieved using interp1() function for efficient table lookup operations. Parameter Estimation: Estimates shape and scale parameters based on the Nakagami distribution model to adapt to varying signal environments. Code implementation typically involves maximum likelihood estimation using mle() function or moment-based methods. Threshold Estimation: Dynamically adjusts detection thresholds through CFAR algorithms (such as Cell-Averaging CFAR) combined with chi-squared distribution characteristics. Implementation often includes sliding window techniques and order statistics processing for background noise estimation.

### Application Scenarios Applicable in radar target detection, wireless communication signal processing, and other fields, particularly in complex noise environments where stable detection performance must be ensured.

The method's advantages include computational efficiency and strong adaptability, but requires careful selection of reference cells and guard cells to avoid target masking effects. Proper implementation should include boundary handling mechanisms and clutter map maintenance for optimal performance.