Optimal Rayleigh Approximation of the K-Distribution via the Kullback–Leibler Divergence

Understanding the validity of distributional approximations is important in radar signal processing. This is certainly exemplified in the context of target detection with X-band maritime surveillance radar. This is due to the fact that if the underlying clutter amplitude model can be assumed to be Rayleigh distributed, then there is a large class of detection processes with the constant false alarm rate property that can be applied. This paper examines the Rayleigh approximation of the K-distribution, since the latter is a popular model in X-band maritime surveillance radar. With an application of ideas from information theory, and in particular the Kullback-Leibler divergence, it is possible to derive the optimal Rayleigh approximation for any given K-distribution. Consequently bounds are derived to measure this approximation. These bounds reveal a necessary interaction between the K-distribution parameters to achieve a good Rayleigh approximation. Some numerical results are included to provide a practical assessment of the approximation.