Sensitivity Analysis of Likelihood Ratio Test in $K$ Distributed and/or Gaussian Noise

In a recent letter we addressed the problem of detecting a fluctuating target in K distributed noise using multiple coherent processing intervals. It was shown through simulations that the performance of the likelihood ratio test is dominated by the snapshot which corresponds to the minimal value of the texture. However, for this particular snapshot the clutter to thermal noise ratio is not large and hence thermal noise cannot be neglected. In the present letter, we continue our investigation with a view to consider detection in a mixture of K distributed and Gaussian noise. Towards this end we study the sensitivity of our previously derived detectors. First, we provide stochastic representations that allow to evaluate their performance in K distributed noise only or Gaussian noise only. Then, their robustness to a mixture is assessed.