Use of perturbation methods in the problem of radar detection against a K-clutter background

The paper studies a model of K-distributed clutter in a radar detection problem. The clutter is modelled with a multidimensional Gaussian probability density function where the variance values are represented by a set of independent random variables distributed with a function. The detection of an a prior known target against the considered K-clutter is studied using the likelihood ratio test. To evaluate the probabilities of false alarm (P_fa) and detection (P_d), we propose, as an alternative to the usual Monte Carlo simulation, a procedure that, resorting to analytical and numerical methods, approximates P_fa and P_d by a power series expansion in terms of a suitable parameter of the model. The numerical work is greatly reduced in the region where the expansion holds. In fact, the high-dimensional integrals involved in the power series expansion are reduced to products of low-dimensional ones. A numerical comparison with the standard Monte Carlo computation has been performed on a test case. The approach used here can be adapted to K-models with correlated Gamma variables