STATISTICAL CHARACTERISATION OF THE MAXIMUM EIGENVALUE OF A WISHART DISTRIBUTION WITH APPLICATION TO MULTI-CHANNEL SAR SYSTEM

Multi-channel SAR system characterise the target with multicomponent Gaussian circular vector whose number of components m is equal to the number of polarimetric and/or interferometric channels of the system. In the case of the multivariate (multi-channel) Gaussian system, the second order statistics known as covariance matrix con-tains all the necessary information to characterise the tar-get vector. In this framework, the eigendecomposition of the covariance matrix have demonstrated as a important analysis in the physical parameter estimation and target detection. Especially, the maximum eigenvalue related to the first eigenvector of the covariance matrix is the most interesting parameter in a wide selection of appli-cation, i.e. polarimetry, GMTI (ground moving target in-dication) and interferometric phase filtering. Related to this, the cornerstone study considering the statistical de-scription of the covariance matrix eigendecomposition in polarimetry has been carried out in [1]. However, the majority of the analysis in [1] was performed on the ba-sis of numerical methods. In this paper we support the results of [1] by addressing analytical solutions. Specif-ically, we derive new exact closed form expressions for Probability Density Function (PDF), for Cumulative Dis-tribution Function (CDF) and for the Moment Generating Function (MGF) of the multi channel SAR system covari-ance matrix maximum eigenvalue, thus enabling the ex-act evaluation of the performance analysis of the estima-tion and the detection problem considering the number of averaged samples and different correlation scenario. Our results are analysed by means of simulated data. Key words: multi-baseline (MB), multi-channel SAR systems, ground moving target indication (GMTI), po-larimetric matching filtering (PMF)