Independent views in MIMO sonar systems

The main advantages of MIMO (Multiple Input Multiple Output) sonar systems come from the assumption of independent observations between each transmitter/receiver pairs.The independence of the observations ensures a unbiased set of measurements and then provides true statistics on the target. In this paper we study the correlation between views in MIMO sonar systems. A traditional tool used to study the dependency between two random variables is the Pearson product-moment correlation coefficient. However this measure suffers numerous defaults: it only estimates linear correlation, it is not a proper distance and in particular a null measure of the Pearson coefficient does not insure the independence of the tested random variables. For these reasons we will use the distance correlation introduced by Szekely. From the distance correlation we will derive the inter-views distance correlation matrix which assess the correlation of the full MIMO system (i.e. the dependencies between each views). This independence measure matrix gives a guideline to how to build truly uncorrelated MIMO sonar systems and then maximise the performances of such system.