In this letter, an adaptive approach to classify the structure of the Interference Covariance Matrix (ICM) is proposed. It extends the framework of [1] to the heterogeneous environment where the secondary radar data used to estimate the ICM share the same covariance structure but different power levels. In particular, the considered classification problem is formulated in terms of a multiple hypothesis test and the Principle of Invariance is exploited to replace original data with a suitable statistic whose distribution is independent of the power scaling factors. Then, classification schemes are devised resorting to model order selection rules. At the analysis stage, the effectiveness of the newly devised classifiers is illustrated over simulated data as well as radar measured data.