A method based on the Bivariate Empirical Mode Decomposition (BEMD) is addressed to facilitate radar scene analysis for cognitive radar, building and expanding upon a previous contribution. The method exploits the response of BEMD to the fractional Gaussian character of coherent sea clutter returns. Second-order properties of the intrinsic mode functions are used to form a null hypothesis, which indicates the absence of target(s) if accepted. Extensive experiments on real-world radar data show that the proposed radar scene analysis procedure leads to significantly enhanced statistical separability for target+clutter and clutter-alone data. The results are judged from an information-theoretic perspective using the Kullback-Leibler distance as well as by visual inspection.