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In this paper, we address the adaptive detection and classification of signals in a homogenous interference environment. The detector assumes the signals belonging to conic regions, and relies on secondary data. To deal with this scenario, we adopt a two-stage detection/classification scheme, enjoying the constant false alarm rate property, to discriminate between target detection and coherent interferer rejection. Finally, we evaluate the system performance via Monte Carlo simulations. The results show that our system has interesting rejection capabilities and satisfactory detection levels, and it could be easily adapted to real scenarios.