This paper proposes a simple Constant False Alarm Rate (CFAR) approach with low computational cost relying on the expectation-maximization algorithm to deal with clutter edges and multiple targets. The possible signal backscattered from a target is modeled as an incoherent pulse train and the proposed CFAR techniques, used to construct an adaptive threshold, are assessed in conjunction with the energy detector, also in comparison to more conventional approaches. The performance analysis shows that the proposed detectors may outperform the state-of-the-art competitors in terms of false alarm control while maintaining satisfying detection performance.