  In this paper, we propose a new solution for the detection problem of a
coherent target in heterogeneous environments. Specifically, we first assume
that clutter returns from different range bins share the same covariance
structure but different power levels. This model meets the experimental
evidence related to non-Gaussian and non-homogeneous scenarios. Then, unlike
existing solutions that are based upon estimate and plug methods, we propose an
approximation of the generalized likelihood ratio test where the maximizers of
the likelihoods are obtained through an alternating estimation procedure.
Remarkably, we also prove that such estimation procedure leads to an
architecture possessing the constant false alarm rate (CFAR) when a specific
initialization is used. The performance analysis, carried out on simulated as
well as measured data and in comparison with suitable well-known competitors,
highlights that the proposed architecture can overcome the CFAR competitors and
exhibits a limited loss with respect to the other non-CFAR detectors.
