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Radar cross-section (RCS) is one of the key parameters in electromagnetic wave sensing and it becomes an interesting field of research when we consider the case where the target is surrounded by a random medium and consequently the backscattering enhancement phenomena arises. We study of the effect of circular wave polarization on the enhancement of RCS (ERCS). In this regard, we consider the case that the incident wave becomes incoherent enough around a conducting cylinder although it keeps a finite spatial coherence length. We present numerical results of normalized RCS (NRCS) for conducting targets of concave-convex shapes with different sizes and also different values of a target shape parameter, concavity index, to observe the behavior of NRCS of such complex targets in random media.