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We deal with the performance prediction of the incoherent radar receiver in the presence of arbitrary correlated, possibly nonidentically-distributed target backscattered echoes. The problem is of interest in some common scenarios that account for frequency agility, and polarization, as well as for spatial diversity. We develop analytic expressions for the detection probability in terms of function series, assuming that a generalized Swerling-chi distribution models the first order probability density function (pdf) of the target amplitude. Moreover, we study the speed of convergence of the resulting series and assess the impact on the detection performance of both the correlation and the nonidentical distribution of the target returns.