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A diffraction-based channel model is developed for characterizing the line-of-sight channel where the receive array is partially blocked by near-field obstacles. An analytic receive signal model is established where the range and size parameters of the blockage are explicitly modeled in the array steering vector. Based on the proposed model, we consider the joint estimation of the direction of arrivals (DoAs) of impinging RF signals and the parameters of interest for the blockage. General analytical expressions are derived for the Cram´er-Rao bounds (CRBs) of both the source-dependent parameters and environmental (common) parameters using both deterministic and stochastic maximum likelihood models. Finally, a Newton’s method-based approach is developed to optimize the maximum likelihood criterion to obtain estimates of the DoAs and blockage range of the sensing problem. Numerical results reveal that the maximum likelihood estimates for the DoAs and the blockage range attain the CRB for the stochastic model.