In this paper, we propose an equivalent channel model for the analysis of passive backscattering systems (e.g., Radio Frequency Identification systems). The proposed framework accurately models radiation efficiencies at the backscattering nodes whose communication channels are affected by spatially correlated shadowing. First, we derive the distribution of interference in the system and the probability that a node will activate as a function of a specific geographical distribution of the nodes. Then, we approximate the capture probability using a multivariate moment matching approach. The rationale is to provide an underlying structure for the cross-layer analysis of current MAC protocols with the perspective of performance enhancement. Numerical results illustrate the performance of a standard MAC protocol for passive RFID systems, including an accurate evaluation of the impact of the channel characterization.