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This paper looks into the modeling of information transmission over cognitive interrogator-sensor networks (CISNs), which represent a novel and important class of sensor networks deployed for surveillance, tracking, and imaging applications. The crux of the problem is to develop a channel model that allows for the evaluation of the sensing channel capacity and error rate performance in CISNs, for which the sensing link is overlaid by the communication link. First, the layered discrete memoryless channel and finite-state Markov channel models are identified as useful tools to capture the essence of information transfer over the communication and sensing links in CISNs. Two different sensor encoding strategies, namely, 1) the amplify-modulate-and-forward (AMF) and 2) decode-modulate-and-forward (DMF) schemes, are considered. Subsequently, the concepts of double-directional channel capacity azimuth spectrum (CCAS) and Chernoff information azimuth spectrum (CIAS) are proposed to facilitate network-level assessment of the communication and sensing link reliability. A study case considering a typical CISN for environmental monitoring, conditioned on different wireless propagation and sensing conditions, is then presented to demonstrate the steps to derive the various model parameters. Finally, the potential applications of the proposed analytical framework in cognitive sensing, network performance assessment, and simulation are briefly discussed.