In this paper the capability of a cognitive radio network to discover available frequency channels in the spectrum licensed to a primary user (e.g., digital TV) is analyzed. We rely on cooperative sensing where fusion of individual sensing outcomes is based on the r-out-of-k decision rule. The study is carried out assuming the point of view of a tagged network of cognitive devices that is surrounded by other uncoordinated transmitters competing for accessing the same portion of the spectrum. The contributions of this work are the following. First, the introduction of a three-state model of the wireless hannel. Second, modeling the sensing process by means of the general framework provided by urn occupancy problems accessed in non-uniform fashion. Third, the evaluation of the number of available channels in the presence of interference limiting spectrum availability. Finally, the proposal of a cognitive protocol to mitigate the interference. Results are given for a specific case of interest where all networks are supposed ECMA- 392 standard compliant.