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Diversity techniques for cognitive radio networks are important since they enable the primary and secondary terminals to efficiently share the spectral resources in the same location simultaneously. In this paper, we investigate a simple, yet powerful, diversity scheme by exploiting the polarimetric dimension. More precisely, we evaluate a scenario where the cognitive terminals use cross-polarized communications with respect to the primary users. Our approach is network-centric, that is, the performance of the proposed dual-polarized system is investigated in terms of link throughput in the primary and the secondary networks. In order to carry out this analysis, we impose a probabilistic coexistence constraint derived from an information-theoretic approach, that is, we enforce a guaranteed capacity for a primary terminal for a high fraction of time. Improvements brought about by the use of our scheme are demonstrated analytically and through simulations. In particular, the main simulation parameters are extracted from a measurement campaign dedicated to the characterization of indoor-to-indoor and outdoor-to-indoor polarization behaviors. Our results suggest that the polarimetric dimension represents a remarkable opportunity, yet easily implementable, in the context of cognitive radio networks.