In this contribution, we investigate the idea of using cognitive radio to reuse locally unused spectrum to increase the total system capacity. We consider a multiband/wideband system in which the primary and cognitive users wish to communicate to different receivers, subject to mutual interference and assume that each user knows only his channel and the unused spectrum through adequate sensing. The basic idea under the proposed scheme is based on the notion of spectrum pooling. The idea is quite simple: a cognitive radio will listen to the channel and, if sensed idle, will transmit during the voids. It turns out that, although its simplicity, the proposed scheme showed very interesting features with respect to the spectral efficiency and the maximum number of possible pairwise cognitive communications. We impose the constraint that users successively transmit over available bands through selfish water filling. For the first time, our study has quantified the asymptotic (with respect to the band) achievable gain of using spectrum pooling in terms of spectral efficiency compared to classical radio systems. We then derive the total spectral efficiency as well as the maximum number of possible pairwise communications of such a spectrum pooling system.