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 perfect sensing. Under this scheme, a cognitive radio will listen to the channel and, if sensed idle, will transmit during the voids. We impose the constraint that users successively transmit over available bands through proper water filling. Within this setting, we derive the total spectral efficiency of the cognitive radio system as well as the spectral efficiency gains and prove that we can improve the overall system spectral efficiency by considering cognitive communications in the system.