A great amount of research has devoted to cognitive radio (CR) in recent years in order to improve spectrum efficiency. In decentralized CR networks, it is not realistic for CR users to sense entire spectrum in practice due to hardware limitations. Consequently, the partially observable Markov decision process (POMDP) can be utilized to provide CR users with sufficient information in partially observable environments. Existing POMDP-based protocols adopt channel aggregation techniques in order to improve spectrum opportunities and system performance. However, the required time for channel sensing is neglected which can result in large sensing time overhead and spectrum opportunity loss in realistic environments. In this paper, based on partially observable channel state with the consideration of sensing overhead, the stochastic multiple channel sensing (SMCS) protocol is proposed to conduct optimal channel selection for maximizing the aggregated throughput of CR users. By adopting the proposed SMCS protocol, CR users can highly accommodate themselves to rapidly varying environment based on the dynamically adjustable channel sensing strategy. Moreover, the channel sensing problem is further extended to imperfect sensing scenario, which can severely degrade system throughput due to packet collision between primary users (PUs) and CR users. Consequently, in addition to channel selection, it is required for CR users to determine the sensing time length in order to address the collision problem. The two-phase SMCS (TSMCS) protocol is proposed to maximize the aggregated throughput of CR users while still fulfilling PUs' quality-of-service (QoS) requirements. Numerical results show that the proposed SMCS and TSMCS protocols can effectively maximize the aggregated throughput for decentralized CR networks.