Cooperative spectrum sensing (CSS) is a promising technique in cognitive radio networks (CRNs) that utilises multi-user diversity to mitigate channel instability and noise uncertainty. In this study, the relationship between `cooperation mechanisms' and `spatial-spectral diversity' over multiple channels jointly sensing is investigated in the presence of an imperfect reporting channel. The multiple channels are sensed at the receiver built on the filter bank-based multi-carrier system. The multi-channel CSS strategies are modelled by the introduced `cooperative ratio' to balance the requirements on `sensing accuracy', `efficiency' and `overhead', which is quantitatively characterised by the energy consumption. The target of CSS is to maximise the aggregate opportunistic throughput of secondary users (SUs) by jointly considering constraints on sensing overhead and the aggregate interference to primary users (PUs). The optimisation is divided into two sequential sub-optimisation processes, `multi-user diversity optimisation' and `multi-channel diversity optimisation'. An approach is developed from generic algorithms to solve the two sub-problems. Numerical results show that the optimal CSS scheme is effective in improving channel utilisation for SUs with low interference to PUs. This study establishes a valuable cooperative model for the design of multi-channel spectrum sensing algorithms in CRNs.