Cognitive radio (CR) allows a secondary user (SU) to utilise the spectrum allocated to the primary user (PU) on the premise of detecting the absence of PU by spectrum sensing. The SU often adopts cooperative spectrum sensing to cope with the hidden terminal problem if the PU is shadowed or in serious multi-path fading; however, the cooperative overhead may decrease the throughput of the SU. In this paper, we consider a wideband CR network that can reuse multiple idle sub-bands after cooperative spectrum sensing and then analyse the total throughput of the SU over all the sub-bands. A multi-variable nonconvex optimisation problem of cooperative spectrum sensing with cooperative overhead and sub-band transmission power is proposed, which maximises the total throughput of the SU subject to the constraints of the false-alarm probability, the detection probability, the cooperative overhead and the maximal total power of the SU. For obtaining the optimal solution, we divide the optimisation problem into two sub-optimisation problems: one for optimising the cooperative spectrum sensing including the sensing time and the number of SUs and the other one for optimising the sub-band transmission power. We have proven the convex optimisation of the two sub-optimisation problems and proposed a joint optimisation algorithm of the sensing time, the number of SUs and the sub-band transmission power. The simulation results show that the proposed joint optimisation algorithm can achieve the largest throughput with the false-alarm probability and the detection probability within their limits. Copyright © 2013 John Wiley & Sons, Ltd.