This paper considers a cognitive radio (CR) system in non-ideal fading wireless channels and proposes cooperative spectrum sensing schemes based on coherent multiple access channels (MAC), serving as an alternative way to improve the cooperative spectrum sensing performance and provide space diversity for spectrum sensing. Sufficient statistics are transmitted using a common channel from the secondary users (SUs) to a fusion center (FC) where the global decision is obtained. The optimal scaling factors of the proposed schemes are obtained by maximizing the detection probability under a target false alarm probability and a transmit power constraint. Because the proposed optimal MAC scheme has high computational complexity, a sub-optimal solution based on maximization of the deflection coefficient (DC) is also proposed. Simulation results show that the proposed algorithms can significantly improve the spectrum sensing performance and approach the detection baseline.