In this paper, a new overlay spectrum sharing protocol based on signal space diversity (SSD), is proposed for cognitive radio networks. The considered network comprises of one licensed primary transmitter/receiver (PT/PR) pair and one secondary transmitter/receiver (ST/SR) pair assisting for cooperation before transmitting its own signal on the licensed primary user's spectrum. The overall transmission is completed in three signaling intervals to avoid any mutual interference between users and the SSD is provided by coordinate interleaved orthogonal design (CIOD) which increases the transmission rate of the primary users. The outage probabilities of both primary and secondary users are analytically derived and supported via computer simulations. The results show that significant performance improvement is provided by the proposed protocol compared to the non-cooperation case and the reference scheme based on the transmission of superimposed primary and secondary signals which causes severe interference at both users.