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In this paper, we consider a cognitive radio network consisting of a primary transmitter-primary receiver pair, and a secondary base station-secondary receiver pair. To improve the performance of both the primary and secondary pair, we propose an overlay spectrum sharing scheme where the primary user (PU) leases half of its time slots to the secondary user (SU) in exchange for the SU cooperatively relaying the PU's data using the amplify and forward scheme. The proposed scheme will involve the design of antenna weights and power allocation to meet a certain error or rate design criterion for both the PU and SU. To analyze the performance of the proposed scheme, we derive new closed form expressions for the rate and bit error rate for arbitrary signal-to-noise ratio (SNR). In addition, we carry out an asymptotic analysis in the high SNR regime to obtain the diversity order. These expressions, along with numerical analysis, reveal that the proposed cooperative overlay scheme can achieve significant performance gains, for both the PU and the SU, compared to a conventional noncooperative underlay scheme, which gives both users the incentive to cooperate.