This paper considers the spectrum sharing multiple-input–multiple-output (MIMO) cognitive radio network, in which multiple primary users (PUs) coexist with multiple secondary users (SUs). Joint transceiver cognitive beam former design is introduced to minimize the transmit power of the SU base station (SBS) while simultaneously targeting lower bounds on the received signal-to-interference-plus-noise ratio (SINR) for the SUs and imposing upper limits on the interference temperature to the PUs. With the perfect knowledge of all links, the optimal secondary transceiver beam former is achieved iteratively. Due to the limited cooperation between SBS and PUs, perfect information of primary links may not be available at SBS which could lead to severe interference to the PUs. Robust designs are developed against the uncertainties in the primary links by keeping the interference to the PU below a prespecified threshold with high probability. Simulation results are presented to validate the effectiveness of the proposed algorithms that minimizes the total transmit power and simultaneously guarantees quality-of-service (QoS) of both SUs and PUs.

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