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This paper focuses on a downlink beamforming problem in the cognitive radio (CR) communication system where primary users (PUs) coexist with secondary users (SUs). It is assumed that the SU transmitter has multiple antennas and transmits data to another SU's single-antenna receiver by employing the beamforming. By properly designing a beamforming vector, a SU can maximize its channel gain while maintaining an interference with PU below a predefined level. Designing a beamforming vector includes steering beamforming vector direction as well as adjusting transmit power. In order to construct the optimal beamforming vector, the SU transmitter requires knowledge of the downlink channel information of both PU and SU receivers sent on the feedback channel. However, it is impractical to assume that the transmitter has the perfect channel state information (CSI) considering the tremendous feedback overhead. One way to tackle this feedback overhead problem is to use a finite number of feedback bits indicating the index of a predefined codeword in the codebook. We analyze interference to the PU receiver and propose an algorithm to design a beamforming vector considering an error attributed to the partial CSI. The simulation shows that the analysis is quite accurate and that the beamforming vector, designed according to the proposed algorithm, keeps interference to PU below a predefined level while taking into account the error owing to the partial CSI. In addition, we propose a feedback bit allocation mechanism, in order to maximize the gain of the SU link. By using the proposed scheme, the CR system become robust against errors attributed to the partial CSI.