We consider the problem of power allocation and linear beamforming design in overlay cognitive radio (CR) networks where the cognitive user is admitted to transmit simultaneously with the primary user. To compensate the interference caused at the primary receiver (PR), the secondary transmitter (ST) uses part of its power to forward the primary user's message. The objective of cognitive user is to design a joint power allocation and beamforming scheme such that the signal-to-interference-plus-noise ratio (SINR) at the secondary receiver (SR) is maximized. We propose algorithms based on uniform quantization and sequential search to solve the corresponding non-convex optimization problems. We perform sequential search over at most three real variables for the case of single-input multiple-output (SIMO) cognitive link, and four real variables for the case of multiple-input single-output (MISO) cognitive link, respectively. It is shown that the computational complexity for solving the formulated problems does not increase significantly with the number of receive (transmit) antennas in the cognitive link. Simulation results show that the multiple-antenna configurations yield improved system performance compared to the case of single-input single-output (SISO) cognitive link. In the case of transmit beamforming, the proposed beamforming scheme shows much better performance than the traditional zero-forcing (ZF) beamforming.