This document presents an optimum transmit beamforming scheme for underlay cognitive radio networks that supports both stationary and mobile secondary users. The scheme formulates the beamforming problem to maximize secondary user transmission power while constraining interference to primary users. It develops solutions for stationary and mobile secondary users by applying convex optimization techniques. Simulation results show the beamforming scheme effectively steers signals to secondary users without interfering with primary users, and significantly improves transmission performance for both stationary and mobile secondary users compared to no beamforming.