To solve the uplink power control problem in underlay cognitive radio network (CRN)

this paper proposes a distributed uplink power control algorithm based on multi-antenna beamforming

which is jointly optimized by cognitive base station and secondary users. The specific steps of joint optimization are as follows. Cognitive base station accomplishes multi-antenna beamforming optimization by solving the maximum generalized eigenvalue problem. Secondary users firstly transform the nonlinear power optimization problem into the geometric programming convex optimization problem

then implement the distributed transmitting power optimization through gradient method. The maximum network utility is realized via the alternating optimization between cognitive base station and secondary users. Numerical simulation results show that compared with the existing uplink power control algorithm which only optimizes the powers of secondary users

the proposed algorithm can not only obtain larger network utility value but also be robust to the effect of the interferences from the primary users.