In this study, the authors consider the application of a system architecture called cognitive radio (CR) with fibre-connected distributed antennas in IEEE 802.22 wireless regional area networks (WRANs) as it could bring the benefits of much shorter wireless transmission distances, lower transmission power and the possibility of utilising multi-antenna transmission techniques. In this architecture, the authors study the secondary user (SU) access problem in uplink, where the SU to primary user (PU) link estimation is subject to random errors because PU could not assist link estimation of SU. This SU access problem is divided into two parts: antenna selection and access control. Thus, first antenna selection problem is modelled as a restless bandit problem, which is solved by the primal-dual index heuristic algorithm based on first order relaxation. In addition, the access control problem is modelled as a stochastic knapsack (SASK) problem with random weight, and then relaxed to be a deterministic second order cone programming problem. With the deduced upper bound, the access control problem is solved by the branch and bound algorithm, which yields the SU access based on SASK scheme. Simulation results illustrate the significant performance improvement of SASK scheme, compared with existing SU access methods.