  In this paper, a general cognitive radio system consisting of a set of users
with different level of spectrum access including two primary transceivers and
several types of secondary users is considered. It is assumed that two
secondary users operate based on an underlay model at the same frequency
bandwidth and at the same time as the primary users based on a multiple access
broadcast channel (MABC) bidirectional beamforming scheme. Other secondary
users provide a relaying service to the primary users in exchange for the
opportunity to send their messages towards their own destinations for a fixed
portion of the communication cycle. In addition, it is assumed that some
interferers are active during the communication cycle and cause interference
for the network. Furthermore, it is assumed that only partial channel state
information (CSI) between interferers and other nodes in the network is
available.
  We provide a robust optimization method against imperfection on the
interferers' CSI to maximize the joint primary and secondary
{signal-to-interference-plus-noise-ratio (SINR)} with the assumption of limited
available power at the secondary relays. An amplify-and-forward (AF) relaying
scheme is deployed at the secondary relays and the optimal beamforming is
obtained using second order convex programming (SOCP) method. The simulation
results show the performance of the proposed beamforming method against the
existence of interferers, and demonstrate the effectiveness of our robust
method against uncertainty in knowledge of interferers' CSIs.
