Opportunistic spectrum sharing in relay-assisted cognitive systems with imperfect CSI

In this paper, we consider spectrum sharing between cognitive radio (CR) users and a licensed primary user (PU) to enhance the spectrum efficiency. In the considered scenario, the PU is not able to successfully transmit data to the intended receiver. In this case, the cognitive base station (CBS) in the vicinity of the primary network offers its help to transmit the primary data. In return, the CR system shares the spectrum with the primary system. In particular, we formulate an opportunistic spectrum sharing approach that determines the optimal beamforming weights at the CBS to maximize the overall worst throughput of the CRs while guaranteeing a certain quality of service (QoS) for the PU. Various formulations of beamforming are proposed, which consider different relaying scenarios, including robust designs that are applicable with imperfect channel state information (CSI) at the PU. The original optimization problems are nonconvex and do not have any closed-form solutions. However, using a convex optimization approach, we transform them into convex forms and find approximate solutions using semidefinite programming (SDP) along with randomization techniques. We consider different examples that demonstrate the efficiency of the proposed approach.