Beamforming and Rate Allocation in MISO Cognitive Radio Networks

We consider decentralized multiantenna cognitive radio networks where the secondary (cognitive) users are granted simultaneous spectrum access along with the license-holding (primary) users. We treat the problem of distributed beamforming and rate allocation for the secondary users such that the minimum weighted secondary rate is maximized. Such an optimization is subject to 1) a limited weighted sum-power budget for the secondary users and 2) guaranteed protection for the primary users in the sense that the interference level imposed on each primary receiver does not exceed a specified level. Based on the decoding method deployed by the secondary receivers, we consider three scenarios for solving this problem. In the first scenario, each secondary receiver decodes only its designated transmitter while suppressing the rest as Gaussian interferers (single-user decoding). In the second case, each secondary receiver employs the maximum likelihood decoder (MLD) to jointly decode all secondary transmissions. In the third one, each secondary receiver uses the unconstrained group decoder (UGD). By deploying the UGD, each secondary user is allowed to decode any arbitrary subset of users (which contains its designated user) after suppressing or canceling the remaining users. We offer an optimal distributed algorithm for designing the beamformers and allocating rates in the first scenario (i.e., with single-user decoding). We also provide explicit formulations of the optimization problems for the latter two scenarios (with the MLD and the UGD, respectively), which, however are nonconvex. While we provide a suboptimal centralized algorithm for the case with MLD, neither of the two scenarios can be solved efficiently in a decentralized setup. As a remedy, we offer two-stage suboptimal distributed algorithms for solving the problem for the MLD and UGD scenarios. In the first stage, the beamformers and rates are determined in a distributed fashion after assuming single user decoding at each secondary receiver. By using these beamformer designs, MLD often and UGD always allow for supporting rates higher than those achieved in the first stage. Based on this observation, we construct the second stage by offering optimal distributed low-complexity algorithms to allocate excess rates to the secondary users such that a notion of fairness is maintained. Analytical and empirical results demonstrate the gains yielded by the proposed rate allocation and the beamformer design algorithms.