Energy Efficient and Robust Beamforming for MISO Cognitive Small Cell Networks

This paper studies a cognitive small cell downlink network, where one cognitive base station (CBS) transmits information to a cognitive user and transfers energy to energy harvesting receivers (EHRs). The spectrum sensing interval, the spectrum sensing time, and the beamforming matrices of the CBS are jointly optimized to maximize the energy efficiency (EE) of the CBS and to minimize the energy cost of the CBS under both the bounded channel state information (CSI) model and the probabilistic CSI model. The interference constraints of the macrocell users, the secrecy rate constraint, the transmit power constraint of the CBS and the energy harvesting constraints of the EHRs are all considered in this paper. All the three formulated optimization problems are nonconvex, for which semidefinite relaxation, a 2-D line search method, S-Procedure, and Bernstein-type inequalities are exploited. This paper also derives the conditions under which the EE maximization problem and the energy cost of the CBS minimization problem using the bounded CSI model have rank-one solutions. Simulation results demonstrate that the proposed algorithms have significant gain on the CBS EE under the perfect CSI and also gain on the CBS energy cost under imperfect CSI, all compared to the benchmark scheme.