Optimal Beamforming Design for Minimal Energy Optimization in Cognitive MIMO System with Perfect/Imperfect Knowledge of PU´s Precoder

In a multi-secondary user (SU) and single primary user (PU) cognitive radio (CR) system, each terminal is equipped with multi-antenna. We propose an optimal beamforming design method aiming for the minimal power budget of SUs´ network, where both the perfect and imperfect knowledge of PU´s precoder are considered, e.g. optimal beamforming vector with perfect PU´s precoder (OBV-perfect), optimal beamforming vector with imperfect PU´s precoder (OBV-imperfect). In a spectrum sharing based CR network, SUs are allowed to coexist with the PU, provided that the interference power from the SUs to the PU is less than an acceptable value, such that the quality of service (QoS) of PU is guaranteed. Meanwhile, the QoS requirement of minimizing signal to interference and noise ratio (SINR) at the secondary receiver is also included as the constraint. Simulation results show that the system power of OBV-perfect is smaller than the imperfect scenario, since OBV-perfect knows of both the PU´s channel state information (CSI) and precoder information, thus contributing to minimize the power under the minimal SINR constraints. However, the system rate of OBV-imperfect is larger than OBV-perfect scenario due to the reason that in our presumed resolution of OBV-imperfect, the employed signal to jamming and noise ratio (SJNR) is a much stricter constraint than SINR for the system. Therefore, both the schemes are optimal beamforming design, and the knowledge of PU´s precoder is favorable for access capability in the cognitive MIMO system.