This paper presents the results of an investigation into bi-directional communication in spectrum sharing-based cognitive radio (Bi-CR) systems. A Bi-CR system can increase the spectral efficiency significantly by sharing the spectrum and through the bi-directional use of spatial resources for two-way communication. On the other hand, the primary user experiences more interference from the secondary users in a Bi-CR system. Satisfying the interference constraint by simply reducing the transmission power results in performance degradation for secondary users. In addition, secondary users also experience self-interference from echo channels due to full duplexing. These imperfections may weaken the potential benefits of the Bi-CR system. Therefore, a new way to overcome these defects in the Bi-CR system is needed. To address this need, this paper proposes some novel power allocation schemes for the Bi-CR system. This contribution is based on two major analytic environments, i.e., noise-limited and interference-limited environments, for providing useful analysis. This paper first proposes an optimal power allocation (OPA) scheme in a noise-limited environment and then analyzes the achievable sum rates. This OPA scheme has an effect in the noise-limited environment. In addition, a power allocation scheme for the Bi-CR system in an interference-limited environment was also investigated. The numerical results showed that the proposed schemes can achieve the full duplexing gain available from the bi-directional use of spatial resources.