Optimal Power Allocation for Bi-Directional Cognitive Radio Networks with Fading Channels

In this paper, we consider a spectrum-sharing cognitive radio network where a bi-directional secondary network is allowed to access the spectrum allocated to a primary user (PU) on condition that the interference power received at the PU receiver is below a predefined threshold. Under such an interference power constraint (IPC), we investigate the optimal power allocation strategies to achieve the fundamental capacity limits of a bi-directional secondary network with fading channels. In particular, both the ergodic capacity and the outage capacity are considered. Closed-form solutions are obtained for both scenarios. Besides, a key parameter referred to as Interference-Transmission-Ratio (ITR) is proposed. It is shown that under a given IPC, ITR is the only factor that affects the transmission policies of the secondary network. In general, the transceiver with lower ITR value has the priority to transmit. We also show that unlike the conventional bi-directional communications network where concurrent transmission is always optimal, concurrent transmission is not always the first choice for bi-directional CRNs in terms of maximizing the ergodic capacity.