Capacity Analysis of Bidirectional AF Relay Selection with Imperfect Channel State Information

In this letter, we analyze the ergodic capacity of bidirectional amplify-and-forward relay selection network. The imperfect channel state information (CSI) is taken into account, which includes outdated CSI and channel estimation error, caused by the time-variation of channel and the imperfect channel estimation, respectively. The lower bound of the ergodic capacity for this network is derived in a closed-form, and verified by the Monte-Carlo simulations. Furthermore, the effects of the imperfect CSI and the number of relays on the ergodic capacity are investigated. The results manifest that imperfect CSI will jeopardize the capacity, and increasing the number of relays contributes to enhance the capacity with imperfect CSI.