Average SNR and ergodic capacity of reactive DF relaying system with outdated channel state information

In this paper, we investigate the effects of outdated channel state information (CSI) in opportunistic relaying systems on the ergodic capacity. The CSI in the data transmission instant may be different from that used in the relay selection instant due to channel variation. When the CSI in the relay-destination link is outdated, the average signal-to-noise ratio (SNR) and the ergodic capacity of the reactive decode and forward (DF) relaying system are derived. In addition, the effective ergodic capacity which is the spectral efficiency of the successful transmissions excluding the outage events is also derived. The numerical results show that if the CSI in the relay-destination link is outdated, the loss in the ergodic capacity is remarkable compared to the perfect CSI case. However, the level of the inaccuracy of the CSI does not affect the performance of the ergodic capacity in the reactive DF relaying system. In other words, no capacity degradation occurs even if the CSI inaccuracy becomes much larger.