Effect of Outdated Channel Estimates on Multiple Antennas Multiple Relaying Networks

In this paper, we propose an intergraded unified imperfect CSI model and investigate the joined effects of feedback delay and channel estimation errors (CEE) for two-hop relaying systems with transmit beamforming and relay selection. We derived closed-form expressions for important performance measures including the exact analysis and lower bounds of outage probability as well as error performance. The ergodic capacity is also included with closed-form results. Furthermore, diversity and coding gains based on the asymptotic analysis at high SNRs are also presented, which are simple and concise and provide new analytical insights into the corresponding power allocation scheme. The analysis indicates that delay effect results in the coding gain loss and the diversity order loss, while CEE will merely cause the coding gain loss. Numerical results verify the theoretical analysis and illustrate the system is more sensitive to transmit beamforming delay compared with relay selection delay and also verify the superiority of optimum power allocation. We further investigate the outage loss due to the CEE and feedback delays, which indicates that the effect of the CEE is more influential at low-to-medium SNR, and then it will hand over the dominate role to the feedback delay.