Performance Analysis of Multiple-Relay AF Cooperative Systems Over Rayleigh Time-Selective Fading Channels With Imperfect Channel Estimation

In this paper, we consider the adaptive-gain M-relay amplify-and-forward (AF) cooperative system with both conventional relaying (cr), as well as a best-relay-selection (br) scheme, and investigate its performance over time-selective fading, due to nodes' mobility, in the presence of channel estimation errors. We first derive exact closed-form expressions for the destination's direct path and overall end-to-end instantaneous signal-to-noise ratios (SNRs). We also derive closed-form tight approximate expressions for the system average bit error rate, outage probability, and Shannon capacity, which are general functions of the cooperating nodes' relative speeds, in terms of the links' correlation parameters, the estimation errors' variances, and the receivers' tracking loops' channel estimation rates, in terms of the transmitted block length. Our analysis reveals that due to the cooperating nodes' mobility, the system performance metrics are severely degraded and, in some particular network circumstances, experience asymptotic limits. In addition, when both of the source and the destination are static, the system performance does not experience asymptotic limits although the relays are in motion. On the other hand, despite that the relays are static, the mobility of either the source or the destination severely impacts the system performance by asymptotic limits, where the difference between their impacts depends on the symmetrical conditions of the network two-hop fading gain power. In addition, we found that the br provides higher asymptotic error limits than that of the cr scheme. We also assumed the special case when the network receivers are equipped with fast estimation loops and showed their effect of reducing the degradation impacts of the nodes' mobility. Simulation and numerical results are provided to verify the accuracy of the derived analytical expressions.