Performance of Multi-Hop Cooperative Networks Subject to Timing Synchronization Errors

In this paper, we propose a mathematical model for timing synchronization errors in a cascaded virtual multi-hop multiple-input multiple-output (MIMO) system that incorporates cooperation at each hop using decode-and-forward (DF) algorithm. Specifically, the DF relays are grouped to form clusters and one cluster transmits the same data to the next cluster over orthogonal fading channels. The proposed error model is used to study the statistics of the timing error from one cluster to the next and it has been shown that the variance of the timing errors gradually increases as the data traverse the multi-hop network. The effects of the timing errors on the bit error probability (BEP) performance of the system have been quantified. For that purpose, the closed-form expressions of the BEP for the network are derived for every hop with a particular number of nodes per hop. The results indicate that the BEP performance of the system degrades as the data propagates from hop to hop. We quantify the minimum required SNR and the optimal number of relays per cluster that guarantee successful traversal of data to a specified number of hop while keeping overall BEP below a defined threshold.