Modeling and analysis of CFO pre-synchronization for STBC-OFDM-based multi-hop cooperative transmissions in WSNs

In this paper, we model and analyze the carrier frequency offset (CFO) pre-synchronization for STBC-OFDM-based multi-hop cooperative transmissions in wireless sensor networks (WSNs). In our scenario, the nodes those can decode the message from the previous cluster correctly are selected as relays, and these relays will do STBC-OFDM encoding and CFO pre-synchronization autonomously before transmission. The CFO estimation at each relay is composed of coarse estimation based on preamble and residual CFOs estimation based on pilot symbols. We model the per-synchronization error for each relay, and apply a first-order dynamic system method is to get the closed forms of the variance, covariance and expected sample variance of the pre-synchronization errors of each hop. The convergent property of the expected sample variance indicates the feasibility of multi-hop transmissions. Numerical simulations validate our theoretical results of the error model and explore the effect of the number of relays to the synchronization performance.