Distributed Time and Carrier Frequency Synchronization for Dense Wireless Networks

Dense networks call for inter-connectivity of a large number of devices, and in this context, the diversity of inter- connected devices introduces challenges to be considered for management and coordination of the network. Synchronization of timing (TO) and carrier frequency offsets (CFO) are critical aspects to be considered to guarantee the proper network inter- connectivity. This paper addresses a distributed synchronization method for dense (say ≥50 nodes), compact and possibly strongly connected wireless network where the inter-node distance is small and prop- agation delay of the entire network is not negligible compared to the inverse of signal bandwidth. Signatures are periodically transmitted by every node to mark the start of the payload and to broadcast the synchronization state that is iteratively minimized by all nodes in aligning jointly the TO/CFO skew with consensus- type algorithms. Here the same signature is broadcasted by every node and it collides with those of the others to perform as a reference (compound) signature for receiving nodes that embeds the reference TO/CFO of the network for synchronization. In view to make distributed TO/CFO synchronization practicable, this paper aims to: i) compensate the propagation delays be- tween nodes to mitigate their impact on the global TO/CFO synchronization of the network; ii) design and validate chirp- like signatures based on Zadoff-Chu sequences that enable the estimate of the TO and CFO mismatch on every node and decouple TO and CFO estimates; and iii) evaluate the mean- square convergence conditions for nodes employing realistic and unstable oscillators. Numerical validations are based on TO/CFO synchronization for OFDM system.