Feedback-Based Closed-Loop Carrier Synchronization: A Sharp Asymptotic Bound, an Asymptotically Optimal Approach, Simulations, and Experiments

Abstract

Abstract-We derive an asymptotically sharp bound on the synchronization speed of a randomized black box optimization technique for closed-loop feedback-based distributed adaptive beamforming in wireless sensor networks. We also show that the feedback function that guides this synchronization process is weak multimodal. Given this knowledge that no local optimum exists, we consider an approach to locally compute the phase offset of each individual carrier signal. With this design objective, an asymptotically optimal algorithm is derived. Additionally, we discuss the concept to reduce the optimization time and energy consumption by hierarchically clustering the network into subsets of nodes that achieve beamforming successively over all clusters. For the approaches discussed, we demonstrate their practical feasibility in simulations and experiments.

Symbol error rate analysis for M-QAM modulated physical-layer network coding with phase errors

“…Therefore, under any signal-to-noise ratio (SNR) value, µ should be restricted by µ ∈ (µ 0 − d, µ 0 + d) for any i, i , j, and j . According to (13), the values of phase errors are directly related to the value of µ. Hence, we can obtain a constraint of the relationship among φ A , φ B and M :…”

“…Progress on phase synchronization has been achieved in both theoretical works [11], [12] and implementations [13], under the context of distributed beamforming, which is a similar superposition-based cooperative technology. A phase synchronization scheme for PNC was also recently proposed in [14].…”

Synchronous Physical-Layer Network Coding: A Feasibility Study

“…Although [15] investigated the impact of imperfect synchronization for binary phase-shift keying (BPSK) modulated PNC, it did not explicitly introduce a synchronization scheme and also did not investigate the interaction between synchronization and data transmission. In the literature, some phase synchronization schemes for distributed beamforming have been studied [16]- [19]. Although both PNC and distributed beamforming make use of signal superposition, the goal of PNC is to increase network throughput, while distributed beamforming is for increasing the signal strength at the receiver.…”

“…The difference between these two techniques can make synchronization schemes for beamforming infeasible for PNC. The limited feedback-based synchronization for beamforming such as [16] may cause large synchronization overhead due to the iterative process, which violates the intention of PNC, since the overhead can reduce the goodput (i.e. effective throughput).…”

Phase-level synchronization for physical-layer network coding

“…A round-trip carrier synchronization scheme for beamforming was studied in [14], and its bit error rate (BER) with phase error was analyzed in [15]. Recently, synchronization schemes for beamforming were implemented both in acoustic communication systems [16] and in RF systems operating at the 2.4 GHz frequency band [17]. However, PNC differs from distributed beamforming in the sense that, in beamforming, multiple end nodes transmit identical data to the destination [16], while in PNC, two end nodes exchange different messages via the relay.…”