Accurate clock synchronization is required for collaborative operations among nodes across wireless networks. Compared with traditional layer-by-layer methods, cooperative network synchronization techniques lead to significant improvement in performance, efficiency, and robustness. This paper develops a framework for the performance analysis of cooperative network synchronization. We introduce the concepts of cooperative dilution intensity (CDI) and relative CDI to characterize the interaction between agents, which can be interpreted as properties of a random walk over the network. Our approach enables us to derive closed-form asymptotic expressions of performance limits, relating them to the quality of observations as well as network topology. Index Terms-Cooperative network synchronization, Cramér-Rao bound (CRB), cooperative dilution intensity (CDI), relative CDI, random walk. ). scalable and insensitive to network topology variations. Existing approaches of this type include consensus-based methods [27]-[29] and Bayesian inference methods [30]-[32]. The convergence of cooperative synchronization methods has been investigated in [33]-[35]. Understanding the performance of cooperative network synchronization can lead to insights into network deployment and network operation techniques. Performance analysis of network synchronization was pioneered by [36] . Early works were influenced by the phase-locked loop (PLL) structure which were widely used in single-link synchronization. Following this line, a body of literature was devoted to the analysis of network-wide PLL-based methods [37]-[39]. The issue with this approach is that it focuses on a specific system structure and thus the results therein do not generalize to other systems. Another body of literature, including the seminal work [40] , focused on the feasibility of network synchronization instead of accuracy. Recently, performance limits derived from the information inequality, also known as the Cramér-Rao lower bound (CRB), are introduced to address the problem. These performance limits are not restricted to certain system structures or determined by specific algorithm implementations. Thus, they can better reflect the relation between synchronization accuracy and network parameters. However, existing works typically provide only complicated expressions that are not in closed form [41] , [42] . Due to the difference among application scenarios, the network synchronization problem takes various forms, as summarized in [40] . In this paper, we consider two variants of the network synchronization problem, namely absolute synchronization and relative synchronization. In absolute synchronization, agents are required to be synchronized to a reference clock in reference nodes. In contrast, in relative synchronization there is no reference node, and agents are allowed to reach agreement on any common clock. In this paper, we develop a novel framework for the performance limit analysis of cooperative network synchronization. Based on this framework, we analyze the asymptotic synchronization performance of large-scale networks for both absolute and relative synchronization. The contributions of this paper are summarized as follows: • We derive the performance limits for both absolute and relative cooperative network synchronization, using the Bayesian Cramér-Rao bound (BCRB) and the constrained Cramér-Rao Bound, respectively. • We propose the concept of cooperative dilution intensity (CDI) to characterize the efficiency of cooperation Nan Wu (M'11) received his B.S., M.S. and Ph.D. degrees from Beijing Institute of Technology (BIT),
Xiong et al. REF propose a framework for cooperative network synchronization analysis and derive closed-form asymptotic expressions under performance limits, which is demonstrated to be applicable to practical wireless networks through results.
Cooperative Network Synchronization: Asymptotic Analysis
ArXiv
ArXiv
Mathematics Computer Science