Dyadic Cooperation in Code Acquisition: a Theoretical Framework

This paper presents a general framework for the analysis of dyadic cooperation of finite-state machines (FSMs) performing code acquisition, as applied to navigation and communication spread-spectrum systems. Our aim is to show how code acquisition performance can be improved by relying on the unidirectional or bidirectional exchange of timing information between two FSMs. We develop an analytical framework based on the flow-graph approach to derive closed forms for the mean and variance of the acquisition time of various cooperating structures. An approximate form of the cumulative distribution function (CDF) is also provided. This framework is suitable for multiple applications, including peer-to-peer navigation, hierarchical codes, assisted global navigation satellite systems (GNSS), multiple navigation signals, and others. As a study case, we provide quantitative results for a dual-band Galileo receiver, which demonstrate the superiority of dyadic cooperation approaches in acquiring synchronization in both the E1 and E5 bands.