General Approach to Analysis of GNSS Signal Acquisition Performance with Application to GALILEO Signals

Abstract

The ranging signals of coming Galileo will make use of chip rates and lengths of pseudorandom noise (PRN) codes which are significantly higher as utilised by the current signals of GPS. While offering very good overall system performance, the use of long ranging codes makes fast and reliable signal acquisition a challenging task. This stems from the fact that acquisition is essentially a two-dimensional search process over the uncertainty region spanned by the PRN code-phase and residual Doppler of a satellite signal to be acquired. Normally, if no assistance information is available, the code-phase uncertainty is equal to the entire PRN code length. With Galileo signals having the PRN code length up to 10230 chip, the resulted acquisition search space is up to 10 times larger than in case of GPS C/A code. In order to cope with the increasing search space, the acquisition techniques must be carefully designed taking into account new features of the Galileo signals such as the presence of pilot channels and binary offset carrier (BOC) modulation. This paper will address the problem of optimum GNSS signal acquisition by introducing a general theoretical approach for the acquisition performance analysis. In this paper we adopt a general structure of the acquisition process consisting of three stages: detection, verification and fine acquisition. Considering these three stages in one structure enables the performance analysis of the complete acquisition process, from very coarse to the fine acquisition. Various acquisition schemes can be formed by applying either serial or parallel or hybrid search strategies at the detection stage. The proposed structure is quite flexible and includes many practical acquisition schemes like double-dwell serial search or all-in-parallel (maximum likelihood) FFT-based acquisition as particular cases. The mathematical model of the acquisition process with the proposed structure will be described. The model utilizes the Markov chains theory and the flow graph technique to obtain analytical results for the main acquisition performance parameters such as the mean acquisition time (MAT), the mean acquisition complexity (MAC), overall probabilities of detection, false alarm and some others. The introduction of the MAC as a performance metric is justified by the fact that it is independent of the search strategy. This metric is derived in a way similar to the MAT, a widely used performance parameter, by associating complexity figures with the decision algorithms used at each acquisition stage. The mean acquisition complexity might be of special interest in software receiver applications with flexible management of computational resources. Also, the specific of Galileo signals will be addressed. The effect of Galileo signal features like pilot channels and BOC modulation on acquisition process design and performance will be discussed. In the case of BOC signals, options used with single and double sideband acquisition will be considered. We will present some simulation results for acquisition performance with different acquisition schemes. The analytical models of decision algorithms used for simulations, e.g. single-dwell, M of N, maximum likelihood, bump-jumping, will be shortly described. The results will be further used to determine potential trade-offs between different acquisition schemes and their options.