# A Cumulant-Based Method for Acquiring GNSS Signals
## 1 Introduction  
As noted by [PERSON], [PERSON], and [PERSON] [1], the Global Navigation Satellite System (GNSS) is a space-based radio positioning system that includes one or more satellite constellations, augmented as necessary to support the intended operation. GNSS provides 24-h, three-dimensional positioning, velocity, and time services to suitably equipped users anywhere on or near the surface of the Earth. In recent years, modern users have gained access to several additional GNSS options due to the development or modernization of systems like Russia's GLObal Navigation Satellite System (GLONASS) and China's COMPASS constellation [2]. GLONASS, which is very similar to GPS, is owned and operated by the military and is designed to function with a full constellation of 24 satellites. Another GNSS system, the Galileo positioning system, is being jointly developed by the European Union (EU) and the European Space Agency (ESA). To efficiently reuse RF bandwidth, Galileo employs a novel modulation technique called Binary Offset Carrier (BOC), which is intended to offer better service than other GNSS systems. However, this technique can introduce multiple side-peaks during the acquisition process. Recent studies [3, 4] have addressed this issue. In a conventional GNSS receiver, the positioning process includes RF front-end processing, acquisition, tracking, and navigation data decoding. The acquisition process aims to identify signals from visible satellites and determine coarse values of Doppler frequencies and code phases of the ranging signals. Code Division Multiple Access (CDMA) is the primary technique used in GNSS signals, allowing users to distinguish each satellite signal obtained from the receiver antenna via different Coarse/Acquisition (C/A) codes, also known as satellite identification numbers or PRN numbers, during the acquisition process. Once the C/A code of a satellite is found, thesignal can be tracked. The purpose of this paper is to introduce a novel acquisition method based on higher-order cumulants that efficiently suppresses side-peaks when acquiring Galileo signals. A cumulant is a higher-order statistical expectation. Over the past few decades, higher-order statistics (HOS) have been applied across various fields, including sonar, radar, speech/image processing, geophysics, and biomedical signal processing [5; 6; 7]. Among these, significant research has focused on time-delay estimation [8; 9; 10]. [PERSON], [PERSON], and [PERSON] [11] extensively discussed the application of HOS to time-delay estimation, particularly useful when the noise in the signal is non-Gaussian. The GNSS signal acquisition process is essentially a time-delay estimation problem. However, the signal model in [PERSON] et al. is not suitable for GNSS signal processing due to the very low signal-to-noise ratio. To overcome this limitation, we propose a new method that allows the use of cumulants to acquire GNSS signals effectively. GNSS signal acquisition involves a two-dimensional search process, requiring the exploration of all potential spreading code phases and Doppler frequencies. To enhance search efficiency, parallel acquisition techniques have been developed. These methods utilize fast Fourier transforms (FFT) to convert the signal from the time domain to the frequency domain, enabling rapid processing. Parallel acquisition methods can be classified into three main types:  
1. Parallel Frequency Search: This approach utilizes FFT to simultaneously explore all or a subset of Doppler frequency bins, allowing for an efficient search across the frequency domain [12; 13]. 2. Parallel Code Search: In this method, FFTs are employed to compute code correlations, enabling the simultaneous examination of all code delay bins, thus expediting the search process within the code domain [14; 15]. 3. Two-Dimensional Search: This technique applies FFTs to both the frequency and code domains, performing a simultaneous search across both dimensions, thereby enhancing acquisition speed and accuracy [16; 17; 18; 19].