# Deep Learning of GNSS Acquisition
## 1 Introduction
In short, deep learning algorithms (for instance, the variety of NN architectures currently available) are data-driven models that, instead of using complex-to-derive physics-based models, use large datasets to learn the correlations in the data. This has been recently considered in order to redesign communication receivers using deep learning models [23] with promising results. In the context of the GNSS (boosted by the ever-increasing computational power of receivers [24]), deep learning has been recently investigated in several domains, with [25] providing an excellent summary. Some works explore the use of DNN as multipath mitigation strategies, one of those situations where a physics-based model is either too complex to be used or not available at all. For instance, ref. [26] presented a deep-learning-based beamforming approach to mitigate multipath. That work highlighted the limitations of conventional beamforming algorithms by developing a DNN-based model and applied it in different environments, showing a root mean-squared error (RMSE) reduction. The work in [27] discussed the benefits of DNN in predicting distortions in the urban area, which cause significant degradation to GNSS performance. This is improved by leveraging a DNN to extract useful features from the data to learn GNSS measurement quality for improved prediction (of satellite visibility and pseudorange errors) in urban areas. The work in [28] proposed an end-to-end deep learning method for satellite selection based on the PointNet and VoxelNet networks as a promising alternative to standard selection procedures. The work in [29] presented a methodology to substitute the CAF calculation (typically performed through local code correlation) by a DNN method that was able to learn the complexities of the multipath channel, with promising results when used in standard tracking loops. Those and other works [30; 31] highlight the relevance and popularity that this topic is gaining in the GNSS multipath mitigation challenge [32; 33]. On another set of GNSS applications, the impact of the deep learning approaches to counteract GNSS spoofing [34; 35; 36; 37; 38] and jamming [39; 40] attacks is presented in several works. In the context of the GNSS for Earth sciences, deep learning was considered for earthquake prediction [41], hurricane monitoring [42], ice detection [43], and ionospheric scintillation [44; 45; 46], as well as in the survey article in [47]. This work investigates the use of Deep Neural Networks (DNNs) for GNSS signal acquisition. In particular, a Convolution Neural Network (CNN) is considered in this paper, used as a binary classifier to determine the presence or absences of signal from a given satellite. The inputs to the CNN are the samples of the CAF, a time/Doppler matrix of correlation values, which can potentially be high-dimensional. The dimensionality prevents its direct use, and thus this paper proposes a divide-and-conquer approach to parallelize the computation employing a bank of CNNs processing smaller CAF portions. The main idea is to split the original image (i.e., the CAF map) into several subimages, such that, for instance, one can operate at the regular sampling frequencies encountered in a GNSS receiver. Each classifier on these subimages produces binary class posteriors that we propose to fuse using a Bayesian rule. The probabilistic results are optimally fused to provide a so-called probability ratio map from which acquisition is decided. The results show remarkable performance, particularly at high signal-to-noise ratio regimes, where the data-driven approach provides enhanced performance when compared with theoretical classification bounds. The reason is related to a more exhaustive use of signal correlation in the neighborhood of the CAF's peak. This work opens the possibility to further methodological advances in addressing challenging GNSS problems, such as attack detection or other forms of waveform distortions. The remainder of the paper is organized as follows.