# Deep Learning of GNSS Acquisition
## 1 Introduction  
The Global Navigation Satellite System (GNSS) [1, 2] is the _de facto_ technology for position, navigation, and timing (PNT) applications [3, 4], when it is available [4, 5, 6]. The GNSS relies on one or more satellite constellations that transmit ranging signals, which a receiver can use to self-localize. Along the signal processing chain, the first step that is performed by a GNSS receiver is signal acquisition. The outcome of this statistical process decides whether the signal from a particular satellite is present or absent in the received signal, as well as providing a rough estimate of its associated code delay and Doppler frequency, if present. All GNSS receivers [7, 8, 9] implement such an acquisition process by evaluating the so-called Cross-Ambiguity Function (CAF) and maximizing it [10]. The CAF is a two-dimensional function that is related to the correlation between the received signal and a local code replica for every possible delay/Doppler pair, which is then maximized for signal detection and coarse synchronization. This acquisition process can be regarded as a signal detection problem, where two hypotheses are available: (1) the null hypothesis \(\mathcal{H}_{0}\) that the signal is not present or not correctly aligned with the local replica; and (2) the alternative hypothesis \(\mathcal{H}_{1}\) that the signal is present and correctly aligned with the local replica. Three probabilities characterize the performance of the acquisition method: detection (the probability of correctly detecting signal/noise when there is signal/noise); false alarm (the probability of wrongly detecting signal when the satellite is not present); and miss detection (the probability of mistakenly deciding for the null hypothesis when the signal is present). Detection and false-alarm probabilities are used to obtain an important figure of merit in hypothesis tests: the Receiver Operating Characteristic (ROC), which is a plot of the probability of detection as a function of the probability of false alarm [11, 12]. Signal acquisition is based on solid statistical grounds, where the approach of maximizing the CAF (i.e., the correlation between the local replica and the incoming signal) can be seen to be optimal under certain model conditions (e.g., Gaussianity of the channel). However, experiments show (e.g., [13]) that reality is typically more challenging and that the assumed nominal model conditions do not always hold true necessarily. Recent attempts to modify the CAF [14; 15] to make it more robust to non-Gaussian behaviors (such as heavy-tailed noise distributions) showed outstanding performance, particularly in the context of the GNSS operation under jamming, for instance considering Cauchy [16] or Laplacian [17] distributions, or robust statistics losses [18] in transformed domains [19] or dual domains [20], as well as understanding the impact on positioning solution [21]. Regardless of its remarkable performance in outlier-rich data, the aforementioned robust approach does not accommodate for more complex situations such as multimodal distributions or moderate-to-severe nonlinearities affecting the received signal. In [22], the authors showed preliminary results that such complex behaviors can be learned by employing efficient data-driven methods, trained over large datasets. In particular, the work proposed to use deep neural network (DNN) models to carry out the detection (or classification) process involved in signal acquisition. The current paper extends the methodology presented in [22] to (_i_) accommodate for enhanced DNN models that improve flexibility and computational complexity through dataset splitting and parallel DNN processing: (_ii_) allow for noncoherent integration times within the DNN framework through an optimal data fusion step; and (_iii_) provide a more detailed discussion of results and design tradeoffs for practitioners. Nowadays, the advent of deep learning as a popular tool has sped up advances in a myriad of disciplines.