## 3 Literature Review and Related Work
### Fingerprinting-Based Positioning Implementing Fingerprint Images Processed Using CNNs  
A 2D CNN operates with an input of values, in our case fingerprints, arranged into a matrix (or, in a more general case, a tensor). In the literature, in the context of fingerprinting-based positioning, the input matrix is often referred to as a _fingerprint image_. In the context of our work, the fingerprint image is that produced by the 2D sensor array. We surveyed research works on fingerprinting-based positioning implementing fingerprint images processed using CNNs in 2D, considering only the case of downlink transmissions in positioning systems based on radio signals. It was out of our scope to study the case of device-free positioning systems, such as that discussed in [84; 85; 86], on the basis that positioning is not performed at the device and that it was not aligned with our goal of transferring the complexity and costs from the infrastructure to the positioning device. The objective is to identify whether some work proposes the use of spatial side information in 2D through a CNN, on the positioning device side, in downlink, and, preferably, through simultaneous sampling of the fingerprints. The works reviewed are listed in Table 3. In some of these articles, the details of the CNN were not provided. Thus, we inferred the CNN's structure from the context, e.g., according to the authors' definition of the fingerprints as the image input to the CNN or the dimensions of the convolution kernel. For more details, refer to the corresponding articles. The fingerprint images reported in the table are, in most of these cases, found in the context of a 2D image (matrix), which is processed using a 2D CNN in the first layer of the adopted NN structure. The actual input to the CNN may have a third dimension, meaning that a set of images is stacked to form a tensor. In most of these cases, the images that form this third dimension are handled independently at the input of the NN. These images are referred to as channels, in a context analogous to the primary color channels in a color image. In the case of fingerprints based on radio signals, the channels are typically the different sources of the fingerprints, such as access points, base stations, or links in general. In the case of fingerprints from geomagnetic measurements, the channels are typically the coordinates measured using a magnetometer. The main purpose of listing the composition of the fingerprint image for each work surveyed is to identify the possible composition of an image implementing information from two coordinates in space. For details of the actual composition of the input to the CNNs, refer to the corresponding articles. Our expectation is to find fingerprint images composed of two spatial dimensions and accordingly observe a 2D CNN operating in two dimensions in space. However, at first glance, we observe from this survey that there are two main trends for the creation of fingerprint images, one applied to the case of RSS-based fingerprints and the other applied to the case of CSI-based fingerprints. In the first trend, most of the works adopting RSS fingerprints compose image-like arrangements of fingerprints that do not possess spatial information. These works instead consider a specific arrangement of the fingerprints into a matrix form, usually arranging sub-vectors of a vector of fingerprints as rows in a matrix. In the second trend, that is, in the case of CSI-based fingerprints, in general, the fingerprint images are composed in one dimension of a time domain component and in the other dimension of a frequency domain component. In the case of Orthogonal Frequency Division Multiplexing systems, the frequency domain component consists of the amplitudes or phases of the subcarriers. Regarding the collection of the fingerprints in the training phase, the works reviewed collect a given number of fingerprint samples at so-called reference positions, also referred to as reference points.