## 3 Literature Review and Related Work
### Discussion on Research Works Using Spatial Side Information  
We reviewed research works that could make use of spatial side information on the device side in 2D, focusing on downlink transmission for the case of fingerprints based on radio signals. From our survey related to 2D CNNs, we identified the use of 2D side information in [120; 133]. From our survey related to time-series of spatially distributed fingerprints, we could not find any research work reporting the use of spatial side information in 2D. From other works, we identified the collection of fingerprints in 2D from portions of the positioning area in [199] and the use of a circular antenna array for 2D positioning in [202]. The above cited works are those with the closest relationship to the approach that we describe in this article; however, these differ in a number of key points. These articles differ in the concept of how to exploit the side information in 2D, in not exploring the possibility of using 2D side information for the creation of a fingerprint image, and in not exploring the possibility of processing the 2D side information using a 2D CNN. Some articles also differ in not simultaneously sampling fingerprints.  
In contrast, there are several works making use of spatial side information in 1D by moving a sensor or receiver along a path or trajectory and handling the fingerprints as a time-series. These approaches have in common with our proposal the use of spatial side information, differing, however, by considering only one dimension. Another difference is the sequential sampling of the fingerprints. With the proposed 2D sensor array, multiple adjacent positions are sampled in parallel.  
We could imagine that between the use of a moving sensor and the use of the proposed 2D sensor array, a hybrid approach could be devised. This would consist of combining the movement of more than one sensor or receiver along a path. In this hybrid approach, a linear array of sensors or a linear antenna array, aligned perpendicularly with the moving direction, would be moved to generate a matrix of fingerprints analogous to those obtained by the 2D sensor array. Such an approach was not found in the literature. Considerations for this case are outside of the scope in our work.  
Many works have composed a so-called fingerprint map or image and handled it as a picture image using a 2D CNN. Our intention was to try to identify whether any research work has proposed composing an image of fingerprints with spatial side information in 2D on the device side. We could not identify such an approach.  
As a general summary from our literature review, we could not find any work discussing spatial side information in two dimensions, on the receiver side, and with downlink transmissions for fingerprinting-based positioning. Nor could we find in the literature any proposals related to the utilization of multiple sensors on the positioning device side for the simultaneous sampling of fingerprints in 2D, analogous to the proposed 2D sensor array, for downlink transmissions (in contrast, for uplink transmissions, there are proposals to arrange the antennas into 2D planar arrays on the base station side [205,206]). Then, possibly as a result of there not being a proposal like ours related to the collection of fingerprints in 2D, we did not find any proposals suggesting the construction of fingerprint images in two dimensions. It follows that there was no proposal to implement a 2D CNN as a pattern-matching method exploiting the 2D side information from such fingerprint images.