## 3 Literature Review and Related Work  
A survey was carried out centered on identifying previous work proposing the use of spatial side information on the device side with downlink transmission (in the case of fingerprints based on radio signals) in 2D and, particularly, aggregating the fingerprints in the fingerprint domain. We aimed to learn the state of the art in this area and to identify whether there is an existing approach equal or similar to that proposed by us. Research works estimating positions through the aggregation of past position estimates using smoothing filters (e.g., moving average filters, Kalman-based filters [79], etc.) are not considered. These works may exploit spatial side information when the fingerprints are collected by the movement of a positioning device along a path. However, the final position estimate relies on aggregation of the positions in the position domain. In contrast, we are interested in the exploitation of spatial side information in the fingerprint domain before mapping the fingerprints to an estimated position. Another consideration in ruling out works utilizing filters is that typically, the fingerprints collected by the movement of a positioning device along a path have associated side information in only one dimension. Even when the displacement is along a 2D path, the relationship of each neighboring position ultimately contributes to the side information in one dimension. Thus, filtering is typically carried out on position estimates that have side information along one dimension. Part of our survey was carried out by looking at research works discussing positioning with 2D antenna arrays, (massive) MIMO, LISs, and RISs. However, these works focus mainly on uplink transmissions (see the references in Section 2.3). Actually, LISs and RISs are considered for the downlink case, although not on the device side but as a complementary and static component to enhance the positioning, as discussed, for example, in [80; 81; 82; 83]. We surveyed research works using two particular approaches that could be related to exploiting spatial side information on fingerprints in 2D. One possible approach to exploiting the side information consists of the use of the convolution operation. Convolution is an operation that relies on the adjacent data, and therefore, it may serve as a keyword for finding works dealing with spatial side information. From a general survey, we identified that in the field of fingerprinting-based positioning, convolution of the fingerprints is generally applied using CNNs. Thus, we surveyed the use of CNNs with fingerprinting-based positioning, focusing particularly on 2D CNNs. A secondary goal of surveying works adopting 2D CNNs was to identify any possible work aligned with our approach, that is, on collecting fingerprints in 2D on the device side, in downlink, and implementing a pattern-matching method based on a 2D CNN to exploit the side information. A second possible approach to exploiting side information consists of the use of time-series or sequences of _spatially distributed fingerprints_. A time-series of fingerprints can be generated by moving a positioning device along a path. In this case, the positioning device may implement a single sensor or receiver, as is commonly found in the literature, to sample the fingerprints. Then, sampling the fingerprints during the movement of the positioning device along a path allows spatially distributed fingerprints to be collected. Thus, we surveyed this category to identify the possible use of spatial side information in 2D. It is noted that some research works gather fingerprints in static positions, without movement, to generate time-series of fingerprints. These works do not contain spatial side information as it is considered in the context of our research; therefore, these works are not considered in our survey. In addition, we surveyed other research works using spatial side information through other methods than those mentioned above.