## 2 Basic Concepts and Work Scope
### Summary of the Key Assumptions and Scope  
The assumptions and scope of our research are summarized below. 1. We focus on fingerprinting-based positioning, with downlink transmission of the fingerprints and fingerprints processing on the positioning device side in 2D. 2. The spatial side information on adjacent fingerprints at the positioning device is considered. 3. The position is estimated considering positioning data aggregation in the position domain in one of the pattern-matching methods proposed and in the fingerprint domain in two of the pattern-matching methods proposed. However, our main interest is processing the fingerprints in the fingerprint domain before their input into the pattern-matching method. 4. The collection of the fingerprints is assumed to be carried out using a two-dimensional sensor array (2D sensor array). 5. The same 2D sensor array is used in the training and testing phases. 6. An actual description of how the 2D sensor array should be built it is out of our scope. Each sensor, in charge of sampling fingerprints, may be an antenna or a receiver with a built-in antenna. Thus, it may be composed of an antenna array or a receiver array. We do not consider the actual antenna design aspects related to the construction of the 2D sensor array. In this context, we work only with the numeric modules of what  
Figure 8: Data aggregation domains, side information, and analogy to communications systems. would be the equivalent of the received signal strength, ignoring the effects of the constructive/destructive phases of the radio-waves, the optimal antenna spacing, the effect on the antenna spacing and the Signal-to-Noise Ratio (SNR), and variable Angles of Arrival (AoAs) of the radio-waves with respect to the 2D sensor array's position. * We carry out positioning in 2D. * We assume that the fingerprint source nodes (transmitters) belong to the positioning system infrastructure, are always present, and are located in stationary positions. * It is assumed that the fingerprints are always collected in the same plane, at the same height. In practice, this assumption is not unrealistic considering that the 2D sensor array may not be suitable as a hand-held positioning device. This requirement could be satisfied in practice by mounting the 2D sensor array onto a trolley, robot, or machine operating at the same height. * Perfect alignment of the 2D sensor array with the positioning area in the scenario considered will be assumed. Rotation and tilting of the 2D sensor array were not considered in our study. * As will be explained in Sections 4 and 5, the positioning area will be fractionated into discretized areas called tiles consistent with the size of the 2D sensor array. These discrete areas, or tiles, are non-overlapping, of square shape, and uniform in size for a given set of parameters. * It is assumed that a subdivision of the tile (called a sub-tile) is the smallest granularity for discretizing the positioning area and the sample positions. These subdivisions are non-overlapping, of a square shape, and uniform in size. * We utilize Monte Carlo methods to generate synthetic RSS fingerprints. We will assume an omnidirectional radiation pattern for the antennas of the transmitters, an LOS radio propagation channel model, and transmitters with a constant transmit power. * The primary goal is to observe whether using the spatial side information on the RSS fingerprints by means of an ideal 2D sensor array produces any gain in terms of minimizing the positioning error. * It is out of the scope of this article to evaluate the computing cost of the pattern-matching methods proposed. * It is not part of our claim that the use of pattern-matching methods based on feedforward and convolutional NNs will outperform any other method. These were selected, and used as a tool, based on the general performance of these in the fields of fingerprinting-based positioning and pattern matching in images.