## 5 Feasibility Study Through System Simulations  
In this section, we carry out a feasibility study using simulations to learn whether the use of spatial side information on the fingerprints can lead to a justifiable gain in terms of minimizing the positioning error. This study is performed using simulations based on Monte Carlo methods with a system simulator, testing the performance of each pattern-matching method with synthetic fingerprints and moving tiles at random positions. Monte Carlo methods are suitable for studying the behavior of complex systems. In the field of telecommunications, Monte Carlo methods are a common way to study the performance of a communications system at the system level. The system-level approach abstracts the actual information transmitted at the bit level over the communication links with a representation at the signal level. In the context of this work, we work with RSS-based fingerprints, which are generated in the same way as they are in system-level simulators for communications systems. Our system is composed of the 2D sensor array used to collect fingerprint samples with adjacent side information (Section 4.1); a scenario constituting four base stations and the area intended for positioning (Section 5.1) discretized into tiles (Section 4.2) of a given size (Section 5.9) in the training phase; and the fingerprinting-based positioning method, based on the mapping of the fingerprints to positions using a pattern-matching method (Figure 5, Section 2.2) by implementing an NN. Four pattern-matching methods are implemented, as described in Section 4.4 and depicted in Figure 10.  
Data collection from field measurements is very costly, in particular for feeding machine-learning-based models as training data. Thus, in this study, we rely on synthetically generated fingerprints in the form of the RSS. Synthetic data generation for positioning is not uncommon in the literature. In [215], synthetic data are generated to augment a small set of measured data for localization purposes, and a simulator is used for the evaluation of the proposed solution. In [216], the generation of fingerprints using radio propagation models is presented as virtual fingerprinting. In [217], an algorithm is validated and tested with the aid of simulations, and synthetic data are generated to complement measured positioning data in the training phase for an NN-based model. Other examples of works implementing synthetic fingerprints are [143; 151; 189]. From another perspective, regardless of the number of channels used to create the fingerprint images for pattern-matching method 4-MultFingIn-ClassOut, the creation of fingerprint images can be considered a subcategory of the more general fields of synthetic image generation and image synthesis [218; 219; 220]. The implemented system simulator comprises the following:  
* The creation of a scenario with transmitting base stations in downlink and the area intended for positioning;
* Tiling of the area intended for positioning (creation of the positioning area);
* The creation of datasets of synthetic fingerprints for fixed and moving tiles (as arrangements that are equivalent to samples of the 2D sensor array) with a radio channel model, published by a standardization body, for a frequency of 2.6 GHz;
* Training of the NN model for a selected pattern-matching method in the training phase;
* Estimation of the positions of moving tiles in the testing phase;
* Storage of the best-performing result. Simulations are carried out for the four pattern-matching methods introduced in Section 4.4 for processing the fingerprints. The first pattern-matching method is based on the traditional approach to pointwise samples, without side information. The other three pattern-matching methods use spatial side information.