## 6 Results of the Simulations
### Observations for Cases with Spatial Side Information and Aggregation in the Fingerprint Domain
#### 6.8.2 Two-Dimensional Sensor Array Sizes and Positioning Errors for the Best Results
Then, this view challenges the idea of benefiting from using spatial side information, suggesting that taking a high number of samples at a single point would produce better results than collecting samples at adjacent points. Yet this generates many questions. The instantaneous and simultaneous collection of samples using multiple sensors or receivers is not physically possible when all of the sensors converge to a single point. Then, we can think about using a single sensor or receiver and taking a high number of samples in the time domain, as has been suggested in some research works in the past. However, the initial observation was based on the assumption of the sampling of the entire positioning area. The sampling of the entire positioning area is realistically feasible if it is performed using a 2D sensor array with a size equivalent to a tile size of, say, above \(300\times 300\) mm\({}^{2}\). The sampling can be achieved using a certain mechanized process. One example could be sampling fingerprints using a robot driven by stepping motors. Another example could be using for the sampling the same machinery that needs the positioning information, taking overlapped samples, which will then be post-processed as training tiles. In contrast, it is not realistic to sample every point in the positioning area when the meaning of a point is defined in a mathematical sense, or even when it is defined as a very small discretized area. Another observation is that if there are no adjacent samples, it is not possible to perform the convolution operation in pattern-matching method 4-MultFingIn-ClassOut. Another line of thought is that in our assumptions, we did not consider the actual antenna design aspects related to the construction of the 2D sensor array, such as the effects and constraints of the inter-antenna spacing. These may counteract the performance gain experienced when reducing the 2D sensor array's size in a real system. It was observed that for the system under consideration, there is a correlation between the reduction in the 2D sensor array's size and the reduction in the positioning error. However, in reality, it could be expected that the physical arrangement of the sensors will introduce constraints that will counteract this trend. For example, in the case of implementing the 2D sensor array with an array of antennas, the inter-antenna spacing will add a constraint. In the case of implementing the 2D sensor array with a mechanical device sampling all of the positions equivalent to the sub-tiles,the precision of the mechanism and possible vibrations in the sequential sampling will add a constraint limiting the smallest possible size of the 2D sensor array. This consideration is discussed in Section 7.2. Yet, another line of thought is based on the idea that it would be beneficial to exploit the side information from adjacent positions as far as possible from the target position. This is based on the idea that the further apart the sensors are, the more the RSS level may vary enough to counteract the variations due to the fading. A possible research direction associated with this line of thought would be to study the use of side information collected using a kind of 2D sensor array with sparse sensors.