# Beyond REM: A New Approach to the Use of Image Classifiers for the Management of 6G Networks
## 3 Proposed System
### Generation of Synthetic Network Images  
A transformation is proposed from a dataset of systematically collected geotagged and timestamped traces into synthetic images. These images encapsulate the network state in a structured manner for a geographical area, as illustrated in Figure 1. Spatial and temporal resolutions are key aspects of this representation, defining the level of detail captured both in space and time. The first step of this process is to define a specific spatial and temporal resolution. This defines the size of the pixels in the synthetic image and the time period each image will cover. The geographical location of each UE at a given interval, denoted as \(Loc_{UE_{i}}(T)\), is expressed as a two-dimensional spatial vector containing x and y coordinates, respectively. Along with this location information, a set of measurements of different Key Performance Indicators is collected:  
\[LM_{UE_{i}}(T)=\left\{Loc_{UE_{i}}(T),KPI_{UE_{i}}^{1}(T),KPI_{UE_{i}}^{2}(T), \ldots,KPI_{UE_{i}}^{k}(T)\right\} \tag{1}\]  
The pixelization step defines the spatial resolution of the scenario by splitting the geographical area of interest \(A\) into a grid of pixels \(P_{i,j}\). The size of each pixel, denoted \(\Delta p\), should be based on the specific application needs:  
\[A=\left\{P_{i,j}|i=1,\ldots,n;\,j=1,\ldots,m\right\} \tag{2}\]  
The set of LMs within each pixel, which contains multiple measurements from the UEs in its vicinity during the period of interest, is defined as:  
\[LM_{P_{i,j}}=\left\{LM_{UE_{k}}(T)|Loc_{UE_{k}}(T)\in P_{i,j},UE_{k}\in U_{T}, T\in T_{t}\right\} \tag{3}\]  
In the MergeLM (merging) step, statistical figures or a linear combination are used to summarize the measurements within each pixel. For instance, the average measurement value \(KPI_{P_{i,j}}\) for each pixel is calculated as:  
\[KPI_{P_{i,j}}=\frac{1}{|LM_{P_{i,j}}|}\sum_{LM_{UE_{k}}(T)\in LM_{P_{i,j}}}KPI _{UE_{k}}(T) \tag{4}\]  
Balancing between high resolution, which allows for a detailed state view of the network but requires more data and computational resources, and low resolution, which offers less detail but is more resource-efficient, is crucial. Factors such as the number of monitored users, their distribution, and movements within the area significantly influence this balance. Figure 2 illustrates how the number of samples (time resolution) influences the construction of an NSI (Figure 1) for an operational consistent state. The process of LM coding in this context could be formulated as the transformation of each pixel \(P_{i,j}\), with its set of local measurements \(LM_{P_{i,j}}\) and their aggregated metrics such as \(K\tilde{P}I^{1}P_{i,j}\), \(K\tilde{P}I^{2}P_{i,j}\), and \(K\tilde{P}I^{3}P_{i,j}\), into a color representation (i.e., in the Red Green Blue (RGB) format). In this case, each color component in RGB corresponds to a different Key Performance Indicator (KPI). For instance, \(K\tilde{P}I^{1}P_{i,j}\) can be mapped to the Red channel, \(K\tilde{P}I^{2}P_{i,j}\) can be mapped to the Green channel, and \(K\tilde{P}I^{3}P_{i,j}\) can be mapped to the Blue channel. The color components are then normalized to fit into an 8-bit integer range, between 0 and 255, to be suitable for the RGB format (or any other format such as YUV or HUE). The transformation for each color component can be represented as follows:  
\[R_{P_{i,j}}=255\cdot\frac{K\tilde{P}I^{1}P_{i,j}-\min(K\tilde{P}I^{1})}{\max (K\tilde{P}I^{1})-\min([PERSON]\tilde{P}I^{1})} \tag{5}\]\[G_{P_{i,j}}=255\cdot\frac{[PERSON]\tilde{P}I^{2}{}_{P_{i,j}}-\min([PERSON]\[PERSON]{P}I^{2})}{\max( [PERSON]\tilde{P}I^{2})-\min([PERSON]\tilde{P}I^{2})} \tag{6}\]  
\[B_{P_{i,j}}=255\cdot\frac{[PERSON]\[PERSON]{P}I^{3}{}_{P_{i,j}}-\min([PERSON]\tilde{P}I^{3})}{\max( [PERSON]\tilde{P}I^{3})-\min([PERSON]\[PERSON]{P}I^{3})} \tag{7}\]  
The specific transformation function can be further refined by using feature engineering techniques to identify the most relevant indicators to map onto the color components.