# Solution for Interference in Hotspot Scenarios Applying Q-Learning on FFR-Based ICIC Techniques
## 8 Preliminary Analysis B: Factorial Design using the Strict Frequency Reuse Algorithm
### 2\({}^{k}\) Factorial Design  
The 2\({}^{k}\) factorial design (2k factor) is a specific case of factorial design that identifies which parameters of an experiment have a significant effect on the desired output [44]. It provides a better understanding of the system, and can simplify future analysis. For example, assume that the 2k factor is conducted for an experiment with a parameter called \(P\). If the 2k factor determines that \(P\) is not relevant, a following full factorial design will need fewer repetitions, since \(P\) does not need to change. A Full Factorial Design consists of replicating an experiment for all possible combinations of parameters. To perform the 2k factor, \(k\) factors (parameters) are chosen, and they assume only two distinct values, preferably a low and a high value close to the upper and lower limits of the parameter's range. Besides, it is usually followed by an Analysis of Variance (ANOVA) that validates the results by statistically rejecting or not the null hypothesis, which is a given parameter does not affect the desired output. ANOVA tests this hypothesis by comparing variances. Consider the value \(F0\) in Equation (1). This value is calculated for each parameter, and it is defined as the division between two Sum of Squares (SSs), which is a non-biased estimator of a population's variance [44]. For example, if a simulation that has a parameter A is repeated \(n\) times for each value of the parameter, \(SS_{treat}\) is the SS that measures the variation between the different values of parameter A and \(SS_{error}\) is the SS that measures the variation between the \(n\) results of a single value of A. If the change of a given parameter  
Figure 11: Scenario for preliminary analysis B, which is similar to the scenario in Figure 6, but without the radius R, since all users are randomly distributed according to a uniform distribution. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Bandwidth (RBs) & 25 \\ \hline UE distribution & Uniform \\ \hline Number of UEs & 80 \\ \hline Distance between eNBs (m) & 1000 \\ \hline Scheduling algorithm & _Proportional Fair_ \\ \hline Channel model & Friss model \\ \hline Error model & MIESM \\ \hline UE mobility & No mobility \\ \hline Traffic model & Non-GBR TCP-based \\  & Video (Buffered Stream) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters for preliminary analysis B: parametric analysis of strict frequency reuse. has a relevant impact on the desired output, the null hypothesis is rejected, and \(SS_{treat}\) is bigger than \(SS_{error}\)[44]. Therefore, the bigger \(F0\) is, the bigger is the parameter's impact. \[F0=\frac{SS_{treat}}{SS_{error}} \tag{1}\]  
However, it is recommended to define a threshold for \(F0\) that guarantees the parameter's relevance. Since \(SS_{treat}\) and \(SS_{error}\) are both chi-square random variables by definition [45], \(F0\) has a Fisher-Snedecor distribution [44; 46]. Defining a level of significance \(\alpha=0.001\), for the evaluated parameters, the threshold value for \(F0\) is 10.83. Thus, \(F0\) is calculated for each parameter. If \(F0\) is greater than 10.83, the parameter has a significant impact on the output. Therefore, the \(2^{k}\) factorial was conducted for the Strict FR's parameters: _CenterPowerOffset_, _RsrqThreshold_, and _BandwidthDistribution_. As detailed in Section 6, they define the power level of the common sub-band, the threshold for allocating users on sub-bands and the number of RBs on each sub-band, respectively. In order to investigate all users and users with the worst performance (most likely cell-edge users), the targeted output is the average throughput and its 10 th percentile. Tables 4 and 5 present the calculated \(F0\) for each parameter and for the interaction between parameters. The nomenclature X* Y represents the interaction between parameters X and Y. CenterPowerOffset is the only parameter that does not have a significant impact on the average of 10 th percentile throughput.