# Factorial Design Analysis for Localization Algorithms
## 2 Related Work
### Experiment Desing Using \(2^{k}\) Factorial  
The statistical experiment design considers a wide variety of experimental strategies that are optimal for generating the information being sought. One of these strategies is the complete \(2^{k}\) factorial design. This method describes the most adequate experiments for simultaneously determining the effect that \(k\) factors have on a response and discovering whether they interact among themselves. These experiments are planned in such a way that various factors vary simultaneously but are kept from always changing in the same direction. The absence of correlated factors serves to avoid redundant experiments. Furthermore, the experiments complement one another in such a way that the information being sought is obtained by combining the responses of all of them. This makes it possible to obtain the information with the lowest number of experiments (and therefore at the lowest cost) and with the least uncertainty possible (because the random errors of the responses are averaged).  
In [27] the author proposes a systematic statistical Design of Experiments (DOE) used for analyzing the factors and performance of Mobile Ad Hoc Networks (MANETs). The \(2^{k}\) factorial method is used to quantify the effects of 7 factors on a performance metric (Mean Opinion Score (MOS) calculated with the Peak Signal-to-Noise Ratio (PSNR) with the EvalVid computer package) [27]. In [28] the authors address the issue of energy consumption optimization, the objective of which is to keep a network connected while transmitting the lowest power from each node; two algorithms are used: PSO and [PERSON]'s algorithm [46]. In this experiment, the \(2^{k}\) factorial method is used to compare the performance of two algorithms according to the metrics of energy savings and processing time. Different network performance factors are used such as sensing area, node density (%) and the PSO and [PERSON]'s algorithms.  
In MANETs, routing is a difficult task due to the changes in network topology, making it difficult to select a particular protocol. Several studies have focused on comparing protocols, paying less attention to other factors such as packet size, node mobility, Direct Sequence Spread Spectrum (DSSS) rate and the mobility pattern, among others [29]. Therefore, it is essential to determine the importance of these factors for network functioning. In [29] the authors consider three factors: the routing protocol (Dynamic MANET On-demand (DYMO) and Ad hoc On-Demand Distance Vector (AODV)), packet size, and DSSS rate. These factors influence the average delay and the average jitter, which are network performance factors that affect the buffering requirements for video devices and downstream networks [29]. This experiment used the Qualnet 5.1 simulator to analyze the DYMO and AODV protocols. After using the \(2^{k}\) factorial methodology for the simulation scenario, the results obtained show that when it comes to the average delay, the routing protocol has an impact of 37.4%, the packet size has an impact of 37.9% and the DSSS rate has no impact. The combination of the routing protocol and the packet size has an impact of 23.6%. Similar results were obtained on average jitter: it was shown that the routing protocol, the packet size, and the combination of the two have a greater impact on this metric [29]. In a networking area, we can find several works that use \(2^{k}\) factorial methodology. In [47] this methodology is used to determine the factors that most affect the Warning Message Dissemination (WMD) in a Vehicular Ad hoc networks (VANET) under real roadmaps; the result shows that the density of vehicles and the type of map used are the factors that most affect, displacing a second term broadcast scheme used and the channel bandwidth. The \(2^{k}\) factorial methodology [48] has also been used to determine which aspects influence the performance of antennas in Body Area Networks (BAN) at 60 GHz.