## 4 Statistical Testing of ENMRA Algorithm
### Magnetic Induction Techniques Used in WUSNs  
The basic principle of mutual magnetic induction is used to transmit and receive communication signals in direct MI communication architecture [50]. As with transformers, the transmitter coil communicates the signal as sinusoidal current, which induces analogous sinusoidal current to the receiving node, completing the communication [51; 52]. Due to mutual induction, the interaction between the coupled coils of the transmitter and receiver is accomplished (See Figure 3). Despite the advantages of direct MI communication, such as a small coil size, low path loss, and stable communication channel, few limitations prevent it from being a viable alternate to WUSN applications. To overcome the limitations of direct MI communication, such as limited communication range, investigators developed waveguide-based MI communication, which proved to be effective in achieving a practical bandwidth of intersensor communication. Moreover, it increased the communication range and reduced the transmission path loss in numerous applications in the underground environment (see Figure 4). This design was made up of a succession of resonant relay nodes [52] that were deployed between underneath transceiver sensor nodes and were wirelessly coupled in MI-based WUSNs. To achieve an effective signal strength increase with a transmission range of 2 m, six or more relay coils were necessary. The following advantages were observed when using this approach: sufficient bandwidth, fewer sensors, increased transmission range, path loss reduction, better robustness, extended system lifetime, a stable MI channel, and easier deployability and maintenance. In practical underground communication applications, coils are not buried in a straight line due to two probable causes: the first one is the inability to deploy in exact planned positions due to rocks or pipes present inside the ground, and second, the positions of already buried coils may get changed during operation of the network due to above-ground pressure or movement of soil. Moreover, it was also well established that received signal strength at the MI transceiver end was affected by the angle between the axes of two adjacently placed coils. Therefore, the option of using multidimensional MI coils in such a complex scenario was worked on for high-quality transmission between sensing nodes [52]. More precisely, three-directional (3D) coils were designed and used, which offered omnidirectional signal coverage, as well as a minimal number of coils, leading to reduced system complexity and cost (see Figure 5). In a 3D MI coil system, three individually fabricated unidirectional (UD) coils were vertically mounted on a cubical structure having each side with a length of 10 cm, such that each UD coil was perpendicularly deployed in relation to others. These three coils were  
Figure 4: Structure of MI waveguide technique. Figure 5: Basic structure of MI waveguide with 3D coils. Figure 3: Structure of direct MI communication. meant to form a powerful beam along the three different axes of a Cartesian coordinate. Due to magnetic flux created by one surrounding coil becoming zero on another two orthogonal coils, these three coils did not interfere with each other, attributing to the field distribution structure of the coils. Like direct MI coils, the 3D MI coils were also made up of 26 AWG wire, and each one of these coils was supported by a serial capacitor for detecting resonance. At the side of the receiving node, all three signals from three coils were introduced. Depending on the channel model, after fixing MI coil parameters and transmission distance, the intersection angle between transmission and receiver nodes determined the signal strength. At least one coil achieved adequate signal strength with three orthogonal coils regardless of how the angle of intersection was changed. Even if MI coils were rotated, or the intersection angle between them changed, a high degree of communication was supposed to be kept by the system in this case [53].