# Performance Analysis of Multihop Underground Magnetic Induction Communication
###### Abstract  
Magnetic induction (MI) is a promising solution for realizing wireless underground sensor networks (WUSNs) for many applications such as smart agriculture, surveillance, and environmental monitoring. In this study, a practical deployment model for a multihop MI-WUSN was developed, and its end-to-end performance was evaluated in terms of the signal-to-noise ratio, channel capacity, and bit error rate. We considered a multihop MI-WUSN and evaluated its end-to-end statistical performance for two scenarios pertaining to the hop state: (1) independent and identical distribution (IID) and (2) independent and non-identical distribution (INID). We derived analytical expressions for the performance evaluation and analysis of both scenarios by varying the number of hops and channel conditions. Our extensive numerical results show that asymptotic performance bounds can be obtained for the IID of hops. An analysis of the INID of hops yielded practical results that can facilitate decisive optimisation trade-offs and that can help reduce the system design overhead. wireless underground sensor network (WUSN); magnetic induction (MI); underground communication; decode-and-forward (DF); end-to-end; multihop; relay; system performance; bit error rate (BER) +
Footnote †: journal: 2021  
* It offers low cost and design efficiency because of the simplistic hardware (a coil) involved. [14; 16]. These benefits can be enhanced by using multihop MI transmission, which is an effective way to divide the communication link from the source to the destination into several hops using relays. Relays have been used to achieve a myriad goals. In [17], the magnetic field detector with high sensitivity was used to achieve a high communication range, and in [18] pulse powered magnetic induction (PPMI) was used to reduce the path loss and thereby increase the communication distance. In multihop communication, relays are primarily used for reducing signal attenuation in long-range communication and for deriving cooperative diversity benefits [19]. Passive relays, which are merely repeaters with small coils that use minimal energy and are cost efficient, were used for MI waveguides in [14] to increase the communication range. The downside to using waveguides is the limited bandwidth they offer. To extend the communication range using relays and without additional power consumption by the WUSN, [20] proposed an optimal relay position related to the system configuration. To extend the range further and gain a bandwidth advantage, [21] used active relays (with the capability to perform some operation on the received signal). Active relays have two major operation modes: amplify and forward (AF) and decode and forward (DF). In the AF mode, the signal received at the non-regenerative relay is amplified (along with noise) and then forwarded. By contrast, the DF mode decodes the signal at the generative relay and then forwards it. Active relaying is an energy-consuming protocol, and therefore it has been used in parallel with simultaneous wireless information and power transfer schemes [22]. Apart from range extension, MI relays have been studied for various other purposes. Some of them are as follows:  
* Diversity gain by using relay selection protocols [23] and network orientation [24]
* Mitigation of interference in the form of crosstalk in MI-based multiple-input multiple-output systems [25]
* Noise modeling [21]
* Network throughput improvement by using an optimal relay position [26]
* Determination of outage probability and analysis of connectivity [27]  
Despite all the studies on MI relays, some assumptions made in previous studies restrict the practicality of the solution. For example, in the range extension techniques proposed in [21] and the data rate improvement technique presented in [28], all the nodes are assumed to be deployed in a homogeneous conductive environment (soil and tunnel, respectively), with constant properties over space and time.