# Performance Analysis of Multihop Underground Magnetic Induction Communication
## 5 Conclusions  
In this paper, we have formulated a performance evaluation methodology for MI-WUSN using SNR, channel capacity and BER. We first studied the single hop communication model and concluded that system performance is directly dependent on the transmission distance for any given channel state. For instance, at high noise power, a shorter communication distance makes desirable system performance achievable and vice versa. Next, we present the end-to-end performance evaluation of a multihop MI-WUSN for a constant (IID) and changing (INID) channel state between hops. We derived analytical expressions for evaluating both scenarios and verified our hypothesis through extensive evaluations. Our results show that the assumption of the IID of hop states is impractical for an underground channel owing to the channel's inherently dynamic nature. For multihop MI-WUSN, more relays correspond to better performance irrespective of the channel  
Figure 10: Multihop underground MI communication system’s performance for INID of channel states between hops. Decreasing noise scenarios across hops were considered for high noise power (\(P_{n}=-83\) dBm) at hop 1, and increasing noise scenarios across hops were considered for low noise power (\(P_{n}=-103\) dBm) at hop 1. The panels show the variation of the **(a)** SNR (dB), **(b)** channel capacity (bps) and **(c)** BER with the noise power across hops.  
conditions due to stronger magnetic coupling. However, a trade-off should be achieved between the deployment cost of more relays and the required system performance. The system evaluation showed that with an increase in the number of links characterised by a low average SNR, the end-to-end BER increases while the overall system performance deteriorates. The more the deviation of channel state across successive hops is, the more the deviation in the system performance is observed.  
Our analysis is general and can be easily extended to any channel model (such as the Rayleigh, Rice, and AWGN models) by adding the corresponding channel fading parameters. In the absence of any reported work on precise channel state modeling for underground communication in the context of multihop MI-WUSNs, our work provides an analytical model that can be used to study the performance of end-to-end MI-WUSNs for a time-varying underground channel. Furthermore, our results show that a margin for unexpected performance degradation should always be considered when modeling a practical MI-WUSN, because of the unpredictable underground channel state, which cannot be assumed to remain constant over space and time.  
In the future, if packet error rate is to be analysed, higher order modulation and detection schemes would have to be employed using the approach proposed in this work. This is also applicable to computing the end-to-end delay of the relay channel which is dependent on parameters like the choice of relay scheme (AF or DF), SNR, the required BER and the decoding scheme applied at relay (DF) or destination (AF). Our work provides the foundation for such extensions.  
[PERSON] and [PERSON] contributed to the main idea of this research. [PERSON] performed the numerical evaluation. [PERSON] and [PERSON] contributed to the writing of this article. This research activity was planned and executed under the supervision of [PERSON]-[PERSON]. Both authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.