## 6 Conclusions  
This study built a single-carrier M-QAM-based SD-PLC system used as a test bed to determine the statistical properties of data transmission errors and obtain error sequences in an indoor PLC environment. The three-state Fritchman-Markov model and the BWA were used to model the error sequences that were found. Analyses were performed to show that the models were correct based on error sequences that were recorded experimentally at the output of a software-defined M-QAM PLC transceiver. This validation was performed for each modulation scheme studied under different loading conditions. Analytical validation metrics for the realized FMMs include log-likelihood ratios, error-free run distribution graphs, and error probability.  
Moreover, the proposed three-state Fritchman-Markov error model was used to study and model how different connected indoor electrical devices affect data transmission on M-QAM-based SD-PLCs working in a noisy environment. The performance evaluation of the M-QAM-based SD-PLC systems for this study showed that the 4-QAM system was the most reliable and the 16-QAM system was the least reliable. As more devices are added to a power line network, the probability of errors and bursts of errors rises. In this study, M-QAM-based SD-PLC system development and experimental channel error assessment led to results that were similar to those in real-world PLN channel situations.  
The statistical behavior of the PLC channel impulse noise error sequence caused by electrical appliances connected together in the network was successfully modeled using a three-state FMM with one error state, and the results were satisfactory. Because the experimental error sequences resemble FMM error sequences, FMMs can be used to simulate impulse noise errors in the NB-PLC channel. The models created can also be used to optimize modulation schemes, reduce or eliminate the effects of impulsive noise, develop error correction methods, and improve the overall efficiency of the PLC system.  
Further work will be carried out in the next phase, where we will focus on enhancing the discrete channel modeling techniques and their applications to facilitate the design of forward error correction techniques to mitigate PLC channel impairments.  
Figure 19: EFRD graph for Case 4 (combination of CFL bulb and hairdryer).  
**Author Contributions:** Conceptualization: A.O.I.; methodology: A.O.I. and A.D.F.; software: A.O.I. and A.D.F.; validation: A.O.I. and A.D.F.; formal analysis: A.O.I. and A.D.F.; investigation: A.O.I.; resources: T.G.S.; data curation: A.O.I. and A.D.F.; writing--original draft: A.O.I.; writing--review and editing: A.D.F., T.G.S. and T.S.; supervision: A.D.F., T.G.S. and T.S.; funding acquisition: T.G.S. and T.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** The financial assistance of UJ Center for Telecommunications towards this research is hereby acknowledged.  
**Conflicts of Interest:** The authors declare no conflict of interest.