An Application of a Semi Markov Model in Predicting the Fading Occurrences in Wireless Communication Channels

Abstract

The most frustrating and troublesome issue in wireless communication is fading. Estimating the fading occurrence for the design of greatly reliable communication link is crucial. In this paper, we present a novel mathematical method for predicting the future signal fading on the basis of current and past data. The application of a Semi Markov Model as a generalization of the Markov Model is discussed for predicting the deep fading occurrence probabilities of the received envelope in wireless communications channels. This flexible model is given for assessing the system performance with the envelope correlation. 142 deep fading data whose amplitudes are lower than a mean of the amplitudes which occurred in a typical wireless system with the Jakes filtering are considered. The transition probability matrix and the holding time mass functions are calculated for the next 1 to 21 unit times. One unit time is regarded as the inverse of sampling frequency; moreover, the core matrix and the cumulative probability distribution of the waiting time are obtained. Calculating the interval transition probabilities for Amplitude to Amplitude transition for these deep fades demonstrates the forecasting occurrence probabilities in the future and the possibility of forecasting the fading occurrences in dimensions of time and amplitude. 

Keywords

• Semi Markov Model,Holding time,Interval transition probability,Fading occurrence

References

1. [1] Zheng Z., Trivedi K. S.,Qiu K., Xia R, "semi Markov models of composite web services for their performance, reliability and bottlenecks," IEEE Transactions on services computing, vol. 10, no. 3, pp. 448-460, (2017).
2. [2] Grabski F., Semi Markov processes: Applications in system reliability and maintenance, Elsevier Inc., (2015).
3. [3] D’Amico G., Petroni F., "A Semi Markov model for price returns," Physica A: Statistical Mechanics and its applications, vol. 391, no. 20, pp. 4867-4876, (2012).
4. [4] Wanneveich M. , Jacqmin-Gadda H., Dartigues J., Joly P., "Prediction of health indicators for chronic disease under a semi Markov assumption," Theoretical population Biology, vol. 119, pp. 83-90, (2018).
5. [5] Ghosh S., Gosavi A., "A Semi-Markov model for post-earthquake emergency response in a smart city," Control Theory and Technology, vol. 15, no. 1, pp. 13-25, February (2017).
6. [6] Niemeyer A., "Safety margins systematic biometric and financial risk in a semi Markov life insurance framework," Risks, vol. 3, pp. 36-60, (2015).
7. [7] Sengathir A., Manoharan R., "A futuristic trust coefficient-based semi-Markov prediction model for mitigating selfish nodes in MANETs," EURASIP Journal on Wireless Communications and Networking, vol. 1, pp. 1-13, (2015).
8. [8] Vishnevskii V. M., Andronov A. M., "Estimating the throughput of wireless hybrid systems operating in a semi-Markov stochastic environment," Automation and Remote Control, vol. 78, no. 12, p. 2154–2164, (2017).

9. [9] Yin R., Liu B., Liu H., Li Y., Dong M., "A quantitative fault tolerance evaluation model for topology in wireless sensor networks based on the semi Markov process," Neurocomputing, vol. 149, pp. 1014-1020, (2015).
10. [10] Chen M., Ekman T., Viberg M., "New approaches for channel prediction based on sinusoidal modeling," EURASIP Journal on Advances in signal process, (2007).
11. [11] Eyceoz T., Duel-Hallen A., Hallen H., "Deterministic Channel Modeling and Long Range Prediction of Fast Mobile Radio Channels," IEEE Communication Metters, vol. 2, no. 9, pp. 254-256, (1998).
12. [12] Schiavone J. A. , Hermiller S. M., "A Regression model for forecasting Microwave Radio fading at palmetto, GA," IEEE Transactions on Antennas and propagation, Vols. AP-34, no. 7, pp. 936-942, (1986).
13. [13] Lavanya V., Sasibhushana Rao G., Bidikar B., "Fast fading mobile channel modeling for wireless communication," Procedia Computer Source, vol. 85, pp. 777-781, (2016).
14. [14] Skima M. A., Ghariani H., Lahiani M., "A multi criteria comparative analysis of different Rayleigh fading channel simulators," AEU Int. J. Electron. Commun, vol. 66, no. 6, pp. 550-560, (2014).
15. [15] Blaunstein N., Cohen V, Hayakawa M., "Prediction of fading phenomena in land-satellite communication links," Radio Science, vol. 45, no. 06, pp. 1-13, (2010).
16. [16] Rodhiah H. A., Hamid E. Y., "ARMA model for multipath Rayleigh fading using Minimum Description Length criterion," in 10th International Conference on Telecommunication Systems Services and Applications(TSSA)., (2016).
17. [17] Olofsson T., Ahlen A., Gidlund M., "Modeling of the fade statistics of wireless sensor network channels in industrial environments," IEEE Transactions on signal processing, vol. 64, no. 12, pp. 3021-3034, (2016).
18. [18] Lutz E., Cygan D., Dippold M., Dolainsky F., Papke W., "The land mobile satellite communication channel-recording, Statistics and channel model," IEEE Trans. Veh. Techol., vol. 40, pp. 375-386, (1991).
19. [19] Lin H. P., Tsai F. S., Tseng M. J.,, "Satellite propagation channel modeling using photogrammetry and hidden Markov model approach," IEEE Proc. Microw. Antennas Propag., vol. 148, no. 6, pp. 550-560, (2001).
20. [20] Sajadieh M., Kschischang F. R., Len-Garciae A., "A block memory model for correlated Rayleigh fading channels," in Proceedings of ICC/SUPERCOMM 96-International Conference on Communications, (1996).
21. [21] Iglesias D.R. , Sanchez M.G., "Semi Markov Model for Low-Elevation Satellite-Earth Radio Propagation Channel," IEEE Transactions on Antennas and Propagation, vol. 60, no. 5, pp. 2481-2490, (2012).
22. [22] Wang J., Cai J., Alfa A. S., "New Channel Model for Wireless Communications: Finite-State Phase-Type Semi-Markov Channel Model," in IEEE International Conference on Communications, May (2008).
23. [23] Georgiadis S., Limnios N., "Nonparametric estimation of the stationary distribution of a discrete time semi Markov process," Communication in Statistics-Theory and Methods, vol. 44, no. 7, pp. 1319-1337, (2015).
24. [24] Girardin V., Limnios N., Applied Probability from Random Sequences to Stochastic Processes, Springer Nature Switzerland AG, (2018).
25. [25] Devolder P. , Janssen J., Manca R., "Homogeneous and non-homogeneous semi Markov models," Basic stochastic processes, pp. 113-163, (2015).
26. [26] Ekwe O. A., Abioye V, Oluwe M.O., Okoro K.C., "Effective Fading Reduction Techniques in Wireless Communication System," OSR Journal of Electronics and Communication Engineering, vol. 9, no. 4, pp. 35-43, (2014).
27. [27] Sachdeva N., Sharma D., "Diversity: A Fading Reduction Technique," International Journal of Advanced Research in Computer Science and Software Engineering, vol. 2, no. 6, June (2012). [28] Özbek B., Ruyet D. L., Feedback Strategies for Wireless Communication, Springer-Verlag New York, (2014).
28. [29] Zhang H., Liu Y., Gao J., "Statistical Analysis of Wireless Fading Channels," in International Conference on Artificial Intelligence and Computational Intelligence: Artificial Intelligence and Computational Intelligence, (2010).