Developing and Utilizing Multivariate Stochastic Wireless Channel Models
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Developing accurate channel models is paramount in designing eﬃcient mobile communication systems. The focus of this dissertation is to understand the small-scale fading characteristics, develop mathematical tools that accurately capture these characteristics and utilize them in three different applications - diversity receivers, scheduling, packet duplication in dual connectivity scenarios. This dissertation develops multivariate stochastic models for Rayleigh fading channels that incorporate factors such as the velocity of the users, angle of arrival distribution of signals, and carrier frequency. The developed models are more comprehensive than the existing ones. They capture the correlation characteristics of signals more accurately and are applicable to more practical scenarios. The developed models are the only ones that incorporate the spatial correlation structure suggested by 3GPP. The models are used to derive analytical expressions for the output SNR of certain diversity receivers. Owing to our expressions, the output SNR performances of these receivers are now studied through their moments. The moments provide insight about the nature of these receivers’ output SNR distribution, which is very useful in their reliability analysis. Secondly, the models are used to capture the temporal evolution of the received iii SNR. Temporal correlation characteristics of the SNR are exploited to decrease the number of variables in the downlink scheduling problem. This is achieved by making scheduling decisions less frequently for users with relatively higher coherence time. The results illustrate that the number of operations it takes to make scheduling decisions can be reduced by 33% with conﬁdence probability of 0.7 and by 58% with conﬁdence probability of 0.4. Finally, fade duration and non-fade duration characteristics of a Rayleigh fading channel are used to partially and randomly duplicate some packets when connected to multiple base stations. This is performed based on the small-scale fading statistics rather than the large-scale fading. Duplication based on large time scales can be wasteful and unnecessary, so it is shown using matrix exponential distributions how with low complexity to duplicate only when necessary. The results indicate that up to 50% of the resources at the duplicating base station can be liberated whilst meeting the target reliability measure.
Table of Contents
Introduction -- Moments of the Quadrivariate Rayleigh Distribution with applications for diversity receivers -- Reducing computational time of a wireless resource scheduler by exploiting temporal channel characteristics -- Partial packet duplication in 5G: control of fade and non-fade duration outages using matrix exponential distributions -- Conclusion and future work -- Appendix A. Derivation of the PDF of the Quadrivariate Rayleigh Distribution -- Appendix B. Derivation of the CDF of the Quadrivariate Rayleigh Distribution -- Appendix C. Derivation of the MGF of the Quadrivariate Rayleigh Distribution -- Appendix D. Derivation of bivariate SNR density -- Appendix E. Derivation of trivariate distribution density of Rayleigh Random variables
Ph.D. (Doctor of Philosophy)