Impulsive self-similar processes, with applications in broadband communication system modeling

In broadband networks, bandwidth requirements of multimedia applications and size ofthe associated files deviate frequently and significantly from their average value and resultin impulsive and self-similar tra±c. Impulsiveness implies that the second- or higher-orderstatistics of the process are infinite. On the other hand, self-similarity translates to strongcorrelation between the process samples. Self-similarity has been traditionally defined basedon second-order statistics, e.g. a power-law decaying autocorrelation. Thus, it is di±cultto integrate self-similarity with impulsiveness, despite the fact that in the case of networktra±c they emerge simultaneously.In this dissertation, we develop a general mathematical framework for dealing withimpulsive and self-similar processes. We extend the conventional definition of self-similarityto a more generalized sense, based on a proposed quantity called the generalized codi®erence.Under this framework, we propose a parsimonious constructive model for broadbandnetwork tra±c, namely the Extended Alternating Fractal Renewal Process (EAFRP). TheEAFRP can model individual sessions in network tra±c and can capture both tra±c impulsivenessand self-similarity. The proposed model enabled us to show, that, despite theexisting view that self-similarity is the dominant factor in shaping the principles of highspeednetwork engineering, impulsiveness is at least as important as self-similarity, mostoften being more dominant.Assuming seamless connectivity between wireless and wired networks, tra±c in wirelessnetworks will have similar characteristics as that of wired networks. High-speed wirelessdata networks are mostly based on spread spectrum principles, where users share the samefrequency range. Interference from other concurrent users is the main factor that a®ectssystem performance and limits system capacity. We propose a statistical-physical model todescribe the interference generation mechanism, and subsequently obtain the instantaneousand joint statistics of the interference. We show that the interference is impulsive, andfurthermore, due to the characteristics of the multimedia tra±c, it is self-similar. In the past,the dependence structure of the interference has been overlooked. However, our analysisshows that the consequences of self-similarity can be very severe, and overlooking them canlead to unexpected performance degradation in the receiver.Ph.D., Electrical Engineering -- Drexel University, 200