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

In broadband networks, bandwidth requirements of multimedia applications and size of the associated files deviate frequently and significantly from their average value and result in impulsive and self-similar traffic. Impulsiveness implies that the second- or higher-order statistics of the process are infinite. On the other hand, self-similarity translates to strong correlation between the process samples. Self-similarity has been traditionally defined based on second-order statistics, e.g. a power-law decaying autocorrelation. Thus, it is difficult to integrate self-similarity with impulsiveness, despite the fact that in the case of network traffic they emerge simultaneously. In this dissertation, we develop a general mathematical framework for dealing with impulsive and self-similar processes. We extend the conventional definition of self-similarity to a more generalized sense, based on a proposed quantity called the generalized codifference. Under this framework, we propose a parsimonious constructive model for broadband network traffic, namely the Extended Alternating Fractal Renewal Process (EAFRP). The EAFRP can model individual sessions in network traffic and can capture both traffic impulsiveness and self-similarity. The proposed model enabled us to show, that, despite the existing view that self-similarity is the dominant factor in shaping the principles of high-speed network engineering, impulsiveness is at least as important as self-similarity, most often being more dominant. Assuming seamless connectivity between wireless and wired networks, traffic in wireless networks will have similar characteristics as that of wired networks. High-speed wireless data networks are mostly based on spread spectrum principles, where users share the same frequency range. Interference from other concurrent users is the main factor that affects system performance and limits system capacity. We propose a statistical-physical model to describe the interference generation mechanism, and subsequently obtain the instantaneous and joint statistics of the interference. We show that the interference is impulsive, and furthermore, due to the characteristics of the multimedia traffic, it is self-similar. In the past, the dependence structure of the interference has been overlooked. However, our analysis shows that the consequences of self-similarity can be very severe, and overlooking them can lead to unexpected performance degradation in the receiver.