archives@tulane.edu / An ongoing effort in the study of microparticle movement in biofluids is the proper characterization of subdiffusive processes i.e. processes whose mean-squared displacement scales as a sublinear power law. In order to describe phenomena that lead to subdiffusive behavior, a few models have been developed: fractional Brownian motion, the generalized Langevin equation, and random walks with dependent increments. We will present perhaps a simpler model that leads to subdiffusion and is designed to characterize systems where a regularly diffusive particle intermittently becomes trapped for long periods of time. By combining ideas from Hybrid Switching Diffusion and queuing systems literature we will describe the law of our process. The major obstacle is the introduction of heavy tail immobilization times and we will overcome it by representing the power law as an infinite mixture of exponentials. The description of the law allows us also to solve the First Passage Problem. Modeling subdiffusion is a very active field of research both in mathematics and physics. Physicists often use a continuous model that originates in the theory of random walks - Brownian motion inversely subordinated to an $\alpha$-stable process. In a similar way we will describe our process. With this description we will show that our process under rescaling is equivalent to the inverse subordinated Brownian motion, i.e., we will present the functional limit theorem for Switching Diffusion. / 1 / Lukasz Sikora

Modern communication systems operate with high peak-to-average-power ratio (PAPR) over wide bandwidth. Linearity requirements force operation in a low efficient highly linear back-off region. Then increasing efficiency is becoming critical. One of the most promising technologies to accomplish this is using supply modulation, e.g. envelope tracking (ET) and envelope elimination and restoration (EER). Supply modulated systems have been studied extensively in the past years, but no systems have been presented with flexibility in the envelope amplifier circuit.   In this work the supply modulator amplifiers have been studied. The focus is on hybrid switching amplifier (HSA) as envelope amplifier. Two envelope amplifier prototypes P-I and P-II have been designed. They are both designed for 15W output but P-II has 28V maximum supply voltage and P-I has 15V maximum supply voltage. P-II developed in version A, using silicon (Si) based switching transistor and version B using gallium-nitride (GaN) switching transistor. The efficiency is limited to a maximum 97 % possible by the circuit components.   The linearity was mainly analyzed by AM-AM diagrams. P-I, P-IIA and P-IIB, were analyzed in simulations and measurements. Results show high possibility of improvement with digital processing, i.e. digital pre-distortion (DPD). Linearization will improve the overall performance in the supply modulator (SM) systems, improving the delay issues and distortion produced by the implementation of the system.   The developed flexible board has made it possible to investigate alternative technologies of ET, focused in the hybrid switching amplifier (HSA). This has given the possibility to compare the overall performance for a traditional Si based switch with the novel Ferdinand Braun Institute’s (FBH) GaN-HEMT based switch with regards to bandwidth, efficiency and non-linearities introduced by the envelope tracking amplifier. P-I and P-II show high efficiency (> 60%) in results. For signals with adequate average power levels the efficiency is high, with around 70% efficiency for WCDMA signals. Phase distortions are evident already at a 5 MHz bandwidth.

Optical fibers have brought fast and reliable data transmission to todays network. The immense fiber build-out over the last few years has generated a wide array of new access technologies, transport and network protocols, and next-generation services in the Local Area Network (LAN), Metropolitan Area Network (MAN), and Wide Area Network (WAN). All these different technologies, protocols, and services were introduced to address particular telecommunication needs. To remain competitive in the market, the service providers must offer most of these services, while maintaining their own profitability. However, offering a large variety of equipment, protocols, and services posses a big challenge for service carriers because it requires a huge investment in different technology platforms, lots of training of staff, and the management of all these networks.<p> In todays network, service providers use SONET (Synchronous Optical NETwork) as a basic TDM (Time Division Multiplexing) transport network. SONET was primarily designed to carry voice traffic from telephone networks. However, with the explosion of traffic in the Internet, the same SONET based TDM network is optimized to support increasing demand for packet based Internet network services (data, voice, video, teleconference etc.) at access networks and LANs. Therefore the service providers need to support their Internet Protocol (IP) infrastructure as well as in the legacy telephony infrastructure. Supporting both TDM and packet services in the present condition needs multilayer operations which is complex, expensive, and difficult to manage. A hybrid switch is a novel architecture that combines packets (IP) and TDM switching in a unified access platform and provides seamless integration of access networks and LANs with MAN/WAN networks. The ability to fully integrate these two capabilities in a single chassis will allow service providers to deploy a more cost effective and flexible architecture that can support a variety of different services.<p> This thesis develops a hybrid switch which is capable of offering bundled services for TDM switching and packet routing. This is done by dividing the switchs bandwidth into VT1.5 (Virtual Tributary -1.5) channels and providing SONET based signaling for routing the data and controlling the switchs resources. The switch is a TDM based architecture which allows each switchs port to be independently configured for any mixture of packet and TDM traffic, including 100% packet and 100% TDM. This switch allows service providers to simplify their edge networks by consolidating the number of separate boxes needed to provide fast and reliable access. This switch also reduces the number of network management systems needed, and decreases the resources needed to install, provision and maintain the network because of its ability to collapse two network layers into one platform.<p> The scope of this thesis includes system architecture, logic implementation, and verification testing, and performance evaluation of the hybrid switch. The architecture consists of ingress/egress ports, an arbiter and a crossbar. Data from ingress ports is carried to the egress ports via VT1.5 channels which are switched at the cross point of the crossbar. The crossbar setup and channel assignments at ingress port are done by the arbiter. The design was tested by simulation and the hardware cost was estimated. The performance results showed that the switch is non-blocking, provide differentiated service, and has an overall effective throughput of 80%. This result is a significant step towards the goal of building a switch that can support multiprotocol and provide different network capabilities into one platform. The long-term goal of this project is to develop a prototype of the hybrid switch with broadband capability.

Optical fibers have brought fast and reliable data transmission to todays network. The immense fiber build-out over the last few years has generated a wide array of new access technologies, transport and network protocols, and next-generation services in the Local Area Network (LAN), Metropolitan Area Network (MAN), and Wide Area Network (WAN). All these different technologies, protocols, and services were introduced to address particular telecommunication needs. To remain competitive in the market, the service providers must offer most of these services, while maintaining their own profitability. However, offering a large variety of equipment, protocols, and services posses a big challenge for service carriers because it requires a huge investment in different technology platforms, lots of training of staff, and the management of all these networks.<p> In todays network, service providers use SONET (Synchronous Optical NETwork) as a basic TDM (Time Division Multiplexing) transport network. SONET was primarily designed to carry voice traffic from telephone networks. However, with the explosion of traffic in the Internet, the same SONET based TDM network is optimized to support increasing demand for packet based Internet network services (data, voice, video, teleconference etc.) at access networks and LANs. Therefore the service providers need to support their Internet Protocol (IP) infrastructure as well as in the legacy telephony infrastructure. Supporting both TDM and packet services in the present condition needs multilayer operations which is complex, expensive, and difficult to manage. A hybrid switch is a novel architecture that combines packets (IP) and TDM switching in a unified access platform and provides seamless integration of access networks and LANs with MAN/WAN networks. The ability to fully integrate these two capabilities in a single chassis will allow service providers to deploy a more cost effective and flexible architecture that can support a variety of different services.<p> This thesis develops a hybrid switch which is capable of offering bundled services for TDM switching and packet routing. This is done by dividing the switchs bandwidth into VT1.5 (Virtual Tributary -1.5) channels and providing SONET based signaling for routing the data and controlling the switchs resources. The switch is a TDM based architecture which allows each switchs port to be independently configured for any mixture of packet and TDM traffic, including 100% packet and 100% TDM. This switch allows service providers to simplify their edge networks by consolidating the number of separate boxes needed to provide fast and reliable access. This switch also reduces the number of network management systems needed, and decreases the resources needed to install, provision and maintain the network because of its ability to collapse two network layers into one platform.<p> The scope of this thesis includes system architecture, logic implementation, and verification testing, and performance evaluation of the hybrid switch. The architecture consists of ingress/egress ports, an arbiter and a crossbar. Data from ingress ports is carried to the egress ports via VT1.5 channels which are switched at the cross point of the crossbar. The crossbar setup and channel assignments at ingress port are done by the arbiter. The design was tested by simulation and the hardware cost was estimated. The performance results showed that the switch is non-blocking, provide differentiated service, and has an overall effective throughput of 80%. This result is a significant step towards the goal of building a switch that can support multiprotocol and provide different network capabilities into one platform. The long-term goal of this project is to develop a prototype of the hybrid switch with broadband capability.