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This paper has established a new theoretical framework that allows us to analyze the ultra-wideband system performance using the closed form formulations. A new generalized time-domain multipath channel based on the geometric theory of diffraction/uniform theory of diffraction (GTD/UTD) framework is incorporated into the system bit-error rate and signal-to-noise ratio by modifying the existing system model. Closed form expressions for important geometric configurations are derived in the time domain for the first time. Some interesting insights into the physical mechanisms and system analysis are observed through explicit expressions and numerical results.