Accurate Closed Form Expressions for The Time-Bandwidth Product and FCC Violation Ratio as New Metrics To Characterize UWB Optical Systems

摘要

In this paper, analytical analysis of the first seven derivatives of the Gaussian and hyperbolic secant pulses is carried out for a basic optical communications system. The analysis is mainly based on two important design metrics, namely the Federal Communications Commission violation ratio (FCC VR), and the time-bandwidth product (TBP). The FCC VR is a new metric introduced in this paper, it computes the average power of the signal violating the FCC mask relative to the average power of the FCC mask over the whole spectrum. FCC VR provides great insight on how a generated UWB pulse obeys the FCC mask. The second metric discussed in this paper is the TBP, which is obtained using a variance-based definition for the pulse width. This definition is advantageous in many aspects compared to other definitions, as discussed in the paper. In this work, a generalized closed-form expressions is obtained for the TBP regarding the aforementioned pulse shapes. Moreover, the analysis of a basic optical communications system is carried out by applying the two metrics which proves their significance in the context of designing a similar system.