Power Spectral Density of Digital Pulse Streams in the Presence of Timing Jitter

The spectral occupancy and composition of a chosen digital signaling technique when the data pulse stream is nonideal, due for instance to implementation imperfections, are important considerations in the design of a practical communication system. One source of imperfection is timing jitter where the rising and falling transitions do not occur at the nominal data transition time instants; nevertheless, the time instants are ofiset by random amounts relative to the nominal one. The amount of timing shift per transmission interval is random and typically is characterized by a discrete random process (independent of the data sequence) with known statistical properties. The purpose of this article is to characterize the power spectral density (PSD) of baseband signaling schemes in the presence of arbitrary timing jitter. Although general PSD results are flrst obtained for arbitrary timing jitter statistics, speciflc results are then given for the cases of practical interest, namely, uniform and Gaussian distributed jitter. Examples of an uncorrelated data pulse stream, an independent identically distributed data stream, and Markov sources are given. Interesting results emerge when the generating sequencefang is uncorrelated. For generating sequences fang that are nonzero mean, timing jitter has the efiect of widening the main lobe of the spectrum and increasing the side lobes. When the generating sequence is zero mean and uncorrelated, a rather surprising result is that the timing jitter does not afiect the PSD. Simulation results are also presented to verify the analysis. I. Introduction The spectral occupancy and composition of a chosen digital signaling technique are important considerations in the design of a communication system. These spectral properties can be derived from knowledge of the technique’s power spectral density (PSD), which in the general case consists of both continuous and discrete components. Evaluation of the PSD for ideal synchronous data pulse streams (a baseband data waveform with a flxed transmission interval and flxed transmission epochs where the underlying data sequence has known statistical properties and the transmitted waveform is a single known pulse shape) is well documented in the literature (see [1, Chapter 2], for example). Most often the data sequence that generates the pulse stream is either wide sense stationary (WSS) or, more generally, wide sense cyclostationary (WSCS), both of which result in a pulse stream that is a WSCS process.