Power spectral density of binary digital pulse streams in the presence of independent uniform 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 offset by random amounts relative to the nominal one. The amount of timing shift per transmission interval is random and is typically characterized by a discrete stationary random process (independent of the data sequence). The purpose of this paper is to characterize the power spectral density (PSD) of baseband binary data streams in the presence of uniform timing jitter. Examples of uncorrelated data pulse stream, and i.i.d. data stream are given. Interesting results emerge when the generating sequence {a_n} is uncorrelated. For generating sequences {a_n} that are non-zero mean, timing jitter has the effect of widening the main lobe of the spectrum and increasing the sidelobes. When the generating sequence is zero mean and uncorrelated, a rather surprising result is that the timing jitter does not effect the PSD. Simulation results are also presented to verify the analysis