On the power spectral density of digital pulse streams generated by M-ary cyclostationary sequences in the presence of stationary 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) with known statistical properties. The purpose of this paper is to characterize the power spectral density (PSD) of baseband signaling schemes in the presence of arbitrary timing jitter. Although general PSD results are first obtained for arbitrary timing jitter statistics, specific 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 a Markov source are given. Interesting results emerge when the generating sequence {a_n} is uncorrelated. For generating sequences {a_n} that are nonzero-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 affect the PSD. Simulation results are also presented to verify the analysis