Effects of low sampling rate in the digital data-transition tracking loop

This article describes the performance of the all-digital data-transition tracking loop (DTTL) with coherent and noncoherent sampling using nonlinear theory. The effects of few samples per symbol and of noncommensurate sampling and symbol rates are addressed and analyzed. Their impact on the probability density and variance of the phase error are quantified through computer simulations. It is shown that the performance of the all-digital DTTL approaches its analog counterpart when the sampling and symbol rates are noncommensurate (i.e., the number of samples per symbol is an irrational number). The loop signal-to-noise ratio (SNR) (inverse of phase error variance) degrades when the number of samples per symbol is an odd integer but degrades even further for even integers.