The performance of the all-digital data transition tracking loop using nonlinear analysis

This paper 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 non-commensurate sampling and symbol rates are addressed and analyzed for perfectly square pulses as well as filtered pulses. 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 irrational). The phase error variance for an even number of samples per symbol is also shown to degrade compared to an odd number of samples per symbol.<>