Markov modelling of digital symbol synchronizers in noise and interference

Symbol timing recovery (STR) is a fundamental synchronization requirement in many digital communication systems. Symbol synchronization is increasingly performed by digital circuitry, and in many implementations this produces a receiver in which the symbol timing error assumes one of a finite number of values, which we call a discrete phase adjustment (DPA) synchronizer. In this thesis, we analyze a DPA synchronizer which uses a binary-quantized version of the Data Transition Tracking Loop (DTTL) timing error estimator. We use Markov chain models and simulations to analyze the performance of the synchronizer when the received signal is impaired by additive white Gaussian noise (AWGN) and cochannel interference (CCI).; The thesis can be divided into two parts. In the first part, we show that a first order Markov model of the synchronizer can be inaccurate when the signal-to-noise ratio (SNR) is small, and that a second order model provides worthwhile improvement over the first order model. We also show that if two conditions are satisfied in receivers which use interpolation to correct the sampling phase error, then the timing error assumes a finite number of values. That is, we give the conditions under which interpolated STR exhibits discrete phase adjustment. We discuss conditions on the timing error estimator and the loop structure, under which the performance of the interpolated STR loop may be accurately modelled by a Markov chain.; In the second part, we examine the performance of the synchronizer in noise and interference for both binary phase shift keying (BPSK) and quaternary phase shift keying (QPSK) modulation. The CCI can be added to the Markov model without increasing the number of states in the chain, but the cost of computing the transition probabilities increases exponentially with the number of interferers. For the BPSK case, the transition probabilities can be computed using a Fourier series, and the computational complexity of this method increases linearly with additional interferers. We show that a first order Markov model and a simulation are in close agreement in some important cases, and we also examine the effects of interferer epoch and excess bandwidth of the signalling pulse on the degradation caused by the interference.