Multi-sampling digital tanlock loop and applications

Abstract

In this dissertation work, an improved digital tanlock loop (DTL) called the multi-sampling DTL (MSDTL) is proposed, its performances in various noisy environments are analyzed, and practical applications for tracking and detecting various digital modulation signals are studied. The proposed MSDTL is based on the multi-sampling scheme in which the two quadrature input signals are sampled more than once in one period of input sinusoidal signal. It has several important advantages over other digital phase locked loops (DPLL``s) and the conventional DTL. These include linear characteristics, wider locking range, faster acquisition behavior. and less steady state phase error mean in the absence of noise. In the presence of Gaussian noise, assuming that the loop phase noise disturbances due to Gaussian noise are mutually independent, we calculate the steady-state phase error probability density functions (pdf``s) of the first- and second-order MSDTL``s with various parameter values by solving numerically the Chapman-Kolmogorov equations. With the pdf``s obtained, we determine the steady-state phase error means and variances of the first-and second-order MSDTL``s by solving their respective system difference equations without approximating the sinusoidal nonlinearity or having numerical computation as is usually done in the case of the sinusoidal DPLL. The results show that as the number of samples in one period of the input sinusoidal signal increases, the steady-state phase error mean of the first-order MSDTL becomes close to zero, and that as the loop gain parameter increases, the steady-state phase error variances of the first- and second-order MSDTL``s are reduced drastically. In the case of fading communication channels, we first find the mathematical models of fading communication channels having characteristics such as log-normal, Rician, or Rayleigh distribution function. We then obtain the pdf``s, means and variances of steady-state phase error of the first...