In this thesis, we propose and study a new suppressed carrier tracking loop called the N-phase digital tanlock loop. This tracking loop is a modified version of the digital tanlock loop and is somewhat similar to the N-phase inphase and quadrature (I-Q) loop. We investigate the performance of the loop in tracking suppressed carrier N-ary phase shift keyed signals and its acquisition behavior in the absence and presence of noise and data phase distortion. In the absence of phase noise, we found the optimal parameter values that give minimum locking time, and determined the locking range of the loop when initial phase error and frequency offset exist. In the presence of phase noise, we determined the variance of phase error that gives a measure of tracking performance of this system and showed the relation between the tracking performance and the arm filter bandwidth by computer simulation.