Timing recovery based on the PAM representation of CPM

A reduced-complexity decision-directed timing recovery method for continuous phase modulation (CPM) is presented. Using the well-known and popular pulse amplitude modulation (PAM) representation-or Laurent representation- of CPM, we develop two different formulations of a PAM-based timing error detector (TED). We consider the general M-ary multi-h CPM model in our development and use the family of aeronautical telemetry CPMs for our numerical examples. We show by analysis that the two TED formulations have identical ldquoS-curverdquo characteristics, and are free of false lock points, but have slightly different performance when applied to specific CPM examples, particularly in the multi-h case. There is no unanimous winner between the two formulations in all cases; however, for both formulations, we show the TEDs are able to perform close to the theoretical limit given by the modified Cramer-Rao bound. As such, the proposed TEDs provide an important synchronization component for reduced-complexity PAM-based CPM receivers that has heretofore been missing.