Reduced-Complexity Joint Frequency, Timing and Phase Recovery for PAM Based CPM Receivers

Abstract

In this thesis, we present a reduced-complexity decision-directed joint timing and phase recovery method for continuous phase modulation (CPM). Using a simple linear modulation--pulse amplitude modulation (PAM)--representation of CPM, more popularly known as the Laurent representation of CPM, we develop formulations of a PAM based joint timing error detector (TED) and a phase error detector (PED). We consider the general M-ary single-h CPM model in our developments and numerical examples. We show by analysis and computer simulations that the PAM based error detector formulations have characteristics similar to the conventional (i.e., non-PAM) formulations and they render reliable performance when applied to specific CPM examples; in fact, we show the error detectors are able to perform close to the theoretical limit given by the modified Cramer-Rao bound (MCRB) and able to provide a bit error rate (BER) close to the theoretical value. Also, we investigate the false lock problem in M-ary CPMs and are able to obtain much improved performance over conventional CPM detectors with our PAM based method. Furthermore, the PAM based receivers perform well in the presence of a large frequency offset (on the order of the symbol rate) and are, in general, much more resistant to small carrier frequency variations compared to conventional CPM receivers. We use an existing PAM based frequency difference detector (FDD) for a large carrier frequency recovery. As such, the proposed method of combining the error detectors (FDD, TED and PED) provides important synchronization components for jointly recovering the respective signal attribute offsets (i.e, carrier frequency, symbol timing and carrier phase) for reduced-complexity PAM based CPM receivers, which have been missing up to this point.