  In this paper, we propose a complete synchronization algorithm for continuous
phase modulation (CPM) signals in burst-mode transmission over additive white
Gaussian noise (AWGN) channels. The timing and carrier recovery are performed
through a data-aided (DA) maximum likelihood algorithm, which jointly estimates
symbol timing, carrier phase, and frequency offsets based on an optimized
synchronization preamble. Our algorithm estimates the frequency offset via a
one dimensional grid search, after which symbol timing and carrier phase are
computed via simple closed-form expressions. The mean-square error (MSE) of the
algorithm's estimates reveals that it performs very close to the theoretical
Cram\'er-Rao bound (CRB) for various CPMs at signal-to-noise ratios (SNRs) as
low as 0 dB. Furthermore, we present a frame synchronization algorithm that
detects the arrival of bursts and estimates the start-of-signal. We simulate
the performance of the frame synchronization algorithm along with the timing
and carrier recovery algorithm. The bit error rate results demonstrate near
ideal synchronization performance for low SNRs and short preambles.
