  Identifying the start time of a sequence of symbols received at the receiver,
commonly referred to as \emph{frame synchronization}, is a critical task for
achieving good performance in digital communications systems employing
time-multiplexed transmission. In this work we focus on \emph{frame
synchronization} for linear channels with memory in which the channel impulse
response is periodic and the additive Gaussian noise is correlated and
cyclostationary. Such channels appear in many communications scenarios,
including narrowband power line communications and interference-limited
wireless communications. We derive frame synchronization algorithms based on
simplifications of the optimal likelihood-ratio test, assuming the channel
impulse response is unknown at the receiver, which is applicable to many
practical scenarios. The computational complexity of each of the derived
algorithms is characterized, and a procedure for selecting nearly optimal
synchronization sequences is proposed. The algorithms derived in this work
achieve better performance than the noncoherent correlation detector, and, in
fact, facilitate a controlled tradeoff between complexity and performance.
