Frame synchronization for M-ary modulation with phase offsets

We study frame synchronization (FS) based on the transmission of known sequences (synchronization words) for M-PSK signals in the presence of additive white Gaussian noise and phase offset due to imperfect carrier phase estimation. In particular, we derive optimal and simple suboptimal metrics for noncoherent FS of M-PSK modulation with M ≥ 4. We show that a simple ℓ1-norm correction of the noncoherent correlation gives large improvements in terms of synchronization error probability. For example, more than 2 dB are gained with respect to usual correlation tests in terms of signal to noise ratio, assuming QPSK with a synchronization error probability 10−3. Finally, we illustrate that the proposed technique is better than correlation based metric also for M-QAM systems, as well as in the presence of small frequency offsets.