Optimum frame synchronization of preamble-less packets surrounded by noise with coherent and differentially coherent demodulation

We present an optimal MAP frame synchronizer for coherent demodulation as well as DPSK for preamble-less packets that are transmitted in time slots. The MAP approach also yields an indication of whether or not a packet was actually present in a slot. The optimal synchronizer uses both the sync word and the energy of the packet to correctly establish the position of the packet. The correlation term alone performs much worse and is limited in the synchronization rate even at infinite SNR-we give an analytical expression for this upper bound on the synchronization rate. In addition, we present a high SNR approximation to the MAP rule which performs almost as well, but is easier to implement. Finally, we illustrate a method of implementing the optimum rules that requires relatively few components by using a recursive definition of the likelihood function