Performance Bound of the Start of Frame Delimiters

Start of frame delimiter (SFD) is of critical importance for frame synchronization of packet communication systems. IEEE 802.15.4f defines the SFD as a 16-bit binary sequence and defines the preamble as a 16-bit alternating $\{+1,-1,\ldots, +1,-1\}$ sequence. In addition, direct current (DC) balance is important and always preferred in circuit design. With respect to the preamble and the DC balance constraints, in this letter, we study the performance bound of frame synchronization via SFD. We provide a mathematical modeling of SFD and show that for any SFD, the strongest side lobe yielded can never be less than 2, regardless of the lengths of the SFD and the preamble. As a special case of the more general case considered in this letter, the SFDs in 802.15.4f, achieves the performance bound for synchronization accuracy.