  In the ultraviolet (UV) scattering communication, the received signals
exhibit the characteristics of discrete photoelectrons due to path loss. The
synchronization is based on maximum Pulse Number-Sequence correlation problem.
First of all, the accuracy of synchronization is vital to channel estimation
and decoding. This article focuses on improving synchronization accuracy by
designing and optimizing synchronization sequences. As for the maximum Pulse
Number-Sequence correlation problem, it is assumed that the correlation values
satisfy the Gaussian distribution and their mathematical expectation, variance
and covariance are derived to express the upper bound of synchronization
offset. The synchronization sequence we designed has two equilong RANDOM parts
(Symbols meet Bernoulli distribution with equal probability.) and a
$\{1,0,1,0,1,0,...,1,0,1,0\}$ part between them with $ \alpha $ as its
proportion of entire sequence. On the premise of ensuring the synchronization
reliability, the synchronization deviation can be reduced by optimizing $
\alpha $.
  There are simulation experiments to verify correctness of the derivation,
reasonableness of the hypothesis and reliability of optimization. Compared with
equilong random sequence, the synchronization accuracy of the optimized
synchronization sequence is significantly improved.
