The design and optimization of synchronization sequence for Ultraviolet communication

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