A Sparse Temporal Synchronization Algorithm of Laser Communications for Feeder Links in 5G Nonterrestrial Networks

Algorithm 2

Modify the DFT result based on Rife and Newton methods.

1: Modify the DFT result by Rife method.

Since denotes the output of SFFT, the modified result is

,

where

2: Further modify the result by the iteration of Newton method.

For a positive integer , the - iteration result is expressed as

, where and denote the first-order

and the second-order derivatives of , respectively, and denotes

the tuning step.

3: Replace    by the latest iteration result, .