Research Article

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

Algorithm 1

Estimate based on the SFFT algorithm.
Input: .
Output: .
1: Zero padding and the length of is changed from to .
2: Let .
3: For  ; ++  do
4:Tear apart the spectrum randomly by and , where and
denote the expressions of and in frequency-domain, respectively, and .
5:Apply a flat window function to expand the spectrum range.
(1) Let be the window function in frequency-domain,
where and denote the cutoff frequencies of the passband and stopband, respectively,
and denotes the ripple amplitude, whose reference value is , where is a positive integer.
(2) Compute , where denotes the expression of in time-domain.
The length of is .
6:Subsample in frequency-domain. Letting be the data length after subsampling,
we have with .
7:Map with a hash function.
(1) Define a hash function .
(2) Define an offset function .
(3) Let denote the support set of the largest coefficients in . The preimage set of is ,
whose size is , where and .
(4) Obtain the largest spectrum coefficients as
(5) Record the nonzero position of .
8: End for
9: Letting be the occurrence times of coordinate in the sets and only retaining the coordinate whose occurrence
times are larger than , we have , and the rest terms are zeroes.
10: For each coordinate in , we obtain the corresponding spectrum coefficients with and .
11: Return  , where denotes computing the median of a sequence.