Consider the frequency synchronization in global niobile satellite coiiiniunications systems. Let fc ( n , %: t ) be the t,raiismitt,ed ca.rrier frequency from the SAN t o the i-th user in the n-th spot bea.m, D c ( t ) be the fractional Doppler of t.he feeder link, fc6 be t,he translation frequency at. t.he sat.ellit,e, J f ( t ) be the fractional satel1it.e translation error, atid D,(n , i , ...