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Total synchronization probabilities of CBTS are rather low, which are 0% when SNR = 10 dB.
But, the proposed one could get almost 99%, even or 100% total synchronization probabilities among the results we achieved.
Therefore, our approach introduces a not high complexity in implementation, but achieves a most 100% total synchronization probabilities improvement.
Meanwhile, the synchronization of our estimator could achieve a total synchronization probability as much as 100% and an exact synchronization probability of 96% in CM1 and TFC1.
In CM2 and TFC3, the proposed estimator could get a total synchronization probability of 100% and an exact probability of 93%.
Figure 16 Synchronization probabily with different SNR in CM1: (A) Preamble 1. (B) Preamble 3. Figure 17 Synchronization probabily with different SNR in CM2: (A) Preamble 1. (B) Preamble 3. The charts indicate that the total synchronization probabilities of the proposed estimators all over 90%, which demonstrates the stability of the proposed estimator once more.
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Nevertheless, let us conservatively consider a total clock synchronization jitter of 20 ps.
Based on graph theory, it derives two sufficient conditions between the network's graph structure and the total system's synchronization, one is delay-independent condition and another is delay-dependant one.
Total and exact synchronization probability could get as much as 100 and 96%.
The maximum total and exact synchronization probabilities of the proposed estimator among the results we achieved are 97 and 95% for TFC1 in CM2.
The initial conditions of the numerical simulations are taken as x 1 ( 0 ) = ( − 1, − 2 ) T, x 2 ( 0 ) = ( − 3, 1 ) T, x 3 ( 0 ) = ( 2, 3 ) T. The synchronization total error of the network are defined as e ( t ) = ∑ 1 ≤ i < j ≤ 3 3 ∑ l = 1 2 | x i ( l ) − x j ( l ) |.
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