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The estimation of the synchronization parameters and the channel state relies on scattered pilots obtained with the auxiliary pilot technique.
The calculation of PSYNC for HIPESYN is conducted according to the estimation of the synchronization error for this algorithm.
The reduction of the intrinsic synchronization error will facilitate a precise estimation of the synchronization between a parent node and its children, or between different neighbors.
Finally, note that this error value is further required to compute the estimation of the synchronization error, as it is explained below.
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And then, based on the finite-time stability theory, a sufficient criterion on the finite-time synchronization of this scheme is rigorously verified in the form of matrix and the corresponding estimation for the synchronization time is analytically given.
The following simulation results prove this by taking a closer look at the estimation performance of the synchronization parameters.
In GNSS receivers, antenna arrays are usually applied to signal tracking, where the algorithms may have access to an initial coarse estimation of the signal synchronization parameters and the array attitude (and thus an estimation of the direction of arrival of the desired signals).
Here the estimation error with iteration of the synchronization part is almost overlaying with the presented results.
The only assumption lies on the perfect estimation of timing synchronization (one sample per symbol, optimum sampling time).
Thus, we propose l = 63 and t = 23 + lk k ∈ Z + to be the estimation of the code length and synchronization positions, which are consistent with the simulation settings.
Taking into account the clock drift of commercial motes (d), the synchronization error in IEEE 802.15.5 (denoted as E ˜ b r o a d c a s t − x ) can be expressed, following the same consideration as the estimation done in the calculation of the synchronization error, by the following equation E ˜ b r o a d c a s t − x = T h r e s h o l d + T current − T lastsynchronization × d (4).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com