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As a verification of the derived CRVB, the MLE of the CFO is simulated with zero frequency offset and a small timing offset of −T s ≤τ≤T s. Figure 7 clearly shows that the MLE yields the derived CRVB, suggesting that the CRVBTD is too optimistic.
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In addition, the discretization of time into equally small timing steps (∆k) is applied to assign the timing index of each node to the corresponding discrete distance.
However, in complex systems where a great number of devices are considered, and/or where several time instants have to be obtained (i.e., the time step h is very small), timing conditions cannot be fulfilled, i.e., the calculations do not finish before t = t 0 + h.
The controlled bandwidth criterion is very important in high speed digital data transmission, while the flat response at the sampling time makes the pulse maximally immune to small timing offset (jittering) at the sampling instant, hence reducing the channel bit error rate.
The present approach is centered on the optimization of a piece-wise rectangular transfer characteristic in order to obtain a minimal value of the error probability when the impulse response is sampled with small timing errors.
The problem was that our control circuit of the interface circuit could allow only very small timing delay.
One aspect of this relationship is the existence of small timing differences in the signals in different regions.
An implementation example of a real filter with improved performance in terms of ISI error probability when sampled with small timing errors is presented.
This can be explained by the ability of the channel equalizer to effectively reduce the distortion of the phase per subchannel caused by small timing offsets.
It may also be concluded that the imagined black swans vary in terms of their impact, either positive or negative, impact (large or small), timing effects (first, then), and level of surprise.
Practically, the random errors on the measurements from three gyros and three accelerometers can be considered statistically independent after ignoring the small timing error and tiny installation error compared to the other error sources.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com