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In order to guarantee detection performance, the maximum timing error is generally about 1% of pulse duration (e.g., about 5 ps).
Therefore, the maximum timing offset with ranging is given by d r n g, m a x = D m a x c. (3).
The maximum timing offset between two transmitters at a receiver is shown in Figure 5 and expressed as Figure 5 The effect of the worst-case propagation delay in synchronization.
When there is timing inaccuracy in UWB receivers, the designed pulses can obtain about 9 dB gain compared to SOCP-based orthogonal pulses, when the maximum timing deviation is about 0.2 nanoseconds in 2-user WDMA network and the BER drops below 10-4.
where P k denotes the set of transmit powers and T is the duration of the cyclically extended OFDMA block, whereas MSE ( θ ̂ k ) = E { | θ ̂ k - θ k | 2 } is the mean-square error (MSE) of the timing estimate θ ̂ k, and MSE ¯ θ is the network QoS requirement in terms of maximum timing estimation MSE.
For example, the maximum TVE is required to be 1% in steady-state synchrophasor measurement and the corresponding maximum timing error of PMU is 26.4 μs for 60 Hz power grid (Assuming PMU has no magnitude measurement error, 1% TVE corresponds to 0.57 degree phase error or 26.4 μs timing error).
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Six dynamic features are shown: the amplitude of the first peak (First Maximum), the timing of the first peak (First Translocation Time), the time between the first and the second peaks (First Period), the level of the first minimum (First Minimum), the amplitude of the second peak (Second Maximum), and the asymptotic Steady State value.
Results showed that most metrics were better simulated by the multi-objective approach than those of the single objective calibration, especially the low and high flow magnitudes, frequency and variation, duration, maximum flow timing and rating.
where θmax and εmax stand for the maximum allowable timing and frequency offsets, respectively.
The full width half maximum (FWHM) timing jitter before irradiation was ≈600 ps for SLiK, ≈550 ps for C30921SH, and ≈700 ps for SAP500S2.
Here, let us assume that θ k ∈ [ 0,θmax] and ε k ∈ [ -εmax,εmax] where θmax and εmax are defined as the maximum allowable timing offset and and absolute frequency offset of the system, respectively.
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