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Computer simulation results show that a fourth-order algorithm will suffice to cover a wide tracking range exceeding half the carrier spacing while producing results with good accuracy.
The reason explains why we make efforts on improving the fine synchronization with wide tracking range, high estimation accuracy, and low computational complexity.
We note here that the development of the fine CFO tracking with wide tracking range while keeping high estimation accuracy and low computational complexity is beneficial to the design of the synchronization algorithms, viewing the fact that different coarse synchronization algorithms lead to different magnitudes of the fine residual frequency offsets.
In [1], by using the linear minimum-mean-square-error (LMMSE) combiner to optimally combine frequency offset estimators based on single time slot pilot samples from a received time-domain OFDM block, they successfully circumvent the multiple solution difficulty and meanwhile achieve very satisfactory joint estimation performance with wide tracking range (up to half the subcarrier spacing).
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To cover a wider tracking range, one can use orders higher than 4.
When a wider tracking range is desired (|δ| > 0.5), we will need at least an order 4 algorithm.
Our first order algorithm is found to be superior to others with faster convergence, wider tracking range, least computation requirement, and estimation accuracies.
However, using orders higher than 4 is not recommended since it will only increase the computation load without much gain except for a wider tracking range which is rarely necessary for fine frequency tracking.
Its tracking range is quite wide up to half the carrier spacing, and convergence speed is very fast, costing only several tens of iterations; moreover, its mean-square error (MSE) performances are very much close to CRLBs at medium-to-high signal-to-noise ratio (SNR) values.
The proposed method leads to a high responding speed and low time-drift in wide range tracking, and greatly decreases the compensation error in the microgravity simulation for space manipulator and moon vehicle.
The global positioning system such as GPS is wide range tracking system; however, the system is not applied to indoor positioning system.
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