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Early-Late Timing Error Detection

Early-Late timing error detection for estimating and compensating timing error.

The Early-Late algorithm works similar to the Gardner algorithm. But its goal is not the detect the roots but the peaks of the received signal. It also makes use of the two times oversampled signal $x_i(n)$. $$ t_\mathrm{err} = \mathrm{Re}\left\{\sum_{n=0}^{N/2-1}\left[x_i(2n)-x_i(2(n+1))\right]x_i^*(2n+1)\right\} $$

As with Gardner, the algorithm runs into issues for Nyquist pulses. $\rightarrow$ 0). The method is also modified to make use of the fourth power $$ t_\mathrm{err} = \sum_{n=0}^{N/2-1}\left[p_i(2n)-p_i(2(n+1))\right]p_i(2n+1). $$