Design of optimal interpolation filter for symbol timing recovery

We propose an optimal interpolation filter for symbol timing recovery in a digital receiver where the input analog-to-digital (A-D) conversion sampling clock is not synchronized to the transmitter symbol clock. The optimal filter is designed by minimizing the mean-square error (MSE) at the output of the receiver, assuming that the correct timing difference between the nonsynchronized input samples and the correct strobe synchronized to the symbol is given. The MSE minimization procedure results in a system of linear equations which can easily be solved to yield the optimal filter coefficients. We also analyze the symbol tracking performance of a symbol synchronizer that employs the proposed optimal interpolation filter. Although the proposed optimal filter is designed assuming the availability of the correct timing difference, we show that it minimizes the timing estimation error variance even when the computed timing difference values deviate from the ideal, we also show that the timing estimation is virtually unbiased if the length of the interpolation filter is greater than or equal to 4. Simulation results are included to show the performance improvement realizable by employing the optimal interpolation filter.