We propose a method to eliminate the bias term present in the timing-error estimator employed in digital receivers where the input signal is sampled by a fixed clock which is not synchronized to the transmitter clock. This bias error results from the nonideal interpolation that precedes the timing-error estimator. We show that it can be derived as a function of the previously estimated symbol timings. An unbiased timing-error estimate can then be obtained by subtracting this bias term from the output of the timing-error detector. Simulation results are included to show the performance improvement realizable by employing this method.

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.

A new method for estimating the frequency of a complex sinusoid in complex white Gaussian noise is proposed. Its computational complexity is comparable to Kay's method [1989], but it attains the Cramer-Rao bound (CRB) down to lower signal-to-noise ratio (SNR) values. Simulation results are included to demonstrate the performance of the proposed method.