A digital transversal postdetection filter for use in differential PSK demodulation is proposed, and a method for optimizing the weighting coefficients is presented. This low-pass filter is implemented using a finely spaced (relative to the symbol rate) tapped delay line whose tap weights are determined so as to minimize the overall mean-square error at the detector outputs. It is shown that even though the detector output signal is quadratic, the optimization problem can be formulated in a way similar to the well-known minimum-mean-square equalizer for linear signals. The filter design technique also accommodates nonideal detector structures, such as those employing hard limiters.

A new approach to echo canceling for two-wire fullduplex data transmission is proposed. The canceling signal is directly synthesized from the binary data, using a transversal filter approach, and the usual multiplications are replaced by additions and subtractions, thus allowing efficient operation of a large number of taps as required for the canceling of distant echoes. As a specific application, a system processing one sample per baud is discussed where timing signals at both communicating stations are assumed to be synchronized. A stochastic adjustment gradient-type algorithm is used for both training and adaptive tracking of the canceler. It is shown that convergence does not depend on intersymbol interference, timing phase, carrier phase, or the energy ratio of the local to the received signal, but is a function only of the number of taps. Convergence time is proportional to that number, and the optimum step size for fastest convergence is equal to the reciprocal of the number of taps. The residual fluctuation noise is proportional to that part of the mean-square (MS) error which cannot be reduced by the canceler and is a simple function of the product of the tap signal and the step size. The predicted convergence properties are verified by simulation results. Finally, it is shown how such an echo canceler might be used to allow two-wire full-duplex transmission for data rates as high as 4800 bit/s.

A new class of fast-converging timing recovery methods for synchronous digital data receivers is investigated. Starting with a worst-case timing offset, convergence with random binary data will typically occur within 10-20 symbols. The input signal is sampled at the baud rate; these samples are then processed to derive a suitable control signal to adjust the timing phase. A general method is outlined to obtain near-minimum-variance estimates of the timing offset with respect to a given steady-state sampling criterion. Although we make certain independence assumptions between successive samples and postulate ideal decisions to obtain convenient analytical results, our simulations with a decision-directed reference and baud-to-baud adjustments yield very similar results. Convergence is exponential, and for small loop gains the residual jitter is proportional and convergence time is inversely proportional to the loop gain. The proposed algorithms are simple and economic to implement. They apply to binary or multilevel PAM signals as well as to partial response signals.