Recent developments in DSP hardware has made it possible to use almost any pulse shape for digital data trans- mission. This resulted in a search for algorithms capable of constructing pulse shapes matching to the properties of a given channel. The projection onto convex sets technique is suitable for the solution of this problem particularly because of its ffexibility in modeling a variety of constraints. The use of the technique for the optimal pulse shape design problem is demonstrated through a detailed example from power line communications. I. INTRODUCTION INCE Nyquist's invention of the intersymbol interference (ISI), the optimal pulse shaping problem for digital data transmission over channels with various properties has been investigated by a number of researchers (1)-(7). The main differences between various digital Nyquist pulse design al- gorithms published in the literature are the type of the filter (FIR or IIR) they choose to generate the pulse shape and the formulation and solution of the optimization problem. Some of these approaches use general optimization techniques and they can handle additional constraints if needed. However, addition of each new constraint requires reformulation of the problem and the solution algorithm. The projections onto convex sets (POCS) technique is an optimization method introduced in the 1960's (8). A number of successful applications of the POCS technique in the signal processing area have been reported in the recent years (9)-(ll). The POCS technique is attractive for optimum pulse shape design particularly because of its modular way of formulating problems with many constraints. In this technique, the addition of new constraints or removal of some of the existing ones does not require reformulation. It is also possible to handle certain inconsistent requirements in the POCS formulation (12). If there are nonintersecting convex sets, it is possible to find the vector which is as close as possible to one set of constraints, while satisfying the rest.

The paper describes a new technique for adaptive cancellation of phase jitter based on IIR filtering. If all the possible sources of phase jitter are known a priori for a given system, then their effect can be interactively filtered out by the proposed algorithm. In addition to offering a cost effective solution for combating the effects of severe phase jitter, this algorithm yields a fast response time to interactive sources of phase jitter. The proposed algorithm will not face any noise/bandwidth conflicts and, hence, it will make no sacrifice in performance.>

A technique for designing stable infinite impulse response (IIR) filters is introduced. An arbitrary order IIR filter can be designed which will very closely model the magnitude and the phase response of a finite impulse response (FIR) filter. Mean field annealing (MFA) is used to estimate the pole and the zero coefficients of the IIR filter. Due to the global optimization nature of the proposed technique, higher performance improvements can be obtained for the same filter order. In addition, the proposed technique will stay away from coefficients which cause the IIR filter to become unstable.>

A technique for adaptive filtering of nonlinear systems with memory has been developed which combines quantized mean field annealing (QMFA) and conventional recursive-least-squares/fast-transversal filter (RLS/FTF) adaptive filtering. Unlike other methods which rely on Volterra and Wiener models, this technique can efficiently handle large order nonlinearities with or without memory. The nonlinear channel is divided into a memory nonlinearity followed by a dispersive linear system. Assuming that the dispersive linear system is stationary during initialization and the nonlinearity does not change while the dispersive linear system varies with time, QMFA is applied to obtain the coefficients and the order of the memory of the nonlinearity and RLS/FTF is applied to determine the weights of the dispersive linear system. This method was applied to a full duplex digital subscriber loop. Simulations show that the performance of the technique is superior to that of ordinary RLS/FTF and steepest descent algorithms.>

A technique is presented for finding transmitter and receiver filters for a wide class of data transmission systems which minimize the bit error rate (BER). The techniques uses Monte Carlo simulation to estimate the BER, coupled with mean field annealing (MFA) to optimize the pulse shapes. Modeling of the link can be as complex as simulation will allow, while MFA is resistant to the statistical scatter in the BER estimate from the simulation. In a complex example, MFA is coupled with Monte Carlo simulation techniques to find near optimal transmit and receive filters for a satellite communications link, taking 6 CPU hours on a DECstation 3100. The bit error rate of the link is found to be as much as three orders of magnitude lower when using the MFA-constructed optimal filters than when using filters constructed by gradient descent and simulated annealing.>

A technique for finding transmitter and receiver filters for a wide class of digital communication systems which minimize the bit-error rate (BER) is presented. The technique uses Monte Carlo simulation to estimate the BER and mean field annealing (MFA) to optimize the pulse shapes. Modeling of the link can be as complex as simulation will allow, while MFA is resistant to the statistical variation in the BER estimate from the simulation. Initially, the MFA technique was applied to a binary symmetric channel in a nonsimulation environment, and an approximate analysis of the behavior of MFA for this problem was performed. In a more complex example, MFA was coupled with Monte Carlo simulation techniques to find near-optimal transmit and receive filters for a satellite communications link, taking 6 CPU hours on a DECstation 3100. The BER of the link was found to be as much as three orders of magnitude lower when using the MFA-constructed optimal filters than when using filters from other comparison results. For this example, the pulse shapes obtained using MFA exhibit a low BER even as the parameter controlling the nonlinearity of the satellite-link model is varied over a wide range, thus showing the solution is robust.>

Recent development in digital signal processing (DSP) hardware has made it possible to use almost any pulse shape for digital data transmission, resulting in a search for design algorithms capable of constructing pulse shapes matching the properties of a given channel. The technique of projection onto convex sets is particularly suitable for the solution of this problem because of its flexibility in modeling a variety of constraints. The use of the technique for the optimal pulse design problem is demonstrated through by an example from power line communications.>

Recently, ways to obtain a new generation of image-coding techniques have been proposed. The incorporation of the human visual system (HVS) models and tools of the image analysis, such as segmentation, are two defining features of these techniques. In this paper, a new image coding technique is presented which utilizes a human visual system model and a image analysis criteria together with the technique of projection onto convex sets (POCS). The human visual system model is used to determine the most probable perceptual information of an image and the removal of irrelevant information. The projection onto convex sets operation is used as a restoration technique aimed at correcting the degradations caused by the conventional coders in the transmitter part of the channel. And finally, the image analysis based technique is used as an interpolator in order to predict the unknown regions of the received image. This new technique can be used in single frame image coding applications to obtain acceptable images at extremely high compression rates.