Optimal pulse shape design for digital communication systems by projections onto convex sets
R.A. Nobakht, M. Reha Civanlar · IEEE Transactions on Communications · 1995
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.