On Channel Equalization Using Piecewise Polynomial Kernels

A recent approach to understanding the channel equalization problem is based on function approximation theory. From this approach, it is known that the optimal equalizer is nonlinear even for linear channels. Moreover, Volter-ra-based equalizers and decision feedback equalizers (DFE) ooer restricted exibility for representing the nonlinear dis-criminant required in many cases. This fact has motivated the study of network-based equalizers (perceptrons and radial basis functions). Despite their universal approximation features, these methods are often impractical since they require nonlinear parameter search procedures which result in slow learning algorithms and a performance extremely dependent on initial conditions. In this paper we introduce a new method for modeling the nonlinear discrimination functions based on combinations of continuous piece-wise polynomial (CPP) kernels. The kernels are constructed using tensor products of either B-splines or localized threshold decomposition (LTD) functions. These methods ooer an increased exibility compared to Volterra equalizers while simultaneously the most relevant parameters, the kernel shape parameters, are still determineded using linear optimization. Simpliied examples involving the recovery of binary signals propagating through a non-minimum phase channel and a nonlinear channel are used to demonstrate the potential of this approach.