Nonlinearity shows up in a variety of different communication system components. Common examples include power amplifiers for wireless communication (cellular, broadcast, and satellite), companding in the telephone channel, and flux interaction in high density magnetic recording systems. In cases such as the telephone and magnetic recording channels, the nonlinearity limits the capacity of the channel. For power amplifiers, nonlinearities effectively restrict their operating range to a low efficiency linear region. Significant efficiency improvements, obtained by sacrificing some linearity, translate directly into prolonged battery life, smaller size devices, and reduced operating costs. The penalty for allowing nonlinearity in the system is that the receiver needs to compensate for nonlinear distortion in addition to intersymbol interference.;This thesis considers Volterra series based models for the nonlinear channel, and proposes new fixed point, decision feedback, and linear multichannel equalizers to compensate for nonlinear intersymbol interference. The fixed point equalizer is based on the method of successive approximations implied by the contraction mapping theorem. New single channel minimum mean-square error, multichannel, and single channel fixed point equalizers with precoding are proposed. Additional bounding functions to prevent divergence and comparisons with the Pth-order inverse are also made.;Decision feedback equalizers for the Volterra series are proposed based on a polynomial formulation of the Volterra series. The problems that existing decision feedback equalizers for Volterra systems have with the nonlinearity associated with the current symbol can be explained by the polynomial formulation. Two decision feedback algorithms are then given which exploit the input symbol set information in different ways to alleviate the problem with nonlinearity associated with the current symbol.;Three linear multichannel equalizers are designed for the Volterra series. The first is a blind iterative algorithm that can be considered an extension of the block-based Bussgang algorithm for multiple linear channels. The second is a multiuser equalizer for time-varying Volterra channels, which exploits a basis function expansion of the time-varying system. The third is a blind equalizer for code division multiple access systems with Volterra channels. The goal of these equalizers is to make nonlinear channel equalization viable for different communication systems.
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