Abstract
Generally, it is difficult to design equalizers for signal reconstruction of nonlinear channels. In this paper, we study the H2, H-infinity and mixed H2/H-infinity filters for equalization of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the nonlinear transmission system is described as a state space model and the input signal is embedded in the state vector such that the equalization problem becomes a state estimation problem, then the Takagi and Sugeno fuzzy linear model is proposed to interpolate the nonlinear channel at different operation points through membership functions. If the statistics of the driving noise and measurement noise are available, the fuzzy H2 filter is employed to treat the state estimation problem. If the statistics of noises are unknown or uncertain, then the fuzzy H-infinity filter is proposed to treat the state estimation problem from the worst-case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the fuzzy mixed H2/H-infinity filter is applied, which takes advantage of both the $H_2$ optimal performance with nominal statistics of noises and the H-infinity robustness performance against the statistical uncertainty of noises. Using LMI approach, the fuzzy H2/H-infinity filter design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.