Robust H sub( infinity ) and mixed H sub(2)/H sub( infinity ) filters for equalization designs of nonlinear communication systems: fuzzy interpolation approach

• Published in: IEEE transactions on fuzzy systems Vol. 11; no. 3
• Main Authors: Chen, Bor-Sen, Tsai, Chang-Lan, Chen, Dow-Shin
• Format: Journal Article
• Language: English
• Published: 01.01.2003
• Subjects: Design engineering; Equalizers; Fuzzy; Fuzzy logic; Fuzzy set theory; Mathematical models; Noise; Nonlinearity
• ISSN: 1063-6706
• DOI: 10.1109/TFUZZ.2003.812698

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H sub( infinity ) and mixed H sub(2)/H sub( infinity ) filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H sub( infinity ) equalizer 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 mixed H sub(2)/H sub( infinity ) equalizer is employed to take the advantage of both H sub(2) optimal performance with nominal statistics of noises and the H sub( infinity ) robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H sub(2)/H sub( infinity ) equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.