Theoretical derivation of minimum mean square error of RBF based equalizer

In this paper, the minimum mean square error (MSE) convergence of the RBF equalizer is evaluated and compared with the linear equalizer based on the theoretical minimum MSE. The basic idea of comparing these two equalizers comes from the fact that the relationship between the hidden and output layers in the RBF equalizer is also linear. For the purpose of theoretically evaluating exact minimum MSE for both RBF and linear equalizer, a linear time dispersive channel whose order is one is selected. As extensive studies of this research, various channel models are selected, which include linearly separable channel, slightly distorted channel, and severely distorted channel models. In this work, the theoretical minimum MSE for both RBF and linear equalizers were computed, compared and the sensitivity of minimum MSE due to RBF center spreads was analyzed. It was found that RBF based equalizer always produced lower minimum MSE than linear equalizer, and that the minimum MSE value of RBF equalizer was obtained with the center spread parameter which is relatively higher (approximately 2–10 times more) than variance of AWGN. As a result of that, it leads to the better bit error rate. This work provides an analytical framework for the practical training of RBF equalizer system.