Among the useful blind equalization algorithms, stochastic-gradient iterative equalization schemes are based on minimizing a nonconvex and nonlinear cost function. However, as they use a linear FIR filter with a convex decision region, their residual estimation error is high. In this paper, four non-linear blind equalization schemes that employ a complex-valued multilayer perceptron instead of the linear filter are proposed and their learning algorithms are derived. After the important properties that a suitable complex-valued activation function must possess are discussed, a new complex-valued activation function is developed for the proposed schemes to deal with QAM signals of any constellation sizes. It has been further proven that by the nonlinear transformation of the proposed function, the correlation coefficient between the real and imaginary parts of input data decreases when they are jointly Gaussian random variables. Last, the effectiveness of the proposed schemes is verified in terms of initial convergence speed and MSE in the steady state. In particular, even without carrier phase tracking procedure, the proposed schemes correct an arbitrary phase rotation caused by channel distortion.
Bibliographical noteFunding Information:
Manuscript received September 24, 1997; revised June 9, 1998. This work was supported by the Korea Research Foundation (#01-E-0840). The authors are with the Department of Electronic Engineering, Yonsei University, Seoul 120-749 South Korea. Publisher Item Identifier S 1045-9227(98)07710-8.
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Computer Networks and Communications
- Artificial Intelligence