Learning Algorithms for Complex-Valued Neural Networks in Communication Signal Processing and Adaptive Equalization as its Application

INTrODUCTION Intersymbol interference (ISI) of the digital communication channel becomes a main drawback to efficient use of frequency bandwidth efficiency and performance improvement. So, it is necessary to use adaptive equalizers to restore the digital signal distorted by ISI. For equalization, many powerful adaptive algorithms have been ABSTrACT In this chapter, the complex Backpropagation (BP) algorithm for the complex backpropagation neural networks (BPN) consisting of the suitable node activation functions having multi-saturated output regions is presented and analyzed by the benchmark testing. And then the complex BPN is utilized as nonlinear adaptive equalizers that can deal with both quadrature amplitude modulation (QAM) and phase shift key (PSK) signals of any constellation sizes. In addition, four nonlinear blind equalization schemes using complex BPN for M-ary QAM signals are described and their learning algorithms are presented. The presented complex BP equalizer (CBPE) gives, compared with conventional linear complex equalizers, an outstanding improvement with respect to bit error rate (BER) when channel distortions are nonlinear. developed such as the least mean squares (LMS) algorithm, the recursive least squares (RLS) algorithm and so on. But, the linear adaptive algorithms were not successful occasionally when channel distortion is nonlinear because of the assumption that the equalizer output is a linear function of the inputs. On this account, nonlinear adaptive equalization techniques have been required and developed. Among these nonlinear adaptive equalization algorithms, the backpropagation (BP) algorithm has occupied an important position because of its ease of implementation and nontrivial mapping capabilities (Arai, 1989, June). On the other hand, in conventional equalizers, we assume that the receiver has knowledge of the transmitted information sequence in forming of the error signal between the desired symbol and its estimate for initially adjusting the equalizer weights. However, there are some applications, such as multipoint communication networks involving a control unit connected to several data terminal equipments (DTEs) and wireless communication systems using digital technology, where it is desirable for the receiver to adjust the equalizer weights without a known training sequence available. Equalization techniques based on initial adjustment of the weights without a training sequence are said to be self-recovering or blind 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 chapter, the complex BP algorithm is …