Least Bit Error Rate Adaptive Nonlinear Equalizers for Binary Signalling

The paper considers the problem of constructing adaptive minimum bit error rate (MBER) neural network equalizers for binary signalling. Motivated from a kernel density estimation of the bit error rate (BER) as a smooth function of training data, a stochastic gradient algorithm called the least bit error rate (LBER) is developed for adaptive nonlinear equalizers. This LBER algorithm is applied to adaptive training of a radial basis function (RBF) equalizer in a channel intersymbol interference (ISI) plus co-channel interference setting. Simulation study shows that the proposed algorithm has a good convergence speed and a small-size RBF equalizer trained by the LBER can closely approximate the performance of the optimal Bayesian equalizer. The results also demonstrates that the standard adaptive algorithm, the least mean square (LMS), performs poorly for neural network equalizers, due to the reason that the minimum mean square error (MMSE) is irrelevant to the equalization goal.

[1]  G. J. Gibson,et al.  Space translation properties and the minimum-BER linear-combiner DFE , 1998 .

[2]  B. Mulgrew,et al.  Complex-valued radial basis function network, Part II: Application to digital communications channel equalisation , 1994, Signal Process..

[3]  Ching-Haur Chang,et al.  A polynomial-perceptron based decision feedback equalizer with a robust learning algorithm , 1995, Signal Process..

[4]  Chris J. Harris,et al.  Decision feedback equaliser design using support vector machines , 2000 .

[5]  S. Siu,et al.  Decision feedback equalisation using neural network structures and performance comparison with standard architecture , 1990 .

[6]  C.F.N. Cowan,et al.  Adaptive equalization of finite nonlinear channels using multilayer perceptron , 1990 .

[7]  Sheng Chen,et al.  Adaptive Bayesian equalizer with decision feedback , 1993, IEEE Trans. Signal Process..

[8]  C.F.N. Cowan,et al.  The application of nonlinear structures to the reconstruction of binary signals , 1991, IEEE Trans. Signal Process..

[9]  Bruce D. Fritchman,et al.  On optimum receivers for channels having memory (Corresp.) , 1968, IEEE Trans. Inf. Theory.

[10]  Sheng Chen,et al.  Adaptive minimum-BER decision feedback equalisers for binary signalling , 2001, Signal Process..

[11]  K. Abend,et al.  Statistical detection for communication channels with intersymbol interference , 1970 .

[12]  Sheng Chen,et al.  Minimum-SER linear-combiner decision feedback equaliser , 1999 .

[13]  Sheng Chen,et al.  Bayesian decision feedback equaliser for overcoming co-channel interference , 1996 .

[14]  Sheng Chen,et al.  Reconstruction of binary signals using an adaptive radial-basis-function equalizer , 1991, Signal Process..

[15]  John G. Proakis,et al.  Digital Communications , 1983 .

[16]  B. Mulgrew,et al.  Stochastic gradient minimum-BER decision feedback equalisers , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[17]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[18]  John R. Barry,et al.  Adaptive minimum bit-error rate equalization for binary signaling , 2000, IEEE Trans. Commun..

[19]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[20]  Rodney A. Kennedy,et al.  Block decision feedback equalization , 1992, IEEE Trans. Commun..

[21]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.

[22]  Tho Le-Ngoc,et al.  Polynomial perceptrons and their applications to fading channel equalization and co-channel interference suppression , 1994, IEEE Trans. Signal Process..

[23]  S. Qureshi,et al.  Adaptive equalization , 1982, Proceedings of the IEEE.

[24]  Saleem A. Kassam,et al.  Channel Equalization Using Adaptive Complex Radial Basis Function Networks , 1995, IEEE J. Sel. Areas Commun..

[25]  R. Chang,et al.  On receiver structures for channels having memory , 1966, IEEE Trans. Inf. Theory.

[26]  Lajos Hanzo,et al.  Adaptive minimum-BER linear multiuser detection for DS-CDMA signals in multipath channels , 2001, IEEE Trans. Signal Process..

[27]  Jack K. Wolf,et al.  Decision-feedback equalization via separating hyperplanes , 2001, IEEE Trans. Commun..