Adaptive minimum bit-error rate equalization for binary signaling

We consider the design and adaptation of a linear equalizer with a finite number of coefficients in the context of a classical linear intersymbol-interference channel with Gaussian noise and a memoryless decision device. If the number of equalizer coefficients is sufficient, the popular minimum mean-squared-error (MMSE) linear equalizer closely approximates the optimal linear equalizer that directly minimizes bit-error rate (BER). However, when the number of equalizer coefficients is insufficient to approximate the channel inverse, the minimum-BER equalizer can outperform the MMSE equalizer by as much as 16 dB in certain cases. We propose a simple stochastic adaptive algorithm for realizing the minimum-BER equalizer. Compared to the least-mean-square algorithm, the proposed algorithm can provide a substantial reduction in BER with no increase in complexity.