Approximate minimum bit-error rate equalization for binary signaling

Although most linear and decision-feedback equalizers are designed to minimize a mean-squared error (MSE) performance metric, the equalizer that directly minimizes bit-error rate (BER) may significantly outperform the minimum-MSE equalizer, especially for binary antipodal signaling and its biorthogonal extensions, such as four quadrature-amplitude modulation. We show that the performance gain of the minimum-BER equalizer over the minimum-MSE equalizer is most pronounced when the number of equalizer coefficients is small relative to the severity of the intersymbol interference. We propose a simple stochastic gradient algorithm that approximately minimizes BER in the presence of linear intersymbol interference and white Gaussian noise. Computer simulations reveal that the proposed algorithm compares favorably to the popular least-mean-square algorithm in terms of both steady-state performance and complexity