Valuation of the effects of intersymbol interference in decision-feedback equalizers

For channels which suffer predominantly from additive noise and intersymbol interference, the decision-feedback equalizer has provided a relatively simple solution for reducing the effects of interfering symbols at the input to the decision device. A technique is developed that enables fast, accurate calculation of the error performance of decision-feedback equalization for a number of channel models. The method is to calculate the n-step transition probability for an associated Markov process and then use this transition probability as an approximation to the stationary probability distribution. For systems with finite memory, it is proved that the method converges. If the signal-to-noise ratio (SNR) is high and the signal amplitude is more than twice the worst-case interference, it is shown that the convergence is rapid. Numerical results indicate that the convergence is rapid enough to make this an efficient method of calculation, even for channels for which the interference does not fully satisfy this condition. Two examples are given here, but the technique has been tested on most of the examples that have been presented in the literature. The method yields results in closer agreement with simulation results than previous results obtained using bounding techniques, especially at low to moderate SNRs, and requires less computation.