A unified theory of data-aided equalization

A unified theory is presented for data-aided equalization of digital data signals passed through noisy linear dispersive channels. The theory assumes that some past and/or future transmitted data symbols are perfectly detected. We use this hypothesis to derive the minimum mean-square error receiver. The optimum structure consists of a matched filter in cascade with a transversal filter combined with a linear intersymbol interference canceler which uses the ideally detected data symbols. The main result is an expression for the optimized mean-square error as a function of the number and location of the canceler coefficients, the s/n, and the channel transfer function. When the number of canceler coefficients is zero, we get the well-known result for linear equalization. When the causal or postcursor canceler approaches infinite length, we obtain the well-known decision feedback result. When both the precursor and postcursor cancelers become infinite, we obtain the very best result possible, namely, the matched-filter bound dictated from fundamental theoretical considerations. Neither the decision feedback nor the matched-filter results can be achieved in practice since their implementation requires infinite memory and storage. Our theory can be used to calculate the rate of approach to these ideals with finite cancelers.