A class of batch-iterative methods for the equalization of intersymbol interference channels

Abstract

A class of nonlinear receivers is proposed to equalize intersymbol interference (ISi) channels in a batch-iterative fashion. The iterated-decision or multipass equalizer uses symbol decisions made during the previous iteration to cancel out both precursor and postcursor ISi during the current iteration. With each successive pass of the equalizer, the probability of symbol error decreases. Eventually, after relatively few iterations, the symbol error rate converges. The structure of the equalizer makes it attractive to use in combination with channel coding, since equalization and coding become largely separable issues. The multipass equalizer is optimized according to a maximum signal-to-interference+noise ratio (SINR) criterion, and, unlike the decision-feedback equalizer, the multipass equalizer is optimized assuming that decisions used for ISi cancellation can be erroneous. Furthermore, even under such an assumption, the performance of the iterated-decision equalizer can still be readily evaluated in the severe-ISi case. With a complexity comparable to the linear equalizer and the decision-feedback equalizer, the multi pass equalizer is shown in theory and in simulations to perform significantly better than either equalizer when the ISi is severe. In particular, for the long channel impulse responses we consider, the iterated-decision equalizer requires 2.507 dB less transmit power at high SNR to achieve the same probability of error as the minimum mean-square error decision-feedback equalizer (MMSE-DFE). Even more remarkably, the iterated-decision equalizer performs at high SNR as if the severeISi channel has been transformed into an ideal bandlirnited additive white Gaussian noise channel (AWGN) with the same receiver SNR. An adaptive version of the multipass equalizer is also proposed, which does not require a priori knowledge of the channel characteristics. Simulations show that only a modest amount of training data is required for the performance of the adaptive equalizer to be comparable to its non-adaptive counterpart. The adaptive equalizer is easily modified into a fractionally spaced adaptive equalizer, which can compensate for a wider range of amplitude and phase distortion. The fractionally spaced equalizer is also generalized to the case of multichannel communication.