Discrete time blind equalization techniques involving higher-order cumulants which are useful in digital communication systems subject to intersymbol interference (ISI) and additive Gaussian noise (ACN), are investigated. The proposed techniques are:​ (i) a batch-type channel identification-equalization method, named tricepstrum identification method (TIM), (ii) an adaptive equalization technique called the tricepstrum equalization algorithm (TEA), and (iii) suboptimum, synchronous, zero-forcing linear and decision feedback (DFE) equalization algorithms. Performance evaluation of the proposed methods and comparisons with existing methods are made by means of Monte-Carlo simulations and analysis.

The proposed schemes make use of the complex cepstrum of the fourth-order cumulants (tricepstrum) of the received signal, which consists of the channel-distorted transmitted signal plus additive Gaussian noise, to estimate the channel (or equalizer) coefficients. Based on the properties of the tricepstrum the proposed schemes are blind to both signal and Gaussian noise and are capable of identifying (equalizing) both the minimum and maximum phase components of communication channels.

It is demonstrated, that the new techniques perform very effectively in both blind channel identification and blind equalization applications. Comparisons with existing methods demonstrate improved performance characterized by faster convergence properties, robustness, and low sensitivity to additive Gaussian noise. However, the improved performance is achieved at the expense of a higher computational complexity.