Direct second-order blind equalization of polyphase channels based on a decorrelation criterion

We consider the problem of linear polyphase blind equalization (BE), i.e. we are interested in equalizing the output of a single-input-multiple-output (SIMO) channel, without observing its input. A previous result by Liu and Dong (see IEEE Trans. on Circuits and Systems, vol.44, no.5, 1997) showed that if the sub-channel polynomials are co-prime in the z-domain, then the equalizer output whiteness is necessary and sufficient for the equalization of a white input. Based on this observation, we propose a simple decorrelation criterion for second-order based BE. Due to its second-order nature, this criterion is insensitive to the distance of the input from Gaussianity, hence it achieves BE even for Gaussian or non-Gaussian inputs. Moreover, unlike other second-order techniques, our approach bypasses channel estimation and computes directly the equalizer. By doing so, it avoids the problem of ill-conditioning due to channel order mismatch which is crucial to other techniques. Combined to its good convergence properties, these characteristics make the proposed technique an attractive option for robust polyphase BE, as evidenced by both our analysis and computer simulation results.