Combined Linear Prediction and Subspace Based Blind Equalizers

A novel hybrid linear prediction (LP) and subspace decomposition based blind equalization algorithm, based on second-order statistics, is proposed in this paper. Previous blind equalization algorithms based on subspace decomposition and LP methods have problems when the channel order is under/over estimated. Previous subspace based algorithms exhibit significantly higher residual output mean square error if the estimation of channel length is off even by one, (Tong et al., 1994), (Li and Fan, 2000). In a practically noisy environment, accurate rank determination may be difficult. Even the linear prediction algorithms (Slock, 1994), (Liavas et al., 2000) are not robust to order over-estimation because solving the Yule Walker equation requires the computation of the pseudo-inverse of the noise free correlation matrix, for which the theoretical rank of the noise-free correlation matrix needs to be known. If the channel order is over-estimated, some of the small eigen-values (corresponding to noise) are erroneously classified in the signal subspace and are then inverted, and the LP algorithms exhibit large mean square errors (Liavas et al., 2000). In this paper, we propose a novel hybrid linear prediction and subspace based blind equalization algorithm. The superior performance of subspace based methods in low signal-to-noise ratio (SNR) is thus integrated into our method. Our algorithm is robust to channel order under/over estimation. Our algorithm is a data based (as opposed to channel based) algorithm and avoids effects of channel estimation errors. Simulations clearly indicate that our algorithm performs very well under channel order under/over-estimation, when LP and subspace based blind equalizers fail.