On-line blind multichannel equalization based on mutually referenced filters

This paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time-varying communication channels. In the context of channel diversity, we introduce the concept of mutually referenced equalizers (MREs) in which several filters are considered, the outputs of which act as training signals for each other. A corresponding (constrained) multidimensional mean-square error (MSE) cost function is derived, the minimization of which is shown to be a necessary and sufficient condition for equalization. The links with a standard linear prediction problem are demonstrated. The proposed technique exhibits properties of important practical concern: 1) the proposed algorithm is globally convergent. 2) Simple closed-form solutions exist for the MREs, but the MREs also lend themselves readily to adaptive implementation. In particular, the recursive least-squares (RLS) algorithm can be used to offer optimal convergence rate. 3) The MRE method provides a solution for all equalization delays, which results in robustness properties with respect to SNR and ill-defined channel lengths.