A geometrical view of blind equalization

A geometrical analysis of the equalization problem is presented. The input signal forms an (m+L)-dimensional hypercube that is mapped via a convolution matrix to an m-D parallelotope, where L is the order of the channel and m is the order of the transversal equalizer. The properties of this mapping are discussed, and a criterion for equalization called the minimum width criterion is proposed. Virtually all of the standard equalizer schemes can be viewed as special cases of this minimum width criterion, including the L/sub infinity /, L/sub 1/, MSE (mean square error), LS (least squares), Sato, Godard, and kurtosis methods. It is possible to build new equalization algorithms by combining the basic distance elements uncovered by this geometric analysis.<>