On the use of kernel structure for blind equalization

The mathematical theory of kernel (null space) structure of Hankel and Hankel-like matrices is applied to the problem of blind equalization of cochannel signals. This approach provides a new perspective on the blind equalization problem and gives insights into the identifiability conditions already presented in the literature. An algorithm is presented that tracks the exact null space of the symbol matrix even in the presence of noise. This work exploits shift structure in the oversampled channel output and the finite alphabet property of the signals. Previously, these two properties were used independently in a two-step (equalize then separate) process. A contribution of the new approach is that it allows simultaneous exploitation of both shift structure and the finite alphabet property of the signals.